INDICE ANEXO MANUAL DIDACTICO DE MATEMATICAS FINANCIERAS INDICE TEMATICO SERIES UNIFORMES SERIES VARIABLES CONVERSION DE TASAS SISTEMAS DE AMORTIZACION INDICADORES DE CONVENIENCIA Anualidades vencida Gradiente aritmético Tasa nominal Cuota fija VPN Anualidades anticipada Gradiente aritmético diferido Tasa efectiva anual Cuotas extraordinarias TIR Anualidad diferida Gradiente geométrico Anualidad diferida TIRM Anualidad perpetua Gradiente geométrico diferido Gradiente aritmético CAUE Gradiente geométrico B/C VENCIDA-ANTICIPADA Valor Presente de una serie uniforme con anualidad vencida Sintaxis (P/A, i%, n) Tasa Per. Nper ANUALIDAD VP 9.00% 12 500,000 3,580,363 Valor Futuro de una serie uniforme con anualidad vencida Sintaxis (F/A, i%, n) Tasa Per. Nper ANUALIDAD VF 2.50% 24 100,000 3,234,904 Valor de la anualidad vencida conociendo el valor presente Sintaxis (A/P, i%, n) Tasa Per. Nper VP ANUALIDAD 1.00% 60 30,000,000 667,333 Valor de la anualidad vencida conociendo el valor futuro Sintaxis (A/F, i%, n) Tasa Per. Nper VF ANUALIDAD 6.50% 8 10,000,000 992,373 Valor Presente de una serie uniforme con anualidad anticipada Sintaxis (P/A, i%, n) Tasa Per. Nper ANUALIDAD VP 4.00% 6 750,000 4,088,867 Valor Futuro de una serie uniforme con anualidad anticipada Sintaxis (F/A, i%, n) Tasa Per. Nper ANUALIDAD VF 1.00% 9 380,000 3,595,641 Valor de la anualidad anticipada conociendo el valor presente Sintaxis (A/P, i%, n) Tasa Per. Nper VP ANUALIDAD 2.50% 12 24,000,000 2,282,625 Valor de la anualidad anticipada conociendo el valor futuro Sintaxis (A/F, i%, n) Tasa Per. Nper VF ANUALIDAD 7.00% 12 5,000,000 261,224 DIFERIDA ANUALIDAD DIFERIDA Valor Presente Con período de gracia (r) y período de pagos (s) Sintaxis P=(P/A , i%, r, s) Tasa Per. r s ANUALIDAD VP 0.50% 23 36 1,000,000 29,308,508 Valor de la anualidad vencida diferida conociendo el valor presente con período de gracia (r) y período de pagos (s) Sintaxis A=(A/P , i%, r, s) Tasa Per. r s VP ANUALIDAD 0.75% 20 28 50,000,000 2,306,618 PERPETUA ANUALIDAD PERPETUA Valor Presente de una anualidad perpetua Sintaxis (P/A, i%) Tasa Per. ANUALIDAD VP 1.39% 750,000 53,956,835 GRADIENTE ARITMETICO GRADIENTE ARITMETICO Valor Presente Gradiente Aritmético Vencido Creciente Sintaxis P=A(P/A ,i%, n) + G(P/G, i%, n) Tasa Per. Nper Pago Gradiente VP 0.75% 180 350,000 3,000 55,185,497 Valor Presente Gradiente Aritmético Vencido Decreciente Sintaxis P=A(P/A ,i%, n) + G(P/G, i%, n) Tasa Per. Nper Pago Gradiente VP 0.75% 180 350,000 -3,000 13,829,889 Valor Presente Gradiente Aritmético Anticipado Creciente Sintaxis P=A(P/A ,i%, n) + G(P/G, i%, n) Tasa Per. Nper Pago Gradiente VP 1.31% 36 120,000 10,000 8,129,035 Valor Presente Gradiente Aritmético Anticipado Decreciente Sintaxis P=A(P/A ,i%, n) + G(P/G, i%, n) Tasa Per. Nper Pago Gradiente VP 1.37% 36 120,000 -1,000 2,979,164 Valor Futuro Gradiente Aritmético Vencido Creciente Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper Pago Gradiente VF 1.00% 12 250,000 20,000 4,535,632 Valor Futuro Gradiente Aritmético Vencido Decreciente Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper Pago Gradiente VF 1.00% 12 250,000 -20,000 1,805,620 Valor Futuro Gradiente Aritmético Anticipado