tag:blogger.com,1999:blog-56928365115868638362024-03-20T00:51:59.216-07:00Finanças com HP e EXCELAprenda a utilizar as calculadoras da HP e o Microsoft Excel em finanças.
Escolha: Matemática Financeira, Análise de Investimentos, Capital de Giro etc.Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.comBlogger71125tag:blogger.com,1999:blog-5692836511586863836.post-48204034119665954112022-07-12T11:44:00.001-07:002022-07-12T11:44:29.400-07:00"Calibragem" e Interpretação do RSI14 para tendência de alta<p>Esta postagem traz a calibragem e a interpretação ideais ao melhor aproveitamento das tendências de alta com o RSI14 no gráfico diário. Não há nada de novo aqui, apenas um exemplos real, situação analisada a partir das contribuições de Welles Wilder (criador do RSI) e Andrew Cardwell (estudioso das faixas de oscilação do RSI em tendências de alta e de baixa).</p><p>Sobre as contribuições de Welles Wilder: seria enxugar gelo dedicar muito tempo explicando a relevância de um dos maiores autores da escola estatística da análise técnica, sendo assim, torna-se suficiente relembrar a faixa de oscilação do RSI14 entre 30 e 70 e o cruzamento ascendente do nível 50 para sinalizar uma possível tendência de alta.</p><p>Sobre algumas contribuições de Andrew Cardwell: a principal está na definição de faixas de oscilação para tendências de alta e de baixa; para tendência de baixa, prevalece o intervalo formado com os valores 20 e 60; no caso da tendência de alta, intervalo com os níveis 40 e 80.</p><p><br /></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4RjRYzGfj1JR5JeeplfdVoeyEuNueT3i5mEYbNN5UXr6KycLPuHsgsm703ieHCuQRgeUB2ooPpXsdXMOGTx3E-XdBf7G71qgmgxFzASeDy-OgBvESH0i0qJcBCppqyvuBSzyQ-WtLTNs/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1080" data-original-width="1916" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4RjRYzGfj1JR5JeeplfdVoeyEuNueT3i5mEYbNN5UXr6KycLPuHsgsm703ieHCuQRgeUB2ooPpXsdXMOGTx3E-XdBf7G71qgmgxFzASeDy-OgBvESH0i0qJcBCppqyvuBSzyQ-WtLTNs/w640-h360/image.png" width="640" /></a></div><br /><br /></div><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMAPpQH2Y04YEadqo9Buj_h6Ufprz54BuXltWbrEnAwsQzEHVS6MOS0UvNO736kFXvAzCjv6ylkLSh1Amirl43jzfgPULhssOPOZkF2yyUUBTye3KuIWkt8PHGELncTRsNL_CMLRzkP9Q/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="768" data-original-width="1366" height="337" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMAPpQH2Y04YEadqo9Buj_h6Ufprz54BuXltWbrEnAwsQzEHVS6MOS0UvNO736kFXvAzCjv6ylkLSh1Amirl43jzfgPULhssOPOZkF2yyUUBTye3KuIWkt8PHGELncTRsNL_CMLRzkP9Q/w600-h337/image.png" width="600" /></a></div></div></div><br /><br />Pegue umas listas de ações e de criptomoedas para praticar, busque períodos de tendência de alta no gráfico diário, perceba o "mapa da mina" contido no RSI14.<div><br /></div><div>Até breve! <br /><div><br /></div><div><br /><p></p><p> </p></div></div>Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-7849277423643870072022-06-29T15:25:00.006-07:002022-06-29T15:25:39.050-07:00ANÁLISE TÉCNICA: figuras de reversão e xícara com alça (continuidade)<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIEuW1ld5-s-oofUk-BLxcp0kldeW0ncYHFpr40pdC_KllkGVeeYyjDSrozrJ856_YUbSNFux7Ji1kf8WDpqibZF1jBqcUYNXnVuI9FOz-yYNkxKtqvhmqm8yBTORDadPv1vyOw1I6jz7Eq_OpyMIIMqhUL1YYwD9VzPNn-ibhv7wTEH7-ZHT1Tr8F/s1431/FIG%2010.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="811" data-original-width="1431" height="363" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIEuW1ld5-s-oofUk-BLxcp0kldeW0ncYHFpr40pdC_KllkGVeeYyjDSrozrJ856_YUbSNFux7Ji1kf8WDpqibZF1jBqcUYNXnVuI9FOz-yYNkxKtqvhmqm8yBTORDadPv1vyOw1I6jz7Eq_OpyMIIMqhUL1YYwD9VzPNn-ibhv7wTEH7-ZHT1Tr8F/w640-h363/FIG%2010.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-XjSEL7p15ECLR4tlS9czi0eg3X2tJMrRQeGuKe8XcTt5nctL3XxeddYZ6A5uHrnpTdVEzhIIa6sE_FZhCBVOU89DKyhUF79tnDjAq4sgwYuvGOQpuJzNEGkXZXKTqHKEUYLE-clqLPI8xVZSglqcgFcFMK5B5Al6LVp7dFanx1xPUbWoUaXMrRc6/s1427/FIG%209.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="812" data-original-width="1427" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-XjSEL7p15ECLR4tlS9czi0eg3X2tJMrRQeGuKe8XcTt5nctL3XxeddYZ6A5uHrnpTdVEzhIIa6sE_FZhCBVOU89DKyhUF79tnDjAq4sgwYuvGOQpuJzNEGkXZXKTqHKEUYLE-clqLPI8xVZSglqcgFcFMK5B5Al6LVp7dFanx1xPUbWoUaXMrRc6/w640-h364/FIG%209.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4B8lS85n-21QZkhXFTNgDCXtwgsLupK-cZBjvY58fVQCBauB_Iqho3DzjGmWMZXJhT3RLfUW4t_85D5wlKfXDYYQQEx9-AFXvyn1sYYu8eOvWBLPMWMhiySD4D4-TQ9I5Or79E_goi2dgyM6oE4redQXtjrBRuvRqVYODQJg_GUD5x8hSWY5zvYqT/s1429/FIG%208.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="811" data-original-width="1429" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4B8lS85n-21QZkhXFTNgDCXtwgsLupK-cZBjvY58fVQCBauB_Iqho3DzjGmWMZXJhT3RLfUW4t_85D5wlKfXDYYQQEx9-AFXvyn1sYYu8eOvWBLPMWMhiySD4D4-TQ9I5Or79E_goi2dgyM6oE4redQXtjrBRuvRqVYODQJg_GUD5x8hSWY5zvYqT/w640-h364/FIG%208.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDv-sZPRGVesi8Cpfj8-p4hDCFkeVHEZIeQ87ag3xbo6lbCOQkNID7Y0hqMLxhh0KnXN9ZmkuRVZdloy8JBnrDQjz036UCjrSyW9XbeIuwVsSkZ-lVoFuLy-JKUKEtinURnMOj6hFv7FxxtQIWCBvNmfASyOabHPj7EWgzTyFVyMivVzdYWA8e2qVv/s1430/FIG%207.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="811" data-original-width="1430" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDv-sZPRGVesi8Cpfj8-p4hDCFkeVHEZIeQ87ag3xbo6lbCOQkNID7Y0hqMLxhh0KnXN9ZmkuRVZdloy8JBnrDQjz036UCjrSyW9XbeIuwVsSkZ-lVoFuLy-JKUKEtinURnMOj6hFv7FxxtQIWCBvNmfASyOabHPj7EWgzTyFVyMivVzdYWA8e2qVv/w640-h362/FIG%207.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXP3944Ni16v1vsDzw0OMpUHjPF0-V2UPGhzBs1YfUOiocq-WwGL6p9UQs2-D1A5nfJJy9fbTAvr0tL46fVZAYK4C0tHoTqZ0u5cPrsVhhF93yvuHzhzaRaVO6Smv_VBzLOHYAg_sJzDtlO3qXXmZrVIg2fAzIAQPMtcz0KZLSGJrIQNfr4slnli1i/s1428/FIG%206.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="811" data-original-width="1428" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXP3944Ni16v1vsDzw0OMpUHjPF0-V2UPGhzBs1YfUOiocq-WwGL6p9UQs2-D1A5nfJJy9fbTAvr0tL46fVZAYK4C0tHoTqZ0u5cPrsVhhF93yvuHzhzaRaVO6Smv_VBzLOHYAg_sJzDtlO3qXXmZrVIg2fAzIAQPMtcz0KZLSGJrIQNfr4slnli1i/w640-h364/FIG%206.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqe6_qpboxA20dQwJoIneYjilxHVqfSU319YIX6CyPOfHYmw8FwFjQlhpVfDwbs1rc1F9wU9e1yLtrG2l0Gy8lUzhTX3U7jDPLZbkwwCdU03MLcfsiU6YoaUs-tSD0ZX1YzN-eCwrJNcm2K4JNKbRm3vGX3S7wutdOLZjSS2Uyw73X6tVtMNvCNo-M/s1430/FIG%205.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="811" data-original-width="1430" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqe6_qpboxA20dQwJoIneYjilxHVqfSU319YIX6CyPOfHYmw8FwFjQlhpVfDwbs1rc1F9wU9e1yLtrG2l0Gy8lUzhTX3U7jDPLZbkwwCdU03MLcfsiU6YoaUs-tSD0ZX1YzN-eCwrJNcm2K4JNKbRm3vGX3S7wutdOLZjSS2Uyw73X6tVtMNvCNo-M/w640-h362/FIG%205.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbLZ4Vj6MJmI52HbY_5LYTugBce4q5Q_7lmwWK03ROdhIxhfrUB6YgY_mAQImsDizMm-MGgrBGDwOw-AhX4unMzH7sJyhMIzJJPBcFOn9MfoBqvDFJ_26dteOMFf1YS3Ych95LYd4p1P98sRSqNUvOYUe6j9_VfyQcryNgPHMWpLe2kpJJ4Vb9Tlpf/s1430/FIG%204.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="820" data-original-width="1430" height="366" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbLZ4Vj6MJmI52HbY_5LYTugBce4q5Q_7lmwWK03ROdhIxhfrUB6YgY_mAQImsDizMm-MGgrBGDwOw-AhX4unMzH7sJyhMIzJJPBcFOn9MfoBqvDFJ_26dteOMFf1YS3Ych95LYd4p1P98sRSqNUvOYUe6j9_VfyQcryNgPHMWpLe2kpJJ4Vb9Tlpf/w640-h366/FIG%204.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcggrgynR4E-Uu8-vvUBLddw2diqx-F5zQPks2kJZ4xRwd00BgF_tHsWJAzxAJpfTmB4jrJ6kDTKkztK4tzUo4PI-D1U1ybNpB01ftm5MtWEBBH_Zeyj96A0DprBIg4sGUAR7_2XTxZeSBkGoEIQ3t1O85nJE93W0rR91XgVzcVS-zzKnBWXrAyoq6/s1431/FIG%203.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="815" data-original-width="1431" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcggrgynR4E-Uu8-vvUBLddw2diqx-F5zQPks2kJZ4xRwd00BgF_tHsWJAzxAJpfTmB4jrJ6kDTKkztK4tzUo4PI-D1U1ybNpB01ftm5MtWEBBH_Zeyj96A0DprBIg4sGUAR7_2XTxZeSBkGoEIQ3t1O85nJE93W0rR91XgVzcVS-zzKnBWXrAyoq6/w640-h364/FIG%203.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZvlBgneTEMnCc_tR0w5Hn4Zyu6JButNcsgocUlLwjOCLnNeUrUhitLLJvhtf1_VVDmu9sZObp8PgMXm8XzpPkyimoCXu4BKAO87Fm3er9KIeUuhkqkEe7ekkT-X5HSn7b6df1hpFQmpjQKnaP86CpFijt5bWAieyv9h6SORWiLz58HDYVT2MyFFDU/s1430/FIG%202.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="815" data-original-width="1430" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZvlBgneTEMnCc_tR0w5Hn4Zyu6JButNcsgocUlLwjOCLnNeUrUhitLLJvhtf1_VVDmu9sZObp8PgMXm8XzpPkyimoCXu4BKAO87Fm3er9KIeUuhkqkEe7ekkT-X5HSn7b6df1hpFQmpjQKnaP86CpFijt5bWAieyv9h6SORWiLz58HDYVT2MyFFDU/w640-h364/FIG%202.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi41Zv34N9RlobN7wlMaJcXNYL_tWjqBuFUgPgnQmFbymBo6YMa6MDuoD41l2Aq0z3Cd4VdpNF7GnMHm_8XzNVThDuwMJfckLLwn8xfXmrKx0qwtla9qiCQ_Q-rfWp_Am76n4bB0Ixt1EYDLfY10chKH7-SczQUAVLFNYniGuWTV1iDyBgKMrA1AI-o/s1435/FIG%201.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="816" data-original-width="1435" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi41Zv34N9RlobN7wlMaJcXNYL_tWjqBuFUgPgnQmFbymBo6YMa6MDuoD41l2Aq0z3Cd4VdpNF7GnMHm_8XzNVThDuwMJfckLLwn8xfXmrKx0qwtla9qiCQ_Q-rfWp_Am76n4bB0Ixt1EYDLfY10chKH7-SczQUAVLFNYniGuWTV1iDyBgKMrA1AI-o/w640-h364/FIG%201.png" width="640" /></a></div><br /><p></p>Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-75535250338259844212020-09-28T16:56:00.003-07:002020-09-28T16:56:35.318-07:00Análise Técnica Empírica: TRIÂNGULOS<p> Olá!</p><p>Primeira postagem sobre Análise Técnica Empírica. Tema: TRIÂNGULOS.</p><p>Adiantei logo as imagens (em 28/09/2020); os comentários serão inseridos amanhã (29/09/2020).</p><p>ATENÇÃO: peço para citar a fonte (este blog) em caso de uso das imagens a seguir. Obrigado! </p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1Q1bCNrt4DNe1DXvs0CHjJem0FHNVl2PWrV4kBEpv2k8uEIcOofY9lGPhBMsj0D47lTps7JMZ09m6u1iH4LTUQF86DW_ocfzeeAqYDg6h8W-GKeaLA5XWSWjJfRxkpP3Os-Zm7lOZ1qs/s1366/T2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="768" data-original-width="1366" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1Q1bCNrt4DNe1DXvs0CHjJem0FHNVl2PWrV4kBEpv2k8uEIcOofY9lGPhBMsj0D47lTps7JMZ09m6u1iH4LTUQF86DW_ocfzeeAqYDg6h8W-GKeaLA5XWSWjJfRxkpP3Os-Zm7lOZ1qs/w400-h225/T2.png" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLRPekdP73WPi_Zdb98u3OZrEd-MlIxm2OC4ZtjgnwmKWSKCVMdrYhBImID_tWPAJdaOtEV-o6syqyK_EZRgPzsZVCnMsFktjSbmJi5NRM3R1qajL21Vp7TGrjJVpVzAc9M8JOGx7FYek/s1366/T3.png" imageanchor="1" style="margin-left: 1em; 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text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNAj9au92qoCxyHPZYen-ssUFLnLH39IYIT2wniIfiw6-dHgVvRD0QmHh3DbPHW_sb-hAL19iu4e2KMGDwJJegIkjXyO_hYwNmEmiJDzRNj6WsqKRRGwnSJOQwVwYhGPEdZrYJWNouqqA/s1366/T13.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="768" data-original-width="1366" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNAj9au92qoCxyHPZYen-ssUFLnLH39IYIT2wniIfiw6-dHgVvRD0QmHh3DbPHW_sb-hAL19iu4e2KMGDwJJegIkjXyO_hYwNmEmiJDzRNj6WsqKRRGwnSJOQwVwYhGPEdZrYJWNouqqA/w400-h225/T13.png" width="400" /></a></div><br /><p><br /></p>Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-20871570073494589752020-09-26T10:47:00.007-07:002022-03-11T09:13:12.380-08:00Modelo Fleuriet: classificação automática da situação financeira para Excel, Calc e Google Planilhas <p>O modelo Fleuriet de análise financeira dispensa apresentação - muito conhecido, um clássico e eficaz à administração financeira empresarial. </p><p>Conhecer as "Estruturas de análise do Modelo Fleuriet" ou "Estratégias de Balanço Patrimonial" é suficiente para o propósito desta postagem (excelente, sólida, insatisfatória, alto risco, muito ruim e péssima). Explicações mais detalhadas podem ser encontradas em diversas publicações referentes ao tema, mas tenho duas sugestões interessantes: https://www.modelo-fleuriet.com/conceitos-avancado/estrategias-de-balanco-patrimonial/ e Mapeamento da produção científica sobre o Modelo Fleuriet no Brasil, de Araújo, Costa e Camargos (2013).</p><p>Agora sim, sobre o objetivo desta postagem: apresentar uma forma de tornar automática a classificação da situação financeira empresarial, segundo o modelo Fleuriet, em planilhas eletrônicas - pode ser usado Excel, Calc ou Google Planilhas.</p><p>Já venho usando há bastante tempo a modelagem em questão nas minhas aulas de Administração Financeira I. Ela requer dados contábeis organizados da forma como disponibiliza o site www.fundamentus.com.br - tenho preferência por fazer uso do histórico trimestral do balanço patrimonial. </p><p>Abaixo, a imagem apresenta as variáveis ACC (ativo circulante cíclico), ACE (ativo circulante errático), PCC (passivo circulante cíclico), PCE (passivo circulante errático), CDG (capital de giro), NCG (necessidade de capital de giro) e T (saldo de tesouraria). A célula B9 deve ser reservada para classificar a situação financeira. </p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNSv82RiEv8AMI0644O1mG-HE2CS7R1F4kR6sQ65nbTU3eKZaVjkLJ3nv2p_mgpj52aLcpi4wRkYMiRecKAgpKjvji12d4S7230BMuMY3c73_a4r5a7pKzVHJaSh1kBq-xfMTIgJh49zY/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="209" data-original-width="211" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNSv82RiEv8AMI0644O1mG-HE2CS7R1F4kR6sQ65nbTU3eKZaVjkLJ3nv2p_mgpj52aLcpi4wRkYMiRecKAgpKjvji12d4S7230BMuMY3c73_a4r5a7pKzVHJaSh1kBq-xfMTIgJh49zY/" width="242" /></a></div><br />Para obter a classificação correta, basta relacionar os saldos do CDG e da NCG - se positivos, negativos e diferentes. Com apenas duas funções é possível providenciar todas as classificações: SE e E. Observe os raciocínios a seguir: <div><ul style="text-align: left;"><li>SE(E(CDG>0;NCG<0);"EXCELENTE";</li><li>SE(E(NCG>0;CDG>NCG);"SÓLIDA";</li><li>SE(E(NCG<0;CDG<0;CDG>NCG);"ALTO RISCO";</li><li>SE(E(NCG>0;CDG>0;NCG>CDG);"INSATISFATÓRIA";</li><li>SE(E(NCG<0;CDG<0;CDG<NCG);"MUITO RUIM";</li><li>SE(E(NCG>0;CDG<0);"PÉSSIMA";</li><li>""))))))</li></ul><div>Combinando as funções SE e E e os sinais > e < não tem erro, a classificação de uma empresa segundo os tipos de estruturas patrimoniais do balanço para o modelo Fleuriet será gerada de modo automático. </div><div><br /></div><div>Como as células B6 e B7 estão reservadas para receber os valores do CDG e da NCG, basta substituir CDG e NCG por B6 e B7, respectivamente. Veja o resultado na imagem abaixo.</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLR-3BunfJDpGjpNpYd95JmhhTzQrLpIDEjCucosSMtdJm5bpd-hXgyj63PSLNkeWxeitXFh2YY5X3NoJum7gyYSkgv7Gh8vxTjYM3yK1XYt15NmkV8IejVX852G1U5nzLDe9vpKGVUHw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="317" data-original-width="591" height="335" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLR-3BunfJDpGjpNpYd95JmhhTzQrLpIDEjCucosSMtdJm5bpd-hXgyj63PSLNkeWxeitXFh2YY5X3NoJum7gyYSkgv7Gh8vxTjYM3yK1XYt15NmkV8IejVX852G1U5nzLDe9vpKGVUHw/w624-h335/image.png" width="624" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Após inserir a fórmula na célula B9, arraste para o lado direito para ter o histórico inteiramente classificado.</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Vamos aos testes: insira =B6-B7 na célula B8; digite 2 e -1 nas células B6 e B7, respectivamente. Confira o resultado na imagem abaixo.</div><div class="separator" style="clear: both; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP0EfNuF_8MgfnuVwHBcI4iguDDG7JFfVnRLXwGyKJm2KxKVvgekllQatvnQNwq2C_kI9rcPsmMCZNDs-4U4djXy_AFXKpG46J8sQFekfls9PoiRm0mSozQEzYaCUqTevhHegeJEl3dQ4/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="211" data-original-width="236" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP0EfNuF_8MgfnuVwHBcI4iguDDG7JFfVnRLXwGyKJm2KxKVvgekllQatvnQNwq2C_kI9rcPsmMCZNDs-4U4djXy_AFXKpG46J8sQFekfls9PoiRm0mSozQEzYaCUqTevhHegeJEl3dQ4/" width="267" /></a></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Digite 2 e 1 nas células B6 e B7, respectivamente. Resultado na imagem abaixo.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXKuYNm4zvfPiugVVlC5zMU-ympAB4ONYcEkgfL1t4PGw2SkTBlsiEHo19rQDO4mh_S3zI0gY1TnY0YpZlCTkJOkP4sArOCcEg7ILLAVL52pVtLavKNbipTjHdI-1IFZzQUkxf7t4YutI/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="212" data-original-width="229" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXKuYNm4zvfPiugVVlC5zMU-ympAB4ONYcEkgfL1t4PGw2SkTBlsiEHo19rQDO4mh_S3zI0gY1TnY0YpZlCTkJOkP4sArOCcEg7ILLAVL52pVtLavKNbipTjHdI-1IFZzQUkxf7t4YutI/" width="258" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: justify;">Digite 3 e 2 nas células B6 e B7, respectivamente. Resultado na imagem abaixo.</div><div style="text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXgZkkNUK-9994tK-p9nk5i9Q9W8yRk3sWUtPj0ilCW76pU7SytykhYS0-4h7N61_9dUo8egTm_VdPuoH2v6P5Sj-2zzvjf0JmMOOUPmWwH0rnwGkwy33JNRWbej9gKMU42Ljb_5s18rQ/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="210" data-original-width="234" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXgZkkNUK-9994tK-p9nk5i9Q9W8yRk3sWUtPj0ilCW76pU7SytykhYS0-4h7N61_9dUo8egTm_VdPuoH2v6P5Sj-2zzvjf0JmMOOUPmWwH0rnwGkwy33JNRWbej9gKMU42Ljb_5s18rQ/" width="266" /></a></div><span style="text-align: justify;"><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Digite -1 e -2 nas células B6 e B7, respectivamente. Resultado na imagem abaixo.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRyow9osakXt_4XxD5Ap4Wa381JDis8_GCLTNpLmvfS5xXx109cXYJvYGQvom_XxU9ihYpWOrXDdzl1BvXgr-N-RQLLdDK9d7r0OMvRhf_HXuX067DUi3Fi3XkMWLB8QddQxI26ZkWCic/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="213" data-original-width="237" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRyow9osakXt_4XxD5Ap4Wa381JDis8_GCLTNpLmvfS5xXx109cXYJvYGQvom_XxU9ihYpWOrXDdzl1BvXgr-N-RQLLdDK9d7r0OMvRhf_HXuX067DUi3Fi3XkMWLB8QddQxI26ZkWCic/" width="266" /></a></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Digite -2 e -1 nas células B6 e B7, respectivamente. Resultado na imagem abaixo.</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpQ4-m6IY51-br2uV_SBotVGEeolTVUamo6_bRA-zQINJzDce20VbI_zXqJDX3vVH7JpC_rN_Jza1nfovCb84fASe91-RGWbntyLXLUMtD2G3BzpRIAi_lJ44wpdegXucZu67GrOF-EbI/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="206" data-original-width="235" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpQ4-m6IY51-br2uV_SBotVGEeolTVUamo6_bRA-zQINJzDce20VbI_zXqJDX3vVH7JpC_rN_Jza1nfovCb84fASe91-RGWbntyLXLUMtD2G3BzpRIAi_lJ44wpdegXucZu67GrOF-EbI/" width="274" /></a></div><br />Digite -2 e 1 nas células B6 e B7, respectivamente. Resultado na imagem abaixo.</div><div class="separator" style="clear: both; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7ShbDKkXtvvMXlU49uz80vxK2ynLby6rLuKPoid1v2zEOoKE0ToXD_g4pSu3wveM1OrHDDvAKKPRVfsAYJMwIdqUmetCSlNVKzpyOv4hFWq9hUhki3R5bdavJVL_IzZCuGb2jX4VlwWk/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="211" data-original-width="232" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7ShbDKkXtvvMXlU49uz80vxK2ynLby6rLuKPoid1v2zEOoKE0ToXD_g4pSu3wveM1OrHDDvAKKPRVfsAYJMwIdqUmetCSlNVKzpyOv4hFWq9hUhki3R5bdavJVL_IzZCuGb2jX4VlwWk/" width="264" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Bem, agora é aproveitar. Lembrando: arraste para o lado direito para completar a classificação do histórico.</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Esta postagem ainda não acabou, vai ter continuação! </div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Até mais! </div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Att.,</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Adail Marcos</div></div></div></span></div></div></div></div></div></div></div></div>Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-56323759612308811132020-07-09T06:34:00.003-07:002020-07-09T09:24:02.918-07:00Estatística com EXCEL: perspectiva bicaudal da aplicação monovariada do teste t <div style="text-align: justify;">Objetivo desta postagem: construir uma pequena modelagem à aplicação monovariada do teste t segundo a perspectiva bicaudal de análise - parâmetro populacional (desvio padrão) desconhecido.</div><div><br /></div><div style="text-align: justify;">A seguir, tabela com uma amostra referente ao histórico do índice de liquidez corrente trimestral de uma grande empresa brasileira. Copie e cole numa nova aba do Microsoft Excel. ATENÇÃO: na hora de COLAR, escolha COLAR ESPECIAL (clicar com o lado direito do mouse na célula A1) e selecione a opção TEXTO UNICODE. Hipótese a ser testada: a amostra origina-se de uma população com média igual a 2,00 (H0).</div><div><br /></div><div><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 139px;">
<colgroup><col style="mso-width-alt: 2742; mso-width-source: userset; width: 56pt;" width="75"></col>
<col style="width: 48pt;" width="64"></col>
</colgroup><tbody><tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt; width: 56pt;" width="75"></td>
<td style="width: 48pt;" width="64"><font size="2">LC</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2009 </font></td>
<td align="right"><font size="2">2,2</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2010</font></td>
<td align="right"><font size="2">2,04</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2010 </font></td>
<td align="right"><font size="2">1,97</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2010</font></td>
<td align="right"><font size="2">2,01</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2010</font></td>
<td align="right"><font size="2">1,73</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2011</font></td>
<td align="right"><font size="2">2,12</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2011</font></td>
<td align="right"><font size="2">1,97</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2011</font></td>
<td align="right"><font size="2">2,15</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2011</font></td>
<td align="right"><font size="2">1,89</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2012</font></td>
<td align="right"><font size="2">2,05</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2012</font></td>
<td align="right"><font size="2">2,24</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2012</font></td>
<td align="right"><font size="2">2,41</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2012</font></td>
<td align="right"><font size="2">1,79</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2013</font></td>
<td align="right"><font size="2">2,01</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2013</font></td>
<td align="right"><font size="2">1,9</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2013</font></td>
<td align="right"><font size="2">2,07</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2013</font></td>
<td align="right"><font size="2">2,54</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2014</font></td>
<td align="right"><font size="2">2,57</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2014</font></td>
<td align="right"><font size="2">2,37</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2014</font></td>
<td align="right"><font size="2">2,05</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2014</font></td>
<td align="right"><font size="2">1,88</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2015</font></td>
<td align="right"><font size="2">1,77</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2015</font></td>
<td align="right"><font size="2">1,74</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2015</font></td>
<td align="right"><font size="2">1,73</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2015</font></td>
<td align="right"><font size="2">1,47</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2016</font></td>
<td align="right"><font size="2">1,51</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2016</font></td>
<td align="right"><font size="2">1,58</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2016</font></td>
<td align="right"><font size="2">1,8</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2016</font></td>
<td align="right"><font size="2">2,01</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2017</font></td>
<td align="right"><font size="2">1,9</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2017</font></td>
<td align="right"><font size="2">1,88</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2017</font></td>
<td align="right"><font size="2">1,86</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2017</font></td>
<td align="right"><font size="2">1,45</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2018</font></td>
<td align="right"><font size="2">1,53</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2018</font></td>
<td align="right"><font size="2">1,68</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2018</font></td>
<td align="right"><font size="2">1,65</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2018</font></td>
<td align="right"><font size="2">1,67</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2019</font></td>
<td align="right"><font size="2">1,21</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/06/2019</font></td>
<td align="right"><font size="2">1,24</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">30/09/2019</font></td>
<td align="right"><font size="2">1,38</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/12/2019</font></td>
<td align="right"><font size="2">1,23</font></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt;"><font size="2">31/03/2020</font></td>
<td align="right"><font size="2">1,72</font></td>
</tr></tbody></table></div><span><a name='more'></a></span><div><br /></div><div style="text-align: justify;">Depois de colar a amostra, a estrutura do modelo aqui sugerido deve seguir a orientação geral da figura abaixo - utilizei as colunas A e B para abrigar o histórico do índice de liquidez corrente.</div><div> </div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img alt="" 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" style="margin-left: auto; margin-right: auto;" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><font size="2">Estrutura do modelo definido à aplicação monovariada do teste t - perspectiva bicaudal.</font></td></tr></tbody></table><div><br /><div style="text-align: justify;">A próxima figura traz todas as fórmulas e funções envolvidas no procedimento, a serem inseridas nas células E4, E5, E6, E7, E8, F8, E10 e E11. </div></div><div><br /></div><div style="text-align: center;"><img alt="" height="270" src="data:image/png;base64,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" width="570" /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td class="tr-caption" style="text-align: center;"><font size="2">Fórmulas e funções do EXCEL à aplicação monovariada do teste t.<br /></font><br /></td></tr></tbody></table></div><div>A interpretação do resultado do teste deve seguir as orientações contidas células F10 e F11.</div><div><br /></div><div>Sim, era só isso mesmo - simples, fácil e objetivo. </div><div><br /></div><div>Tema da próxima postagem? Uma incógnita... </div><div><br /></div><div>Até mais!</div>Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com2tag:blogger.com,1999:blog-5692836511586863836.post-9321715233969805052020-04-17T06:48:00.000-07:002020-04-17T06:49:49.509-07:00Modelagem para Durbin-Watson no Microsoft Excel<div style="text-align: justify;">
Se você gosta de utilizar o Microsoft Excel para desenvolver aplicações envolvendo regressão linear, certamente já sentiu falta de uma ferramenta automática para analisar a autocorrelação dos resíduos com Durbin-Watson. Esta postagem traz exatamente uma proposta de modelo para inferência quanto à autocorrelação dos resíduos com Durbin-Watson. </div>
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Sem muita conversa, vamos direto ao assunto. Os resíduos apresentados no exemplo a seguir são originários de um exercício contido no livro de Iudícibus e Mello (2012), intitulado "Análise de Custos - uma abordagem quantitativa". </div>
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Monte a estrutura destacada na <b>Figura 1,</b> onde: <b>d</b>, estatística do teste de Durbin-Watson, calculada a partir da fórmula inserida na célula <b>E3</b>; <b>Rho</b>, valor da autocorrelação dos resíduos, com resposta apurada a partir da fórmula da célula <b>E3</b>; <b>dl</b> e <b>du</b>, valores obtidos da tabela de valores críticos de Durbin-Watson (o exemplo é alusivo a uma regressão linear simples, com significância de 0,05); <b>1º Int</b>, primeiro intervalo de <b>d</b>, de <b>0,00</b> até <b>dl</b>; <b>2º Int</b>, segundo intervalo de <b>d</b>, de <b>dl</b> até <b>du</b>; <b>3º Int</b>, terceiro intervalo de <b>d</b>, de <b>dl</b> até <b>4-du</b>; <b>4º Int</b>, quarto intervalo de <b>d</b>, de <b>4-du</b> até <b>4-dl</b>; <b>5º Int</b>, quinto intervalo de <b>d</b>, de <b>4-dl</b> até <b>4,00</b>. </div>
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<b><span style="font-size: large;">Figura 1</span></b> </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNgT1iIkSOqkZrLRf1vRixqbYbKsbWUL47ovRzhniWv_rPLm9Kbtca9j4lExFUfClB8oqzj6UhQtcpH6OMHDIYCCP1BeIl6RMpDXdd0ZNUdz0beod5rRLXPiMN8MKGfA9YD4A9LOiRNaM/s1600/DW+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="541" data-original-width="1233" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNgT1iIkSOqkZrLRf1vRixqbYbKsbWUL47ovRzhniWv_rPLm9Kbtca9j4lExFUfClB8oqzj6UhQtcpH6OMHDIYCCP1BeIl6RMpDXdd0ZNUdz0beod5rRLXPiMN8MKGfA9YD4A9LOiRNaM/s640/DW+1.png" width="640" /></a></div>
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A <b>Figura 2</b> mostra como criar uma identificação automática do intervalo onde se encontra o valor de <b>d</b>: utilizar as células <b>G7</b> até <b>G11</b>; cada célula deve receber sua respectiva fórmula (observar anotações do Excel na <b>Figura 2</b>).</div>
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<b><span style="font-size: large;">Figura 2</span></b> </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqX62WC2QVQZgA3f7azUpC2JlGhJMhAiFg5PuQATN2aD8X3BEW25QBZXnD9Cm6Bxneo3pxeicHanDCbEUFj9dIZsvcKxL4FAGF_3cTuGsDnacohMSiC31acJoML4j_DEXP3UEANBfQgyQ/s1600/DW+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="574" data-original-width="1199" height="304" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqX62WC2QVQZgA3f7azUpC2JlGhJMhAiFg5PuQATN2aD8X3BEW25QBZXnD9Cm6Bxneo3pxeicHanDCbEUFj9dIZsvcKxL4FAGF_3cTuGsDnacohMSiC31acJoML4j_DEXP3UEANBfQgyQ/s640/DW+2.png" width="640" /></a></div>
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Por fim, a <b>Figura 3</b> traz uma sugestão para lançar, também de forma automática, a conclusão final sobre o resultado do teste: utilizar as células <b>H7</b> até <b>H11</b>; cada célula deve receber sua respectiva fórmula condicional (observar anotações do Excel na <b>Figura 3</b>).</div>
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<b><span style="font-size: large;">Figura 3</span></b> </div>
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Pronto! Fácil e rápido, portanto, objetivo! Com o resultado da célula <b>E3</b> mudando, a identificação do intervalo e a conclusão sobre o teste mudam automaticamente. </div>
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Deixe sugestões, dúvidas e outras observações nos comentários. </div>
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Até mais! </div>
Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-71997212131178585142017-08-30T18:50:00.004-07:002022-05-27T12:45:49.758-07:00Definição das proporções da carteira de risco mínimo com 5 ativos: aplicação da ferramenta SOLVER do Microsoft EXCEL<div style="text-align: justify;">
Depois de explorar bastante a análise risco/retorno para ativos isolados e carteiras com dois ativos de risco, agora chegou a vez de carteiras com mais de dois ativos. A teoria fundamental encontra-se em <i>portfolio selection</i>, de Harry Markowitz.<br />
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Nsta postagem trago um procedimento específico com o SOLVER do EXCEL para determinar as proporções ideais de até cinco ativos numa mesma carteira. Qual seria o significado de "proporções ideias"? Refiro-me aos valores dos pesos encarregados de gerar o menor risco possível, então, trata-se da iniciativa de encontrar as proporções da carteira de risco mínimo para cinco ativos. É um método específico para ser trabalhado com planilhas, fundamentado nos ensinamentos de Moore e Weatherford (2005) em Tomada de Decisão em Administração com Planilhas Eletrônicas; venho adotando em sala de aula há muito tempo; também já o recomendei em minhas orientações de trabalhos de conclusão de curso em duas oportunidades; pode ser adaptado para quantos ativos você desejar, mas aqui demonstrarei o desenvolvimento com cinco ativos de risco.</div>
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Utilizei os seguintes ativos como cobaias: NATU3, CIEL3, KLBN11, JBSS3 e VLID3. Representando o mercado, o IBOVESPA. Por questão de facilidade de acesso, coletei os dados do google finance; baixei seis planilhas com os históricos das cotações diárias; período de 30/12/2014 até 31/07/2017; trabalhei somente com retornos ao mês, então selecionei apenas as cotações de fechamento do último dia útil de cada mês; como são 32 meses, obtive seis amostras com 31 valores do retorno ao mês (de 30/01/2015 até 31/07/2017).</div>
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Veja o modelo de planilha na Figura 1 - faça logo o download antes de continuar com a leitura desta postagem, assim você poderá seguir todos os passos na prática (<a href="https://docs.google.com/spreadsheets/d/0B6NoDCpMf4EvTGJmUV9jM2pGVzg/edit?usp=sharing&ouid=104522420965306549003&resourcekey=0-Bxt-rhasKe0R3dBicldk1Q&rtpof=true&sd=true" target="_blank"><span style="background-color: blue; color: white;"><b>clique aqui</b></span></a>). </div>
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<b style="background-color: red;"><span style="color: white;">Figura 1</span></b></div>
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Definir os históricos mensais dos retornos dos ativos NATU3, CIEL3, KLBN11, JBSS3 e VLID3 e do mercado (IBOV) é o primeiro passo a ser implementado. Veja a sequência de imagens na Figura 2: inserir =(Q3/Q4-1)*100 na célula I2; arrastar/copiar copiar a fórmula da célula I2 até N2; selecionar e depois arrastar até a linha 33 o intervalo I2:N2. </div>
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<b style="background-color: red;"><span style="color: white;">Figura 2</span></b></div>
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Observe a Figura 3: a matriz das proporções nesta postagem é uma matriz linha com cinco colunas (1x5); trata-se do intervalo A3:E3; como todos sabem, a soma das proporções dos ativos numa carteira deve ser sempre igual a 1,00 (100%); insira =SOMA(A3:E3) na célula F3, pois será necessário confirmar a resposta da soma dos pesos no final do processo, além de ser uma restrição para usar o SOLVER.</div>
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<b><span style="background-color: red; color: white;">Figura 3</span></b> </div>
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A segunda matriz, a matriz das covariâncias, tem cinco linhas e cinco colunas (5x5). Siga atentamente as instruções indicadas na Figura 4: nas células B7, B8, B9, B10 e B11, insira as fórmulas =COVARIAÇÃO.P($J$3:$J$33;J3:J33), =COVARIAÇÃO.P($K$3:$K$33;J3:J33), =COVARIAÇÃO.P($L$3:$L$33;J3:J33), =COVARIAÇÃO.P($M$3:$M$33;J3:J33) e =COVARIAÇÃO.P($N$3:$N$33;J3:J33), respectivamente; em seguida, selecione e arraste até a coluna F o intervalo B7:B11; no final, a matriz covariância será o intervalo B7:F11.</div>
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<b style="background-color: red;"><span style="color: white;">Figura 4</span></b></div>
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Terceira matriz, a matriz dos betas dos ativos, também é uma matriz linha com cinco colunas (1x5). Observe a Figura 5: insira =INCLINAÇÃO(J3:J33;$I$3:$I$33) na célula A15 (calcula o beta da NATU3); o congelamento do intervalo I3:I33 ($I$3:$I$33) tem a ver com o fato de ser o histórico do retorno mensal do mercado; arraste/copie a fórmula da célula A15 até a coluna E. </div>
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<b style="background-color: red;"><span style="color: white;">Figura 5</span></b></div>
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Agora vamos para a melhor parte, explicada a partir da Figura 6: para calcular a variância, o desvio padrão e o beta da carteira com cinco ativos, insira nas células A19, C19 e E19 as fórmulas =SOMARPRODUTO(MATRIZ.MULT(A3:E3;B7:F11);A3:E3), =RAIZ(A19) e =SOMARPRODUTO(A15:E15;A3:E3), respectivamente. </div>
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<b style="background-color: red;"><span style="color: white;">Figura 6</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgI3q68u9nGg2BeC0e9iIRX7lOsyPFYJM2GxCmeaQpd8RC918xd6glo8D8TWyXk94ncMwhDyxz5AyQKJvyzGO_yVz_lfGOGMDZYVw6jkvXD1gBmBzeXKEjCs6nJ3QcmPO-VI-wvFmIRYhY/s1600/C5+6.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="267" data-original-width="413" height="412" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgI3q68u9nGg2BeC0e9iIRX7lOsyPFYJM2GxCmeaQpd8RC918xd6glo8D8TWyXk94ncMwhDyxz5AyQKJvyzGO_yVz_lfGOGMDZYVw6jkvXD1gBmBzeXKEjCs6nJ3QcmPO-VI-wvFmIRYhY/s640/C5+6.png" width="640" /></a></div>
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Só para ter como melhorar a compreensão do conceito de diversificação, nas linhas 21 a 23 inseri mais uma matriz, também do tipo linha com cinco colunas (1x5), com os valores dos desvios padrões dos ativos. Observe a Figura 7: insira =DESVPAD.P(J3:J33) na célula A23 para calcular o risco da NATU3; arraste/copie o procedimento até a célula E3.</div>
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<b style="background-color: red;"><span style="color: white;">Figura 7</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_KWL7rscg3F3Of1sWCAHIWK4OmDWaXsjG5klK-eeSRZWOwTxD8ZdQ7eNFxuA5fpVYiYdDVmGVCUa-nHTuyEtuvhjTrTyPq31jUCIHl9LAojS8yJ4C40VHb_U17ypF87BvGGcYLEc5u2s/s1600/C5+7.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="278" data-original-width="390" height="456" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_KWL7rscg3F3Of1sWCAHIWK4OmDWaXsjG5klK-eeSRZWOwTxD8ZdQ7eNFxuA5fpVYiYdDVmGVCUa-nHTuyEtuvhjTrTyPq31jUCIHl9LAojS8yJ4C40VHb_U17ypF87BvGGcYLEc5u2s/s640/C5+7.png" width="640" /></a></div>
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Nada mais faltando, vamos agora à aplicação do SOLVER. Siga as instruções das 8 a 11. </div>
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Na Figura 8: em Dados, clique em <b style="background-color: blue;"><span style="color: white;">?Solver</span></b> - se você não encontrar no local indicado, então instale o suplemento a partir das opções do Microsoft Excel (<b>Opções / Suplementos / Ir / habilitar Solver</b>). </div>
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<b><span style="background-color: red; color: white;">Figura 8</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7zg_aSR4iCRBa1H15zoGhFg3qVcCD9wi16Wc1TJ79qT9wcXSF2yk5BrJeOdBJeeqhCfpjgIyrWYzVxFxDv_sbYfdHgDMBLisMu6vmrCYNwcs-XwG-VIv4sviY0d-1XmlIAjzG4P7PZcM/s1600/C5+8.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="266" data-original-width="851" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7zg_aSR4iCRBa1H15zoGhFg3qVcCD9wi16Wc1TJ79qT9wcXSF2yk5BrJeOdBJeeqhCfpjgIyrWYzVxFxDv_sbYfdHgDMBLisMu6vmrCYNwcs-XwG-VIv4sviY0d-1XmlIAjzG4P7PZcM/s640/C5+8.png" width="640" /></a></div>
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Na Figura 9: após clicar em <b style="background-color: blue;"><span style="color: white;">?Solver</span></b>, utilize a célula A19 (variância da carteira) como referência à solução; em "Definir Objetivo:", habilite "Mín." (para encontrar a variância da carteira de risco mínimo); em "Alterando Células Variáveis", inclua o intervalo A3:E3 (matriz das proporções); em "Sujeito às Restrições":, adicione a necessidade de a soma das proporções ser igual a 1, portanto, F3=1 (clique em "Adicionar" para inserir a restrição); não desabilite, sob nenhuma hipótese, "Tornar Variáveis Irrestritas Não Negativas"; e o método deve ser GRG Não Linear; clique em Resolver.</div>
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<b style="background-color: red;"><span style="color: white;">Figura 9</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip3hfuVSv6SNP2XoYZ-e4dlnLRWz5g7EFBCMeZbRjQD9KF2d3Y5ZAGZNEMMqBMMC_QwjrlW3I92oWUUX8G7Gf-YjZO8fKmv_yxqEICo9vJWfQrkH4HTpmrXwDNI1_ZeWIpbruH1WfFoPk/s1600/C5+9.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="587" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip3hfuVSv6SNP2XoYZ-e4dlnLRWz5g7EFBCMeZbRjQD9KF2d3Y5ZAGZNEMMqBMMC_QwjrlW3I92oWUUX8G7Gf-YjZO8fKmv_yxqEICo9vJWfQrkH4HTpmrXwDNI1_ZeWIpbruH1WfFoPk/s640/C5+9.png" width="558" /></a></div>
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Na Figura 10: depois de clicar em Resolver, a janela "Resultados do Solver" perguntará se você deseja manter a solução do SOLVER; sua resposta deve ser afirmativa, então pressione OK para aceitar. </div>
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<b style="background-color: red;"><span style="color: white;">Figura 10</span></b></div>
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Vamos analisar o resultado final, exposta na Figura 11: o intervalo A3:E3 traz as proporções obtidas com o SOLVER; se um investidor adotar as mesmas, aceitando como válida a hipótese de os níveis de risco percebidos para cada ativo no período de análise (passado) se repetirem no futuro, NATU3, CIEL3, KLBN11, JBSS3 e VLID3 deverão compor uma carteira com 15,32%, 37,72%, 36,22%, 8,31% e 2,42%, respectivamente. Lembre-se: trata-se da composição responsável por gerar o menor risco possível dentre todas as possibilidades, portanto, trate-a como carteira de risco mínimo. Analise agora a qualidade da diversificação: o risco da carteira, estimado em aproximadamente 4,26%, é bem inferior ao risco do ativo de menor risco, a CIEL3, com desvio padrão de 7,07%. </div>
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<b style="background-color: red;"><span style="color: white;">Figura 11</span></b></div>
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Pronto, mais uma postagem finalizada! E tome análise risco/retorno! Esta é a quarta postagem seguida sobre o tema.</div>
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Façam bom proveito. Registrem dúvidas e sugestões nos comentários. </div>
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Cordialmente,</div>
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Adail Marcos</div>
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<br />Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-2682406432060893592017-08-29T19:43:00.001-07:002017-08-30T08:11:07.673-07:00Gráficos do conjunto de oportunidades de investimento de carteiras com 2 ativos de risco: aplicações com o Microsoft EXCEL<div style="text-align: justify;">
Antes de mais nada, gostaria de fazer o seguinte registro: esta é a terceira postagem consecutiva sobre análise risco/retorno com Excel, continuação da postagem <a href="http://adailmarcos.blogspot.com.br/2017/08/esta-postagem-faz-parte-do-grupo.html" target="_blank">Carteira de Risco Mínimo com 2 Ativos: aplicações com o Microsoft Excel</a> - é praticamente a mesma planilha, ensinarei agora como incluir nela a tabela e os gráficos do conjunto de oportunidades de investimento para carteiras com 2 ativos. Então, vamos lá!</div>
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O desenvolvimento do modelo tem a ação preferencial do Itaú Unibanco (ITUB4) e a <i>unit</i> da Klabin (KLBN11) como "cobaias"; representando o mercado, o IBOVESPA. Por questão de facilidade de acesso, coletei os dados do google finance; baixei três planilhas com os históricos das cotações diárias do IBOVESPA, da KLBN11 e da ITUB4; os históricos pertencem ao período de 30/12/2014 até 31/07/2017; como preferi trabalhar com retornos ao mês, selecionei apenas as cotações do último dia útil de cada mês; então, como são 32 meses, obtive três amostras, cada uma com 31 valores do retorno ao mês (de 30/01/2015 até 31/07/2017).</div>
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Observe a Figura 1 com a estrutura da planilha; está praticamente igual ao modelo da postagem anterior, acrescentei apenas a estrutura da tabela do conjunto de oportunidades de investimento (colunas O a T). Ainda sobre a Figura 1: a soma das proporções dos ativos numa carteira deve ser sempre 1,00 (100%); resolvi trabalhar com 21 carteiras, a primeiro com 100% de KLBN11 e 0% de ITUB4; a última, 0% de KLBN11 e 100% de ITUB4; as demais, são composições obtidas com 5% de variação para as proporções (de cima para baixo, redução da participação de KLBN11 e aumento para ITUB4); você pode trabalhar com mais ou menos carteiras, vai depender da taxa de variação definidas às proporções. Lembre-se de acessar a postagem anterior para baixar o arquivo com a estrutura básica da planilha.</div>
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<b style="background-color: red;"><span style="color: white;">Figura 1</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJeVtOaAGhuYc6BlicayQWA_w9L2h5GP_HUwyzkn2abJj4b3knR0VmJvdqSo2eklDWtVKy4JgRbL9Fi6TPB0nC4JJU9TwWYLEuqDgOda4s-JjRgIext8OMZJNAtXRynfBVWbVsRhclU5Q/s1600/COI+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="501" data-original-width="1077" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJeVtOaAGhuYc6BlicayQWA_w9L2h5GP_HUwyzkn2abJj4b3knR0VmJvdqSo2eklDWtVKy4JgRbL9Fi6TPB0nC4JJU9TwWYLEuqDgOda4s-JjRgIext8OMZJNAtXRynfBVWbVsRhclU5Q/s640/COI+1.png" width="640" /></a></div>
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Conforme apresenta a Figura 2, insira as fórmulas para calcular à carteira 1 as variáveis risco, retorno e beta, respectivamente nas células R4, S4 e T4. Na célula R4, duas fórmulas podem ser usadas: uma com a correlação entre os ativos, sendo =RAIZ((P4*$L$4)^2+(Q4*$M$4)^2+2*P4*Q4*$L$7); ou com a covariância, =RAIZ((P4*$L$4)^2+(Q4*$M$4)^2+2*P4*Q4*$L$7); como as fórmulas das células R4, S4 e T4 devem ser arrastadas/copiadas até a última carteira, então os valores comuns a todos os cálculos precisam participar com suas células fixadas (aquelas com cifrões); os dois cifrões aparecem quando você pressiona a tecla F4 uma vez durante a edição da fórmula dentro da célula; se você pressionar F4 duas vezes, a fixação mudará para =RAIZ((P4*L$4)^2+(Q4*M$4)^2+2*P4*Q4*L$7) e =RAIZ((P4*L$4)^2+(Q4*M$4)^2+2*P4*Q4*L$7), com o cifrão entre a coluna (letra) e a linha (número) de cada célula, sem haver qualquer prejuízo aos cálculos. Em S4 e T4 devem ser congeladas as células com os valores dos retornos e dos betas dos ativos; =P4*$L$3+Q4*$M$3 para o retorno da carteira, podendo ser =P4*L$3+Q4*M$3; =P4*$L$5+Q4*$M$5 para o beta, com iguais resultados quando =P4*L$5+Q4*M$5.<br />
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<b style="background-color: red;"><span style="color: white;">Figura 2</span></b> </div>
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A Figura 3 tem apenas um propósito: informar a necessidade de arrastar/copiar as fórmulas das células R4, S4 e T4 até a última carteira.<br />
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<b style="background-color: red;"><span style="color: white;">Figura 3</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQqgBfndAfCc1iFcJcZ77GpGt_OmlBrIQRVjyhDbo1MmXSrS7TI6xWTp-AUoJD3Rt35FGdgNmHXQ3BC84ISBXvsgiIo9qSnSBqBjfg0eMf7gNhxiosLF3f2WKrxsJzCIFJrRcN7Hc2Rw8/s1600/COI+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="472" data-original-width="492" height="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQqgBfndAfCc1iFcJcZ77GpGt_OmlBrIQRVjyhDbo1MmXSrS7TI6xWTp-AUoJD3Rt35FGdgNmHXQ3BC84ISBXvsgiIo9qSnSBqBjfg0eMf7gNhxiosLF3f2WKrxsJzCIFJrRcN7Hc2Rw8/s320/COI+3.png" width="320" /></a></div>
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Após o preenchimento dos intervalos R4:R24 e S4:S24, 21 pares ordenados estarão disponíveis: X para o risco da carteira; Y, retorno da carteira. Proceda agora da forma como sugere o conteúdo da Figura 4: selecione o intervalo R4:S24; insira o gráfico de dispersão com linhas suaves para obter a primeira versão do gráfico do conjunto de oportunidades de investimento, representado pela relação desvio padrão da carteira (X) e retorno da carteira (Y).<br />
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Resolvi melhorar a aparência do gráfico alterando o padrão de cores e inserindo os títulos dos eixos horizontal (risco da carteira) e vertical (retorno da carteira), exatamente como ratifica a Figura 5. Você pode (deve) fazer a mesma coisa!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgedfwK56uu1MdfiwAkMtGIKQyY7fErJQjifDsr8Lj7xr6uO0_wnrO0UqmdfQc7bYg2zoJGlmg-h7sBKfXCFDrhFdrNxApbhsTyJvoS7DGMS2VYom2pFXutn0CYcl9fIUBNX6AIh6h0cl8/s1600/COI+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="434" data-original-width="593" height="466" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgedfwK56uu1MdfiwAkMtGIKQyY7fErJQjifDsr8Lj7xr6uO0_wnrO0UqmdfQc7bYg2zoJGlmg-h7sBKfXCFDrhFdrNxApbhsTyJvoS7DGMS2VYom2pFXutn0CYcl9fIUBNX6AIh6h0cl8/s640/COI+5.png" width="640" /></a></div>
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Ainda não acabou! Falta inserir a carteira de risco mínimo no gráfico. Seguindo a orientação exposta na Figura 6, insira uma nova série no gráfico, na verdade o par ordenado da carteira de risco mínimo (assunto da postagem anterior) - acesse Selecionar Dados ao clicar com o lado direito do mouse sobre o gráfico para começar a inserir os dados da carteira de risco mínimo (K14 e I14 são, respectivamente, o risco e o retorno).<br />
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<b style="background-color: red;"><span style="color: white;">Figura 6</span></b></div>
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Para fazer o par ordenado da carteira de risco mínimo aparecer na curva, com gráfico selecionado clique em Formatar (veja menu), depois selecione Série "CRM" para Formatar Seleção e inserir um marcador. Instruções demonstradas na Figura 7. CRM é a sigla para carteira de risco mínimo, obviamente.<br />
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<b style="background-color: red;"><span style="color: white;">Figura 7</span></b></div>
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Aparência final do gráfico na Figura 8.<br />
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<span style="background-color: red;"><span style="color: white;"><b>Figura 8</b></span></span></div>
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Você agora deve fazer mais um gráfico, agora com a relação entre beta e retorno da carteira. Repita todos os passos demonstrado à elaboração do gráfico anterior, mas com os intervalos T4:T24 (beta, no eixo horizontal) e S4:S24 (retorno, no eixo vertical). Veja o resultado final na Figura 9.<br />
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<span style="background-color: red;"><span style="color: white;"><b>Figura 9</b></span></span></div>
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Resultado final da planilha na Figura 10.</div>
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<b style="background-color: red;"><span style="color: white;">Figura 10</span></b></div>
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Pronto, trabalho encerrado!<br />
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Registre dúvidas e sugestões nos comentários.<br />
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Cordialmente,<br />
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Adail Marcos<br />
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-89042115319401666162017-08-28T15:07:00.005-07:002022-05-27T12:52:21.597-07:00Carteira de Risco Mínimo com 2 Ativos: aplicações com o Microsoft Excel<div style="text-align: justify;">
Esta postagem faz parte do grupo temático risco/retorno deste blog, sendo uma continuação de<u> <a href="http://adailmarcos.blogspot.com.br/2017/08/risco-e-retorno-de-ativos-isolados.html" target="_blank">Risco e Retorno de Ativos Isolados: cálculo de medidores com o Microsoft Excel</a></u>. Então, caso você tenha alguma dúvida sobre as principais medidas estatísticas usadas para aferir e analisar o risco de ativos isolados, e tudo feito a partir do Microsoft Excel, recomendo clicar no link acima para estudar o conteúdo mais básico, necessário à iniciação em formação de carteiras (objetivo desta postagem).<br />
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Enfatiza-se aqui a formação da carteira de risco mínimo com dois ativos de risco. Trago um modelo de planilha do Microsoft Excel, também adaptável para o Calc, útil para diversos públicos: graduandos, pós-graduandos, investidores iniciantes e professores, por exemplo.</div>
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A apresentação do desenvolvimento do modelo tem as ações preferenciais da Gol (<b>GOLL4</b>) e da Suzano (<b>SUZB5</b>) como "cobaias"; representando o mercado, o <b>IBOVESPA</b>. Por questão de facilidade de acesso, coletei os dados do <i>google finance</i>; baixei três planilhas com os históricos das cotações diárias do <b>IBOVESPA</b>, da <b>GOLL4</b> e da <b>SUZB5</b>; os históricos pertencem ao período de 30/12/2014 até 31/07/2017; como preferi trabalhar com retornos ao mês, selecionei apenas as cotações do último dia útil de cada mês; então, como são 32 meses, obtive três amostras, cada uma com 31 valores do retorno ao mês (de 30/01/2015 até 31/07/2017).</div>
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A Figura <b>1</b> mostra como defini a aparência geral da planilha - <a href="https://docs.google.com/spreadsheets/d/0B6NoDCpMf4EvMDU4bmQ4c2JhMDA/edit?usp=sharing&ouid=104522420965306549003&resourcekey=0-cQtitVk6MSOeYdwRQArXJA&rtpof=true&sd=true" target="_blank">CLIQUE AQUI</a> para baixar o arquivo .xlsx com a estrutura básica, assim você terá como trabalhar imediatamente.<br />
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<b style="background-color: red;"><span style="color: white;">Figura 1</span></b></div>
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Considerei neste exemplo os históricos dos preços de fechamento das ações, bem como a cotação do IBOVESPA - de cada mês do período completo, selecionei apenas o último dia útil. <br />
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<b style="background-color: red;"><span style="color: white;">Figura 2</span></b></div>
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Para cada mês, calcule o retorno de acordo com a fórmula discreta. Na Figura 3, por exemplo, mostro o procedimento para o IBOV; repeita-o para os dois ativos, mas lembre-se de fazer as alterações das células; no caso da ação <b>SUZB5</b>, use =(C3/C4-1)*100), para <b>GOLL4</b>, =(D3/D4-1)*100; arraste as três fórmulas das células E3, F3 e G3 até a linha 33.<br />
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<b style="background-color: red;"><span style="color: white;">Figura 3</span></b> </div>
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Bem, a parte da planilha destacada na Figura 4 tem a ver com a postagem sobre cálculos básicos de risco e retorno para ativos isolados. Utilize as funções MÉDIA(), DESVPAD.P(), INCLINAÇÃO(), CORREL() e COVARIÂNCIA exatamente como instruído. Exemplos: retorno médio mensal da ação <b>GOLL4</b> com =MÉDIA(G3:G33), na célula M3; desvio padrão da ação <b>SUZB5</b> com =DESVPAD.P(F3:F33), na célula L4; beta da ação <b>GOLL4</b> com =INCLINAÇÃO(G3:G33;E3:E33), em M5; correlação entre os ativos com =CORREL(F3:F33;G3:G33); covariância entre os ativos com =COVARIAÇÃO.P(F3:F33;G3:G33).<br />
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<b style="background-color: red;"><span style="color: white;">Figura 4</span></b> </div>
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Veja a Figura 5 para entender como proceder quanto ao cálculo das proporções das duas ações na carteira de risco mínimo. Na célula I11: =(M4^2-L4*M4*L6)/(L4^2+M4^2-2*L4*M4*L6), fórmula voltada à definição da proporção da <b>SUZB5</b> na carteira de risco mínimo. Na célula J11: tem o mesmo propósito da célula I11, mas utiliza outra fórmula, exatamente =(M4^2-L7)/(L4^2+M4^2-2*L7). Diferença entre as fórmulas das células I11 e J11: na I11 participa do cálculo a correlação; na J11, a covariância entre os ativos. Sendo assim, para achar a proporção da <b>GOLL4</b> na carteira de risco mínimo, basta utilizar, na célula K11, =1-I11 ou =1-J11. Finalmente, lembre-se de somar as duas proporções na célula L11, pois se faz preciso conferir se a resposta é mesmo igual a 1 - utilize =I11+K11 ou =J11+K11. <br />
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<b style="background-color: red;"><span style="color: white;">Figura 5</span></b></div>
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Explicações sobre como calcular retorno, risco (desvio padrão) e beta, tudo para a carteira de risco mínimo, estão contidos na Figura 6. Observe: no caso do riso da carteira, duas fórmulas podem ser aplicadas, uma com a covariância e outra com a correlação; na célula K14 tem o cálculo com a covariância, por isso =RAIZ((I11*L4)^2+(K11*M4)^2+2*I11*K11*L7); na L14, com =RAIZ((I11*L4)^2+(K11*M4)^2+2*I11*K11*L4*M4*L6), a correlação. Beta e retorno da carteira são duas médias ponderadas, respectivamente calculadas, nas células I14 e J14, com =J11*L3+K11*M3 e =J11*L5+K11*M5. Como as células I11 e J11 tem a mesma resposta, em todas as fórmulas (Figura 6) I11 pode ser substituído por J11, sem nenhum problema.<br />
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<span style="background-color: red;"><span style="color: white;"><b>Figura 6</b></span></span></div>
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Pronto! Concluída a planilha, resta tirar dúvidas sobre interpretações diversas. Registre-as nos comentários ou procure um docente da área de finanças da sua instituição de ensino.<br />
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Na próxima postagem: tabela e gráfico do conjunto de oportunidades de investimentos da carteira com <b>SUZB5</b> e <b>GOLL4</b> para definir a fronteira eficiente.<br />
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Cordialmente,<br />
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Adail Marcos<br />
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-40543031285839160552017-08-27T12:57:00.002-07:002021-12-03T04:59:35.830-08:00Risco e Retorno de Ativos Isolados: cálculo de medidores com o Microsoft Excel<div style="text-align: justify;">
Muito em função de ser uma possibilidade à aplicação de estatística ao conteúdo de finanças, considero a tradicional análise risco/retorno de ativos isolados e de carteiras um dos temas mais interessantes. Torna-se ainda mais prazeroso quando as demonstrações práticas são realizadas com a colaboração de planilhas eletrônicas, modeladas no Microsoft Excel ou no Calc.</div>
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Esta postagem volta-se ao desenvolvimento de um modelo básico de planilha no Microsoft Excel ao estudo específico da relação risco/retorno de ativos isolados. O conjunto das ilustrações distribuídas a seguir fornece todos os passos, contemplando retorno médio, risco (variância e desvio padrão), beta, covariância, correlação e determinação - os quatro últimos derivam da explicação da relação existente entre ativo isolado e mercado, amparada na regressão linear simples.</div>
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A apresentação do desenvolvimento do modelo tem a ação preferencial da Petrobras (<b>PETR4</b>) como "cobaia"; representando o mercado, o <b>IBOVESPA</b>. Por questão de facilidade de acesso, coletei os dados do <i>google finance</i>; baixei duas planilhas, uma com o histórico da cotação diária do <a href="https://www.google.com/finance/historical?cid=851377182412228&startdate=dec+30%2C+2014&enddate=jul+31%2C+2017&num=30&ei=kwijWejUEJS4esebkSg" target="_blank">IBOVESPA</a> e outra, com a <a href="https://www.google.com/finance/historical?cid=868181216622781&startdate=Dec+30%2C+2014&enddate=Jul+31%2C+2017&num=30&ei=vAmjWYDbNYW9erjKkbAC" target="_blank">PETR4</a>; os históricos são referentes ao período de 30/12/2014 até 31/07/2017; como preferi trabalhar com retornos ao mês, selecionei apenas as cotações do último dia útil de cada mês; então, como são 32 meses, gerei duas amostras, cada uma com 31 valores para o retorno ao mês (de 30/01/2015 até 31/07/2017).</div>
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A Figura <b>1</b> mostra como defini a aparência geral da planilha - <a href="https://docs.google.com/spreadsheets/d/0B6NoDCpMf4EvWGUxLW1hcFdOb2s/edit?usp=sharing&ouid=104522420965306549003&resourcekey=0-688M4_1vzBSn5DmMjYFLyg&rtpof=true&sd=true" target="_blank">clique aqui</a> para baixar o arquivo (.xlsx) com a estrutura básica da planilha. </div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 1</b></span></span></div>
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Primeiro passo, de acordo como mostra as ilustrações da Figura <b>2</b>, calcular o retorno discreto ao mês do <b>IBOVESPA</b> e da <b>PETR4</b> - depois de inserir as fórmulas nas células <b>D3</b> e <b>E3</b>, lembre-se de selecioná-las para arrastar os dois procedimentos até a penúltima linha; se optar por expandir o conteúdo da seleção (clique duplo no canto inferior da seleção), na última linha, a de número 34, os erros surgidos nas células <b>D34</b> e <b>E34</b> devem ser apagados (selecionar e deletar).</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 2</b></span></span></div>
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Segundo passo, calcular os retornos médios do <b>IBOVESPA</b> e da <b>PETR4</b>, exatamente como mostra a Figura <b>3</b> - basta utilizar a função <b>MÉDIA()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>, respectivamente nas células <b>I3</b> e <b>J3</b>.</div>
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<b><span style="color: white;"><span style="background-color: red;">Figura 3</span></span></b></div>
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Quarto passo, calcular a variância do retorno para <b>IBOVESPA</b> e <b>PETR4</b>, seguindo as orientações da Figura <b>4</b> - aplicar, nas células <b>I4</b> e <b>J4</b>, a função <b>VAR.A()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>; preferi o procedimento populacional, pois concordo com as explicações prestadas por Elton, Gruber, Brown e Goetzmann (2012) em Moderna Teoria de Carteiras e Análise de Investimentos, precisamente nas páginas 49 e 50.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 4</b></span></span></div>
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Quinto passo, calcular o desvio padrão do retorno para <b>IBOVESPA</b> e <b>PETR4</b>, seguindo as orientações da Figura <b>5</b> - aplicar, nas células <b>I4</b> e <b>J4</b>, a função <b>DESVPAD.P()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 5</b></span></span></div>
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Sexto passo, calcular a covariância entre <b>IBOVESPA</b> e <b>PETR4</b>, de acordo com a Figura <b>6</b> - utilizar, na célula <b>J6</b>, a função <b>COVARIAÇÃO.P()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 6</b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw5WScxTBtihWqp6LMdRqMme5QbA9slAv-AQvUmh73y47APS53-ps2IDg3d6vgOAJQ4kFVPO7QGfDEWL2xEe5yNli6sZhoxVkUpQNobU0GsxSK9055nHBMVdGZDLRQTwbfNR3Wsc_Kl7Y/s1600/Risco+e+Retorno+Ativo+8.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="178" data-original-width="719" height="158" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw5WScxTBtihWqp6LMdRqMme5QbA9slAv-AQvUmh73y47APS53-ps2IDg3d6vgOAJQ4kFVPO7QGfDEWL2xEe5yNli6sZhoxVkUpQNobU0GsxSK9055nHBMVdGZDLRQTwbfNR3Wsc_Kl7Y/s640/Risco+e+Retorno+Ativo+8.png" width="640" /></a></div>