Creciente Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper Pago Gradiente VF 1.00% 12 250,000 20,000 4,580,988 Valor Futuro Gradiente Aritmético Anticipado Decreciente Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper Pago Gradiente VF 1.00% 12 250,000 -20,000 1,823,676 Valor de la primera cuota Gradiente Aritmético Vencido Creciente dado VP Sintaxis (A/P, G ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.02% 180 224,000,000 5,000 2,411,677 Valor de la primera cuota Gradiente Aritmético Vencido Decreciente dado VP Sintaxis (A/P, G ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.02% 180 224,000,000 -5,000 3,046,042 Valor de la primera cuota Gradiente Aritmético Vencido Creciente dado VF Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper VF Gradiente CUOTA 4.00% 12 100,000,000 500,000 4,138,043 Valor de la primera cuota Gradiente Aritmético Vencido Decreciente dado VF Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper VF Gradiente CUOTA 4.00% 12 100,000,000 -500,000 9,172,391 Valor de la primera cuota Gradiente Aritmético Anticipado Creciente dado VP Sintaxis (A/P, G ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.02% 180 224,000,000 5,000 2,384,034 Valor de la primera cuota Gradiente Aritmético Anticipado Decreciente dado VP Sintaxis (A/P, G ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.02% 180 224,000,000 -5,000 3,018,399 Valor de la primera cuota Gradiente Aritmético Anticipado Creciente dado VF Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper VF Gradiente CUOTA 4.00% 12 100,000,000 500,000 3,882,073 Valor de la primera cuota Gradiente Aritmético Anticipado Decreciente dado VF Sintaxis F=A(F/G ,i%, n) + G(F/G, i%, n) Tasa Per. Nper VF Gradiente CUOTA 4.00% 12 100,000,000 -500,000 8,916,421 Valor Presente Gradiente Aritmético Diferido Sintaxis P=(P/G ,i%, r,s) Tasa Per. Nper r s CUOTA G VP 2.50% 42 6 36 250,000 75,000 27,731,203 Valor de la primera cuota Gradiente Aritmético Diferido Sintaxis A=(A/P ,i%, r,s) ir is n r s G VP CUOTA 3.00% 4.00% 19 4 15 800,000 105,000,000 5,611,428 GRADIENTE GEOMETRICO GRADIENTE GEOMETRICO Valor Presente de una serie Gradiente Geométrico Vencido Creciente Sintaxis (P/G, A, i%, n) Tasa Per. Nper Pago Gradiente VP 1.50% 5 300,000 10% 1,746,962 Valor Presente de una serie Gradiente Geométrico Vencido Decreciente Sintaxis (P/G, A, i%, n) Tasa Per. Nper Pago Gradiente VP 0.50% 7 120,000 -5% 710,450 Valor Presente de una serie Gradiente Geométrico Anticipado Creciente Sintaxis (P/G, A, i%, n) Tasa Per. Nper Pago Gradiente VP 1.00% 12 1,250,000 5% 18,739,644 Valor Presente de una serie Gradiente Geométrico Anticipado Decreciente Sintaxis (P/G, A, i%, n) Tasa Per. Nper Pago Gradiente VP 3.02% 28 1,500,000 -1% 25,828,735 Valor Futuro de una serie Gradiente Geométrico Vencido Creciente Sintaxis (F/G, A, i%, n) Tasa Per. Nper Pago Gradiente VF 2.36% 12 80,000 1% 1,153,823 Valor Futuro de una serie Gradiente Geométrico Vencido Decreciente Sintaxis (F/G, A, i%, n) Tasa Per. Nper Pago Gradiente VF 2.36% 12 80,000 -1% 1,039,388 Valor Futuro de una serie Gradiente Geométrico Anticipado Creciente Sintaxis (F/G, A, i%, n) Tasa Per. Nper Pago Gradiente VF 1.00% 12 1,250,000 5% 21,116,300 Valor Futuro de una serie Gradiente