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Sétimo passo, calcular a correlação entre <b>IBOVESPA</b> e <b>PETR4</b>, da forma como mostra a Figura <b>7 </b>- inserir, na célula <b>J7</b>, a função <b>CORREL()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 7</b></span></span> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUdAbipzeYfifQ5FX5pIe-s1GVZywHNswdM6aWXowRM12OiOIpA9Mz9pilUSXANKp0jVnrNnkAVFoxWzouEkUZ6jeQGh-IbIv88ZUAWix-x33E_zCAgCNnphBNmVZPjXP970KpujLDCYA/s1600/Risco+e+Retorno+Ativo+9.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="191" data-original-width="657" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUdAbipzeYfifQ5FX5pIe-s1GVZywHNswdM6aWXowRM12OiOIpA9Mz9pilUSXANKp0jVnrNnkAVFoxWzouEkUZ6jeQGh-IbIv88ZUAWix-x33E_zCAgCNnphBNmVZPjXP970KpujLDCYA/s640/Risco+e+Retorno+Ativo+9.png" width="640" /></a></div>
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Oitavo passo, calcular o coeficiente de determinação para o ativo (resulta da relação linear entre <b>IBOVESPA</b> e <b>PETR4</b>), seguindo as orientações da Figura <b>8</b> - aplicar a função <b>RQUAD()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>,<b> </b>respectivamente os valores conhecidos de X e Y, na célula <b>J8</b>.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 8</b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8DPcdTZWCWrLU3uqmYJi6B7o2N_iGeuqGGaMLQL_tGHRRVSpKq2Pl55tN2S2_TkPEB2s-s3-iS5EwPGF9klOkqNdfLUdh6E07h3e_C8pmjXnOVjuMD0vxEOj_NKnPx1c6UfKlzkGVJc8/s1600/Risco+e+Retorno+Ativo+10.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="219" data-original-width="657" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8DPcdTZWCWrLU3uqmYJi6B7o2N_iGeuqGGaMLQL_tGHRRVSpKq2Pl55tN2S2_TkPEB2s-s3-iS5EwPGF9klOkqNdfLUdh6E07h3e_C8pmjXnOVjuMD0vxEOj_NKnPx1c6UfKlzkGVJc8/s640/Risco+e+Retorno+Ativo+10.png" width="640" /></a></div>
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Nono passo, calcular o beta do ativo (coeficiente angular da equação da reta capaz de ilustrar a relação linear entre <b>IBOVESPA</b> e <b>PETR4</b>), de acordo com a Figura <b>9</b> - aplicar a função <b>INCLINAÇÃO()</b> com os intervalos <b>D3:D33</b> e <b>E3:E33</b>, respectivamente os valores conhecidos de X e Y, na célula <b>J9</b>.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 9</b></span></span></div>
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Por fim, ainda sugiro inserir um gráfico de dispersão com ajuste linear para melhor avaliar a relação entre <b>IBOVESPA</b> e <b>PETR4</b>. As Figuras <b>10</b> a <b>15</b> trazem instruções sobre como inserir o referido gráfico.</div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 10</b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b>gerar gráfico em branco com a primeira opção do gráfico de dispersão </b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZw0b92F9hNs-06xWg843PvmhZtF2rfnd7VOIFkTQf61N-8vDVSpNFRiBhjmrwJn4Y55nbjwDZ6m53lxA1p-eEeubEOUmQS_jPGwYk19oamTRwY6FSMPwzI2J3WHrrJGs6pVZlCm26qNQ/s1600/Risco+e+Retorno+Ativo+13.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="518" data-original-width="898" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZw0b92F9hNs-06xWg843PvmhZtF2rfnd7VOIFkTQf61N-8vDVSpNFRiBhjmrwJn4Y55nbjwDZ6m53lxA1p-eEeubEOUmQS_jPGwYk19oamTRwY6FSMPwzI2J3WHrrJGs6pVZlCm26qNQ/s640/Risco+e+Retorno+Ativo+13.png" width="640" /></a></div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 11</b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b> clicar com o lado direito do mouse para acessar <span style="color: yellow;">Selecionar Dados... </span> </b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja9_WVFKlwBDnEWMWEvOiaXKmG_CvpTC668zvwhTMkjqgtWSZUsV6tv_cIlBYLffYeaiAKqvWNdWC2i7H-qJqhuppjspirE_ghCKnmkj7JQ3pBP9_ezPeAqb8EOoPFTMF0c7makFKveRs/s1600/Risco+e+Retorno+Ativo+14.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="348" data-original-width="477" height="291" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja9_WVFKlwBDnEWMWEvOiaXKmG_CvpTC668zvwhTMkjqgtWSZUsV6tv_cIlBYLffYeaiAKqvWNdWC2i7H-qJqhuppjspirE_ghCKnmkj7JQ3pBP9_ezPeAqb8EOoPFTMF0c7makFKveRs/s400/Risco+e+Retorno+Ativo+14.png" width="400" /></a></div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 12</b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b> acessar <span style="color: yellow;">Adicionar</span>, em <span style="color: yellow;">Entrada de Legenda (Série) </span></b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 13</b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b> histórico do IBOVESPA em <span style="color: yellow;">Valores de X</span> / histórico da PETR4 em <span style="color: yellow;">Valores de Y </span> </b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDTtoq6mFQc4SM4aXjnejfQTXOiE8b0-ErCUuxpNK7A_GD7GkZZxFFUnHCtZpK3N-OCGcrIrB6fkDCj6mn3uZKwIUO_7agB2GxeMn7aWWx9TdV4Po_xPUIuKSNqUiNusbyi_9mx1kakpA/s1600/Risco+e+Retorno+Ativo+16.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="197" data-original-width="345" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDTtoq6mFQc4SM4aXjnejfQTXOiE8b0-ErCUuxpNK7A_GD7GkZZxFFUnHCtZpK3N-OCGcrIrB6fkDCj6mn3uZKwIUO_7agB2GxeMn7aWWx9TdV4Po_xPUIuKSNqUiNusbyi_9mx1kakpA/s400/Risco+e+Retorno+Ativo+16.png" width="400" /></a></div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 14</b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b> clicar com o lado direito do mouse em qualquer par ordenado para Adicionar <span style="color: yellow;">Linha de Tendência... </span> </b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 15</b></span></span></div>
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<span style="color: white;"><span style="background-color: red;"><b> habilitar <span style="color: yellow;">Linear</span>, <span style="color: yellow;">Exibir Equação no gráfico</span> e <span style="color: yellow;">Exibir valor de R-quadrado no gráfico</span> </b></span></span> </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMfDcj-feRwzwUpJ83clIblxO8q-2PvifIlsnjMvOZDzJfqmUX9ZBoulRyIkRuIlxWy8DI_OmshBptkNm34NP5_uv9KHxwBKEqbQFgkGGtf2YOs2P63f9IUVKq5OlvnyO2oARzJppIYWQ/s1600/Risco+e+Retorno+Ativo+18.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="541" data-original-width="254" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMfDcj-feRwzwUpJ83clIblxO8q-2PvifIlsnjMvOZDzJfqmUX9ZBoulRyIkRuIlxWy8DI_OmshBptkNm34NP5_uv9KHxwBKEqbQFgkGGtf2YOs2P63f9IUVKq5OlvnyO2oARzJppIYWQ/s400/Risco+e+Retorno+Ativo+18.png" width="187" /></a></div>
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Agora formate o gráfico para obter uma aparência melhor.</div>
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Finalmente, a Figura <b>16</b> mostra o resultado final do modelo de planilha, inclusive com o gráfico formatado segundo as minhas preferências. Observe o seguinte: o coeficiente angular da equação contida no gráfico é o beta; logo abaixo, o coeficiente de determinação. </div>
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<span style="color: white;"><span style="background-color: red;"><b>Figura 16</b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcgdb6jK61Pwf6MSSbIIBtma_IeFXg_bgGGPDZfH6Cm4gp4dkWT0O_VyzrTkZ2f5OcNxUW5ASKhS750BCLCdHbA7tVFZvx7qk4OeUCuGIoHn39Kbppnwkc14rTHA7fNh9pAHKJLRZjK7M/s1600/Risco+e+Retorno+Ativo+19.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="493" data-original-width="666" height="472" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcgdb6jK61Pwf6MSSbIIBtma_IeFXg_bgGGPDZfH6Cm4gp4dkWT0O_VyzrTkZ2f5OcNxUW5ASKhS750BCLCdHbA7tVFZvx7qk4OeUCuGIoHn39Kbppnwkc14rTHA7fNh9pAHKJLRZjK7M/s640/Risco+e+Retorno+Ativo+19.png" width="640" /></a></div>
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Um resumo sobre a situação mensal da <b>PETR4</b>, de 30/01/2015 até 31/07/2017: retorno mensal médio de 2,47%; risco de 18,60%, amparado no desvio padrão (perspectiva simétrica de análise da clássica abordagem média/variância); forte correlação positiva com o mercado (0,92), quase perfeita; beta muito acima de 1,00, exatamente 2,62, acusando um nível de risco 1,62 vezes superior ao risco de mercado; influência sistemática de 84% sobre o risco total do ativo (interpretação resultante da transformação do coeficiente de determinação numa porcentagem).</div>
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Dúvidas sobre o modelo de planilha? Registre-as nos comentários. Queres aprender mais sobre as interpretações? Pergunte nos comentários (responderei quando possível) e peça ajuda aos docentes da sua instituição de ensino. </div>
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Cordialmente,</div>
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Professor Adail Marcos</div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-59910653252607467762017-02-26T07:34:00.001-08:002019-01-26T18:51:37.223-08:00Juros Simples: como calcular juros e montantes com a HP-17bII+<div class="MsoNormal" style="text-align: justify;">
Esta postagem dedicada-se à utilização da calculadora
financeira <b>HP-17bII+</b> na resolução de exercícios de juros simples, precisamente
quanto ao cálculo de valores para juros e montantes.<br />
<br />
Início da atualização - 27 de janeiro de 2019.<br />
<br />
Trata-se de uma pequena amostra do primeiro volume da coleção "HP-17bII+ para Matemática Financeira", já disponível no site da AMAZON para venda. Todos os procedimentos detalhados na coleção são inteiramente compatíveis com a calculadora HP-19bII+, portanto, os usuários de ambas encontrarão na coleção um suporte completo e objetivo. O ponto de maior destaque está na formulação de uma equação no SOLVER com a função condicional IF para resolver praticamente tudo de Juros Simples, sem a necessidade de fazer adaptações cansativas ou cálculos manuais complicados.<br />
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Clique na imagem destacada a seguir para ser direcionado diretamente ao site da AMAZON.<br />
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<a href="https://www.amazon.com.br/dp/B07N54KKPS/ref=sr_1_1?s=digital-text&ie=UTF8&qid=1548555542&sr=1-1" style="text-align: center;" target="_blank"><img border="0" data-original-height="1600" data-original-width="1111" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixLbfYXWsmjOrsw4XLEm18eFlKdkijDklpAwbSrPV7KbuVZJhx24e-DtOun8NYjCRRTBE3nWbG9NWuraZqOrgv8Ywgn4QF4F_NSgLUsrl69SwXuPaHVMWJca3J90RIRHp8THS8PDCm43g/s320/CAPA.png" width="222" /></a><br />
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Fim da atualização - 27 de janeiro de 2019.<br />
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Dois menus podem ser empregados: <b><span style="background-color: black; color: white;">VAR%</span></b> e <b><span style="background-color: black; color: white;">%TOT</span></b>; são menus
embutidos no menu <b><span style="background-color: black; color: white;">COM</span></b>, originalmente
destinado à solução de questões envolvendo percentagens comerciais; <b><span style="background-color: black; color: white;">VAR%</span></b> visa calcular variações
percentuais, como a mudança ocorrida no preço de venda de uma dada mercadoria em
duas datas diferentes, por exemplo; <b><span style="background-color: black; color: white;">%TOT</span></b> define o quanto uma variável representa de outra, como o percentual da margem
de contribuição unitária em relação ao preço de venda, por exemplo.</div>
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O Quadro 1 esclarece como acessar o menu <b><span style="background-color: black; color: white;">VAR%</span></b>.</div>
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Por sua vez, o Quadro 2 esclare como acessar o menu <b><span style="background-color: black; color: white;">%TOT</span></b>.</div>
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Para retroceder ao menu anterior, basta pressionar a tecla <b style="background-color: black;"><span style="color: white;">EXIT</span></b>. Se necessário retornar diretamente ao menu principal, deve-se acionar a tecla de prefixo azul (na versão prateada da calculadora) ou dourada (na versão da calculadora nas cores preto e dourado) e a tecla com a função secundária <b><span style="background-color: black; color: white;">MAIN</span></b> (abaixo da tecla com a função primária <b style="background-color: black;"><span style="color: white;">EXIT</span></b>); também dá para retornar ao menu principal a partir da tecla <b style="background-color: black;"><span style="color: white;">EXIT</span></b>, basta pressioná-la mais de uma vez, em quantidade suficiente ao alcance do referido objetivo.</div>
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Os procedimentos demonstrados a seguir devem ser preferencialmente realizados com a máquina programada para a notação aritmética de cálculo; pode ser feito com a função secundária (azul ou dourada) localizada na parte inferior da tecla <b style="background-color: black;"><span style="color: white;">DSP</span></b>; depois de pressionar em sequência a tecla de prefixo e a tecla da função secundária <b style="background-color: black;"><span style="color: white;">MODES</span></b>, basta escolher o rótulo <b style="background-color: black;"><span style="color: white;">ALG</span></b> – realizado o procedimento, usa-se <b style="background-color: black;"><span style="color: white;">EXIT</span></b> para voltar ao menu principal.</div>
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Agora sim! Depois de prestados os esclarecimentos preliminares à utilização da HP-17bII+, os quadros apresentados a seguir explicam como resolver questões de juros simples com os menus <b><span style="background-color: black; color: white;">VAR%</span></b> e <b><span style="background-color: black; color: white;">%TOT</span></b>, com ênfase na obtenção de respostas para juros e montantes. </div>
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Se uma questão fornecer <b>I</b> (taxa de juros), <b>N</b> (prazo) e <b>P</b> (principal ou capital inicial) para calcular <b>J</b> (juro) e <b>M</b> (montante), no Quadro 3 constam todos os passos exigidos à solução com o menu <b><span style="background-color: black; color: white;">VAR%</span></b>: 1º passo, inserir o produto entre <b>I</b> e <b>N</b> em <b><span style="background-color: black; color: white;">VAR%</span></b> (digite a taxa, acione a tecla de multiplicação, digite o prazo e pressione a tecla de rótulo abaixo de <b><span style="background-color: black; color: white;">VAR%</span></b>); 2º passo, inserir o <b>P</b> em <b><span style="background-color: black; color: white;">ANT</span></b> (digite o valor do capital inicial, posteriormente pressione a tecla de rótulo abaixo de <b><span style="background-color: black; color: white;">ANT</span></b>); 3º passo, calcular o valor do <b>M</b> (pressione a tecla de rótulo abaixo de <b><span style="background-color: black; color: white;">NOVA</span></b>, o resultado será o montante); 4º passo, calcular o valor do <b>J</b> (pressione a tecla de subtração, recupere o valor do <b>P</b> pressionando em sequência as teclas <b><span style="background-color: black; color: white;">RCL</span></b> e a do rótulo <b><span style="background-color: black; color: white;">ANT</span></b> e utilize a tecla de igualdade); no final do procedimento, o valor destacado no visor será <b>J</b>; sendo preciso visualizar novamente o valor do <b>M</b>, pressione em sequência as teclas <b><span style="background-color: black; color: white;">RCL</span></b> e a do rótulo <b><span style="background-color: black; color: white;">NOVA</span></b>.</div>
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Conhecidos os valores de <b>I</b>, <b>N</b> e <b>P</b> para calcular <b>J</b> e <b>M</b>, o Quadro 4 traz os passos sugeridos à solução com o menu <b><span style="background-color: black; color: white;">%TOT</span></b>: 1º passo, inserir o produto entre <b>I</b> e <b>N</b> em <b><span style="background-color: black; color: white;">%TOT</span></b> (digite a taxa, acione a tecla de multiplicação, digite o prazo e pressione a tecla de rótulo abaixo de <b><span style="background-color: black; color: white;">%TOT</span></b>); 2º passo, inserir o <b>P</b> em <b><span style="background-color: black; color: white;">TOTAL</span></b> (digite o valor do capital inicial e pressione a tecla de rótulo abaixo de <b><span style="background-color: black; color: white;">TOTAL</span></b>); 3º passo, calcular o valor do <b>J</b> (pressione a tecla de rótulo abaixo de <b><span style="background-color: black; color: white;">PARCL</span></b>, o resultado será o juro); 4º passo, calcular o valor do <b>M</b> (pressione a tecla de adição, recupere o valor do <b>P</b> com as teclas <b><span style="background-color: black; color: white;">RCL</span></b> e a do rótulo <b><span style="background-color: black; color: white;">TOTAL</span></b> e finalize com a tecla de igualdade); o valor destacado no visor, ao término de todos os passos, será <b>M</b>; sendo preciso visualizar novamente o valor do <b>J</b>, pressione em sequência as teclas <b><span style="background-color: black; color: white;">RCL</span></b> e a do rótulo <b><span style="background-color: black; color: white;">PARCL</span></b>.</div>
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Para demonstrar o uso dos dois procedimentos expostos com os Quadros 3 e 4, observe o exercício abaixo (a ficha catalográfica esclarece a fonte): capital inicial, taxa de juros e prazo de R$5.000,00, 12% aa e 2 anos, respectivamente; a partir dos dados em destaque, tem-se como calcular os valores de <b>J</b> e <b>M</b>.</div>
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O Quadro 3.1 apresenta os cálculos das variáveis <b>J</b> e <b>M</b> com o menu <b><span style="background-color: black; color: white;">VAR%</span></b>.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic5rwP4w1ED9L-DvnKeRn4zeSTY3K-AYfXS0_IBkiZ4DOZlUzePAV-aqXoczXE1yf-ILtSYQfTLBaRjG3YeZ9G-m6GmodUHL02qiexXv3DoYC2m3iFm96trTHGoBQ-HKomPTlAF2-8JBQ/s1600/Quadro+3_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic5rwP4w1ED9L-DvnKeRn4zeSTY3K-AYfXS0_IBkiZ4DOZlUzePAV-aqXoczXE1yf-ILtSYQfTLBaRjG3YeZ9G-m6GmodUHL02qiexXv3DoYC2m3iFm96trTHGoBQ-HKomPTlAF2-8JBQ/s1600/Quadro+3_1.png" /></a></div>
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Por fim, o Quadro 4.1 apresenta os cálculos das variáveis <b>J</b> e <b>M</b> com o menu <b><span style="background-color: black; color: white;">%TOT</span></b></div>
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Espero que esta postagem tenha sido útil aos usuários da calculadora <b>HP-17bII</b>+.</div>
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Em breve, mais exercícios serão explorados em vídeos do canal <b>MAFIN.</b></div>
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<b><a href="https://www.youtube.com/channel/UCBjheB5Oe3h1bcO_98CLjmQ" target="_blank"><span style="font-size: x-large;">Canal MAFIN</span></a></b></div>
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Até a próxima postagem! </div>
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Cordialmente,</div>
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Adail Marcos</div>
Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-74510340277974165192015-04-22T07:01:00.001-07:002015-04-22T07:02:03.979-07:00ATENÇÃO: o conteúdo desde blog também será explorado no Canal MAFIN (YOUTUBE). <br />
Link para o Canal MAFIN: <a href="https://www.youtube.com/channel/UCBjheB5Oe3h1bcO_98CLjmQ/feed">https://www.youtube.com/channel/UCBjheB5Oe3h1bcO_98CLjmQ/feed</a><br />
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Serão 5 vídeos por semana até contemplar todo o conteúdo desde blog.<br />
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Cordialmente,<br />
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Adail MarcosAdail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-60279756344582666242014-06-11T20:13:00.001-07:002014-06-12T07:40:55.259-07:00Risco e Retorno com o uso do Microsoft Excel: gráfico explicativo dos benefícios da diversificação (correlação) em carteiras com dois ativos de risco<div style="text-align: justify;">
Em minhas aulas na disciplina Administração Financeira do curso de Administração da UFCG, especialmente no semestre 2014.1, tenho percebido um excelente nível de interesse por parte dos alunos em relação ao assunto "Diversificação em Carteiras com dois Ativos de Risco" quando, logo após as exposições teóricas, executo as demonstrações práticas com o Microsoft Excel. A possibilidade de mostrar instantaneamente as mudanças no conjunto de oportunidades de investimento a partir de simples alterações no valor da correlação, isso depois de pronto um bom modelo de planilha, aguça consideravelmente a curiosidade até mesmo dos discentes menos afeitos ao conteúdo de finanças. Todos se mostram inconformados em apenas observar o gráfico sendo alterado, querem aprender a fazer seus próprios modelos de planilhas - e conseguem, inclusive com a promoção de incrementos didáticos substanciais aos gráficos (alguns exageram só um pouquinho com as cores). </div>
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Sendo assim, resolvi fazer uma postagem dedicada exclusivamente à elaboração de um modelo simples de planilha ao estudo dos benefícios da diversificação em carteiras com dois ativos de risco. Por motivos didáticos, evitei substituir as fórmulas usuais do assunto por funções do Microsoft Excel - mas já estou finalizando outra postagem, com duas blue chips de empresas brasileiras, na qual mostrarei como usar somente funções. </div>
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Antes de começar a desenvolver o modelo básico exposto a seguir, faça uma breve revisão do tópico diversificação em carteiras com dois ativos de risco. </div>
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Para começar, construa o modelo de planilha apresentado nas Figuras 1 e 2. Detalhe: a Figura 2 não está errada; considerei 10.001 carteiras em virtude da possibilidade de obtenção de um único gráfico capaz de agrupar todos os conjuntos de oportunidades de investimento para correlações 1, 0,5, 0, -0,5 e -1 e, também, por permitir considerar precisamente todas as carteiras de risco mínimo; para elencar 10.001 composições, utilizei uma diferença entre as proporções dos ativos "A" e "B" de apenas 0,0001 (0,01%). Ainda, "W RM", coluna "A", refere-se aos valores das proporções dos ativos nas carteiras de risco mínimo. </div>
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Figura 1</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXFixhL7fx70WDXx68oH9OWNpiArNP4cLlBdMSmXT039m0yHEI3NOB5kbU4w-f1z8e47ROohV2fx-r7A1qR3ho44hR8JsKJIItf6B95ihdu6wcheKIFEzDdX1O6hVvtTLKVspC9OgBDC4/s1600/BLOG+CARTEIRA+7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXFixhL7fx70WDXx68oH9OWNpiArNP4cLlBdMSmXT039m0yHEI3NOB5kbU4w-f1z8e47ROohV2fx-r7A1qR3ho44hR8JsKJIItf6B95ihdu6wcheKIFEzDdX1O6hVvtTLKVspC9OgBDC4/s1600/BLOG+CARTEIRA+7.png" height="419" width="640" /></a></div>
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Figura 2</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDaUKOzxf_44uCrILqSwxj_6uHdmyeRkKnd0aBE0CFoRfHX20XIgTIHavvLEv6K-GG3axuhVarShcnDPGkVhsGFMqA-b7SbbA1pmNUe4V1FgzI_Qjef4997orpQUnsgVzv7_hMAXRrVFE/s1600/BLOG+CARTEIRA+8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDaUKOzxf_44uCrILqSwxj_6uHdmyeRkKnd0aBE0CFoRfHX20XIgTIHavvLEv6K-GG3axuhVarShcnDPGkVhsGFMqA-b7SbbA1pmNUe4V1FgzI_Qjef4997orpQUnsgVzv7_hMAXRrVFE/s1600/BLOG+CARTEIRA+8.png" height="320" width="640" /></a></div>
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Comecemos então com as composições responsáveis pelas carteiras de risco mínimo:</div>
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<li style="text-align: justify;">para dois ativos perfeitamente correlacionados, a carteira de risco mínimo tem o mesmo risco do ativo de menor risco, por isso atribua 0,00% para o ativo "A", por ter o maior risco, e 100% para "B", exatamente como descrito na Figura 3;</li>
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Figura 3</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrSnvtleEuxg5x4TioNYTsh2YW6IWaOdmDg33WYUls0wjeqVsyjYlkyKO5GF4wTqqoPO2s6XFG7WMGarFKBta49NkiJcMNknQyZJUPpH4M4ZW8QxexU-T01ZPuFaf70yZBD2Kk_yD7oaQ/s1600/BLOG+CARTEIRA+9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrSnvtleEuxg5x4TioNYTsh2YW6IWaOdmDg33WYUls0wjeqVsyjYlkyKO5GF4wTqqoPO2s6XFG7WMGarFKBta49NkiJcMNknQyZJUPpH4M4ZW8QxexU-T01ZPuFaf70yZBD2Kk_yD7oaQ/s1600/BLOG+CARTEIRA+9.png" height="197" width="400" /></a></div>
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<li style="text-align: justify;">de acordo com a Figura 4, para a hipótese de os ativos apresentarem correlação de 0,5, a fórmula de cálculo das proporções de risco mínimo já pode ser aplicada - recomendo arredondar para 4 casas decimais a resposta, por isso inseri a fórmula dentro da função "ARRED" (0,00% para "A" significa um conjunto de oportunidades de investimento sem a presença de uma carteira com risco inferior ao risco do ativo de menor risco, sendo a mesma situação quando a correlação é perfeitamente positiva, todavia, como será mostrado mais adiante, benefícios da diversificação são percebidos quando a correlação está abaixo de 1,00);</li>
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Figura 4</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHkgdVjicl2pZHA0tgz-27MJ0i74Xx_Hk40PLpDYSr8cO8mPVD4jsF-3GtC9F0ED2NIpmetB9l9VI_O5TlDxhh005zR35iNKARzDUkwRD4vRM7Z82gl3RcPcMP_G1xUF31oPX59wwGo5k/s1600/BLOG+CARTEIRA+10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHkgdVjicl2pZHA0tgz-27MJ0i74Xx_Hk40PLpDYSr8cO8mPVD4jsF-3GtC9F0ED2NIpmetB9l9VI_O5TlDxhh005zR35iNKARzDUkwRD4vRM7Z82gl3RcPcMP_G1xUF31oPX59wwGo5k/s1600/BLOG+CARTEIRA+10.png" /></a></div>
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<li style="text-align: justify;">a Figura 5 traz a hipótese de a correlação entre os ativos ser 0,0, neste caso a fórmula de cálculo das proporções de risco mínimo assume uma versão mais simples (20,00% para "A", diferente das duas circunstâncias anteriores, significa um conjunto de oportunidades de investimento com a presença de carteiras com riscos inferiores ao risco do ativo de menor risco, situação onde os benefícios da diversificação são bem mais intensos aos constatados com a correlação 0,5);</li>
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Figura 5</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL9-5f3gA7-Pxoz2cFfxJqvWiVxdhQGYASHHLy1RxECZjXpOULqWRIxca18UQBINxtebDkF39M9BqaXK6mjYHt7MknEYbxQZT3LTZYrNkH8G5TaSlBcwqn2po_Tv9VxzrYp3OKKygMG_k/s1600/BLOG+CARTEIRA+11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL9-5f3gA7-Pxoz2cFfxJqvWiVxdhQGYASHHLy1RxECZjXpOULqWRIxca18UQBINxtebDkF39M9BqaXK6mjYHt7MknEYbxQZT3LTZYrNkH8G5TaSlBcwqn2po_Tv9VxzrYp3OKKygMG_k/s1600/BLOG+CARTEIRA+11.png" /></a></div>
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<li style="text-align: justify;">sendo de -0,5 a correlação, Figura 6, aplica-se novamente a fórmula tradicional de cálculo das proporções de risco mínimo (28,57% para "A" informa um conjunto de oportunidades de investimento com a presença de mais carteiras com riscos inferiores ao risco do ativo de menor risco, indicando maior incidência de benefícios da diversificação);</li>
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Figura 6<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6lswvbIbJ9Fi5OUOCUfK5h3wHn4RqKlDakQlXuWckjE8q_d6S2_KpXPIJ67TUJ6AcBMfN2Rm3NWaEHsJ3KcIkRdeUekTlvifcg1rT3N8vmXF895eKXln-nH39kioK-0DgKK0sDgYQmrA/s1600/BLOG+CARTEIRA+12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6lswvbIbJ9Fi5OUOCUfK5h3wHn4RqKlDakQlXuWckjE8q_d6S2_KpXPIJ67TUJ6AcBMfN2Rm3NWaEHsJ3KcIkRdeUekTlvifcg1rT3N8vmXF895eKXln-nH39kioK-0DgKK0sDgYQmrA/s1600/BLOG+CARTEIRA+12.png" /></a></div>
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<li style="text-align: justify;">finalmente, com correlação -1,0, retratada na Figura 7, aplica-se novamente mais uma versão simplificada da fórmula dedicada ao cálculo das proporções de risco mínimo (33,33% para "A" informa um conjunto de oportunidades de investimento com a presença de mais carteiras com riscos inferiores ao risco do ativo de menor risco e, ainda, 33,33% é exatamente a proporção a ser atribuída ao ativo "A" à obtenção do benefício máximo da diversificação, com o risco da carteira totalmente anulado).</li>
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Figura 7</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy87zesyPc4_kYJoueaBEn-jZz1O_31UC5bb4SFcrgzjPd8t7GtsECGGQk_PKVQ-9dQ5rucGZylgP3XpPGLb0QAvJj0MMIQaFRlZ7FFu28iSqBrcsXdzNDBcYSXEZ2N8l6VX3B2jt5tKM/s1600/BLOG+CARTEIRA+13.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy87zesyPc4_kYJoueaBEn-jZz1O_31UC5bb4SFcrgzjPd8t7GtsECGGQk_PKVQ-9dQ5rucGZylgP3XpPGLb0QAvJj0MMIQaFRlZ7FFu28iSqBrcsXdzNDBcYSXEZ2N8l6VX3B2jt5tKM/s1600/BLOG+CARTEIRA+13.png" /></a></div>
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Calculadas as carteiras de riscos mínimos para as correlações 1, 0,5, 0, -0,5 e -1, o próximo passo no estudo dos benefícios da diversificação deve ser direcionado à definição dos conjuntos de oportunidades de investimento. </div>
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As Figuras 8 a 17 detalham as formações dos conjuntos de oportunidades de investimento, onde: </div>
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<li style="text-align: justify;">como mostra a Figura 8, as proporções dos ativos "A" e "B" devem ser inseridas nas colunas "F" e "G" - a primeira carteira, justamente a carteira de risco mínimo para as correlações 1 e 0,5, tem como composição 0% para "A" e 100% para "B" (digite a fórmula 1 menos a proporção de "A" na célula "G4"); </li>
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Figura 8</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBf5uDvDorttbXCPzmcHVV0oXMOKWXAGFzo67sY6byL2XQ66cIgL_7knqWJ8fyR49PZDdIdrIuzpUYcMQZTMv70gh_oeIqAvKWL4329m6AShL1-BYrVOXbDdLmEAa9HvRV2Ebl4ci9Wwc/s1600/BLOG+CARTEIRA+14.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBf5uDvDorttbXCPzmcHVV0oXMOKWXAGFzo67sY6byL2XQ66cIgL_7knqWJ8fyR49PZDdIdrIuzpUYcMQZTMv70gh_oeIqAvKWL4329m6AShL1-BYrVOXbDdLmEAa9HvRV2Ebl4ci9Wwc/s1600/BLOG+CARTEIRA+14.png" /></a></div>
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<li>as Figuras 9 e 10 ensinam como criar a série de proporções para "A", a ser iniciada com 0,00% e finalizada com 100,00% e com variação de 0,0001 (0,01%) - segundo a Figura 9, em "Página Inicial" procure por "Preencher", depois, conforme a explicação da Figura 10, defina as características da série; </li>
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Figura 9</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg5v6HZOpt_jz7Ld4dSu5R5mPVGTy7f_88mi3OGO0oCpHTAToymgXIaDrfor9wR9kfs1sgzs36aQHyQwR1j3cXkPoVE8Qok-evPoQNmf6DTcms7zQNLxl5aZGkNJ5OP0_YkMit4SQD6-8/s1600/BLOG+CARTEIRA+15.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg5v6HZOpt_jz7Ld4dSu5R5mPVGTy7f_88mi3OGO0oCpHTAToymgXIaDrfor9wR9kfs1sgzs36aQHyQwR1j3cXkPoVE8Qok-evPoQNmf6DTcms7zQNLxl5aZGkNJ5OP0_YkMit4SQD6-8/s1600/BLOG+CARTEIRA+15.png" height="152" width="640" /></a></div>
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Figura 10</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR4jqsTw1fejXoV3hXBOMbf2uO-gqWWbz2BVBBr8Ip97sxLYgzNVrfORx2MhR0vWAl1ykrwICbineR-k96jgwkzxFJpw7zfjZqE0Mnv4EWsAJXu9SuiebzAchEb0CiAnKQFyZF8T6IWZE/s1600/BLOG+CARTEIRA+16.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR4jqsTw1fejXoV3hXBOMbf2uO-gqWWbz2BVBBr8Ip97sxLYgzNVrfORx2MhR0vWAl1ykrwICbineR-k96jgwkzxFJpw7zfjZqE0Mnv4EWsAJXu9SuiebzAchEb0CiAnKQFyZF8T6IWZE/s1600/BLOG+CARTEIRA+16.png" height="229" width="640" /></a></div>
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<li><span style="text-align: justify;">a Figura 11 orienta a clicar duas vezes rápido na extremidade direita inferior da célula "G4", correspondente ao valor da proporção do ativo "B" na primeira carteira, assim o procedimento "1 menos a proporção do ativo A" será expandido até a última carteira;</span></li>
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Figura 11</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvIkZlE0bUrDuyEokN4Z_gtwWDfXxyLUvFInl4N2-FzV6PV56mLx2jKdfm7EN67UmwmTHvjOOGq0rQfX_VKOkBuUqguqp58yllIiUEaKJiQCkX_4deP48iRELE09ayZMEWy0iQgbwBk40/s1600/BLOG+CARTEIRA+17.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvIkZlE0bUrDuyEokN4Z_gtwWDfXxyLUvFInl4N2-FzV6PV56mLx2jKdfm7EN67UmwmTHvjOOGq0rQfX_VKOkBuUqguqp58yllIiUEaKJiQCkX_4deP48iRELE09ayZMEWy0iQgbwBk40/s1600/BLOG+CARTEIRA+17.png" /></a></div>
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<li style="text-align: justify;">conforme a demonstração da Figura 12, calcule o retorno da primeira carteira através da média ponderada envolvendo os retornos isolados dos ativos e suas respectivas proporções (pesos), depois clique duas rápido no lado direito inferior da célula "H4" para expandir o procedimento - não esqueça de fixar as células com os valores dos retornos dos ativos;</li>
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Figura 12</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUeQz7hWzDc2tOPk6Sj7l-djlJToe0qQXMsDToLrDW1vUlvA6OnQhU0Ny4YYTI3cSYqjVLIduaOoXisqtKLfaJrPyJAxfZrf1DjUHQOE4gGSApE9qh4tWw5NR4gEWwR4dvXmKaD4kWWO8/s1600/BLOG+CARTEIRA+18.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUeQz7hWzDc2tOPk6Sj7l-djlJToe0qQXMsDToLrDW1vUlvA6OnQhU0Ny4YYTI3cSYqjVLIduaOoXisqtKLfaJrPyJAxfZrf1DjUHQOE4gGSApE9qh4tWw5NR4gEWwR4dvXmKaD4kWWO8/s1600/BLOG+CARTEIRA+18.png" height="190" width="640" /></a></div>
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<li style="text-align: justify;">na Figura 13 constam as instruções ao cálculo dos riscos de todas as carteiras sob a hipótese de correlação perfeitamente positiva, sendo assim, e somente com correlação 1,00, a fórmula tradicionalmente empregada na apuração do risco de uma carteira (em amarelo) pode ser substituída por uma versão simplificada (fórmula em verde), procedimento muito semelhante ao cálculo dos retornos das carteiras (média ponderada) - digite a fórmula simplificada tendo o cuidado de fixar as células dos riscos dos ativos, na sequência clique duas vezes rápido no lado direito inferior da célula "I4" para calcular os riscos de todas as carteiras;</li>
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Figura 13</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGWgx4dWze9kZxuIHHr1zwNdtrVlGokVkn_zErj4LwMbN-yHpnHeLkbcGYmzJV1cYhId-2rTNZkZgP9DRpFccU1v2DMhBImYo4a9Gq3W-Es155gxYdv2tw5wUlXOv-QnbnsOmFh6lxqX4/s1600/BLOG+CARTEIRA+19.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGWgx4dWze9kZxuIHHr1zwNdtrVlGokVkn_zErj4LwMbN-yHpnHeLkbcGYmzJV1cYhId-2rTNZkZgP9DRpFccU1v2DMhBImYo4a9Gq3W-Es155gxYdv2tw5wUlXOv-QnbnsOmFh6lxqX4/s1600/BLOG+CARTEIRA+19.png" height="146" width="640" /></a></div>
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<li style="text-align: justify;">a Figura 14 detalha os passos ao cálculo dos riscos de todas as carteiras sob a hipótese de correlação estimada em 0,5, justificativa ao emprego direto da fórmula clássica do risco de uma carteira - digite a fórmula fixando as células com os riscos dos ativos e a correlação entre ambos, posteriormente clique duas vezes rápido no lado direito inferior da célula "J4" para calcular os riscos das carteiras distribuídas abaixo;</li>
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Figura 14</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR_6X_EaZpLrjRgzEeOmbojDkj1RDA19IoQJ4eOzqF3AnrsxQUwcmjYMVh7rwxzyPKMp9IUK5m4L8ZenfkgGtpzJ2nSJgRWRwLrrwErSjdYbT1Elsv4qRQrU5hsE-gNxxKBonCutVTA2o/s1600/BLOG+CARTEIRA+20.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR_6X_EaZpLrjRgzEeOmbojDkj1RDA19IoQJ4eOzqF3AnrsxQUwcmjYMVh7rwxzyPKMp9IUK5m4L8ZenfkgGtpzJ2nSJgRWRwLrrwErSjdYbT1Elsv4qRQrU5hsE-gNxxKBonCutVTA2o/s1600/BLOG+CARTEIRA+20.png" height="158" width="640" /></a></div>
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<li style="text-align: justify;">a Figura 15 mostra como calcular os riscos de todas as carteiras sob a hipótese de correlação nula, sendo assim, a fórmula clássica do risco de uma carteira (em amarelo) pode ser substituída por outra versão simplificada (fórmula em verde) - lembre-se de digitar a fórmula fixando as células dos riscos dos ativos, depois clique duas vezes rápido no lado direito inferior da célula "K4" para calcular os riscos de todas as carteiras;</li>
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Figura 15</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNMBIFlzEP-9gbAFXVRcykIxkb_WGdaWcvRNsVVKO0bo8F6upkbF-gghhDuJmUm2Qzm-xLuGktFYoK_I6Ya7s3j1TY5rQovgQLWV5vXfTMnNXkBe4wP4gEWIrBH51u5F0JtlgLvWlk79U/s1600/BLOG+CARTEIRA+21.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNMBIFlzEP-9gbAFXVRcykIxkb_WGdaWcvRNsVVKO0bo8F6upkbF-gghhDuJmUm2Qzm-xLuGktFYoK_I6Ya7s3j1TY5rQovgQLWV5vXfTMnNXkBe4wP4gEWIrBH51u5F0JtlgLvWlk79U/s1600/BLOG+CARTEIRA+21.png" height="226" width="640" /></a></div>
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<li style="text-align: justify;">as Figuras 16 e 17 expõem os passos para calcular os riscos de todas as carteiras sob as hipóteses de correlações estimadas em -0,5 e -1, respectivamente, sendo suficiente em ambos os casos aplicar a fórmula clássica do risco de uma carteira - é necessário fixar as células com os riscos dos ativos e as correlações entre ambos.</li>
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Figura 16</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOSeJwYrwl4UNc4QAgGSItoYMNgt51MOBngRlf2EpTb1CT0SVmnOjSBihTyKLQkz2L2NaoxavrHN5HvDK_sKHyeQapOpqx14tNufrvekDZasW6brZP0COeNwAaSLaGFIrcx33af6PIvtU/s1600/BLOG+CARTEIRA+22.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOSeJwYrwl4UNc4QAgGSItoYMNgt51MOBngRlf2EpTb1CT0SVmnOjSBihTyKLQkz2L2NaoxavrHN5HvDK_sKHyeQapOpqx14tNufrvekDZasW6brZP0COeNwAaSLaGFIrcx33af6PIvtU/s1600/BLOG+CARTEIRA+22.png" height="196" width="640" /></a></div>
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Figura 17</div>
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Definidas as carteiras com os menores riscos e formados os conjuntos de oportunidades de investimento para correlações 1, 0,5, 0, -0,5 e -1, agora basta construir o gráfico explicativo usado no estudo dos benefícios da diversificação.</div>
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As próximas Figuras, 18 a 31, expõem todos os passos à construção do gráfico com todos os conjuntos de oportunidades de investimento: </div>
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<li style="text-align: justify;">com base na Figura 18, clique numa célula em branco duas colunas distante dos conjuntos de oportunidades de investimento, em seguida insira um gráfico de "Dispersão com Linhas Suaves" - sem especificar os pares ordenados, o gráfico permanecerá provisoriamente sem dados; </li>
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Figura 18</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Cdd3tZFFZ2QcV76NDCtrRphZn_mEusFwymQYIcxt7hNM3cUSbQu45c3vBWAppWVa-NIoEyvQqYoa8v5VoDJEz9BIZ7rmrTtzaGWx13Wtrxzhkig2htroLosBsFhXe1cMwsQMsbJLaPo/s1600/BLOG+CARTEIRA+24.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Cdd3tZFFZ2QcV76NDCtrRphZn_mEusFwymQYIcxt7hNM3cUSbQu45c3vBWAppWVa-NIoEyvQqYoa8v5VoDJEz9BIZ7rmrTtzaGWx13Wtrxzhkig2htroLosBsFhXe1cMwsQMsbJLaPo/s1600/BLOG+CARTEIRA+24.png" height="436" width="640" /></a></div>
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<li style="text-align: justify;">como mostra a Figura 19, clique com o lado direito do mouse sobre o gráfico para acionar "Selecionar Dados";</li>
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Figura 19</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWbjb5e2H3arbPOX0dCRvZ9M9P4bpvclAhpyktb1aycphlCGdWYFOECxRq871A1o-z7Ok19fkV8e7_yONgCLx4BO3F8KO1c28qwbs71BsTJdKYG7DnxaNuSVaAr74JKnTZOP4g0k-xprs/s1600/BLOG+CARTEIRA+25.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWbjb5e2H3arbPOX0dCRvZ9M9P4bpvclAhpyktb1aycphlCGdWYFOECxRq871A1o-z7Ok19fkV8e7_yONgCLx4BO3F8KO1c28qwbs71BsTJdKYG7DnxaNuSVaAr74JKnTZOP4g0k-xprs/s1600/BLOG+CARTEIRA+25.png" height="516" width="640" /></a></div>
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<li style="text-align: justify;">como na Figura 20, clique em "Adicionar" para inserir a primeira série de pares ordenados;</li>
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Figura 20</div>
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<li style="text-align: justify;">proceda da forma como esclarece a Figura 21 para inserir os pares ordenados do conjunto de oportunidades de investimento sob a hipótese de correlação perfeitamente positiva - preencha "Nome da série" com a célula reservada ao tipo de correlação, "Valores de X da série" com todos os riscos e "Valores de Y da série" com todos os retornos;</li>
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Figura 21</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDdhZTA7zn06_hF5bu6QAkVcwDvXu9reqT5km5p1TwmqVjEJfNnAzWdDNQ9lH2a44Zk0j4DbeswPJ6Kes9k0kPH04xl4qJj0EKSgM0edLsLJrwpfBUrw9QYKUreLrjRkyfYwXiPpBnD5s/s1600/BLOG+CARTEIRA+27.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDdhZTA7zn06_hF5bu6QAkVcwDvXu9reqT5km5p1TwmqVjEJfNnAzWdDNQ9lH2a44Zk0j4DbeswPJ6Kes9k0kPH04xl4qJj0EKSgM0edLsLJrwpfBUrw9QYKUreLrjRkyfYwXiPpBnD5s/s1600/BLOG+CARTEIRA+27.png" /></a></div>
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<li style="text-align: justify;">a Figura 22 representa a primeira versão do gráfico, somente com o conjunto de oportunidades de investimento para a correlação perfeitamente positiva - não esqueça de inserir o título do gráfico e os rótulos dos eixos e de mudar a cor da reta para vermelho (com a correlação 1 para os dois ativos, as carteiras possíveis têm riscos distribuídos entre o risco do ativo de menor risco e o risco do ativo de maior risco, assim não há sequer uma carteira com risco inferior ao risco do ativo de menor risco, pois a correlação mencionada não se enquadra na possibilidade de gerar benefícios por meio da diversificação);</li>
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Figura 22</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1kW4U92Vx86ag6g6XnOHLPzmkv8V7Xkt0Y3JqQv4tW9xGVfUfBuqLPlUnNVJuQlqdGrtgBkSCn5Ht4dFSFWO6iR3-xiBc4gcOg8oYAK9_uUFMeliRRMwIUzJTUqNouLwxYq8SHJRl-Yw/s1600/BLOG+CARTEIRA+28.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1kW4U92Vx86ag6g6XnOHLPzmkv8V7Xkt0Y3JqQv4tW9xGVfUfBuqLPlUnNVJuQlqdGrtgBkSCn5Ht4dFSFWO6iR3-xiBc4gcOg8oYAK9_uUFMeliRRMwIUzJTUqNouLwxYq8SHJRl-Yw/s1600/BLOG+CARTEIRA+28.png" /></a></div>
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<li style="text-align: justify;">a Figura 23 reproduz a instrução da Figura 21, mas agora para a hipótese de correlação estimada em 0,5;</li>
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Figura 23</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwy_n2TwiIyJwYE6mjuPKWsZIl4XxHlfowdolKQbMraEXDp6zT5YFO7bs6o5FsgXaDAGwuEovL6IyvnUr7dmW6bhvnlIwFHAcvKBtqIz8P9C3D0GuFqynW0KREu3VHR37_SobFE54rs_w/s1600/BLOG+CARTEIRA+30.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwy_n2TwiIyJwYE6mjuPKWsZIl4XxHlfowdolKQbMraEXDp6zT5YFO7bs6o5FsgXaDAGwuEovL6IyvnUr7dmW6bhvnlIwFHAcvKBtqIz8P9C3D0GuFqynW0KREu3VHR37_SobFE54rs_w/s1600/BLOG+CARTEIRA+30.png" /></a></div>
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<li style="text-align: justify;">a Figura 24 mostra a segunda versão do gráfico, agrupando os conjuntos de oportunidades de investimento para correlações 1 e 0,5 - mude a cor da representação do conjunto da correlação 0,5 para azul (mesmo sem a correlação 0,5 conseguir produzir com os ativos A e B uma combinação com risco inferior ao risco do ativo de menor risco, o benefício da diversificação já pode ser percebido, basta observar a possibilidade de serem alcançados retornos maiores no conjunto em azul para riscos do conjunto em vermelho ou, se preferir, de serem suportados riscos menores no conjunto em azul para retornos do conjunto em vermelho);</li>
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Figura 24</div>
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<li>a Figura 25 ilustra como inserir no gráfico o conjunto de oportunidades com correlação estimada em 0;</li>
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Figura 25</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1cmz5wHWG9GgqxzJCCK3nMv5-5V04h90W8ukfipq8x6SrFQAXw6zvaJogbOuUDBDo9HSal8catpd3yMEUwIlPBWJoGbqZpZq41UCFee0x0pKOUqME05TJyv3tl6Diqht75z-UEXjq5S4/s1600/BLOG+CARTEIRA+31.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1cmz5wHWG9GgqxzJCCK3nMv5-5V04h90W8ukfipq8x6SrFQAXw6zvaJogbOuUDBDo9HSal8catpd3yMEUwIlPBWJoGbqZpZq41UCFee0x0pKOUqME05TJyv3tl6Diqht75z-UEXjq5S4/s1600/BLOG+CARTEIRA+31.png" /></a></div>
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<li style="text-align: justify;">a Figura 26 expõe a terceira versão do gráfico, agrupando os conjuntos de oportunidades de investimento para correlações 1, 0,5 e 0 - mude a cor da representação do conjunto da correlação 0 para amarelo (além da intensificação da vantagem explicada com a correlação reduzida de 1 para 0,5, a variação para 0 consegue gerar o benefício adicional de fazer constar no conjunto em amarelo carteiras com riscos inferiores ao risco do ativo de menor risco, mas é preciso ter cuidado com as composições abaixo da carteira de risco mínimo, pois seus respectivos riscos também formam pares ordenados com retornos maiores, constituindo os pontos da curva distribuídos entre a carteira de risco mínimo e a composição com risco igual ao risco mínimo quando a correlação é perfeitamente positiva);</li>
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Figura 26</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcYtOQHmyXtWOqTU6ot9QqSxsqvbVN90PRYPXfXdXwk2ft9cimFVA-FmkO7qPj761IeYX9wWUV5F94Mz6_TTULGv9Ak606vhySZ73boqhjIz2lVzVSARXUaolNMQV0SPXG56wxyK2DNyo/s1600/BLOG+CARTEIRA+32.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcYtOQHmyXtWOqTU6ot9QqSxsqvbVN90PRYPXfXdXwk2ft9cimFVA-FmkO7qPj761IeYX9wWUV5F94Mz6_TTULGv9Ak606vhySZ73boqhjIz2lVzVSARXUaolNMQV0SPXG56wxyK2DNyo/s1600/BLOG+CARTEIRA+32.png" /></a></div>
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<li>a Figura 27 demonstra como inserir no gráfico o conjunto de oportunidades com correlação estimada em -0,5;</li>
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Figura 27</div>
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<li style="text-align: justify;">a Figura 28 apresenta a quarta versão do gráfico, agrupando os conjuntos de oportunidades de investimento para correlações 1, 0,5, 0 e -0,5 - mude a cor da representação do conjunto da correlação -0,5 para cinza (todos os benefícios relatados quando da redução da correlação de 0,5 para 0 são aprimorados com a variação até -0,5);</li>
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Figura 28</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_Da2x4zZ6Lg-U1aq3U9CdV0b1dBLp0_E8anTaIrObkpVDE6mEh-SsC6BkO92N8GkJHVwxTSpPMhpQ_U6ZbZ1PayUrEJkdfGcSNVqAPo5rNPfXukqkYdkBz4k0VWsxsMUNzIdSp0Az5TY/s1600/BLOG+CARTEIRA+34.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_Da2x4zZ6Lg-U1aq3U9CdV0b1dBLp0_E8anTaIrObkpVDE6mEh-SsC6BkO92N8GkJHVwxTSpPMhpQ_U6ZbZ1PayUrEJkdfGcSNVqAPo5rNPfXukqkYdkBz4k0VWsxsMUNzIdSp0Az5TY/s1600/BLOG+CARTEIRA+34.png" /></a></div>
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<li>a Figura 29 mostra como inserir no gráfico o conjunto de oportunidades com correlação estimada em -1;</li>
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Figura 29</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-WPBW031vVwjJDgTalNmB0tlPVMc__GyaHV11F9KQxyY3QeePstnQSDbw0blTgrnoI5NsrdMXChb0FQ5VzgIAo_KQDmAKuMwAVZXudqPi3SfH9oeDXwTgFVNT10kYq9mZnV-PEXoKn0A/s1600/BLOG+CARTEIRA+35.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-WPBW031vVwjJDgTalNmB0tlPVMc__GyaHV11F9KQxyY3QeePstnQSDbw0blTgrnoI5NsrdMXChb0FQ5VzgIAo_KQDmAKuMwAVZXudqPi3SfH9oeDXwTgFVNT10kYq9mZnV-PEXoKn0A/s1600/BLOG+CARTEIRA+35.png" /></a></div>
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<li style="text-align: justify;">finalmente, com o gráfico da Figura 30 pronto, agrupando os conjuntos de oportunidades de investimento para correlações 1, 0,5, 0, -0,5 e -1, o estudo dos benefícios da diversificação pode ser realizado satisfatoriamente - mude a cor da representação do conjunto da correlação -1 para verde (a correlação perfeitamente negativa exprime a configuração de onde se pode extrair o máximo de benefícios resultantes da diversificação, inclusive com a promoção de uma carteira de risco mínimo com risco nulo, ilustrado no encontro das duas retas de sua representação gráfica no eixo correspondente ao retorno da carteira).</li>
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Figura 30</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifdCEOo5agw7SKLe2jojCbmkfspAoSUSJRl90bQYK09TP3N0osPtw35be0pdbHxYOfEsK35hUL08Kqn5iF08zcSe86DM1fVD3giPpd0g34e8Pl_kwdbVmuVQ-udY3AbS9LdHEE4tBvcR4/s1600/BLOG+CARTEIRA+36.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifdCEOo5agw7SKLe2jojCbmkfspAoSUSJRl90bQYK09TP3N0osPtw35be0pdbHxYOfEsK35hUL08Kqn5iF08zcSe86DM1fVD3giPpd0g34e8Pl_kwdbVmuVQ-udY3AbS9LdHEE4tBvcR4/s1600/BLOG+CARTEIRA+36.png" /></a></div>
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Pronto!!! Minha planilha ficou igual ao modelo da Figura 31.</div>
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Figura 31</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh25XumZkr8X_CfeI9gbsE7F0EZL6mq5qJCkOMHPyGUFd7JaOicTsot3GNDB0Rvk-SEKhmLQBwDELc-YZ7W5GQ12t5HsRQIj65ixuez0PlhXT552ISn9FFCaJvJI_MzibzykXrqqbMkSVM/s1600/BLOG+CARTEIRA+38.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh25XumZkr8X_CfeI9gbsE7F0EZL6mq5qJCkOMHPyGUFd7JaOicTsot3GNDB0Rvk-SEKhmLQBwDELc-YZ7W5GQ12t5HsRQIj65ixuez0PlhXT552ISn9FFCaJvJI_MzibzykXrqqbMkSVM/s1600/BLOG+CARTEIRA+38.png" height="250" width="640" /></a></div>
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Estudar os benefícios da diversificação em carteiras com dois ativos de risco usando o Microsoft Excel é muito mais instrutivo - minha opinião.</div>
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Cordialmente,</div>
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Adail Marcos</div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-61881041967737135882012-11-19T18:17:00.003-08:002018-12-02T06:07:11.376-08:00Payback Period: aprenda a calcular 7 (sete) versões com o Microsoft EXCEL<div style="text-align: justify;">
Antes do início desta postagem, recomendo o eBook (vendido na Amazon) "Funções do Excel Aplicadas à Matemática Financeira - VOLUME I". Traz 70 (SETENTA) exercícios resolvidos e comentados. Tem dois capítulos especiais, exclusivamente elaborados para você aprender, de uma vez por todas, os conceitos e as diferenças envolvendo as taxas nominal, efetiva, equivalente e proporcional. Se você trabalha no setor bancário ou nos diversos setores financeiros das empresas, por exemplo, trata-se de um material de apoio indispensável. Aproveite a oportunidade, o preço está muito convidativo.<br />
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<a href="https://www.amazon.com.br/dp/B07KSWXF25/ref=cm_cr_dp_d_vote_lft?ie=UTF8&voteInstanceId=R3KZ8ANEDI3DC6&voteValue=1&csrfT=gvLdIrwLc7NFqCR68yVGog2SkybnZmosU%2Bs0iSIAAAABAAAAAFv4XBRyYXcAAAAA%2B4kUEk%2F7iMGR3xPcX6iU#R3KZ8ANEDI3DC6&" target="_blank"><img border="0" data-original-height="1600" data-original-width="1107" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSTATByENYK-V8r77l6vDoYzNiwPvpp1q-N_v0CHg_4D_RGBLkStmvWcatSar2TM9WN1qsJe8GIa4T6YWf6GHyMDzt0xPWdcCNvBAw8Pt6v-8gy7mTQpmMYN8DWVcvJ4gJeTqJe0JaxXs/s320/CAPA+1.jpg" width="221" /></a></div>
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Esta postagem é a continuação de <a href="http://adailmarcos.blogspot.com.br/2012/06/payback-period-aprenda-calcular-7-sete.html" target="_blank">Payback Period: aprenda a calcular 7 (sete) versões com a HP-12C</a></div>
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Em relação ao manuseio da HP-12c, calcular as 7 (sete) versões do<i> </i><span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue;"><b><span style="color: white;">Period</span><span style="color: blue;">.</span></b></span> com o Microsoft EXCEL é uma tarefa incomparavelmente mais simples. As funções envolvidas são: </div>
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<li style="text-align: justify;"><b>ABS</b> (absoluto), retorna o valor absoluto de um número;</li>
<li style="text-align: justify;"><b>SOMA</b>, retorna o resultado da soma dos valores contidos em um intervalo;</li>
<li style="text-align: justify;"><b>VP</b>, retorna o valor presente de um dado valor futuro;</li>
<li style="text-align: justify;"><b>VF</b>, retorna o valor futuro de um dado valor presente;</li>
<li style="text-align: justify;"><b>TAXA</b> (taxa de juros), retorna a taxa de juros efetiva para séries simples de fluxo de caixa - situação caracteriza pela ocorrência de fluxos apenas nas datas-focais inicial e final - e séries de prestações uniformes postecipadas e antecipadas;</li>
<li style="text-align: justify;"><b>PGTO</b> (pagamento), retorna o valor da prestação para séries uniformes postecipadas e antecipadas;</li>
<li style="text-align: justify;"><b>NPER</b> (número de períodos), retorna o número de períodos de uma série simples de fluxo de caixa ou a quantidade de prestações para séries uniformes postecipadas e antecipadas. </li>
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Para acompanhar as explicações associadas aos cálculos das 7 (sete) versões do <span style="background-color: blue; text-align: justify;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; text-align: justify;"><b><span style="color: white;">Period</span><span style="color: blue;">.</span></b></span> com o Microsoft EXCEL, monte o modelo do exemplo descrito na <b><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">1</span><span style="background-color: orange; color: orange;">.</span></b>, onde:</div>
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<li style="text-align: justify;">coluna "<b>A</b>", mostra todas as datas-focais do fluxo de caixa;</li>
<li style="text-align: justify;">coluna "<b>B</b>", apresenta a distribuição dos valores dos fluxos;</li>
<li style="text-align: justify;">coluna "<b>C</b>", utilizada para o cálculo do valor acumulado dos fluxos nominais em cada data-focal do fluxo de caixa;</li>
<li style="text-align: justify;">coluna "<b>D</b>", usada para distribuir o fluxo de caixa dos valores descontados;</li>
<li style="text-align: justify;">coluna "<b>E</b>", utilizada para o cálculo do valor acumulado dos fluxos descontados em cada data-focal do fluxo de caixa; </li>
<li style="text-align: justify;">coluna "<b>G</b>", destaca os valores assumidos pelas variáveis <b>TMA</b> (taxa mínima de atratividade) e <b>TR</b> (taxa de reinvestimento); </li>
<li style="text-align: justify;">colunas "<b>I</b>" a "<b>K</b>", destacadas à identificação dos valores assumidos pelos indicadores explorados nesta postagem. </li>
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<b style="background-color: orange;"><span style="color: orange;">.</span><span style="color: white;">Figura </span><span style="color: orange;">.</span><span style="color: white;">1</span><span style="color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8x0Ygl9RJb_wjMgIQhWPqkWucU_FwYbnf_rmtr84-gQnrXIKuSW9waEFbuNe9lMdtp-xibygLdXsTL1AA6qe0k9PgjuHY9W1dZ1E73FN5RRSGyoqDw8rcHjvx8EJNPgWXpyAouuL9aKA/s1600/Payback+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8x0Ygl9RJb_wjMgIQhWPqkWucU_FwYbnf_rmtr84-gQnrXIKuSW9waEFbuNe9lMdtp-xibygLdXsTL1AA6qe0k9PgjuHY9W1dZ1E73FN5RRSGyoqDw8rcHjvx8EJNPgWXpyAouuL9aKA/s640/Payback+1.png" width="640" /></a></div>
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As <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">2</span><span style="background-color: orange; color: orange;">.</span></b> e <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">3</span><span style="background-color: orange; color: orange;">.</span></b> mostram as duas etapas exigidas ao cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Original</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">:</span></div>
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<li><b style="text-align: center;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">2</span><span style="background-color: orange; color: orange;">.</span><span style="background-color: white;">:</span></b></li>
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<li>digite na célula "<b>C3</b>" a fórmula "<b>=SOMA($B$3:B3)</b>";</li>
<li>arraste a fórmula da célula "<b>C3</b>" até a célula "<b>C13</b>";</li>
<li>em virtude de a primeira aparição da célula do fluxo de caixa correspondente ao investimento inicial figurar na fórmula de modo fixo (<b>$B$3</b>), o procedimento indicado no tópico anterior garante o cálculo do valor acumulado dos fluxos nominais para todas as datas-focais;</li>
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<b style="background-color: orange;"><span style="color: orange;">.</span><span style="color: white;">Figura </span><span style="color: orange;">.</span><span style="color: white;">2</span><span style="color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOTL-odf-sFTFSY2245x2WRcD61wOm8MoYbX1vdY9L7g9b6gTZHv_FozPxJMkO1OfVyvG124n8waAi3yHpgmbZvhDhXkCXVoFZ97yHftDVvnzQPflH6OjLUN-3ASERc9ZgJU9XquY4L9c/s1600/Payback+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="282" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOTL-odf-sFTFSY2245x2WRcD61wOm8MoYbX1vdY9L7g9b6gTZHv_FozPxJMkO1OfVyvG124n8waAi3yHpgmbZvhDhXkCXVoFZ97yHftDVvnzQPflH6OjLUN-3ASERc9ZgJU9XquY4L9c/s400/Payback+2.png" width="400" /></a></div>
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<li><b style="text-align: center;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">3</span><span style="background-color: orange; color: orange;">.</span><span style="background-color: white;">:</span></b></li>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: white;">a coluna "<b>C</b>" indica a recuperação do investimento inicial entre as datas-focais "<b>5</b>" e "<b>6</b>" - o somatório cronológico dos valores nominais dos fluxos aponta o ano "<b>5</b>" como o último a apresentar valor negativo;</span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: white;">o valor absoluto do resultado contido na célula "<b>C8</b>", "<b>-10.000,00</b>", mostra a parcela do valor nominal do fluxo da data-focal "<b>6</b>" empregada na recuperação plena do investimento inicial;</span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: white;">a fórmula "</span><b style="background-color: white;">=A8+ABS(C8)/B9</b><span style="background-color: white;">", inserida na célula "<b>I5</b>", calcula com exatidão a versão </span><span style="text-align: justify;"><b><span style="background-color: #274e13; color: #274e13;"> </span><span style="background-color: #274e13; color: white;">Original</span><span style="color: #274e13;"><span style="background-color: #274e13;">.</span><span style="background-color: white;"> </span></span></b><span style="background-color: white;">do </span></span><span style="background-color: blue; text-align: justify;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="text-align: justify;"><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;">;</span></span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><span style="background-color: white;">a participação da célula "<b>A8</b>" na fórmula serve para apontar o ano imediatamente anterior à recuperação plena, ou seja, corresponde ao ano do último valor negativo cronológico presente na coluna "<b>C</b>";</span></span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><span style="background-color: white;">o quociente "<b style="text-align: center;">ABS(C8)/B9</b><span style="text-align: center;">" calcula a fração do valor nominal do fluxo contido na data-focal <span style="text-align: justify;">correspondente ao ano de ocorrência do primeiro valor positivo na coluna "</span><b style="text-align: justify;">C</b><span style="text-align: justify;">"</span> comprometida com a recuperação plena do investimento. </span> </span></span><span style="background-color: white;"> </span><b style="background-color: white;"> </b></span></li>
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<b style="background-color: orange;"><span style="color: orange;">.</span><span style="color: white;">Figura </span><span style="color: orange;">.</span><span style="color: white;">3</span><span style="color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiDxBR-qK29vMxfilzjE5sH9GGE8ND8GhVOjeuvTKO1aOvyuXLy6QNjBlkBj569AdbDIHK7XOmY4jhaCwUeTEkUUhgXuysQgKZJd6GplPStSaowYEOw3B76P5WPBMk4asPcbpEBGavRnM/s1600/Payback+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiDxBR-qK29vMxfilzjE5sH9GGE8ND8GhVOjeuvTKO1aOvyuXLy6QNjBlkBj569AdbDIHK7XOmY4jhaCwUeTEkUUhgXuysQgKZJd6GplPStSaowYEOw3B76P5WPBMk4asPcbpEBGavRnM/s640/Payback+3.png" width="640" /></a></div>
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A <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">4</span><span style="background-color: orange; color: orange;">.</span></b> demonstra o cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Médio</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">:</span></div>
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<li>a fórmula inserida na célula "<b>J5</b>", "<b>=ABS(B3)/MÉDIA(B4:B13)</b>", explica a versão mais fácil de ser calculada;</li>
<li>a divisão do valor absoluto do investimento inicial, "<b>ABS(B3)</b>", pelo valor nominal médio dos fluxos distribuídos após a data-focal "<b>0</b>", "<b>MÉDIA(B4:B13)</b>", representa o procedimento completo. </li>
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<b style="background-color: orange;"><span style="color: orange;">.</span><span style="color: white;">Figura </span><span style="color: orange;">.</span><span style="color: white;">4</span><span style="color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZs4iNcW4XYsTJpCPoioJn8GluiND1leFhJfdDGJtuBICkLhOl_HOiglpoitn7bxpPOOQX-61GJvxHpgalIUMls41vWR-EWfqxVQZJ2sNuZLQosQd5j3TfvkIc_S0SBVn6wZpy3U_iGm4/s1600/Payback+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZs4iNcW4XYsTJpCPoioJn8GluiND1leFhJfdDGJtuBICkLhOl_HOiglpoitn7bxpPOOQX-61GJvxHpgalIUMls41vWR-EWfqxVQZJ2sNuZLQosQd5j3TfvkIc_S0SBVn6wZpy3U_iGm4/s640/Payback+4.png" width="640" /></a></div>
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As <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">5</span><span style="background-color: orange; color: orange;">.</span></b>, <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">6</span><span style="background-color: orange; color: orange;">.</span></b> e <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">7</span><span style="background-color: orange; color: orange;">.</span></b> destacam as três etapas necessárias ao cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Descontado</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">:</span></div>
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<li style="text-align: justify;"><b style="text-align: center;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">5</span><span style="background-color: orange; color: orange;">.</span><span style="background-color: white;">:</span></b></li>
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<li style="text-align: justify;">digite a fórmula "<b>=VP($G$3;A3;;-B3)</b>" na célula "<b>D3</b>";</li>
<li style="text-align: justify;">arraste a fórmula da célula "<b>D3</b>" até a célula "<b>D13</b>";</li>
<li style="text-align: justify;">por figurar na função "<b>VP</b>" como taxa de juros, a célula correspondente ao valor da <b>TMA</b>, "<b>G3</b>", deve ser fixada ("<b>$G$3</b>");</li>
<li style="text-align: justify;">como a distribuição dos fluxos ocorre em datas-focais distintas, o período de desconto não pode ser fixado ("<b>A3</b>");</li>
<li style="text-align: justify;">além de não ser possível fixá-lo, o valor nominal deve ser inserido com sinal invertido ("<b>-B3</b>"); </li>
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<b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">5</span><span style="background-color: orange; color: orange;">.</span></b></div>