Geométrico Anticipado Decreciente Sintaxis (F/G, A, i%, n) Tasa Per. Nper Pago Gradiente VF 1.00% 12 1,250,000 -5% 12,340,200 Valor de la primera cuota Gradiente Geomético Vencido Creciente dado VP Sintaxis (A/G, P ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.00% 15 3,000,000 5% 151,767 Valor de la primera cuota Gradiente Geomético Vencido Decreciente dado VP Sintaxis (A/G, P ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.00% 15 3,000,000 -5% 299,529 Valor de la primera cuota Gradiente Geomético Anticipado Creciente dado VP Sintaxis (A/G, P ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.00% 15 3,000,000 5% 150,265 Valor de la primera cuota Gradiente Geomético Anticipado Decreciente dado VP Sintaxis (A/G, P ,i%, n) Tasa Per. Nper VP Gradiente CUOTA 1.00% 15 3,000,000 -5% 296,563 Valor de la primera cuota Gradiente Geomético Vencido Creciente dado VF Sintaxis (A/G, F ,i%, n) Tasa Per. Nper VF Gradiente CUOTA 3.33% 8 20,000,000 10% 1,580,599 Valor de la primera cuota Gradiente Geomético Vencido Decreciente dado VF Sintaxis (A/G, F ,i%, n) Tasa Per. Nper VF Gradiente CUOTA 3.33% 8 20,000,000 -10% 3,067,407 Valor de la primera cuota Gradiente Geomético Anticipado Creciente dado VF Sintaxis (A/G, F ,i%, n) Tasa Per. Nper VF Gradiente CUOTA 3.33% 8 20,000,000 10% 1,529,662 Valor de la primera cuota Gradiente Geomético Anticipado Decreciente dado VF Sintaxis (A/G, F ,i%, n) Tasa Per. Nper VF Gradiente CUOTA 3.33% 8 20,000,000 -10% 2,968,554 Valor Presente Gradiente Geométrico Diferido Sintaxis P=(P/k ,A, i%, r,s) Tasa Per. Nper r s CUOTA k VP 2.50% 21 3 18 800,000 2.0% 12,518,589 Valor de la primera cuota Gradiente Geométrico Diferido Sintaxis A=(A/k ,P,i%, r,s) Tasa Per. Nper r s k VP CUOTA 10% 12 2 10 8% 30,000,000 4,330,684 TASA NOMINAL MODELO CONVERSION DE TASAS CALCULO TASA NOMINAL Ingreso de datos Tasa Efectiva Anual 18.5% TASA Efectiva Nominal TIPO Vencido Vencido Período capitalización Mes RESULTADOS Tasa Nominal Anual vencida 17.09% Tasa periódica vencida 1.42% Tasa periódica anticipada 1.40% Tasa Nominal Anual anticipada 16.85% TASA TIPO PERIODO CAPITALIZACION No. PERIODOS EN UN AÑO Nominal Vencido Día 365 17.09% Efectiva Anticipado Mes 12 Bimestre 6 EA RESULTADO FUENTE Trimestre 4 0.00% 17.09% 0.00% Semestre 2 18.50% 0.00% 18.50% Anual 1 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 18.50% TEA 17.09% PERIODO (n) 1 12 PERIODO Anual TASA EFECTIVA MODELO CONVERSION DE TASAS CALCULO TASA EFECTIVA ANUAL Ingreso de datos Tasa Nominal 18.00% TASA Nominal Período capitalización Mes TIPO Vencido RESULTADO Tasa Efectiva Anual 19.56% FUENTE EA CALCULO RESULTADO CONVERTIR Tasa Nominal Anual vencida 18.00% 19.56% 19.56% 0.00% 19.56% Tasa periódica vencida 0.00% 0.00% 19.56% 19.56% Efectiva Tasa periódica anticipada 0.00% 0.00% 16.36% 0.00% Tasa Nominal Anual anticipada 0.00% 0.00% 16.36% 0.00% Anual TEA 19.56% PERIODO (n) 12 1 Vencido TASA TIPO Nominal Vencido Efectiva Anticipado PERIODO CAPITALIZACION No. PERIODOS EN UN AÑO Día 365 Mes 12 Bimestre 6 Trimestre 4 Semestre 2 Anual 1 C.FIJA SISTEMA DE AMORTIZACION CUOTA FIJA VR.CREDITO Tasa Per. Nper ANUALIDAD FORMULA EXCEL 15,000,000 2.00% MV 12 Meses 1,418,394 1,418,394 Tabla de amortización Cuota Nº Cuota Interés Capital Saldo Capital 0 15,000,000 1 1,418,394 300,000 1,118,394 13,881,606 2 1,418,394 277,632 1,140,762 12,740,844 3 1,418,394 254,817 1,163,577 11,577,267 4 1,418,394 231,545 1,186,849 10,390,419 5 1,418,394 207,808 1,210,586 9,179,833 6 1,418,394 183,597 1,234,797 7,945,036 7 1,418,394 158,901 1,259,493 6,685,542 8 1,418,394 133,711 1,284,683 5,400,859 9 1,418,394 108,017 1,310,377 4,090,483 10 1,418,394 81,810 1,336,584 2,753,898 11 1,418,394 55,078 1,363,316 1,390,582 12 1,418,394 27,812 1,390,582 -0 C.EXTRAS SISTEMA DE AMORTIZACION CUOTAS EXTRAORDINARIAS VR.CREDITO Tasa Per. Nper 70,000,000 2.00% MV 36 Meses C. Extras Tasa Per. Nper 4,000,000 26.82% EA 3 Años PRIMERO Hallar el valor presente de las cuotas extras Tasa Per. Nper ANUALIDAD VP FORMULA EXCEL 26.82% 3 Años 4,000,000 7,601,751 7,601,751 SEGUNDO Hallar el valor a diferir VR.DIFERIR 62,398,249 Rafael Serna: $70.000.000 -7.601.751 TERCERO Construir tabla de amortización cuotas mensuales y cuotas anuales VR.CREDITO Tasa Per. Nper ANUALIDAD Tasa Per. Nper ANUALIDAD FORMULA EXCEL 62,398,249 2.00% MV 36 Meses 2,448,061 2,448,061 26.82% 3 Años 4,000,000 Tabla de amortización cuotas mensuales Tabla de amortización cuotas anuales Cuota Nº Cuota Interés Capital Saldo Capital Cuota Nº Cuota Interés Capital Saldo Capital 0 62,398,249 0 7,601,751 1 2,448,061 1,247,965 1,200,096 61,198,152 1 7,601,751 2 2,448,061 1,223,963 1,224,098 59,974,054 2 7,601,751 3 2,448,061 1,199,481 1,248,580 58,725,474 3 7,601,751 4 2,448,061 1,174,509 1,273,552 57,451,922 4 7,601,751 5 2,448,061 1,149,038 1,299,023 56,152,899 5 7,601,751 6 2,448,061 1,123,058 1,325,003 54,827,896 6 7,601,751 7 2,448,061 1,096,558 1,351,503 53,476,393 7 7,601,751 8 2,448,061 1,069,528 1,378,533 52,097,859 8 7,601,751 9 2,448,061 1,041,957 1,406,104 50,691,755 9 7,601,751 10 2,448,061 1,013,835 1,434,226 49,257,529 10 7,601,751 11 2,448,061 985,151 1,462,911 47,794,618 11 7,601,751 12 2,448,061 955,892 1,492,169 46,302,449 12 4,000,000 2,039,107 1,960,893 5,640,859 13 2,448,061 926,049 1,522,012 44,780,437 13 5,640,859 14 2,448,061 895,609 1,552,453 43,227,984 14 5,640,859 15 2,448,061 864,560 1,583,502 41,644,483 15 5,640,859 16 2,448,061 832,890 1,615,172 40,029,311 16 5,640,859 17 2,448,061 800,586 1,647,475 38,381,836 17 5,640,859 18 2,448,061 767,637 1,680,425 36,701,411 18 5,640,859 19 2,448,061 734,028 1,714,033 34,987,378 19 5,640,859 20 2,448,061 699,748 1,748,314 33,239,065 20 5,640,859 21 2,448,061 664,781 1,783,280 31,455,785 21 5,640,859 22 2,448,061 629,116 1,818,946 29,636,839 22 5,640,859 23 2,448,061 592,737 1,855,325 27,781,515 23 5,640,859 24 2,448,061 555,630 1,892,431 25,889,084 24 4,000,000 1,513,114 2,486,886 3,153,973 25 2,448,061 517,782 1,930,280 23,958,804 25 3,153,973 26 2,448,061 479,176 1,968,885 21,989,919 26 3,153,973 27 2,448,061 439,798 2,008,263 19,981,656 27 3,153,973 28 2,448,061 399,633 2,048,428 17,933,228 28 3,153,973 29 2,448,061 358,665 2,089,397 15,843,831 29 3,153,973 30 2,448,061 316,877 2,131,185 13,712,646 30 3,153,973 31 2,448,061 274,253 2,173,808 11,538,838 31 3,153,973 32 2,448,061 230,777 2,217,285 9,321,553 32 3,153,973 33 2,448,061 186,431 2,261,630 7,059,923 33 3,153,973 34 2,448,061 141,198 2,306,863 