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<img border="0" height="372" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQjbL_ydmGa10TrUv7UQam4-aYGItzbaS8D6dQ_bGOtIzxFIUujlySQhikdN1V_7Vpxg1dxVDz54l98k8N9Dacx7M112IJl6UPsvPP_LGjhlEXHQrsAU_Fl56nyoze6NGohk171HjnoiU/s640/Payback+5.png" width="640" /></div>
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<li style="text-align: justify;"><b style="text-align: center;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">6</span><span style="background-color: orange; color: orange;">.</span><span style="background-color: white;">:</span></b></li>
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<li style="text-align: justify;">digite a fórmula "<b>=SOMA($D$3:D3)</b>" na célula "<b>E3</b>";</li>
<li style="text-align: justify;">arraste a fórmula da célula "<b>D3</b>" até a célula "<b>D13</b>";</li>
<li style="text-align: justify;">como a primeira aparição da célula correspondente ao investimento inicial indica fixação (<b>$D$3</b>), o procedimento mencionado no tópico anterior garante o cálculo do valor acumulado dos fluxos descontados para todas as datas-focais;</li>
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<b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">6</span><span style="background-color: orange; color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivqFyGwGI_e6_6c1Yks68CH9ri1xUmc7h00Ttmn7NyQ52t2ReX_N_5QPlYsEM502ldlh1kT68MlgyxWRxAaqHlWOIdHmNsnvhe7cVNTORKex8Gnn8qi5DBQUi8oAiVkFIhCIEEe-TZrR8/s1600/Payback+6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivqFyGwGI_e6_6c1Yks68CH9ri1xUmc7h00Ttmn7NyQ52t2ReX_N_5QPlYsEM502ldlh1kT68MlgyxWRxAaqHlWOIdHmNsnvhe7cVNTORKex8Gnn8qi5DBQUi8oAiVkFIhCIEEe-TZrR8/s1600/Payback+6.png" /></a></div>
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<li style="text-align: justify;"><b style="text-align: center;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">7</span><span style="background-color: orange; color: orange;">.</span><span style="background-color: white;">:</span></b></li>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: white;">a coluna "<b>E</b>" indica a recuperação do investimento inicial entre as datas-focais "<b>7</b>" e "<b>8</b>" - o somatório cronológico dos valores descontados dos fluxos mostra o ano "<b>7</b>" como o último a apresentar valor negativo;</span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: white;">o valor absoluto do resultado contido na célula "<b>E10</b>", "<b>-6.377,19</b>", informa a parcela do valor descontado do fluxo da data-focal "<b>8</b>" comprometida com a recuperação plena do investimento inicial;</span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: white;">a fórmula "</span><b style="background-color: white;">=A10+ABS(E10)/D11</b><span style="background-color: white;">", célula "<b>K5</b>", calcula com exatidão o tipo </span><span style="text-align: justify;"><b><span style="background-color: #274e13; color: #274e13;"> </span><span style="background-color: #274e13; color: white;">Descontado</span><span style="color: #274e13;"><span style="background-color: #274e13;">.</span><span style="background-color: white;"> </span></span></b><span style="background-color: white;">do </span></span><span style="background-color: blue; text-align: justify;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="text-align: justify;"><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;">;</span></span></span></li>
<li style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><span style="background-color: white;">a célula "<b>A10</b>" corresponde ao ano de ocorrência do último valor negativo na coluna "<b>E</b>";</span></span></span></li>
<li style="text-align: justify;"><span style="text-align: center;">o quociente "<b style="text-align: center;">ABS(E10)/D11</b>" calcula a fração do valor descontado do fluxo da data-focal correspondente à ocorrência do primeiro valor positivo na coluna "<b style="text-align: justify;">E</b>" comprometida com a recuperação plena do investimento.</span></li>
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<b><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">7</span><span style="background-color: orange; color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4DCtl4uJWHX-UlLDuzlNcZO9Ks0B0m0j2HlQ_dqvGQO_h3AcPx9YLCA1J4_gL7IjKGeqn506AO_85nxAErLCVf1teDgKJFitYeyIAc5Dt3UssBWus6roZJgbM1yto0_4WR39P0j0szeA/s1600/Payback+7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4DCtl4uJWHX-UlLDuzlNcZO9Ks0B0m0j2HlQ_dqvGQO_h3AcPx9YLCA1J4_gL7IjKGeqn506AO_85nxAErLCVf1teDgKJFitYeyIAc5Dt3UssBWus6roZJgbM1yto0_4WR39P0j0szeA/s640/Payback+7.png" width="640" /></a></div>
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As <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span></b><b style="text-align: start;"><span style="background-color: orange; color: white;">8</span><span style="background-color: orange; color: orange;">.</span></b> e <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">9</span><span style="background-color: orange; color: orange;">.</span></b> mostram as duas etapas exigidas ao cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Descontado Médio</span><span style="color: #274e13;">.</span></b><span style="background-color: white;"> (também conhecido como duração):</span></div>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">8</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: white;">:</span></span></li>
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<li style="text-align: justify;">insira a fórmula "<b>=VPL($G$3;B4:B13)</b>" na célula "<b>I3</b>";</li>
<li style="text-align: justify;">o resultado contido na célula "<b>I3</b>" esclarece o valor presente dos fluxos distribuídos após a data-focal "<b>0</b>";</li>
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<b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span></b><b style="text-align: start;"><span style="background-color: orange; color: white;">8</span><span style="background-color: orange; color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIhYk7rXGKQUA9urng3LJr0QriPkKGBd1ByhvFoc_zPa3tlclXHajDyuRXDdv0Xypnp5QXrD5OijmhUAAm-7E1AH75UrV3Zn74AHa45okcWy3sJpwT-ISK1-sCMZPX_-0bNHizxnzpRok/s1600/Payback+8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIhYk7rXGKQUA9urng3LJr0QriPkKGBd1ByhvFoc_zPa3tlclXHajDyuRXDdv0Xypnp5QXrD5OijmhUAAm-7E1AH75UrV3Zn74AHa45okcWy3sJpwT-ISK1-sCMZPX_-0bNHizxnzpRok/s640/Payback+8.png" width="640" /></a></div>
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<li><span style="text-align: center;"><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">9</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: white;">:</span></span></li>
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<li>insira a fórmula "<b>=ABS(B3)/(I3/A13)</b>" na célula "<b>I7</b>";</li>
<li style="text-align: justify;">o resultado contido na célula "<b>I7</b>" retorna a extensão alcançada pelo tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Descontado Médio</span><span style="color: #274e13;">.</span></b>;</li>
<li style="text-align: justify;">a divisão do valor absoluto do fluxo equivalente ao investimento inicial, "<b style="text-align: left;">ABS(B3)</b><span style="text-align: left;">"</span>, pelo valor descontado médio dos fluxos situados depois da data-focal zero, <b style="text-align: left;">I3/A13 </b><span style="text-align: left;">(<b>VP</b> dividido pelo número total de períodos do fluxo de caixa),</span> descreve o procedimento completo.</li>
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<b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span></b><b style="text-align: start;"><span style="background-color: orange; color: white;">9</span><span style="background-color: orange; color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYsWoCza7QnY5EM7OzTLuuOWv9bQuHxAGI2QPlbr7ZngwZW_mFDdbQr2wD0cqWoWXYFnKHQMWxFaeMUIt83u5T0SJNYpusacFkOwVyL4v32cMeNNgh9ba3vZazuLeYjE9Cg4CtEMTPs7U/s1600/Payback+9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="242" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYsWoCza7QnY5EM7OzTLuuOWv9bQuHxAGI2QPlbr7ZngwZW_mFDdbQr2wD0cqWoWXYFnKHQMWxFaeMUIt83u5T0SJNYpusacFkOwVyL4v32cMeNNgh9ba3vZazuLeYjE9Cg4CtEMTPs7U/s640/Payback+9.png" width="640" /></a></div>
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A <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">10</span><span style="background-color: orange; color: orange;">.</span></b> detalha o procedimento dedicado ao cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Anuidade</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">:</span></div>
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<li style="text-align: justify;">a fórmula inserida na célula "<b>J7</b>", "<b>=ABS(B3)/PGTO(G3;A13;-I3;;0)</b>", calcula o indicador de forma direta;</li>
<li style="text-align: justify;">"<b>PGTO(G3;A13;-I3;;0)</b>" converte o valor presente dos fluxos distribuídos após a data-focal "0" em uma anuidade postecipada - o valor presente deve ser inserido com sinal invertido ("<b>-I3</b>") e o tipo de anuidade, postecipada, deve ser informado com a presença de "<b>0</b>" no último termo da função; </li>
<li style="text-align: justify;">portanto, a divisão do valor absoluto do investimento inicial, "<b>ABS(B3)</b>", pelo valor da anuidade postecipada, "<b>PGTO(G3;A13;-I3;;0)</b>", retorna o valor do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Anuidade</span><span style="color: #274e13;">.</span></b>.</li>
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<b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">10</span></b><b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV9Xfqfrdqm4Fb20MG6VSB-3-1jrwdFI8XHKDmYI4xr37qlnyQx1X8WrFOR0oVSBsmWmoPJRuDDwCET6BkEX_Zjg3U3DNSMJqRp_b_cl_2bkE4-2iXrC5q_P1-QALu99ofzBNt-njWy-Q/s1600/Payback+10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV9Xfqfrdqm4Fb20MG6VSB-3-1jrwdFI8XHKDmYI4xr37qlnyQx1X8WrFOR0oVSBsmWmoPJRuDDwCET6BkEX_Zjg3U3DNSMJqRp_b_cl_2bkE4-2iXrC5q_P1-QALu99ofzBNt-njWy-Q/s640/Payback+10.png" width="640" /></a></div>
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As <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span></b><b style="text-align: start;"><span style="background-color: orange; color: white;">11</span><span style="background-color: orange; color: orange;">.</span></b> e <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">12</span><span style="background-color: orange; color: orange;">.</span></b> apresentam as duas etapas exigidas ao cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Taxa Interna de Retorno</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">:</span></div>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">11</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: white;">:</span></span></li>
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<li style="text-align: justify;">insira a fórmula "<b>=TIR(B3:B13)</b>" na célula "J<b>3</b>";</li>
<li style="text-align: justify;">o resultado contido na célula "<b>I3</b>" tem a propriedade de informar a taxa interna de retorno do fluxo de caixa;</li>
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<b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figura </span><span style="background-color: orange; color: orange;">.</span></b><b style="text-align: start;"><span style="background-color: orange; color: white;">11</span><span style="background-color: orange; color: orange;">.</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG5Aq6AiPMY_GTHaCGLGwjubtWNEKD6dKoN2IPtj_PyAceXrt0cj0nhvc2ke1FwneaLwpPCxTwbKZwnG9AkzJXnPczoXtquamogyTOF8SYGeBZr2NnDyplqX16ATLDABeJSu3b0u1OGGs/s1600/Payback+11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG5Aq6AiPMY_GTHaCGLGwjubtWNEKD6dKoN2IPtj_PyAceXrt0cj0nhvc2ke1FwneaLwpPCxTwbKZwnG9AkzJXnPczoXtquamogyTOF8SYGeBZr2NnDyplqX16ATLDABeJSu3b0u1OGGs/s640/Payback+11.png" width="640" /></a></div>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">12</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: white;">:</span></span></li>
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<li style="text-align: justify;">insira a fórmula "<b>=NPER(J3;;-1;2)</b>" na célula "<b>K7</b>";</li>
<li style="text-align: justify;">do modo como encontra-se configurada na célula "<b>K7</b>", a função "<b>NPER</b>" retorno o período de tempo exigido pela taxa interna de retorno à obtenção de um volume de juros igual ao valor do próprio investimento inicial - "<b>-1</b>" representa o investimento inicial, enquanto "<b>2</b>" informa o valor futuro (o valor "2" resulta da soma entre o investimento inicial, representado por "<b>1</b>", e o volume dos juros formados com a taxa interna de retorno, igualmente representado por "<b>1</b>");</li>
<li style="text-align: justify;">o resultado da célula "<b>K7</b>" informa o tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Taxa Interna de Retorno</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">.</span> </li>
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<span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">12</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span></div>
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As <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">Figuras </span><span style="background-color: orange; color: orange;">.</span></b><b style="text-align: start;"><span style="background-color: orange; color: white;">13</span><span style="background-color: orange; color: orange;">.</span></b> e <b style="text-align: start;"><span style="background-color: orange; color: orange;">.</span><span style="background-color: orange; color: white;">14</span><span style="background-color: orange; color: orange;">.</span></b> divulgam as duas etapas empregadas no cálculo do tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Taxa Interna de Retorno Modificada</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">:</span></div>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">13</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: white;">:</span></span></li>
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<li style="text-align: justify;">insira a fórmula "<b>=TAXA(A13;;B3;VF(G5;A13;;-VPL(G5;B4:B13)))</b>" na célula "<b>K3</b>" - "<b>A13</b>" representa a última data-focal do fluxo de caixa, "<b>B13</b>" o investimento inicial, "G5" a taxa de reinvestimento e "<b>B4:B13</b>" a sequência cronológica dos fluxos situados depois da data-focal "<b>0</b>";</li>
<li style="text-align: justify;">a resposta obtida com a fórmula inserida na célula "<b>K3</b>" informa a taxa interna de retorno modificada;</li>
<li style="text-align: justify;">com a taxa de reinvestimento, "<b>VPL(G5;B4:B13)</b>" calcula o valor presente dos fluxos distribuídos após a data-focal "<b>0</b>";</li>
<li style="text-align: justify;">"<b>VF(G5;A13;;-VPL(G5;B4:B13)))</b>" calcula, também com a taxa de reinvestimento, o valor futuro, na última data-focal, do valor presente dos fluxos distribuídos após a data-focal "<b>0</b>";</li>
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<span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">13</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span></div>
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<li style="text-align: justify;"><span style="text-align: center;"><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">14</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: white;">:</span></span></li>
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<li style="text-align: justify;">insira a fórmula "<b>=NPER(K3;;-1;2)</b>" na célula "<b>I9</b>";</li>
<li style="text-align: justify;">a função "<b>NPER</b>" retorno o período de tempo exigido pela taxa interna de retorno modificada à obtenção de um volume de juros igual ao valor do próprio investimento inicial - "<b>-1</b>" representa o investimento inicial, enquanto "<b>2</b>" informa o valor futuro (o valor "2" resulta da soma entre o investimento inicial, representado por "<b>1</b>", e o volume dos juros formados com a taxa interna de retorno modificada, também representado por "<b>1</b>");</li>
<li style="text-align: justify;">o resultado da célula "<b>I9</b>" informa o tipo de <span style="background-color: blue;"><b><span style="color: blue;">.</span><span style="color: white;">Payback </span></b></span><span style="background-color: blue; color: white; font-weight: bold;">Period</span><span style="background-color: blue; color: blue; font-weight: bold;">.</span><span style="background-color: white;"><b> </b>classificado como </span><b style="background-color: #274e13;"><span style="color: #274e13;"> </span><span style="color: white;">Taxa Interna de Retorno Modificada</span><span style="color: #274e13;">.</span></b><span style="background-color: white;">.</span> </li>
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<span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">14</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZeVDONFe7CLPwNQrpbMyE8V0mt4FvnggwB4h-4jcFxl3bIkGtuWskIwqWsYn8Fy4UBHHJarx6iOkUiyxZDq0D8-H-vMTl7lMZ_3iP87ECKBckk1fTy6KQGrdEZdDEra_PvQgOmIWnRtA/s1600/Payback+14.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZeVDONFe7CLPwNQrpbMyE8V0mt4FvnggwB4h-4jcFxl3bIkGtuWskIwqWsYn8Fy4UBHHJarx6iOkUiyxZDq0D8-H-vMTl7lMZ_3iP87ECKBckk1fTy6KQGrdEZdDEra_PvQgOmIWnRtA/s640/Payback+14.png" width="640" /></a></div>
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Confira se todos os indicadores têm as mesmas respostas contidas na <span style="background-color: orange; color: orange; font-weight: bold; text-align: center;">.</span><span style="background-color: orange; color: white; font-weight: bold; text-align: center;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold; text-align: center;">.</span><span style="background-color: orange; color: white; font-weight: bold; text-align: center;">15</span><span style="background-color: orange; color: orange; font-weight: bold; text-align: center;">.</span>. </div>
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<span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">Figura </span><span style="background-color: orange; color: orange; font-weight: bold;">.</span><span style="background-color: orange; color: white; font-weight: bold;">15</span><span style="background-color: orange; color: orange; font-weight: bold;">.</span></div>
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Além de vários tipos de payback, o vídeo a seguir mostra como calcular outros medidores. São QUINZE medidores de desempenho para avaliar projetos de investimentos. </div>
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<span style="background-color: lime;"><b><span style="font-size: large;">Assista ao vídeo do canal MAFIN. </span></b></span></div>
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<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/pOmaj7ZdT3g/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/pOmaj7ZdT3g?feature=player_embedded" width="320"></iframe><br />
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Utilize o espaço dedicado aos comentários para sugerir novas postagens.</div>
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Cordialmente,</div>
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Adail Marcos</div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com6tag:blogger.com,1999:blog-5692836511586863836.post-59503793380854387672012-09-18T09:29:00.001-07:002012-09-18T09:29:53.346-07:00SIMULAÇÃO DE MONTE CARLO COM O USO DO EXCEL (NÍVEL BÁSICO) - CANAL DE FINANÇAS NO YOUTUBE - Prof. Adail Marcos - UFCG<br />
Resolvi criar um canal no youtube sobre o uso do Microsoft EXCEL em Finanças.<br />
<br />
Tem por objetivo geral prestar suporte às atividades de ensino que desenvolvo nas disciplinas ADMINISTRAÇÃO FINANCEIRA I e ADMINISTRAÇÃO FINANCEIRA II, ambas pertencentes ao currículo do curso de Administração da Universidade Federal de Campina Grande (UFCG). <br />
<br />
Primeira lista de reprodução disponibilizada: "Simulação de Monte Carlo com o uso do Microsoft EXCEL - Nível Básico". Conteúdo abordado no III Estágio das disciplinas ADMINISTRAÇÃO FINANCEIRA I e ADMINISTRAÇÃO FINANCEIRA II (gestão do risco em finanças), também será utilizado como curso de extensão. Procura encerrar a seguinte questão: como implementar aplicações do método de simulação de Monte Carlo no Microsoft EXCEL?<br />
<br />
Bem, espero que seja útil.<br />
<br />
<a href="http://www.youtube.com/user/FinancasUFCG/featured"><span style="font-size: large;"><b>http://www.youtube.com/user/FinancasUFCG/featured</b></span></a><br />
<br />
Sem mais,<br />
<br />
Adail MarcosAdail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-3815228326523236462012-06-20T07:34:00.001-07:002018-12-02T06:03:17.363-08:00Payback Period: aprenda a calcular 7 (sete) versões com a HP-12C<div style="text-align: justify;">
Antes do início desta postagem, recomendo o eBook (vendido na Amazon) "Funções do Excel Aplicadas à Matemática Financeira - VOLUME I". Traz 70 (SETENTA) exercícios resolvidos e comentados. Tem dois capítulos especiais, exclusivamente elaborados para você aprender, de uma vez por todas, os conceitos e as diferenças envolvendo as taxas nominal, efetiva, equivalente e proporcional. Se você trabalha no setor bancário ou nos diversos setores financeiros das empresas, por exemplo, trata-se de um material de apoio indispensável. Aproveite a oportunidade, o preço está muito convidativo.</div>
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<a href="https://www.amazon.com.br/dp/B07KSWXF25/ref=cm_cr_dp_d_vote_lft?ie=UTF8&voteInstanceId=R3KZ8ANEDI3DC6&voteValue=1&csrfT=gvLdIrwLc7NFqCR68yVGog2SkybnZmosU%2Bs0iSIAAAABAAAAAFv4XBRyYXcAAAAA%2B4kUEk%2F7iMGR3xPcX6iU#R3KZ8ANEDI3DC6&" target="_blank"><img border="0" data-original-height="1600" data-original-width="1107" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSTATByENYK-V8r77l6vDoYzNiwPvpp1q-N_v0CHg_4D_RGBLkStmvWcatSar2TM9WN1qsJe8GIa4T6YWf6GHyMDzt0xPWdcCNvBAw8Pt6v-8gy7mTQpmMYN8DWVcvJ4gJeTqJe0JaxXs/s320/CAPA+1.jpg" width="221" /></a></div>
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<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><br /></span>
<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">O
emprego do <span style="color: blue;"><i><b>Payback Period</b></i> </span>no estudo
da viabilidade de projetos de investimentos busca conhecer o tempo total exigido à
recuperação plena do volume de capital demandado. Quanto
menor o </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">, situação desejada, maior o
potencial de a recuperação plena do capital ocorrer de forma célere. Dito de outra forma:
quanto menor o </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">, mais
extenso o intervalo de tempo dedicado à remuneração das fontes de capital e à
criação de riqueza – objetivos econômicos das empresas. <o:p></o:p></span></div>
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<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">É possível encontrar 7 (sete) versões distintas ao </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i> <span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">:</span></div>
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</div>
<ul>
<li style="text-align: justify;"><i style="text-indent: -18pt;"><span style="background-color: blue; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><b><span style="color: white;">payback</span></b></span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"><b style="background-color: blue;"><span style="color: white;">
original</span></b><span style="background-color: white;"> (</span><b style="background-color: white;">PO</b><span style="background-color: white;">) – instante do fluxo de caixa onde o somatório (a partir da data focal “</span><b style="background-color: white;">1</b><span style="background-color: white;">”) dos valores <i>nominais</i> das entradas de caixa operacionais assume o mesmo valor do investimento inicial;</span></span></li>
<li style="text-align: justify;"><i style="text-indent: -18pt;"><span style="background-color: blue; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><b><span style="color: white;">payback</span></b></span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"><b><span style="background-color: blue; color: white;">
médio</span></b><span style="background-color: white;"> (</span><b style="background-color: white;">PM</b><span style="background-color: white;">) – resultado da divisão do
investimento inicial pelo valor nominal médio de todas as entradas de caixa
operacionais;</span></span></li>
<li style="text-align: justify;"><span style="background-color: blue;"><span style="color: white;"><b><i style="text-indent: -18pt;"><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">payback</span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;">
descontado</span></b></span></span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"> (<b>PD</b>) – </span>
<span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px; text-indent: -24px;">instante do fluxo de caixa onde o somatório (a partir da data focal “</span><b style="background-color: white; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px; text-indent: -24px;">1</b><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px; text-indent: -24px;">”) dos valores <i>descontados</i> das entradas de caixa operacionais assume o mesmo valor do investimento inicial;</span></li>
<li style="text-align: justify;"><span style="background-color: blue;"><span style="color: white;"><b><i style="text-indent: -18pt;"><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">payback</span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;">
descontado médio ou <i>payback</i> duração</span></b></span></span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"> (<b>PDM</b>) – resultado da divisão do
investimento inicial pelo valor médio de todas as entradas de caixa
operacionais descontadas, ou resultado da multiplicação da data focal “<b>n</b>” pelo quociente envolvendo o investimento inicial (numerador) e o valor presente de um projeto de investimento (denominador);</span></li>
<li style="text-align: justify;"><i style="text-indent: -18pt;"><span style="background-color: blue; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><span style="color: white;"><b>payback</b></span></span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"><span style="background-color: blue; color: white;"><b> anuidade</b></span><span style="background-color: white;">
(</span><b style="background-color: white;">PA</b><span style="background-color: white;">) – divisão do investimento
inicial pelo valor da anuidade correspondente ao valor presente de um projeto
de investimento;</span></span></li>
<li style="text-align: justify;"><i style="text-indent: -18pt;"><span style="background-color: blue; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><span style="color: white;"><b>payback</b></span></span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"><span style="background-color: blue; color: white;"><b>
taxa interna de retorno</b></span><span style="background-color: white;"> (</span><b style="background-color: white;">PTIR</b><span style="background-color: white;">) –
prazo exigido pela taxa interna de retorno de um projeto de investimento à
formação de um volume de juros equivalente ao investimento inicial, ou seja,
indica o período de tempo necessário à recuperação plena do capital com juros
derivados da taxa efetiva do fluxo de caixa;</span></span></li>
<li style="text-align: justify;"><span style="background-color: blue;"><span style="color: white;"><b><i style="text-indent: -18pt;"><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">payback</span></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;">
taxa interna de retorno modificada</span></b></span></span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-indent: -18pt;"> (<b>PTIRM</b>)
– tem a mesma interpretação do <b>PTIR</b>,
mas a taxa interna de retorno deve ser substituída pela taxa interna de
retorno modificada.</span></li>
</ul>
<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-align: justify;"><br /></span>
<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-align: justify;"><br /></span>
<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%; text-align: justify;"><br /></span>
<span style="font-size: large;"><span style="font-family: "arial" , sans-serif; line-height: 115%; text-align: justify;"><b><span style="background-color: black;"><span style="color: white;">ATENÇÃO:</span></span><span style="color: orange;"> </span></b></span><span style="background-color: blue; color: white; font-family: "arial" , sans-serif; line-height: 115%; text-align: justify;"><b>todas
as versões do</b> </span><span style="background-color: blue; color: white; text-align: justify;">
</span><i style="background-color: blue; color: white; font-family: Arial, sans-serif; line-height: 18px; text-align: justify;"><b>Payback Period</b></i><span style="background-color: blue; color: white; text-align: justify;"> </span><span style="background-color: blue; color: white; font-family: "arial" , sans-serif; line-height: 115%; text-align: justify;"><b>podem ser calculadas com a</b> <b>HP-12c</b>.</span></span><br />
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<b style="font-family: Arial, sans-serif; font-size: x-large; line-height: 27px;"><span style="background-color: black;"><span style="color: white;">NÃO DUVIDE!!!!!!!!!</span></span></b><br />
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<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">Considere
o exemplo descrito na Figura 1.<o:p></o:p></span></div>
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<span style="background-color: #274e13; font-family: "arial" , sans-serif; line-height: 115%;"><b><span style="color: white; font-size: x-small;">Figura 1</span></b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbwyzrIJhcC3ooXSOWdSzs-vjgw7Vo-4vPCHkmeKEr-9azPTNzRtxuGNjXK82QhjR_fryva4JwExDmrMUNxmSwQU1Sm2-jajgRMXqmb9Bha_1VfewhYVm5baJQACO3JnJ3gbFDTaq2A4Q/s1600/payback+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="337" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbwyzrIJhcC3ooXSOWdSzs-vjgw7Vo-4vPCHkmeKEr-9azPTNzRtxuGNjXK82QhjR_fryva4JwExDmrMUNxmSwQU1Sm2-jajgRMXqmb9Bha_1VfewhYVm5baJQACO3JnJ3gbFDTaq2A4Q/s400/payback+1.png" width="400" /></a></div>
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<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">Para calcular as 7 (sete) versões do </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i><span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">, do original ao taxa interna de retorno modificada, basta seguir as orientações das Figuras 2 a 10. </span></div>
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<span style="font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;"><span style="color: white;"><b style="background-color: blue;">Importante:</b><span style="background-color: white;"> </span></span>o <b>fluxo de caixa</b> deve ser <b>inserido</b> na <b>HP-12C</b> <b>apenas uma vez</b>, exatamente como sugere o processo detalhado na Figura 2; <b>não é necessário</b> <b>apagar</b> tudo (<span style="background-color: orange;"><b><span style="color: orange;">..</span>f<span style="color: orange;">..</span></b></span> <span style="background-color: black;">.<span style="color: orange;"><b>REG</b></span>. </span><span style="background-color: white;">ou </span></span><span style="background-color: orange; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;"><b><span style="color: orange;">..</span>f<span style="color: orange;">..</span></b></span><span style="font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;"> </span><span style="background-color: black; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;">.<span style="color: orange;"><b>FIN</b></span>.</span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 12pt; line-height: 115%;">) antes de calcular um novo tipo de </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;">; as Figuras 2 a 9 tratam dos <b>cálculos isolados</b> de cada tipo de </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;">; a Figura 10 apresenta um procedimento capaz de calcular todos os </span><span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;">tipos de </span>
<i style="color: blue; font-family: Arial, sans-serif; font-size: 16px; line-height: 18px;"><b>Payback Period</b></i> <span style="background-color: white; font-family: "arial" , sans-serif; font-size: 16px; line-height: 18px;"><b>em sequência</b>; <b>A ORIENTAÇÃO DOS PROCEDIMENTOS (FIGURAS 2 A 10) É DA ESQUERDA PARA A DIREITA (LINHAS).</b></span></div>
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<b style="font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 2 - INSERIR O FLUXO DE CAIXA NA </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<b style="font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 3 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK MÉDIO</span></span><span style="background-color: #274e13; color: white;"> COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA0l5v0qt90g1TKKPaCvHECWyBmwn-bTnShFAXF5yUbt4_ZwBUi38vHs0SjIWV4in9pvCIdDzgZ8z9QpRUvgllKiO2rliI5iwHOH55TNn7V-S6jVA2_OpHvs0yodVBtvrAn25YSfhO3IU/s1600/payback+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA0l5v0qt90g1TKKPaCvHECWyBmwn-bTnShFAXF5yUbt4_ZwBUi38vHs0SjIWV4in9pvCIdDzgZ8z9QpRUvgllKiO2rliI5iwHOH55TNn7V-S6jVA2_OpHvs0yodVBtvrAn25YSfhO3IU/s640/payback+3.png" width="640" /></a></div>
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<b style="font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 4 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK ORIGINAL</span></span><span style="background-color: #274e13; color: white;"> COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOsdsCvZF5zouKIvVQJWsdWlJWV7WkCCtT9ACr0cPbIAR6e2qGqL8DDzQbR4xZqvwGxnIyIfZ2q50hyAiXdYi4P1d8sXqcFRrNl8lP_9XvRQFiyShMt8axVvNwbb2lUJt4D4QFsyGCIfo/s1600/payback+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="336" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOsdsCvZF5zouKIvVQJWsdWlJWV7WkCCtT9ACr0cPbIAR6e2qGqL8DDzQbR4xZqvwGxnIyIfZ2q50hyAiXdYi4P1d8sXqcFRrNl8lP_9XvRQFiyShMt8axVvNwbb2lUJt4D4QFsyGCIfo/s640/payback+4.png" width="640" /></a></div>
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<b style="background-color: white; font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 5 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK DURAÇÃO</span></span><span style="background-color: #274e13; color: white;"> COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn8xhmyNAxe5eluKx8Aql-0QIQlYon_r8JAWDNsQj8wda7tPv8he8Eq19Pb5dZY3uutY5yViGg_ChlrwjLXZLfT916Oe7s2gyx1vrtpcKFvtQBBBPHIRPp55OB88nBHJ_mBOPfSVDH0dM/s1600/payback+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn8xhmyNAxe5eluKx8Aql-0QIQlYon_r8JAWDNsQj8wda7tPv8he8Eq19Pb5dZY3uutY5yViGg_ChlrwjLXZLfT916Oe7s2gyx1vrtpcKFvtQBBBPHIRPp55OB88nBHJ_mBOPfSVDH0dM/s640/payback+5.png" width="640" /></a></div>
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<b style="background-color: white; font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 6 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK ANUIDADE</span></span><span style="background-color: #274e13; color: white;"> COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiw1iYkPhNVVxEiDn2AZKTk8tDyQ1ChuO1hcmMbGiul3JGGuNocMBLCK-1_oyQBDq7kLtV0dL22GBZYSKzFoXlC7b8KU8MxV3QWV1gdOpTAZTAGGWRfBFPKWmdJcEs59yH2S_ZZ_OyKSI/s1600/payback+6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiw1iYkPhNVVxEiDn2AZKTk8tDyQ1ChuO1hcmMbGiul3JGGuNocMBLCK-1_oyQBDq7kLtV0dL22GBZYSKzFoXlC7b8KU8MxV3QWV1gdOpTAZTAGGWRfBFPKWmdJcEs59yH2S_ZZ_OyKSI/s640/payback+6.png" width="640" /></a></div>
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<b style="background-color: white; font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 7 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK TAXA INTERNA DE RETORNO</span></span><span style="background-color: #274e13; color: white;"> COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<b style="background-color: white; font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 8 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK TAXA INTERNA DE RETORNO MODIFICADA</span></span><span style="background-color: #274e13; color: white;"> COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<b style="background-color: white; font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 9 - CALCULAR O </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK DESCONTADO </span></span><span style="background-color: #274e13; color: white;">COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<b style="background-color: white; font-family: Arial, sans-serif; line-height: 18px;"><span style="background-color: #274e13; color: white;">Figura 10 - CALCULAR TODOS OS TIPOS DE </span><span style="background-color: #274e13;"><span style="color: orange;">PAYBACK</span></span><span style="background-color: #274e13; color: white;"> EM SEQUÊNCIA COM A </span><span style="background-color: #274e13; color: orange;">HP-12C</span></b>
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<span style="background-color: white;">Indicadores explorados nesta postagem: 7 (sete) versões do </span><b style="background-color: white;"><i><span style="color: blue;">Payback Period </span></i></b><span style="background-color: white;">e outros 5 (cinco) indicadores - valor presente, valor presente anuidade, valor presente líquido, taxa interna de retorno e taxa interna de retorno modificada. O procedimento detalhado na </span><b style="background-color: #274e13;"><span style="color: white;">Figura 10 consegue CALCULAR 12 (DOZE) INDICADORES EM SEQUÊNCIA COM A HP-12C.</span></b></div>
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Além de vários tipos de payback, o vídeo a seguir mostra como calcular
outros medidores. São QUINZE medidores de desempenho para avaliar
projetos de investimentos com planilha eletrônica. </div>
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<span style="background-color: lime;"><b><span style="font-size: medium;">Assista ao vídeo do canal MAFIN. </span></b></span></div>
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<b><br /></b><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/pOmaj7ZdT3g/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/pOmaj7ZdT3g?feature=player_embedded" width="320"></iframe></div>
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<b>Bom trabalho!</b>
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<b>Adail Marcos</b></div>
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<b><span style="background-color: blue; color: white; font-size: large;">ATENÇÃO!</span> <a href="http://adailmarcos.blogspot.com.br/2012/11/payback-period-aprenda-calcular-7-sete.html" target="_blank">Payback com o uso do Microsof</a></b><b><a href="http://adailmarcos.blogspot.com.br/2012/11/payback-period-aprenda-calcular-7-sete.html" target="_blank">t EXCEL</a></b></div>
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<span style="color: orange; font-family: "arial" , sans-serif;"><span style="line-height: 18px;"><b>!!!!!</b></span></span></div>
Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com8tag:blogger.com,1999:blog-5692836511586863836.post-88452073133621772592012-06-18T09:44:00.004-07:002013-03-18T12:16:20.158-07:00Utilização da HP-12c na análise do risco de ações<div class="separator" style="clear: both; text-align: justify;">
A classificação financeira pode sugerir a falsa ideia de o manuseio da HP-12c restringir-se ao desenvolvimento de aplicações envolvendo matemática financeira e engenharia econômica. A verdade: a <b><span style="color: blue;">HP-12c</span></b> é uma calculadora com funções financeiras e estatísticas; a classificação financeira deriva de seu manuseio abranger uma maior quantidade de aplicações em matemática financeira (pura e aplicada) e engenharia econômica; as funções estatísticas contemplam fragmentos de estatística básica (média, variância, desvio padrão, correlação e regressão linear simples). </div>
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Um usuário desavisado pode considerar improvável o emprego da <span style="color: blue;"><b>HP-12c</b></span> na análise do risco de ações, por exemplo, onde quase todas as funções estatísticas são utilizadas na formação do seguinte conjunto de medidores: risco de uma ação (desvio padrão), beta de uma ação (coeficiente angular), correlação entre uma ação e o mercado (correlação linear) e interferência do risco sistemático sobre o risco total de uma ação (coeficiente de determinação). </div>
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Em relação ao processamento do conjunto de medidores empregados na análise do risco de ações:</div>
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<ul>
<li>esta postagem explora dois casos reais;</li>
<li><span style="background-color: white;">ações<span style="color: blue; font-weight: bold;"> GGBR3</span></span> e <b><span style="background-color: white; color: blue;">AMBV3</span></b>.</li>
</ul>
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Duas observações importantes:</div>
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<ul>
<li>os medidores foram apurados a partir dos retornos discretos mensais do ano de 2011;</li>
<li style="text-align: justify;">os cálculos dos retornos discretos mensais seguiram os históricos das cotações mensais <span style="color: blue;"><b>AJUSTADAS</b></span> da ações (<b style="background-color: white;"><span style="color: blue;">Tabela 1</span></b>).</li>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6aop5f118JobX4ZvQ-kLzM-i6RZmnEk7oBOOrLQiI9LCPh_azf5bEBfjqFwspFlSJYpsEfRZwQbV9liCi-oxscFByndpZWl5D5G5npe5ZnnQAr7VIJti0fZFmAVfkDDn01Ux9N8GYx7A/s1600/cota%C3%A7%C3%B5es+mensais.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6aop5f118JobX4ZvQ-kLzM-i6RZmnEk7oBOOrLQiI9LCPh_azf5bEBfjqFwspFlSJYpsEfRZwQbV9liCi-oxscFByndpZWl5D5G5npe5ZnnQAr7VIJti0fZFmAVfkDDn01Ux9N8GYx7A/s640/cota%C3%A7%C3%B5es+mensais.png" width="524" /></a></div>
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<b><span style="background-color: blue;"><span style="color: white;">Primeira Parte:</span></span></b> </div>
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<ul>
<li>calcular (<b><span style="color: blue;">Figuras 1, 2 e 3</span></b>) e organizar (<b><span style="color: blue;">Tabela 2</span></b>) os retornos discretos mensais do mercado (<span style="background-color: white;"><span style="color: blue;"><b>IBOVESPA</b></span></span>) e das ações (<b><span style="color: blue;">GGBR3</span></b> e <b><span style="color: blue;">AMBV3</span></b>).</li>
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<b><span style="color: blue;">Figura 1 </span></b></div>
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<b><span style="color: blue;">(ordem invertida na TABELA 1)</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisoe5cG9yEIAtUV3KkS934KMECIrDYI8-FFNP0HI1BALpeuFuwfza4BXnwnGwtagn09J3rqnVoEsDae-g1fSAZsZzPC_9ll6IgHkXKjEgUkm9eOsm8m3dVX1TaC4yro75cSumMWN-UuG4/s1600/An%C3%A1lise+de+risco+hp12c+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisoe5cG9yEIAtUV3KkS934KMECIrDYI8-FFNP0HI1BALpeuFuwfza4BXnwnGwtagn09J3rqnVoEsDae-g1fSAZsZzPC_9ll6IgHkXKjEgUkm9eOsm8m3dVX1TaC4yro75cSumMWN-UuG4/s1600/An%C3%A1lise+de+risco+hp12c+1.png" /></a></div>
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<b><span style="color: blue;">Figura 2</span></b>
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<b><span style="color: blue;">(ordem invertida na TABELA 1)</span></b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7TNGe2faML9xYK2KBQhoX7luvhgp6uYj6JkxZ8PMeeig6J8IViNCiyxY7i2QQYlV3IZrt8nMTMd1tSYO7CAVNtrAQzbzVsH0aZpv8pucBd_G9GezTbVWNID6NakiENNTcVSyDnq1qeqs/s1600/An%C3%A1lise+de+risco+hp12c+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7TNGe2faML9xYK2KBQhoX7luvhgp6uYj6JkxZ8PMeeig6J8IViNCiyxY7i2QQYlV3IZrt8nMTMd1tSYO7CAVNtrAQzbzVsH0aZpv8pucBd_G9GezTbVWNID6NakiENNTcVSyDnq1qeqs/s1600/An%C3%A1lise+de+risco+hp12c+2.png" /></a></div>
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<b><span style="color: blue;">Figura 3</span></b>
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<b><span style="color: blue;">(ordem invertida na TABELA 1)</span></b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1KqV5_0S7GofhT2TVU4ZXpi__Hdc8AK7GGTxVM1w_FS1XGfW6xjV4z2eu06w3VB2588iDkuhtCYj2RKeH9geXfA_kfrnm-bDOBCDHcZy0OKBRZUTkTckjKaoAvPvXxbY8x3qge0EvGz8/s1600/An%C3%A1lise+de+risco+hp12c+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1KqV5_0S7GofhT2TVU4ZXpi__Hdc8AK7GGTxVM1w_FS1XGfW6xjV4z2eu06w3VB2588iDkuhtCYj2RKeH9geXfA_kfrnm-bDOBCDHcZy0OKBRZUTkTckjKaoAvPvXxbY8x3qge0EvGz8/s1600/An%C3%A1lise+de+risco+hp12c+3.png" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3M9Zjopw9TrGwN5M9QTjJ4Q_uFSeGDxceLpTR0yX31T1YSzJ2Go2n0cY2kLepoXsIaikd2dfl38vcmBiTVKNGyhFqR9c0ZPVz9sSjQIBzhpbgY1ssyH28QC5phIjz8kltMtt9EaVnyfg/s1600/retornos+mensais.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3M9Zjopw9TrGwN5M9QTjJ4Q_uFSeGDxceLpTR0yX31T1YSzJ2Go2n0cY2kLepoXsIaikd2dfl38vcmBiTVKNGyhFqR9c0ZPVz9sSjQIBzhpbgY1ssyH28QC5phIjz8kltMtt9EaVnyfg/s640/retornos+mensais.png" width="543" /></a></div>
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<b><span style="background-color: blue;"><span style="color: white;">Segunda Parte:</span></span></b> </div>
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<ul>
<li style="text-align: justify;">calcular os medidores de risco com os valores dos retornos discretos mensais (<b style="color: blue;">TABELA 2</b>);</li>
<li>o <b><span style="color: blue;">Quadro 1</span></b> apresenta a lista dos medidores calculados;</li>
<li>as <b><span style="color: blue;">Figuras 4 </span>e<span style="color: blue;"> 5</span></b> descrevem os procedimentos.
</li>
</ul>
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<b><span style="color: blue;">Quadro 1</span></b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1X-0HyItw8NG-jl5IGncd8UScBhStrHIE-06tF0H7mD30_z7ImD5R6aCQ4S7GKZbgcWAH_bIDqL0telUAJJZPcSJLWg2vRUs7yyrFpi_56x6LKkQmvOvCHiuBbdo7jsz_bWINUllbK8o/s1600/medidas+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1X-0HyItw8NG-jl5IGncd8UScBhStrHIE-06tF0H7mD30_z7ImD5R6aCQ4S7GKZbgcWAH_bIDqL0telUAJJZPcSJLWg2vRUs7yyrFpi_56x6LKkQmvOvCHiuBbdo7jsz_bWINUllbK8o/s640/medidas+3.png" width="640" /></a></div>
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<b><span style="color: blue;">Figura 4</span></b>
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<b style="color: blue; text-align: justify;">(ordem invertida na </b><b style="color: blue; text-align: justify;">TABELA 2</b><b style="color: blue; text-align: justify;">)</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf5lUmmlBUuq4oSf5n0iC0DihQSL2D1cSa7Sd8MCaBj9igN45rAys4BwaxwgpNjVMIlHd9e_Hhxap57-66Hiy5CAz5vPIIFyKt9S5wwT9b59uz98jmiz6wh-4P6sA_W411T6O_Y-2h574/s1600/An%C3%A1lise+de+risco+hp12c+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf5lUmmlBUuq4oSf5n0iC0DihQSL2D1cSa7Sd8MCaBj9igN45rAys4BwaxwgpNjVMIlHd9e_Hhxap57-66Hiy5CAz5vPIIFyKt9S5wwT9b59uz98jmiz6wh-4P6sA_W411T6O_Y-2h574/s1600/An%C3%A1lise+de+risco+hp12c+4.png" /></a></div>
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<b><span style="color: blue;">Figura 5</span></b>
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<b style="color: blue; text-align: justify;">(ordem invertida na </b><b style="color: blue; text-align: justify;">TABELA 2</b><b style="color: blue; text-align: justify;">)</b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNHP9i5PFwkzRzkXVbApzt_ghPbxxP3fHOztsujR65bvX1cCdG9NjgYnLXw5dxGSFNVc4Yp_VCOUi7T2hTucDwTcHYUychpeAhXG23cz6h8TFHcoW9fQP7LZof4WZFJ3tAFKxPTNYBIjo/s1600/An%C3%A1lise+de+risco+hp12c+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNHP9i5PFwkzRzkXVbApzt_ghPbxxP3fHOztsujR65bvX1cCdG9NjgYnLXw5dxGSFNVc4Yp_VCOUi7T2hTucDwTcHYUychpeAhXG23cz6h8TFHcoW9fQP7LZof4WZFJ3tAFKxPTNYBIjo/s1600/An%C3%A1lise+de+risco+hp12c+5.png" /></a></div>
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Boa sorte com a elaboração dos relatórios analíticos. </div>
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Cordialmente,</div>
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Adail Marcos</div>
Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-78270558627967428162012-03-21T09:21:00.000-07:002012-04-26T09:46:24.278-07:00Análise das operações de desconto de duplicatas com a utilização da HP-12c<div class="separator" style="clear: both; text-align: center;">
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<div class="MsoNormal">
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A contratação do desconto de
duplicatas em bancos comerciais, uma operação de captação de crédito oneroso de
curto prazo muito popular entre as empresas brasileiras, funciona da seguinte
da forma:</div>
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<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">as empresas enviam aos bancos comerciais borderôs
de descontos, formados por duplicatas a receber selecionadas a partir de
critérios ancorados em uma satisfatória condição de adimplência;</span></li>
</ul>
<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">sobre o valor nominal do borderô de desconto,
resultado do somatório dos valores nominais de todas as duplicatas a receber
selecionadas, os bancos comerciais aplicam um deságio, formado por encargos com juros (descontos), fiscais (<b>IOF</b>) e operacionais (tarifas), visando definir o
valor a ser efetivamente creditado na conta corrente da empresa contratante.</span></li>
</ul>
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<div class="MsoListParagraphCxSpFirst" style="text-indent: -18pt;">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="text-indent: -18pt;">
<o:p></o:p></div>
<span style="text-align: justify;">As empresas contratam o desconto
de duplicatas em bancos comerciais de duas maneiras:</span><br />
<div class="MsoNormal">
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<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">aleatória, quando o custo efetivo total da
operação não interfere no processo de definição do banco comercial a ser
requisitado;</span></li>
</ul>
<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">racional, quando o custo efetivo total da
operação figura como principal critério no processo de definição do banco
comercial a ser requisitado à contratação do desconto de duplicatas.</span> </li>
</ul>
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<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
Se todas as variáveis necessárias
ao cômputo do custo efetivo total de uma operação de desconto de duplicatas
podem ser identificadas antes da efetivação de um contrato de crédito, a partir
de consultas informais aos bancos comerciais interessados, a contratação
racional deve ser praticada sem maiores dificuldades. <o:p></o:p></div>
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Ao cálculo do custo efetivo total de uma operação são respeitadas as seguintes etapas:</div>
<div class="MsoNormal">
</div>
<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">cálculo do valor nominal do borderô de desconto
(</span><b style="text-indent: -18pt;">VNB</b><span style="text-indent: -18pt;">) – somatório dos valores
nominais de todas as duplicatas selecionadas (</span><b style="text-indent: -18pt;">VN1</b><span style="text-indent: -18pt;"> + ... + </span><b style="text-indent: -18pt;">VNn</b><span style="text-indent: -18pt;">);</span></li>
</ul>
<div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTSSc2w02i9l86fhjQQ9HccogLCh7apr2hWT4O7o5-WYGU6fbvyURVYwz6lCqIUzXl6d9TPu8RapY6MCIGsgFbegffo09zYRpzpUgi-DDTZRGAlEIeoziqd7TIx5xv_3iz3IgJAd6CReg/s1600/DESCONTO+DE+DUPLICATAS+HP12C+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTSSc2w02i9l86fhjQQ9HccogLCh7apr2hWT4O7o5-WYGU6fbvyURVYwz6lCqIUzXl6d9TPu8RapY6MCIGsgFbegffo09zYRpzpUgi-DDTZRGAlEIeoziqd7TIx5xv_3iz3IgJAd6CReg/s200/DESCONTO+DE+DUPLICATAS+HP12C+5.png" width="200" /></a> </div>
<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">cálculo do prazo médio de recebimento do borderô
de desconto (</span><b style="text-indent: -18pt;">PMRB</b><span style="text-indent: -18pt;">) – média ponderada
envolvendo os valores nominais e os prazos de recebimento (</span><b style="text-indent: -18pt;">PR</b><span style="text-indent: -18pt;">) de todas as duplicatas inseridas no borderô de desconto;</span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSoI8I5YIdgSeGqV4zDBVyHCuIZ5C73N0NtqFLEnNaDiN_z5DQAxl1LnKZPFpeX1DGdk1srmicugFYJb1uQblSx8xZ_xkYnBf2puaTqs5-gdvqRsJPfhjAXYXBA8TVGs-qyGhGLebeIbY/s1600/DESCONTO+DE+DUPLICATAS+HP12C+6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSoI8I5YIdgSeGqV4zDBVyHCuIZ5C73N0NtqFLEnNaDiN_z5DQAxl1LnKZPFpeX1DGdk1srmicugFYJb1uQblSx8xZ_xkYnBf2puaTqs5-gdvqRsJPfhjAXYXBA8TVGs-qyGhGLebeIbY/s320/DESCONTO+DE+DUPLICATAS+HP12C+6.png" width="320" /></a></div>
<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">cálculo do encargo com juros da operação (</span><b style="text-indent: -18pt;">EJ</b><span style="text-indent: -18pt;">) – procedimento similar ao desconto
comercial simples, com a taxa de desconto (</span><b style="text-indent: -18pt;">d</b><span style="text-indent: -18pt;">)
incidindo sobre o </span><b style="text-indent: -18pt;">VNB</b><span style="text-indent: -18pt;">;</span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1w0b5dSLD36i3lXWPzQrRsu2s0cJ6Zip18T2J1081fHk3CzyG3BmzdGoeMpXQkEvsfk1T-tKcCVdkwkbVl8U35qt-49eUqEczjNVu6RkignfRh4kfyERHE8qC56JfVhXCqfMGXGAKAz0/s1600/DESCONTO+DE+DUPLICATAS+HP12C+7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="118" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1w0b5dSLD36i3lXWPzQrRsu2s0cJ6Zip18T2J1081fHk3CzyG3BmzdGoeMpXQkEvsfk1T-tKcCVdkwkbVl8U35qt-49eUqEczjNVu6RkignfRh4kfyERHE8qC56JfVhXCqfMGXGAKAz0/s320/DESCONTO+DE+DUPLICATAS+HP12C+7.png" width="320" /></a></div>
<ul>
<li style="text-align: justify;"><span style="text-indent: -18pt;">cálculo do encargo operacional da operação (</span><b style="text-indent: -18pt;">EO</b><span style="text-indent: -18pt;">) – soma entre a tarifa de
contratação (</span><b style="text-indent: -18pt;">TCT</b><span style="text-indent: -18pt;">) e o total a ser
pago de tarifa de cobrança (</span><b style="text-indent: -18pt;">TCB</b><span style="text-indent: -18pt;">,
exigida sobre cada duplicata contida no borderô de desconto);</span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXrloAQgmSbguVzLDOCKGGp3DH_D8yDl2PMXg_J2s_FtlC-SDBDPPkhg-oxkaZC7txzyIHITle-DDg7vWmYBtneE4on00V7xwOHSoGwtKHCfhYp5YjmF2LRsW8B5Gw5ViXu0UgQ_EV5ig/s1600/DESCONTO+DE+DUPLICATAS+HP12C+8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXrloAQgmSbguVzLDOCKGGp3DH_D8yDl2PMXg_J2s_FtlC-SDBDPPkhg-oxkaZC7txzyIHITle-DDg7vWmYBtneE4on00V7xwOHSoGwtKHCfhYp5YjmF2LRsW8B5Gw5ViXu0UgQ_EV5ig/s1600/DESCONTO+DE+DUPLICATAS+HP12C+8.png" /></a></div>
<ul>
<li><span style="text-align: justify; text-indent: -18pt;">cálculo do encargo fiscal da operação (</span><b style="text-align: justify; text-indent: -18pt;">EF</b><span style="text-align: justify; text-indent: -18pt;">) – total de </span><b style="text-align: justify; text-indent: -18pt;">IOF</b><span style="text-align: justify; text-indent: -18pt;"> a ser pago, processado a partir das incidências das taxas
variável (</span><b style="text-align: justify; text-indent: -18pt;">IOFV</b><span style="text-align: justify; text-indent: -18pt;">) e fixa (</span><b style="text-align: justify; text-indent: -18pt;">IOFF</b><span style="text-align: justify; text-indent: -18pt;">) sobre o </span><b style="text-align: justify; text-indent: -18pt;">VNB</b><span style="text-align: justify; text-indent: -18pt;"> líquido do </span><b style="text-align: justify; text-indent: -18pt;">EJ</b><span style="text-align: justify; text-indent: -18pt;">;</span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiamDW7jQ4rIQitJO_jS0TWdN-8lPP5wwEfAErxa7b3mudI42E2qYOybiZd2zFu2FZXS5FO60diDJkmiFhPSSbJScW5wTAnMseTKMV0MZxOfVu0QK5doqd1Ly1OoOg8ebRUWoKRKI4rr4k/s1600/DESCONTO+DE+DUPLICATAS+HP12C+9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="62" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiamDW7jQ4rIQitJO_jS0TWdN-8lPP5wwEfAErxa7b3mudI42E2qYOybiZd2zFu2FZXS5FO60diDJkmiFhPSSbJScW5wTAnMseTKMV0MZxOfVu0QK5doqd1Ly1OoOg8ebRUWoKRKI4rr4k/s400/DESCONTO+DE+DUPLICATAS+HP12C+9.png" width="400" /></a></div>
<ul>
<li><span style="text-align: justify; text-indent: -18pt;">cálculo do valor creditado (</span><b style="text-align: justify; text-indent: -18pt;">VC</b><span style="text-align: justify; text-indent: -18pt;">) – valor efetivamente creditado na conta corrente do contrate ao
término de uma operação de desconto de duplicatas;</span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoiBcy0tjoiHlatNVtdDtnvR9Aaz4vhkdTXNUhAPrIg1gyE8PeflC_Q0mvAfO5NeZV1NahMhhBuWdv5pRAdyS4UF5k8g9_xq0fAPk5gh2b7bsKUpC5cm3miwuyLmT-ElHpwQvw5V9qd4o/s1600/DESCONTO+DE+DUPLICATAS+HP12C+10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="76" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoiBcy0tjoiHlatNVtdDtnvR9Aaz4vhkdTXNUhAPrIg1gyE8PeflC_Q0mvAfO5NeZV1NahMhhBuWdv5pRAdyS4UF5k8g9_xq0fAPk5gh2b7bsKUpC5cm3miwuyLmT-ElHpwQvw5V9qd4o/s320/DESCONTO+DE+DUPLICATAS+HP12C+10.png" width="320" /></a></div>
<ul>
<li><span style="text-align: justify; text-indent: -18pt;">cálculo do custo efetivo total da operação (</span><b style="text-align: justify; text-indent: -18pt;">CET</b><span style="text-align: justify; text-indent: -18pt;">) – ao dia, ao mês e ao ano.</span></li>
</ul>
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Seguindo o critério da contratação racional do desconto de duplicatas em bancos comerciais, fundamentado na análise antecipada do <b>CET</b> das operações, a calculadora financeira <b>HP-12c</b> representa uma ferramenta de grande utilidade. A manipulação combinada das funções estatísticas e financeiras consegue extrair de uma suposta operação de desconto de duplicatas todas as informações necessárias à implementação de uma metodologia racional de análise. </div>
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Considere o borderô de desconto detalhado abaixo, a ser descontado em um banco comercial sob as condições a seguir: R$120,00 de <b>TCT</b>; R$3,00 de <b>TCB</b>; 2,70% de <b>d</b>; <b>IOFV</b> de 0,0041% ao dia; <b>IOFF</b> de 0,38%. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnelB8c34QVfXk-_R7tvFCHWKdU8DrepuE3M8KuOERXDiFbTNlx3BObydKht2nnlNRV0JWAy0gr3fKWNMQrkgkSJFFFzW3o2MoMknwx7_QcuNIBqaftMlhusiRH7OVUlwRH9nOTVZesgw/s1600/DESCONTO+DE+DUPLICATAS+HP12C+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnelB8c34QVfXk-_R7tvFCHWKdU8DrepuE3M8KuOERXDiFbTNlx3BObydKht2nnlNRV0JWAy0gr3fKWNMQrkgkSJFFFzW3o2MoMknwx7_QcuNIBqaftMlhusiRH7OVUlwRH9nOTVZesgw/s400/DESCONTO+DE+DUPLICATAS+HP12C+3.png" width="400" /></a></div>
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A figura abaixo apresenta o procedimento completo a ser empregado no processamento de informações relevantes à contratação racional do desconto de duplicatas em bancos comerciais. Algumas instruções elementares: o tratamento quantitativo a ser trabalhado com as funções estatísticas visa identificar o <b>VNB</b> (somatório de "x", obtido com <b><span style="background-color: black;"><span style="color: white;">RCL</span></span> <span style="background-color: black;">..<span style="color: white;">2</span>..</span></b>), quantidade de duplicatas contidas no borderô de desconto (identificada com
<b><span style="background-color: black;"><span style="color: white;">RCL</span></span> <span style="background-color: black;">..<span style="color: white;">1</span>..</span></b> ) e <b>PMRB </b>(obtido a partir de uma média ponderada, esclarecida através de <span style="background-color: cyan;"><span style="color: cyan;">..</span><b>g</b><span style="color: cyan;">..</span></span> <span style="background-color: black;">.<b><span style="color: cyan;">xw</span>.</b></span>). </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhhIxEE_yPqvF-qpNkeDa2jSiZYSDY1CTpvKpfFh7Ute_63PAPqVKw1y1jIGCsFNAUBPiOCeuWLwCG91qrbsPiH3JHp8mg-3QPEoq-utNehXQIndiSIveTuddCTEaU5IaSR3OcFTe6v0c/s1600/DESCONTO+DE+DUPLICATAS+HP12C+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhhIxEE_yPqvF-qpNkeDa2jSiZYSDY1CTpvKpfFh7Ute_63PAPqVKw1y1jIGCsFNAUBPiOCeuWLwCG91qrbsPiH3JHp8mg-3QPEoq-utNehXQIndiSIveTuddCTEaU5IaSR3OcFTe6v0c/s1600/DESCONTO+DE+DUPLICATAS+HP12C+1.png" /></a></div>
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A figura anterior demonstra nos mínimos detalhes a utilização da <b>HP-12c</b> no suporte à análise das operações de desconto de duplicatas em bancos comerciais. Quando da necessidade de aplicar o procedimento mais de uma vez, ou seja, quando o processamento de informações relevantes à contratação racional do desconto assumir a condição de uma atividade corriqueira, passa a ser mais conveniente fazer uso de uma programação específica. A figura abaixo apresenta uma proposta de programação bem interessante. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpOQ7KcJz5x7NnjUd94AqB02n6nEUpYHkjI8AzvvSLOzg96JIHkC_n_7NpSyDZZqk8XXxkXSZceOy4kBN61A0qctKseaAjhyphenhyphenFwQuDwYItlXmUrw3A4U7wwbz_FoPvN6nuBHFzYZVq_sCQ/s1600/DESCONTO+DE+DUPLICATAS+HP12C+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpOQ7KcJz5x7NnjUd94AqB02n6nEUpYHkjI8AzvvSLOzg96JIHkC_n_7NpSyDZZqk8XXxkXSZceOy4kBN61A0qctKseaAjhyphenhyphenFwQuDwYItlXmUrw3A4U7wwbz_FoPvN6nuBHFzYZVq_sCQ/s1600/DESCONTO+DE+DUPLICATAS+HP12C+2.png" /></a></div>
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A figura abaixo apresenta o processamento de informações relevantes à contratação racional do desconto de duplicatas em bancos comerciais a partir da aplicação da programação especificamente desenvolvida. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm7gqGdrZYBtsb9GQzipxnoFomF5GS6QLZAzmHMcODAAqwjo7TAQzuCyJAG3NajOvlGclDQDO3azbgL3aCV9iLdMIDNV82CFUljY0gHcPafNbAmmyt1u5KGWGiFMY5SRFnf7gYPKPFePE/s1600/DESCONTO+DE+DUPLICATAS+HP12C+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm7gqGdrZYBtsb9GQzipxnoFomF5GS6QLZAzmHMcODAAqwjo7TAQzuCyJAG3NajOvlGclDQDO3azbgL3aCV9iLdMIDNV82CFUljY0gHcPafNbAmmyt1u5KGWGiFMY5SRFnf7gYPKPFePE/s1600/DESCONTO+DE+DUPLICATAS+HP12C+4.png" /></a></div>
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Boa sorte!</div>
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Adail Marcos</div>
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<br />Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com1tag:blogger.com,1999:blog-5692836511586863836.post-72916213161907666962012-02-06T14:55:00.000-08:002014-08-12T19:41:48.062-07:00Análise de Custos: emprego do gráfico de dispersão do Microsoft EXCEL no desenvolvimento de aplicações envolvendo o estudo do Comportamento do Custo da Atividade<div style="text-align: justify;">
<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">Esta postagem visa demonstrar o emprego do gráfico de dispersão do Microsoft EXCEL no desenvolvimento de aplicações envolvendo o estudo do Comportamento do Custo da Atividade.</span></b></div>
<div style="text-align: justify;">
<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas"><br /></span></b></div>
<div style="text-align: justify;">
<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">Comportamento do Custo da Atividade representa um tópico básico das disciplinas Análise de Custos e Gestão de Custos.</span></b></div>
<div style="text-align: justify;">
<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas"><br /></span></b></div>
<div style="text-align: justify;">
<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">Observe o caso descrito na Figura 1:</span></b></div>
<br />
<ul>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>uma empresa precisa estimar o custo total a ser desembolsado com o cumprimento de um conjunto de 350 movimentos - necessários à execução
<b>de uma determinada operação</b>;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>a dificuldade reside no fato de não existir em seus relatórios de controle referências ao custo total derivado de 350 movimentos;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>os únicos registros disponíveis viabilizam a elaboração de um histórico mensal, perfazendo os últimos dez meses - janeiro a outubro;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>portanto, a solução exige a manipulação dos dados contidos no histórico visando a estimação do custo total para 350 movimentos;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>como o conjunto dos movimentos representa a variável independente e o custo total a variável dependente, a construção da equação de regressão linear pode viabilizar a estimação do custo total para 350 movimentos.</b></span><b style="color: blue; font-family: arial, sans-serif;"> </b></li>
</ul>
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<span style="color: blue; font-family: arial, sans-serif;"><b>Figura 1</b></span><br />
<span style="color: blue; font-family: arial, sans-serif;"><b><br /></b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggICsTJZMdL7PMbYGX-T_Mq2FBezgRZZsXrbp5COwZR8KzxmN6LcZ5A5LLUUeXGJt3D5APs-OA9c75je5AaPPDwQX827vTDChmYF5AAOMKtSfG6pDLrNTMA0pV806X3q9TTBL-k5uDyX8/s1600/An%25C3%25A1lise+de+Custos+Exemplo+Enunciado.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggICsTJZMdL7PMbYGX-T_Mq2FBezgRZZsXrbp5COwZR8KzxmN6LcZ5A5LLUUeXGJt3D5APs-OA9c75je5AaPPDwQX827vTDChmYF5AAOMKtSfG6pDLrNTMA0pV806X3q9TTBL-k5uDyX8/s1600/An%25C3%25A1lise+de+Custos+Exemplo+Enunciado.png" /></a>
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<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">O gráfico de dispersão do Microsoft EXCEL representa uma alternativa rápida e prática à resolução do problema descrito anteriormente. O gráfico deve ser elaborado com base no exemplo da Figura 2, onde:</span></b></div>
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<ul>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>y = ax + b, equação de regressão linear;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>x, variável independente;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>y, variável dependente;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>a, parâmetro de inclinação ou coeficiente angular ou declive;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>b, intercepto-y ou coeficiente linear; </b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>R2, coeficiente de determinação.</b></span></li>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 2</b>
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<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">A adaptação do gráfico de dispersão à previsão do custo total deve seguir o modelo da Figura 3, onde:</span></b></div>
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<ul>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>CT = CVu Q + CF, equação de regressão linear - empregada na previsão do custo total com base em valores previamente definidos ao nível de atividade;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>Q, nível de atividade - variável independente;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>CT, custo total - variável dependente;</b></span></li>
<li style="text-align: justify;"><span style="color: blue; font-family: arial, sans-serif;"><b>CVu, custo variável unitário - </b></span>
<b style="color: blue; font-family: arial, sans-serif;">parâmetro de inclinação ou coeficiente angular ou declive;</b></li>
<li style="text-align: justify;"><b style="color: blue; font-family: arial, sans-serif;"><b>CF, custo fixo - intercepto-y ou coeficiente linear;</b>
</b></li>
<li style="text-align: justify;"><b style="color: blue; font-family: arial, sans-serif;"><b><b>R2, coeficiente de determinação - identifica a porcentagem da variação do CT explicada pela variação do Q (quanto mais próximo de 100%, maior a capacidade de a equação de regressão prever valores confiáveis ao CT).</b>
</b></b></li>
</ul>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 3</b>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis8m0UbqK-OXWFnda8bEmjWo2yuLP50T-4peomqybMQgVqTK6_zTFGIIzIDQnAVIQcfwNSHIW7K9W0wTq9ZwGHTqJmBzVqtQSrTwVyON9aAA5WaeNtFhfXErAr45vWH2k-4gDPV7MiCDU/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis8m0UbqK-OXWFnda8bEmjWo2yuLP50T-4peomqybMQgVqTK6_zTFGIIzIDQnAVIQcfwNSHIW7K9W0wTq9ZwGHTqJmBzVqtQSrTwVyON9aAA5WaeNtFhfXErAr45vWH2k-4gDPV7MiCDU/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+3.png" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">As figuras 4 a 11 explicam o processo de elaboração do gráfico de dispersão capaz de solucionar a caso descrito na figura 1. </span></b></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 4 - escolher o tipo de gráfico</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUh92nLqYvw-qmBb2Yp08K5tRsIyQ4wJoZqop68phgjcS4DaT7tJRMTIX_GtD1s44V5f-MpBqYaLYSA5f84tAiAwq5s7YRysrmLjClU-pRza0Bn08hPTo1A5HNnF2T02qWGzuDqZXR_0w/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUh92nLqYvw-qmBb2Yp08K5tRsIyQ4wJoZqop68phgjcS4DaT7tJRMTIX_GtD1s44V5f-MpBqYaLYSA5f84tAiAwq5s7YRysrmLjClU-pRza0Bn08hPTo1A5HNnF2T02qWGzuDqZXR_0w/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+1.png" height="426" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 5 - clicar em Selecionar Dados (depois de clicar com o lado direito do mouse sobre o gráfico em branco) </b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirR_w6T76i9MyvCtUIualZF76VaI8CUj7QkGzdxI3_xRdPXzF4PPf3f2rl_LSlLLSA4vU_Z01F7winGYOLPpSOOIy7UCJ8TKFT2owDCU5CfARFoKtLFZ5Oa-pwonNrndx1CrDiSEvgShw/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirR_w6T76i9MyvCtUIualZF76VaI8CUj7QkGzdxI3_xRdPXzF4PPf3f2rl_LSlLLSA4vU_Z01F7winGYOLPpSOOIy7UCJ8TKFT2owDCU5CfARFoKtLFZ5Oa-pwonNrndx1CrDiSEvgShw/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+2.png" height="359" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 6 - em </b><b style="color: blue; font-family: arial, sans-serif;">Entradas de Legenda (Série), </b><b style="color: blue; font-family: arial, sans-serif;">clicar em Adicionar</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiU9idCT6-0XmkzcEtxFYH8g-uHNFqGgK-yzEoWauESAdsnzoEbR3wFCp5zc1oEBe_ywu7WoAcpxSg1gsSiSG-27gQQ1LsqCbjHFKkoh_fITUASRjRh7_MTF_iHlq3eAbnwzruLM3kpD4/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiU9idCT6-0XmkzcEtxFYH8g-uHNFqGgK-yzEoWauESAdsnzoEbR3wFCp5zc1oEBe_ywu7WoAcpxSg1gsSiSG-27gQQ1LsqCbjHFKkoh_fITUASRjRh7_MTF_iHlq3eAbnwzruLM3kpD4/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+4.png" height="354" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 7 - inserir os valores de "x" (Q) e de "y" (CT)</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj79E5zT4WGvJlv0zwG0U0fXsOl7VZnWlh0bo1uNFljgIeJBSK5O9Gs07c65XA7SainxXNaILk_3K_HyQAkFS0EKRmvzwrlzAd6YShs692WlKos50FY_zB2nMvL5oZl_MurzPM_L7mwKUU/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj79E5zT4WGvJlv0zwG0U0fXsOl7VZnWlh0bo1uNFljgIeJBSK5O9Gs07c65XA7SainxXNaILk_3K_HyQAkFS0EKRmvzwrlzAd6YShs692WlKos50FY_zB2nMvL5oZl_MurzPM_L7mwKUU/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+6.png" height="372" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 8 - modificar a aparência do gráfico</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtSVyN1jh_DI1kWC6yiO0H8CLdotz7ggjdhixs0SfM-k7dx1-Wc5fIyBH_D2TYxU1o0Rhl09l5c-3IJjcJoyF27__W6AQnYfwb_aaSZ_5DLYJbaPPytxPl6MeonYKVCep8DGdmxld2w04/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtSVyN1jh_DI1kWC6yiO0H8CLdotz7ggjdhixs0SfM-k7dx1-Wc5fIyBH_D2TYxU1o0Rhl09l5c-3IJjcJoyF27__W6AQnYfwb_aaSZ_5DLYJbaPPytxPl6MeonYKVCep8DGdmxld2w04/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+8.png" height="356" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 9 - em Layout, selecionar mais Opções de Linha de Tendência</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBaoMioj1m2pzAGLLQtIFw1EbNSCGf8rlwY1XMregw9rVDrxjzWb7Intv7r5uhTlL5BA8_OHIb551Dxcp2IOrAOXy0e19i2fNh6of2cpC55kBn9tiwiGrcOw7UPMzaVEOMZ9Kpq3D02AU/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBaoMioj1m2pzAGLLQtIFw1EbNSCGf8rlwY1XMregw9rVDrxjzWb7Intv7r5uhTlL5BA8_OHIb551Dxcp2IOrAOXy0e19i2fNh6of2cpC55kBn9tiwiGrcOw7UPMzaVEOMZ9Kpq3D02AU/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+4+10.png" height="368" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 10 - observar as indicações</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2fy-Qt71zBKVF3jIv_bwVgQF6wPoYit8DG7v7cB0ZSnXsh8Wt1MfkuhHNiEo0-Xv3M87TJcAvRG8SVZNEIh09C6uJVj380F8jykZZzD7jHCRCHBjusbFmNMNQH4eTwRApnYrcpJ9zcq8/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2fy-Qt71zBKVF3jIv_bwVgQF6wPoYit8DG7v7cB0ZSnXsh8Wt1MfkuhHNiEo0-Xv3M87TJcAvRG8SVZNEIh09C6uJVj380F8jykZZzD7jHCRCHBjusbFmNMNQH4eTwRApnYrcpJ9zcq8/s400/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+12.png" height="393" width="400" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif;">Figura 11 - versão final do gráfico de dispersão</b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaRS2qay5aAropH04BXv64KAGYmSPU7zIfsvjD4WykbPkVPmDcUfkKPbicfDZbjsgvV5st8es5vN4XCO7zVlmcy0SXWqLsKpQCvYc7HQ0vUjbr90F80559AbfTvJ8T-_NmKMxv9Ou-WxY/s1600/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+14.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaRS2qay5aAropH04BXv64KAGYmSPU7zIfsvjD4WykbPkVPmDcUfkKPbicfDZbjsgvV5st8es5vN4XCO7zVlmcy0SXWqLsKpQCvYc7HQ0vUjbr90F80559AbfTvJ8T-_NmKMxv9Ou-WxY/s640/An%C3%A1lise+Custos+Dispers%C3%A3o+XY+14.png" height="308" width="640" /></a></div>
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<b style="color: blue; font-family: arial, sans-serif; text-align: center;"><span class="hps" title="Clique para mostrar traduções alternativas">Para o caso a ser solucionado, referente à previsão do CT para um Q de 350 movimentos, a aplicação do gráfico de dispersão do Microsoft EXCEL subsidia a obtenção dos esclarecimentos destacados abaixo:</span></b></div>
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<ul style="text-align: -webkit-auto;">
<li><span style="color: blue; font-family: arial, sans-serif;"><b>CT = 12,392 Q + 854,5, equação a ser empregada na previsão do CT;</b></span></li>
<li><span style="color: blue; font-family: arial, sans-serif;"><b>12,392, custo variável unitário (para cada movimento executado)</b></span><b style="color: blue; font-family: arial, sans-serif;">;</b></li>
<li><b style="color: blue; font-family: arial, sans-serif;"><b>854,5, custo fixo (para qualquer quantidade de movimentos);</b></b></li>
<li><b style="color: blue; font-family: arial, sans-serif;"><b>5191,7 = </b></b>
<b style="color: blue; font-family: arial, sans-serif;">12,392 x 350 + 854,5, CT esperado (para um total de 350 movimentos);</b></li>
<li><b style="color: blue; font-family: arial, sans-serif;"><b><b>a variação de Q consegue explicar
<b><b><b>86,29%</b></b></b> da variação do CT.</b></b></b></li>
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<span style="color: blue; font-family: arial, sans-serif;"><span style="font-weight: 900;">
Cordialmente,</span></span><br />
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<span style="color: blue; font-family: arial, sans-serif;"><span style="font-weight: 900;"><br /></span></span></div>
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<span style="color: blue; font-family: arial, sans-serif;"><span style="font-weight: 900;">Adail Marcos</span></span><br />
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<span style="color: blue; font-family: arial, sans-serif;"><span style="font-weight: 900;"><br /></span></span></div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-2303329283757809292011-12-27T14:53:00.000-08:002012-12-14T00:57:16.308-08:00Aplicação do gráfico de "Eclipse" na análise custo/volume/lucro<br />
<div style="text-align: justify;">
Esta postagem visa demonstrar a aplicação do gráfico de <b><span style="color: blue;">Eclipse</span></b> na tradicional Análise Custo/Volume/Lucro - conteúdo básico das disciplinas Análise de Custos, Gestão de Custos, Gestão Estratégica de Custos e Gestão e Análise de Custos.</div>
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<span style="background-color: white;">Se você compreende de forma satisfatória os conceitos elementares da tradicional Análise Custo/Volume/Lucro (equilíbrios financeiro, operacional e econômico):</span><span style="background-color: white;"> </span><span style="background-color: blue;"><span style="color: white;"><b>despreze a revisão descrita abaixo, siga direto ao parágrafo anterior à Figura 2</b></span></span><span style="background-color: white;">. </span><br />
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<span style="background-color: white;">A Figura 1 auxilia na revisão dos seguintes conceitos:</span></div>
<ul style="text-align: start;">
<li><span style="background-color: white;">o ponto de equilíbrio financeiro (<b><span style="color: orange;">PEF</span></b>) representa o volume de vendas responsável por tornar o</span><span style="background-color: white;"> lucro operacional (</span><b style="background-color: white;"><span style="color: orange;">LO</span></b><span style="background-color: white;">) equivalente ao valor negativo da depreciação (</span><span style="background-color: white; color: orange;"><b>DEP</b></span><span style="background-color: white;">) - receita de vendas igual ao custo gerencial total (<span style="color: orange;"><b>CGT</b></span>), mas sem a </span><span style="background-color: white;"><b style="color: orange;">DEP</b>;</span></li>
<li><span style="background-color: white;">o ponto de equilíbrio operacional (<b><span style="color: orange;">PEO</span></b>) indica o volume vendas responsável</span><span style="background-color: white;"> por conferir valor nulo ao </span><b style="background-color: white;"><span style="color: orange;">LO</span></b> <span style="background-color: white;">- receita de vendas igual ao custo gerencial total (<span style="color: orange;"><b>CGT</b></span>)</span><span style="background-color: white;">;</span></li>
<li><span style="background-color: white;">o ponto de equilíbrio econômico (<b><span style="color: orange;">PEE</span></b>) sugere o volume de vendas encarregado de providenciar ao </span><b style="background-color: white;"><span style="color: orange;">LO</span></b><span style="background-color: white;"> o valor necessário ao cumprimento dos objetivos econômicos das empresas (remuneração do capital e criação de riqueza) - receita de vendas atinge o nível equivalente ao valor da soma entre o </span><span style="background-color: white; color: orange; font-weight: bold;">CGT</span><span style="background-color: white;"> e o patamar incremental de vendas exigido ao alcance do lucro operacional planejado (</span><b style="background-color: white;"><span style="color: orange;">LOP</span></b><span style="background-color: white;">).</span></li>
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<b style="background-color: white; color: blue;">Figura 1</b></div>
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<a href="http://3.bp.blogspot.com/-7rcF2RSs4kY/TvkpbQ6oKgI/AAAAAAAAAZk/kNY3GusSgaM/s1600/An%25C3%25A1lise+CustoVolumeLucro+Gr%25C3%25A1fico+dos+Pontos.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="404" src="http://3.bp.blogspot.com/-7rcF2RSs4kY/TvkpbQ6oKgI/AAAAAAAAAZk/kNY3GusSgaM/s640/An%25C3%25A1lise+CustoVolumeLucro+Gr%25C3%25A1fico+dos+Pontos.png" width="640" /></a></div>
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Pronto! Com os conceitos elementares de Análise Custo/Volume/Lucro devidamente revisados, vamos aprender a construir o gráfico ilustrado na Figura 2.<br />
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<b style="color: blue;">Figura 2</b>
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<a href="http://3.bp.blogspot.com/-UagTduJYHVw/Tvo-ELPBYnI/AAAAAAAAAas/HqvQqkBr-pY/s1600/Eclipse+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://3.bp.blogspot.com/-UagTduJYHVw/Tvo-ELPBYnI/AAAAAAAAAas/HqvQqkBr-pY/s400/Eclipse+1.png" width="351" /></a></div>
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Não é possível entender como o gráfico da Figura 2 pode representar um <b><span style="color: blue;">Eclipse</span></b>? Calma! Observe:<br />
<ul>
<li>as variáveis
<span style="color: orange;"><b>PEE</b></span>, <span style="color: orange;"><b>PEO</b></span> e <b><span style="color: orange;">PEF</span></b> simulam o <a href="http://pt.wikipedia.org/wiki/Eclipse">alinhamento em linha reta de corpos celestes em um mesmo sistema gravitacional</a>;</li>
<li> o valor acumulado das <span style="color: orange;"><b>VENDAS</b></span> também simula um corpo celeste em alinhamento com os demais - <span style="color: orange;"><b>PEE</b></span>, <b><span style="color: orange;">PEO</span></b> e <b><span style="color: orange;">PEF</span></b>;</li>
<li>por enquanto, devido ao valor nulo digitado na célula correspondente, não há como visualizar na Figura 2 o "corpo celeste" representado pela variável <b><span style="color: orange;">VENDAS</span></b>; </li>
<li><span style="background-color: white;">o valor acumulado assumido pela variável </span><b style="background-color: white;"><span style="color: orange;">VENDAS</span></b><span style="background-color: white;"> encobrirá total ou parcialmente as variáveis </span><b style="background-color: white;"><span style="color: orange;">PEF</span></b><span style="background-color: white;">, </span><span style="background-color: white; color: orange;"><b>PEO</b></span><span style="background-color: white;"> e</span><span style="background-color: white; color: orange;"><b> PEE</b></span><span style="background-color: white;">;</span></li>
<li><span style="background-color: white;">portanto, com a alimentação da célula correspondente ao valor acumulado da variável </span><span style="background-color: white; color: orange;"><b>VENDAS</b></span><span style="background-color: white;">, </span><span style="background-color: white;">automaticamente surgirá uma área central em perfeito alinhamento com as variáveis </span><b style="background-color: white;"><span style="color: orange;">PEF</span></b><span style="background-color: white;">, </span><span style="background-color: white; color: orange;"><b>PEO</b></span><span style="background-color: white;"> e </span><b style="background-color: white;"><span style="color: orange;">PEE</span></b><span style="background-color: white;">, conferindo ao gráfico um comportamento análogo ao de um </span><b style="background-color: white;"><span style="color: blue;">Eclipse</span></b><span style="background-color: white;">. </span></li>
</ul>
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Observe os exemplos das figuras 3 a 6: </span><br />
<ul>
<li><span style="background-color: white;">a figura 3 divulga uma receita de vendas incapaz de superar o </span><b style="background-color: white; color: orange;">PEF</b><span style="background-color: white;">; </span></li>
</ul>
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<b style="color: blue;">Figura 3</b>
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<a href="http://4.bp.blogspot.com/-u5FtckGzUkU/TvpHaTYJngI/AAAAAAAAAa4/6R5dUBQyIgY/s1600/Eclipse+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://4.bp.blogspot.com/-u5FtckGzUkU/TvpHaTYJngI/AAAAAAAAAa4/6R5dUBQyIgY/s400/Eclipse+2.png" width="356" /></a></div>
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<ul>
<li><span style="background-color: white;">a figura 4 sugere valores negativos ao </span><b style="background-color: white; color: orange;">LO</b><span style="background-color: white;"> - valor acumulado das vendas inferior ao </span><b style="background-color: white; color: orange;">PEO</b><span style="background-color: white;">; </span></li>
</ul>
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<b style="color: blue;">Figura 4</b>
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<a href="http://4.bp.blogspot.com/-kRC8wDqGoYE/TvpHux-xaII/AAAAAAAAAbE/ah1rcOmQfpY/s1600/Eclipse+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://4.bp.blogspot.com/-kRC8wDqGoYE/TvpHux-xaII/AAAAAAAAAbE/ah1rcOmQfpY/s400/Eclipse+3.png" width="355" /></a></div>
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<ul>
<li><span style="background-color: white;">a figura 5 ratifica a incursão do </span><b style="background-color: white; color: orange;">LO</b><span style="background-color: white;"> em uma faixa de resultados positivos - valor acumulado das vendas superior ao </span><b style="background-color: white; color: orange;">PEO</b><span style="background-color: white;">; </span></li>
</ul>
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<b style="color: blue;">Figura 5</b>
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<a href="http://2.bp.blogspot.com/-8au-AQZl3NI/TvpH_uvPDcI/AAAAAAAAAbQ/gzaaxwvSAc8/s1600/Eclipse+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://2.bp.blogspot.com/-8au-AQZl3NI/TvpH_uvPDcI/AAAAAAAAAbQ/gzaaxwvSAc8/s400/Eclipse+4.png" width="356" /></a></div>
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<ul>
<li><b style="background-color: white; color: blue;"><span style="background-color: white; color: black; font-weight: normal; text-align: justify;">a figura 6 indica um mês de excelente desempenho - valor acumulado das vendas superior ao </span><span style="background-color: white; color: orange; font-weight: normal; text-align: justify;"><b>PEE</b></span><span style="background-color: white; color: black; font-weight: normal; text-align: justify;">.</span></b></li>
</ul>
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<b style="background-color: white; color: blue;">Figura 6</b></div>
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<a href="http://1.bp.blogspot.com/-htovhkjNcyI/TvpIc_6R6YI/AAAAAAAAAbc/acVK3ODvJGs/s1600/Eclipse+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://1.bp.blogspot.com/-htovhkjNcyI/TvpIc_6R6YI/AAAAAAAAAbc/acVK3ODvJGs/s400/Eclipse+5.png" width="356" /></a></div>
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Para aprender a construir um gráfico de <b><span style="color: blue;">Eclipse</span></b>: <span style="color: blue;"><b>ASSISTA AO VÍDEO!</b></span></div>
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<b style="color: blue;">Construção do Gráfico ECLIPSE em Custo/Volume/Lucro</b></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/OpNWO-l2AhY?feature=player_embedded' frameborder='0'></iframe></div>
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Cordialmente,</div>
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<br /></div>
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<br /></div>
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Adail Marcos</div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-30724707236679833502011-12-26T19:38:00.000-08:002012-12-14T00:57:19.813-08:00Aplicação do gráfico de "Termômetro" na análise custo/volume/lucro<div style="text-align: justify;">
A partir de uma contribuição do especialista em modelagem de planilhas Fábio Vianna à Revista PC World, exatamente em 10 de agosto de 2006, tive a oportunidade de conhecer o gráfico de <span style="color: blue;"><b>Termômetro</b></span>, uma ferramenta
muito útil ao monitoramento de desempenho.</div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
Esta postagem visa demonstrar a aplicação do gráfico de <b><span style="color: blue;">Termômetro</span></b> na tradicional Análise Custo/Volume/Lucro - conteúdo básico das disciplinas Análise de Custos, Gestão de Custos, Gestão Estratégica de Custos e Gestão e Análise de Custos.<br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Se você compreende de forma satisfatória os conceitos elementares da tradicional Análise Custo/Volume/Lucro (equilíbrios financeiro, operacional e econômico):</span><span style="background-color: white;"> </span><span style="background-color: blue;"><span style="color: white;"><b>despreze a revisão descrita abaixo, siga direto ao parágrafo anterior à Figura 2</b></span></span><span style="background-color: white;">. </span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">A Figura 1 auxilia na revisão dos seguintes conceitos:</span></div>
<ul>
<li><span style="background-color: white;"><span style="background-color: white;">o ponto de equilíbrio financeiro (</span><b style="background-color: white;"><span style="color: orange;">PEF</span></b><span style="background-color: white;">)</span> representa o volume de vendas responsável por tornar o</span><span style="background-color: white;"> lucro operacional (</span><b style="background-color: white;"><span style="color: orange;">LO</span></b><span style="background-color: white;">) equivalente ao valor negativo da depreciação (</span><span style="background-color: white; color: orange;"><b>DEP</b></span><span style="background-color: white;">) - receita de vendas igual ao custo gerencial total (<span style="color: orange;"><b>CGT</b></span>), mas sem a </span><span style="background-color: white;"><b style="color: orange;">DEP</b>;</span></li>
<li><span style="background-color: white;"><span style="background-color: white;">o ponto de equilíbrio operacional (</span><b style="background-color: white;"><span style="color: orange;">PEO</span></b><span style="background-color: white;">)</span> indica o volume vendas responsável</span><span style="background-color: white;"> por conferir valor nulo ao </span><b style="background-color: white;"><span style="color: orange;">LO</span></b>
<span style="background-color: white;">- receita de vendas igual ao custo gerencial total (<span style="color: orange;"><b>CGT</b></span>)</span><span style="background-color: white;">;</span></li>
<li><span style="background-color: white;"><span style="background-color: white;">o ponto de equilíbrio econômico (</span><b style="background-color: white;"><span style="color: orange;">PEE</span></b><span style="background-color: white;">)</span> sugere o volume de vendas encarregado de providenciar ao </span><b style="background-color: white;"><span style="color: orange;">LO</span></b><span style="background-color: white;"> o valor necessário ao cumprimento dos objetivos econômicos das empresas (remuneração do capital e criação de riqueza) - receita de vendas atinge o nível equivalente ao valor da soma entre o </span><span style="background-color: white; color: orange; font-weight: bold;">CGT</span><span style="background-color: white;"> e o patamar incremental de vendas exigido ao alcance do lucro operacional planejado (</span><b style="background-color: white;"><span style="color: orange;">LOP</span></b><span style="background-color: white;">).</span></li>
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</ul>
</ul>
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<b style="color: blue;">Figura 1</b></div>
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<a href="http://3.bp.blogspot.com/-7rcF2RSs4kY/TvkpbQ6oKgI/AAAAAAAAAZk/kNY3GusSgaM/s1600/An%25C3%25A1lise+CustoVolumeLucro+Gr%25C3%25A1fico+dos+Pontos.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="404" src="http://3.bp.blogspot.com/-7rcF2RSs4kY/TvkpbQ6oKgI/AAAAAAAAAZk/kNY3GusSgaM/s640/An%25C3%25A1lise+CustoVolumeLucro+Gr%25C3%25A1fico+dos+Pontos.png" width="640" /></a></div>
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Pronto! Com os conceitos elementares de Análise Custo/Volume/Lucro devidamente revisados, vamos aprender a construir o gráfico da Figura 2. </div>
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<span style="color: blue;"><b>Figura 2</b></span></div>
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<a href="http://3.bp.blogspot.com/-ZLMsAxVWDhc/Tvk1gtVQFrI/AAAAAAAAAZw/r3A25vvM5hQ/s1600/Term%25C3%25B4metro+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="207" src="http://3.bp.blogspot.com/-ZLMsAxVWDhc/Tvk1gtVQFrI/AAAAAAAAAZw/r3A25vvM5hQ/s640/Term%25C3%25B4metro+1.png" width="640" /></a></div>
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Não é possível entender como o gráfico da Figura 2 pode representar um <b><span style="color: blue;">Termômetro</span></b>? Calma! Encontramos na Figura 2 as seguintes variáveis: </div>
<div style="text-align: justify;">
</div>
<ul>
<li><b><span style="color: orange;">PEF</span></b> mensal, R$100.000,00;</li>
<li><span style="color: orange;"><b>PEO</b></span> mensal, R$150.000,00;</li>
<li><b><span style="color: orange;">PEE</span></b> mensal, R$200.000,00;</li>
<li><span style="color: orange;"><b>VENDAS</b></span> do mês. </li>
</ul>
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<div style="text-align: justify;">
Ao digitar um valor qualquer na célula correspondente ao valor acumulado das vendas: <span style="background-color: blue;"><span style="color: white;"><b> surgirá um barra central sobreposta, sugerindo a funcionalidade básica de um termômetro</b></span></span>.<br />
<br />
Observe os exemplos das figuras 3, 4 e 5:<br />
<br />
<ul>
<li><span style="background-color: white;">a figura 3 indica a superação do </span><b style="background-color: white; color: orange;">PEF</b><span style="background-color: white;">; </span></li>
</ul>
</div>
<div style="text-align: center;">
<span style="color: blue;"><b>Figura 3</b></span></div>
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<a href="http://2.bp.blogspot.com/-7_PTXCqj_LI/Tvk4yIFyPbI/AAAAAAAAAZ8/2H1GuJNmKLM/s1600/Term%25C3%25B4metro+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="206" src="http://2.bp.blogspot.com/-7_PTXCqj_LI/Tvk4yIFyPbI/AAAAAAAAAZ8/2H1GuJNmKLM/s640/Term%25C3%25B4metro+2.png" width="640" /></a></div>
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<div>
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<ul>
<li><span style="background-color: white;">a figura 4 sustenta valores positivos ao </span><b style="background-color: white; color: orange;">LO </b><span style="background-color: white;">(valor acumulado das vendas superior ao </span><b style="background-color: white; color: orange;">PEO</b><span style="background-color: white;">); </span></li>
</ul>
</div>
</div>
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<span style="color: blue;"><b>Figura 4</b></span></div>
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<a href="http://3.bp.blogspot.com/-0wNq24Vm6SI/Tvk7D0X76QI/AAAAAAAAAaI/gDxUVNnyPGU/s1600/Term%25C3%25B4metro+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="204" src="http://3.bp.blogspot.com/-0wNq24Vm6SI/Tvk7D0X76QI/AAAAAAAAAaI/gDxUVNnyPGU/s640/Term%25C3%25B4metro+3.png" width="640" /></a></div>
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<div style="text-align: justify;">
<ul>
<li><span style="background-color: white;">a figura 5 indica um mês de excelente desempenho (valor acumulado das vendas superior ao </span><span style="background-color: white; color: orange;"><b>PEE</b></span><span style="background-color: white;">).</span></li>
</ul>
</div>
</div>
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<b><span style="color: blue;">Figura 5</span></b></div>
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<a href="http://1.bp.blogspot.com/-umyCL-Uhz3Q/Tvk7qg4eiTI/AAAAAAAAAaU/X4duttV6Vv4/s1600/Term%25C3%25B4metro+4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="206" src="http://1.bp.blogspot.com/-umyCL-Uhz3Q/Tvk7qg4eiTI/AAAAAAAAAaU/X4duttV6Vv4/s640/Term%25C3%25B4metro+4.png" width="640" /></a></div>
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E agora, é possível entender como pode ser aplicado o gráfico de <b><span style="color: blue;">Termômetro</span></b> em Análise Custo/Volume/Lucro? Ótimo! Assista ao vídeo abaixo. <br />
<br />
<div style="text-align: center;">
<span style="color: blue;"><b>Aplicação do Gráfico de Termômetro em Custo/Volume/Lucro </b></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/qwTfZGICb40?feature=player_embedded' frameborder='0'></iframe></div>
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Cordialmente,<br />
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<br />
Adail Marcos</div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-50220994942657949822011-12-24T09:47:00.000-08:002011-12-24T09:47:05.139-08:00Finanças com HP e EXCEL: Cálculo da taxa de juros equivalente com as calcul...<a href="http://adailmarcos.blogspot.com/2011/12/calculo-da-taxa-de-juros-equivalente.html?spref=bl">Finanças com HP e EXCEL: Cálculo da taxa de juros equivalente com as calcul...</a>: Em relação ao manuseio básico da calculadora financeira HP-12 C , a conversão de taxas de juros com os modelos 10bII e 10bII+ torn...Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com0tag:blogger.com,1999:blog-5692836511586863836.post-77776585163442824302011-12-23T19:29:00.000-08:002012-07-09T16:17:10.130-07:00Cálculo da taxa de juros equivalente com as calculadoras HP-10BII e HP-10BII+<div style="text-align: justify;">
Em relação ao manuseio básico da calculadora financeira <span style="color: blue;"><b>HP-12</b>C</span>, a conversão de taxas de juros com os modelos <b><span style="color: blue;">10bII</span></b> e <b><span style="color: blue;">10bII+</span></b> torna-se um trabalho menos complicado. Enquanto a utilização da <b><span style="color: blue;">HP-12C</span></b> para os cálculos das taxas efetiva e equivalente (juros compostos) exige adaptações na manipulação das funções financeiras tradicionais (<b><span style="color: orange;">PV</span></b>,<span style="color: orange;"> <b>FV</b></span>, <b><span style="color: orange;">i</span></b> e<span style="color: orange;"> <b>n</b></span>), nas calculadoras <b><span style="color: blue;">HP-10bII</span></b> e <b><span style="color: blue;">HP-10bII+</span></b> existem funções específicas à prática de tais conversões. </div>
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A Figura 1 apresenta as funções financeiras das calculadoras <b><span style="color: blue;">HP-10bII</span></b> e <b><span style="color: blue;">HP-10bII+</span></b> designadas aos cálculos das taxas equivalente e efetiva, onde: </div>
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</div>
<ul>
<li style="text-align: justify;">as funções <b><span style="color: orange;">NOM%</span></b>, <b><span style="color: orange;">EFF%</span></b> e <b><span style="color: orange;">P/YR</span></b> figuram em laranja, destacadas nas partes inferiores das teclas onde constam as funções primárias <b><span style="color: orange;">I/YR</span></b>, <b><span style="color: orange;">PV</span></b> e<span style="color: orange;"> <b>PMT</b></span>, respectivamente;</li>
<li style="text-align: justify;">os empregos das funções <b><span style="color: orange;">NOM%</span></b>, <b><span style="color: orange;">EFF%</span></b> e <b><span style="color: orange;">P/YR</span></b> exigem o acionamento antecipado da tecla de prefixo laranja - <i>shift down</i>.</li>
</ul>
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<div style="text-align: center;">
<b><span style="color: red;">Figura 1</span></b></div>
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<a href="http://2.bp.blogspot.com/-4rsmd-2o5aU/TvVGes0xn7I/AAAAAAAAAX4/pogLb_RXKuI/s1600/Convers%25C3%25B5es+de+Taxas+de+Juros+10BII+e+10BII%252B++1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="http://2.bp.blogspot.com/-4rsmd-2o5aU/TvVGes0xn7I/AAAAAAAAAX4/pogLb_RXKuI/s640/Convers%25C3%25B5es+de+Taxas+de+Juros+10BII+e+10BII%252B++1.png" width="640" /></a></div>
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<div style="text-align: justify;">
Especificamente sobre os manuseios das calculadoras <b><span style="color: blue;">HP-10bII</span></b> e <span style="color: blue; font-weight: bold;">HP-10bII+ </span>no cálculo da <b><span style="color: orange;">Taxa Equivalente</span></b>:</div>
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<ul>
<li style="text-align: justify;">uma dada taxa de juros apresenta frequência de capitalização anual (X% ao ano, por exemplo); </li>
<li style="text-align: justify;">sua taxa equivalente ao mês pode ser calculada a partir da aplicação da fórmula 100*((1+X/100)^(1/12)-1), onde 12 representa a quantidade de reproduções da frequência de capitalização menor (mensal) pela frequência de capitalização maior (anual);</li>
<li style="text-align: justify;">o valor da taxa de juros anual (X) deve ser armazenado em
<span style="background-color: black; color: orange; font-weight: bold;">EFF%</span> (digitar "X" e acionar <span style="background-color: orange; color: orange;">......</span> <span style="background-color: black; color: orange; font-weight: bold;">EFF%</span>);</li>
<li>o número 12, exatamente a quantidade de reproduções da frequência de capitalização menor (mensal) pela frequência de capitalização maior (anual), deve ser armazenado em <span style="background-color: black; color: orange; font-weight: bold;">P/YR</span> (digitar "12" e acionar <span style="background-color: orange; color: orange;">......</span> <span style="background-color: black; color: orange; font-weight: bold;">P/YR</span>);
<span style="text-align: justify;"> </span></li>
<li style="text-align: justify;">o valor obtido com <span style="background-color: orange; color: orange;">......</span> <span style="background-color: black; color: orange; font-weight: bold;">NOM%</span> divido por 12 (quantidade de reproduções da frequência de capitalização
menor pela frequência de capitalização maior) divulga o resultado exato da taxa de juros equivalente ao mês. </li>
</ul>
<div style="text-align: justify;">
Nas resoluções dos exercícios selecionados à demonstração das conversões de taxas de juros: os valores em <span style="color: red;">vermelho</span> indicam inserção de dados nas calculadoras; os valores em <span style="color: blue;">azul</span> representam soluções às questões. </div>
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Sobre a questão 108:</div>
<ul>
<li style="text-align: justify;">trata da aplicação direta do procedimento de cálculo da
<b style="color: orange; text-align: justify;">Taxa Equivalente</b><span style="text-align: justify;"> com as</span><span style="text-align: justify;"> calculadoras <b><span style="color: blue;">HP-10bII</span></b> e <span style="color: blue; font-weight: bold;">HP-10bII+</span></span>;</li>
<li style="text-align: justify;">12%, taxa com a maior frequência de capitalização (anual);</li>
<li style="text-align: justify;">a frequência prevista à capitalização é semestral; </li>
<li style="text-align: justify;">2, quantidade de reproduções da frequência de capitalização
menor (semestral) pela frequência de capitalização maior (anual).</li>
</ul>
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<a href="http://1.bp.blogspot.com/-PfJSb8zd2bI/TvVPbWrp7zI/AAAAAAAAAYE/UvW-Dt5EQqI/s1600/Convers%25C3%25B5es+de+Taxas+de+Juros+10BII+e+10BII%252B++2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="440" src="http://1.bp.blogspot.com/-PfJSb8zd2bI/TvVPbWrp7zI/AAAAAAAAAYE/UvW-Dt5EQqI/s640/Convers%25C3%25B5es+de+Taxas+de+Juros+10BII+e+10BII%252B++2.png" width="640" /></a></div>
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<span style="text-align: justify;"> Acerca da questão 109:</span><br />
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<ul style="text-align: justify;">
<li style="text-align: justify;">não trata de uma simples aplicação direta do procedimento de cálculo da <b style="color: orange; text-align: justify;">Taxa Equivalente</b>;</li>
<li style="text-align: justify;">a relação entre as frequências menor, de 7 meses, e maior, de 12 meses, indica um resultado não inteiro (12 dividido por 7);</li>
<li style="text-align: -webkit-auto;"><span style="text-align: justify;">as calculadoras <b><span style="color: blue;">HP-10bII</span></b> e <span style="color: blue; font-weight: bold;">HP-10bII+</span></span> consideram inválida a inserção de valores não inteiros em
<span style="color: orange; font-weight: bold;">P/YR</span>, justificando a impossibilidade de ser aplicado o procedimento direto;</li>
<li style="text-align: justify;">primeiramente, é preciso calcular a taxa equivalente ao mês da taxa nominal de 6,5% ao período de 7 meses;</li>
<li style="text-align: justify;">em seguida, calcula-se a taxa nominal anua a partir da equivalente mensal - taxa equivalente mensal vezes 12;</li>
<li style="text-align: -webkit-auto;"><span style="text-align: justify;">12, indica a quantidade de repetições da frequência menor (mensal) no período correspondente à frequência maior (anual);</span></li>
<li style="text-align: -webkit-auto;"><span style="text-align: justify;">com os dados devidamente tratados, conforme explicado até o ponto anterior, é possível aplicar diretamente o manuseio convencional das calculadoras </span>
<span style="text-align: justify;"><b><span style="color: blue;">HP-10bII</span></b> e <span style="color: blue; font-weight: bold;">HP-10bII+</span></span>.</li>
</ul>
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<span style="text-align: justify;"> Acerca da questão 111:</span><br />
<div style="text-align: justify;">
</div>
<ul style="text-align: justify;">
<li style="text-align: justify;">pode ser solucionada de duas maneiras;</li>
<li style="text-align: justify;">a primeira resolução sugere a conversão da taxa anual, referente à situação <b>(i)</b>, de 21%, à taxa semestral, exigindo a simples aplicação direta do procedimento de cálculo da <b style="color: orange;">Taxa Equivalente</b> ao semestre - a taxa da situação <b>(i)</b> convertida ao semestre apresenta o mesmo valor da taxa semestral da situação <b>(ii)</b>, indicando uma situação de indiferença entre as duas alternativas;</li>
<li style="text-align: justify;">a segunda resolução sugere a conversão da taxa semestral, referente à situação <b>(ii)</b>, de 10%, à taxa anual, exigindo a simples aplicação direta do procedimento de cálculo da <b style="color: orange; text-align: justify;">Taxa Equivalente</b><span style="text-align: justify;"> ao ano - a taxa da situação </span><b style="text-align: justify;">(ii)</b><span style="text-align: justify;"> convertida ao ano apresenta o mesmo valor da taxa anual da situação </span><b style="text-align: justify;">(i)</b><span style="text-align: justify;">, ratificando a indiferença anteriormente mencionada.</span></li>
</ul>
<span style="text-align: justify;"> </span><a href="http://2.bp.blogspot.com/-jwV-2OOBp3g/TvVw3Lrkb3I/AAAAAAAAAZM/aNFzwQWB3sE/s1600/111+enunciado.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="172" src="http://2.bp.blogspot.com/-jwV-2OOBp3g/TvVw3Lrkb3I/AAAAAAAAAZM/aNFzwQWB3sE/s640/111+enunciado.png" width="640" /></a><div style="text-align: center;">
<a href="http://2.bp.blogspot.com/-e_7eXaKuZOw/TvVWbjaCuDI/AAAAAAAAAYc/TbaKrpFV2sU/s1600/Convers%25C3%25B5es+de+Taxas+de+Juros+10BII+e+10BII%252B++4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="466" src="http://2.bp.blogspot.com/-e_7eXaKuZOw/TvVWbjaCuDI/AAAAAAAAAYc/TbaKrpFV2sU/s640/Convers%25C3%25B5es+de+Taxas+de+Juros+10BII+e+10BII%252B++4.png" width="640" /></a></div>
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<span style="text-align: justify;"> Sobre a questão 113:</span><br />
<div style="text-align: justify;">
</div>
<ul style="text-align: justify;">
<li style="text-align: justify;">a situação indicada na questão 113 exige o manuseio mais simples das calculadoras;</li>
<li style="text-align: justify;">o procedimento demonstrado consegue apurar o valor da taxa proporcional anual (taxa nominal) capaz de gerar uma dada taxa equivalente anual (taxa efetiva).</li>
</ul>
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Temas abordados nesta postagem:<br />
<br />
<ul>
<li>conversões de taxas de juros;</li>
<li>taxa de juros equivalente;</li>
<li>taxa de juros efetiva;</li>
<li>cálculo da taxa equivalente com as <span style="text-align: justify;">calculadoras financeiras</span> <span style="text-align: justify;"><b><span style="color: blue;">HP-10bII</span></b> e <span style="color: blue; font-weight: bold;">HP-10bII+</span></span>;</li>
<li>cálculo da taxa efetiva com as <span style="text-align: justify;">calculadoras financeiras</span> <span style="text-align: justify;"><b><span style="color: blue;">HP-10bII</span></b> e <span style="color: blue; font-weight: bold;">HP-10bII+</span></span>.
</li>
</ul>
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Fonte dos exercícios:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQtY68oS6OMCFJ-DUrZzbc58Egbtrg_h3Rk2fRvAP7wSsyIfvlTujsZQuzwjN7pkuMijMT4gkd3TVGLIM_183827JBFHO8783tVw1V0oTPp72eedHrykOpgDWUb1Xouf6u9FrsJAFpdfo/s1600/Ficha+catalogr%25C3%25A1fica.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="176" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQtY68oS6OMCFJ-DUrZzbc58Egbtrg_h3Rk2fRvAP7wSsyIfvlTujsZQuzwjN7pkuMijMT4gkd3TVGLIM_183827JBFHO8783tVw1V0oTPp72eedHrykOpgDWUb1Xouf6u9FrsJAFpdfo/s320/Ficha+catalogr%25C3%25A1fica.png" width="320" /></a></div>
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Cordialmente,<br />
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<span style="color: blue;"><b><i>Adail Marcos</i></b></span> <br />
<br />
<br />Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com1tag:blogger.com,1999:blog-5692836511586863836.post-33336287884241763312011-09-28T16:11:00.000-07:002011-09-30T18:12:01.992-07:00Estudo da viabilidade dos equilíbrios operacional e econômico - uma abordagem estocástica fundamentada na simulação de Monte Carlo<span class="Apple-style-span" style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"></span><br />
<div style="color: #074a30; font-weight: bold; text-align: justify;">
Esta postagem tem por objetivo demonstrar a utilização do Microsoft EXCEL na aplicação da tradicional análise custo/volume/lucro sob condições de incerteza. </div>
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<span class="Apple-style-span" style="background-color: white; color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;"><b><span class="Apple-style-span" style="background-color: yellow; color: blue;">Assunto:</span></b> Análise de Custos</span><span class="Apple-style-span" style="background-color: white;"></span><br />
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<span class="Apple-style-span" style="background-color: white;"><b style="background-color: yellow;"><span class="Apple-style-span" style="color: blue;">Tema explorado</span>:</b> Viabilidade dos equilíbrios operacional e econômico. </span></div>
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</span><br />
<div style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px; text-align: justify;">
<span class="Apple-style-span" style="background-color: white;">Uma melhor compreensão do conteúdo abordado no vídeo explicativo exige:</span></div>
<span class="Apple-style-span" style="background-color: white;">
</span><br />
<div style="text-align: justify;">
<ul><span class="Apple-style-span" style="background-color: white;">
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>conhecimento básico referente ao conteúdo da tradicional análise custo/volume/lucro;</b></span></span></li>
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>conhecimento básico atinente ao emprego da simulação de Monte Carlo no estudo do risco.</b></span></span></li>
</span></ul>
<div>
<span class="Apple-style-span" style="background-color: white;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span></span></div>
<div>
<span class="Apple-style-span" style="background-color: white;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>Descrição do exemplo abordado:</b></span></span></span></div>
<div>
<ul><span class="Apple-style-span" style="background-color: white;">
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>o proprietário de uma pequena indústria decidiu utilizar de forma mais sofisticada a tradicional análise custo/volume/lucro;</b></span></span></li>
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>ao considerar prudente contar com o auxílio de um profissional, com experiência comprovada na aplicação da análise custo/volume/lucro sob condições de incerteza, o empresário contratou um consultor; </b></span></span></li>
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>logo na primeira reunião o empresário deixou explícito o conjunto de suas pretensões:</b></span></li>
<ul>
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>analisar a viabilidade do ponto de equilíbrio operacional;</b></span></li>
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><span class="Apple-style-span" style="font-weight: normal;"><b>analisar a viabilidade do ponto de equilíbrio econômico</b></span>.</b></span></span></li>
</ul>
</span></ul>
</div>
</div>
<span class="Apple-style-span" style="background-color: white;">
</span><span class="Apple-style-span" style="background-color: white; color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b></b></span><br />
<div style="text-align: justify;">
<span class="Apple-style-span" style="background-color: white; color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b><span class="Apple-style-span" style="background-color: white; color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b><br /></b></span></b></span></div>
<span class="Apple-style-span" style="background-color: white; color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>
</b></span><span class="Apple-style-span" style="background-color: white; color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>As primeiras providências implementadas pelo consultor e sua equipe resultaram nas informações listadas a seguir:</b></span><br />
<div>
<ul>
<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>a empresa trabalha somente com um produto, negociado em "kg";</b></span></span></li>
<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>pesquisas apontam variações no preço de venda praticado pela própria empresa e seus concorrentes, onde cada "kg" pode ser vendido pelos valores listados na Tabela 1 - distribuição de frequência elaborada com base nos preços observados no mercado; </b></span></span></li>
</ul>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>Tabela 1</b></span></span></div>
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<ul>
<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>para os 3 tipos de matéria-prima foram feitas pesquisas visando obter resultados semelhantes aos da Tabela 1 (Tabelas 2 a 4), contemplando os preços praticados pelos fornecedores;</b></span></li>
</ul>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"></span><br />
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; font-weight: bold; line-height: 20px;">Tabela 2</span></span></div>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;">Tabela 3</span></div>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;">Tabela 4</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnCywWUX0nJ5oeHGkgt4HOSi8Tilwo-hzeXuJakwYrUWdOsBCOHKTIrN0-9dcy0q4WAOYC4TcvFPJC2aKfp0sJj-DcmRZjb-Wuh_CeP0cR1hAG93vW0doUkfsQDkC4VfeAFQb3ZPnk090/s1600/mat%25C3%25A9ria+prima+3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnCywWUX0nJ5oeHGkgt4HOSi8Tilwo-hzeXuJakwYrUWdOsBCOHKTIrN0-9dcy0q4WAOYC4TcvFPJC2aKfp0sJj-DcmRZjb-Wuh_CeP0cR1hAG93vW0doUkfsQDkC4VfeAFQb3ZPnk090/s1600/mat%25C3%25A9ria+prima+3.png" /></a></div>
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<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>o histórico das quantidades vendidas, em "kg", apresentou um comportamento semelhante ao de uma distribuição normal (Tabela 5);</b></span></li>
</ul>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;">Tabela 5</span></div>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;"><span class="Apple-style-span" style="color: black; font-family: 'Times New Roman'; font-size: small; font-weight: normal; line-height: normal;"></span></span></div>
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<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>considerando as variações esperados aos preços controlados (energia, por exemplo) e ao salário mínimo, outros custos e despesas fixas podem apresentar a variação indicada na Tabela 6;</b></span></li>
</ul>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;">Tabela 6</span></div>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"></span><br />
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<ul><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;">
<li><b>considerando o conjunto das deduções impostas ao faturamento, o valor destacado na Tabela 7 indica o percentual exato;</b></li>
</span></ul>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;">Tabela 7</span></div>
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</span><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"></span><br />
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwjF8ohPRDleVVuSFvE2OYcHSMHBVb3beuZpG-pLK0rg-E7sTFPE4Y0xgRrPpK5s8ghM93q7l9P_vHk71OWkNOa4SBhCHXlTsDDYJKclHnWsm6i00pURRZAM1gCtcxvxrQf17mLeKMbao/s1600/dedu%25C3%25A7%25C3%25B5es.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwjF8ohPRDleVVuSFvE2OYcHSMHBVb3beuZpG-pLK0rg-E7sTFPE4Y0xgRrPpK5s8ghM93q7l9P_vHk71OWkNOa4SBhCHXlTsDDYJKclHnWsm6i00pURRZAM1gCtcxvxrQf17mLeKMbao/s1600/dedu%25C3%25A7%25C3%25B5es.png" /></a></span></div>
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</span><br />
<ul>
<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>de acordo com os resultados das pesquisas realizadas, contidos nas tabelas 1 a 7, o consultor resolveu elaborar um modelo estocástico fundamentado na simulação de Monte Carlo, justamente por considerar a referida metodologia capaz de atender ao conjunto das exigências destacadas pelo proprietário;</b></span></li>
<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>a Figura 1 divulga o formato do modelo elaborado;</b></span></span></li>
</ul>
<div style="text-align: center;">
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>Figura 1</b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVOmGtqVDPYxdvXez2Mfgv1BXImmkakauaIg3-c280cDuoDPOU84N3-6CsdDiTpA3XNujUYxZxMG7uVqhZcXfq8MHQv4b2yHL73SeXjVhA7T69GoOh44d_1Awb06qSJ1rCxXxr8t7AWfw/s1600/ponto+de+equil%25C3%25ADbrio+risco.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVOmGtqVDPYxdvXez2Mfgv1BXImmkakauaIg3-c280cDuoDPOU84N3-6CsdDiTpA3XNujUYxZxMG7uVqhZcXfq8MHQv4b2yHL73SeXjVhA7T69GoOh44d_1Awb06qSJ1rCxXxr8t7AWfw/s640/ponto+de+equil%25C3%25ADbrio+risco.png" width="640" /></a></div>
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<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span></div>
<ul>
<li style="text-align: justify;"><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>com o modelo devidamente configurado, o consultor deu início à simulação de Monte Carlo seguido os passos detalhados no vídeo abaixo - somente a dedução sobre as vendas assume a condição de variável determinística, enquanto as demais podem ser randomizadas, pois representam as variáveis estocásticas do modelo;</b></span></span></li>
</ul>
<div style="text-align: center;">
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b>Elaboração do Modelo Simulação</b></span></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/70AXiHGjK7I?feature=player_embedded' frameborder='0'></iframe></div>
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span></div>
<br />
<ul>
<li><span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; line-height: 20px;"><b>o vídeo abaixo finaliza a análise da viabilidade dos equilíbrios operacional e econômico da empresa.</b></span></li>
</ul>
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<div style="margin-left: 1em; margin-right: 1em; text-align: center;">
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;">Análise da Viabilidade dos Equilíbrios</span><br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/aLKGaEbgvLQ?feature=player_embedded' frameborder='0'></iframe></div>
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif; font-size: 15px; font-weight: bold; line-height: 20px;"> </span></div>
<br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="background-color: yellow; font-size: 15px; line-height: 20px;"><b>Se devidamente expandido o modelo estocástico explorado nesta postagem pode ser aplicado em todas as empresas; o sucesso da aplicação fica por conta da capacidade de o analista (administrador, contador ou economista) conseguir adaptar o procedimento respeitando as particularidades de cada situação - as distribuições contínuas de probabilidade podem mudar, por exemplo. </b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="background-color: yellow; font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="background-color: yellow; font-size: 15px; line-height: 20px;"><b>Cordialmente,</b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="background-color: yellow; font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="background-color: yellow; font-size: 15px; line-height: 20px;"><b>Prof. Adail Marcos</b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="background-color: yellow; font-size: 15px; line-height: 20px;"><b><br /></b></span></span><br />
<span class="Apple-style-span" style="color: #074a30; font-family: Verdana, Geneva, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 20px;"><b><br /></b></span></span></div>
</div>
Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com2tag:blogger.com,1999:blog-5692836511586863836.post-88650329323626397892011-09-26T11:25:00.000-07:002012-09-22T08:17:15.589-07:00Análise do Conflito VPL x TIR com o uso do Microsoft EXCEL: cálculo da taxa de rentabilidade de Fisher e construção do gráfico da Cruz de Fisher<div style="text-align: justify;">
<b><span class="Apple-style-span" style="background-color: yellow; color: blue;">Assunto:</span></b> </div>
<div style="text-align: justify;">
<br />
<ul>
<li><b><span style="background-color: blue; color: yellow;">Técnicas de Orçamento de Capital</span></b>.</li>
</ul>
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b style="background-color: yellow;"><span class="Apple-style-span" style="color: blue;">Tema explorado</span>:</b><br />
<br />
<ul>
<li><span style="color: yellow;"><b style="background-color: red;">Utilização do Gráfico da Cruz de Fisher na Análise do Conflito entre VPL x TIR</b></span>. </li>
</ul>
</div>
<div style="text-align: justify;">
<br />
<span style="background-color: yellow;"><span style="color: blue;"><b><br /></b></span></span>
<span style="background-color: yellow;"><span style="color: blue;"><b>Recursos do Microsoft EXCEL explorados nesta postagem:</b></span></span><br />
<br />
<ul>
<li><b>No cálculo da <span style="background-color: red; color: yellow;">TAXA DE RENTABILIDADE DE FISHER</span>:</b></li>
<ul>
<li><b style="background-color: blue; color: white;">ATINGIR META</b><span style="background-color: white;">;</span></li>
</ul>
</ul>
<ul>
<li><b>Na elaboração do gráfico da <span style="background-color: red; color: yellow;">CRUZ DE FISHER</span>:</b></li>
<ul>
<li><b><span style="background-color: blue; color: white;">GERAÇÃO DE NÚMERO ALEATÓRIO</span></b>;</li>
<li><span style="color: white;"><b style="background-color: blue;">GRÁFICO DE DISPERSÃO</b></span>.</li>
</ul>
</ul>
<br />
<br class="Apple-interchange-newline" /></div>
<div style="text-align: justify;">
Uma melhor compreensão do conteúdo abordado no vídeo explicativo exige o conhecimento prévio do tema explorado - utilização da cruz de Fisher na análise do conflito entre VPL x TIR.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
De qualquer forma:</div>
<div style="text-align: justify;">
</div>
<ul>
<li style="text-align: justify;">existem duas alternativas de investimento;</li>
<li style="text-align: justify;">Projeto "A" e Projeto "B";</li>
<li style="text-align: justify;">situação mutuamente exclusiva;</li>
<li style="text-align: justify;">cada Projeto teve seu VPL calculado a partir do custo de capital definido pela empresa;</li>
<li style="text-align: justify;">com base na interpretação do VPL, efetivamente um medidor de riqueza, o Projeto "A" deve ser implementado - <b style="background-color: yellow;"><span style="color: blue;">VPL "A" > VPL "B"</span></b>;</li>
<li style="text-align: justify;">segundo a TIR, um medidor de desempenho encarregado de indicar a taxa efetiva ligada ao cumprimento combinado da remuneração do capital e da criação de riqueza (justificando o valor nulo assumido pelo VPL quando calculado com a própria TIR), o Projeto "B" é mais atrativo - <span style="background-color: yellow;"><span style="color: blue;"><b>TIR "A" < TIR "B"</b></span></span>;</li>
<li style="text-align: justify;">conflito entre VPL e TIR;</li>
<li style="text-align: justify;">causas do conflito: </li>
<ul>
<li style="text-align: justify;">discrepâncias entre os valores dos fluxos dos dois projetos;</li>
<li style="text-align: justify;">diferenças nas formas de distribuição dos fluxos de caixa ao longo do tempo.</li>
</ul>
<li style="text-align: justify;">o conflito pode ser solucionado com a análise do gráfico da <b style="background-color: yellow;"><span style="color: blue;">Cruz de Fisher</span></b>.</li>
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<span style="text-align: justify;">por meio da </span><b style="background-color: yellow; text-align: justify;"><span style="color: blue;">intersecção ou cruz de Fisher</span></b><br />
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<li style="text-align: justify;">deve ser calculada uma taxa de desconto capaz de promover a igualdade entre VPL "A" e VPL "B";</li>
<li style="text-align: justify;">a taxa de desconto capaz de viabilizar a igualdade entre VPL "A" e VPL "B" deve ser classificada como taxa de rentabilidade de Fisher;</li>
<li style="text-align: justify;">o conflito entre VPL e TIR ocorre quando da utilização de taxas de desconto inferiores à taxa de rentabilidade de Fisher;</li>
<li style="text-align: justify;">o conflito entre VPL e TIR deixa de existir quando da utilização de taxas de desconto superiores à taxa de rentabilidade de Fisher;</li>
<li style="text-align: justify;">para uma melhor análise recomenda-se construir o gráfico da "Cruz de Fisher". </li>
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<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;">A situação descrita na Figura 1, voltada à definição da melhor alternativa de investimento entre os projetos A e B, representa um exemplo clássico concernente ao conflito VPL x TIR.</span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;"><b>Para resolver a questão com o </b> <span style="background-color: blue;"><span style="color: white;"><b>ATINGIR META</b></span></span> <b>do Microsoft EXCEL</b>:</span><br />
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<li><span style="background-color: red; font-size: large;"><b><span style="color: white;">elabore uma planilha semelhante ao modelo destacado na </span><span style="color: yellow;">Figura 1</span></b></span>;</li>
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<b style="background-color: red;"><span style="color: yellow;">Figura 1</span></b><br />
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<span style="background-color: red;"><span style="font-size: large;"><b><span style="color: white;"><br /></span></b></span></span></div>
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<li style="text-align: left;"><span style="background-color: red;"><span style="font-size: large;"><b><span style="color: white;">siga todos os passos implementados no </span><span style="color: yellow;">Vídeo 1.</span></b></span></span> </li>
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<span style="background-color: red; color: yellow;"><b>Vídeo 1</b></span><br />
"Taxa de Rentabilidade de Fisher" e "Gráfico de Cruz de Fisher"</div>
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Até mais,</div>
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Prof. Adail Marcos</div>
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Adail Marcoshttp://www.blogger.com/profile/09115685934360491880noreply@blogger.com1