4,753,060 34 3,153,973 35 2,448,061 95,061 2,353,000 2,400,060 35 3,153,973 36 2,448,061 48,001 2,400,060 -0 36 4,000,000 846,027 3,153,973 0 CUARTO Construir tabla de amortización total (cuotas mensuales + cuotas anuales) Tabla de amortización total Cuota Nº Cuota Interés Capital Saldo Capital 0 70,000,000 1 2,448,061 1,400,000 1,200,096 68,799,904 2 2,448,061 1,375,998 1,224,098 67,575,805 3 2,448,061 1,351,516 1,248,580 66,327,225 4 2,448,061 1,326,545 1,273,552 65,053,673 5 2,448,061 1,301,073 1,299,023 63,754,651 6 2,448,061 1,275,093 1,325,003 62,429,647 7 2,448,061 1,248,593 1,351,503 61,078,144 8 2,448,061 1,221,563 1,378,533 59,699,610 9 2,448,061 1,193,992 1,406,104 58,293,506 10 2,448,061 1,165,870 1,434,226 56,859,280 11 2,448,061 1,137,186 1,462,911 55,396,369 12 6,448,061 1,107,927 3,453,062 51,943,308 13 2,448,061 1,038,866 1,522,012 50,421,296 14 2,448,061 1,008,426 1,552,453 48,868,843 15 2,448,061 977,377 1,583,502 47,285,341 16 2,448,061 945,707 1,615,172 45,670,170 17 2,448,061 913,403 1,647,475 44,022,695 18 2,448,061 880,454 1,680,425 42,342,270 19 2,448,061 846,845 1,714,033 40,628,237 20 2,448,061 812,565 1,748,314 38,879,923 21 2,448,061 777,598 1,783,280 37,096,643 22 2,448,061 741,933 1,818,946 35,277,698 23 2,448,061 705,554 1,855,325 33,422,373 24 6,448,061 668,447 4,379,317 29,043,056 25 2,448,061 580,861 1,930,280 27,112,777 26 2,448,061 542,256 1,968,885 25,143,891 27 2,448,061 502,878 2,008,263 23,135,628 28 2,448,061 462,713 2,048,428 21,087,200 29 2,448,061 421,744 2,089,397 18,997,804 30 2,448,061 379,956 2,131,185 16,866,619 31 2,448,061 337,332 2,173,808 14,692,810 32 2,448,061 293,856 2,217,285 12,475,526 33 2,448,061 249,511 2,261,630 10,213,896 34 2,448,061 204,278 2,306,863 7,907,033 35 2,448,061 158,141 2,353,000 5,554,033 36 6,448,061 111,081 5,554,033 -0 ANUALIDAD DIFERIDA SISTEMA DE AMORTIZACION ANUALIDAD DIFERIDA Vr. Préstamo 50,000,000 Plazo total 36 MESES Periodo gracia 12 MESES Número pagos 24 MESES Tasa nominal 21% NMV TPM 1.8% MV METODO 1 Hallar el valor de la anualidad por fórmula Valor de la anualidad vencida diferida conociendo el valor presente con período de gracia (r) y período de pagos (s) Tasa Per. r s VP ANUALIDAD 1.8% MV 12 24 50,000,000 3,163,916 METODO 2 Hallar el valor futuro de $50.000.000 en el período 12 Tasa Per. n VP VF 1.8% MV 12 50,000,000 61,571,966 A partir de este valor hallar el valor de la anualidad Valor de la anualidad vencida conociendo el valor presente Tasa Per. Nper VP ANUALIDAD FORMULA EXCEL 1.75% 24 61,571,966 3,163,916 3,163,916 Tabla de amortización anualidad diferida Cuota Nº Cuota Interés Capital Saldo Capital 0 PERIODO DE GRACIA PERIODO DE GRACIA 50,000,000 1 875,000 50,875,000 2 890,312 51,765,313 3 905,893 52,671,205 4 921,746 53,592,952 5 937,877 54,530,828 6 954,289 55,485,118 7 970,990 56,456,107 8 987,982 57,444,089 9 1,005,272 58,449,361 10 1,022,864 59,472,225 11 1,040,764 60,512,988 12 1,058,977 61,571,966 13 3,163,916 1,077,509 2,086,406 59,485,560 14 3,163,916 1,040,997 2,122,918 57,362,641 15 3,163,916 1,003,846 2,160,069 55,202,572 16 3,163,916 966,045 2,197,871 53,004,702 17 3,163,916 927,582 2,236,333 50,768,368 18 3,163,916 888,446 2,275,469 48,492,899 19 3,163,916 848,626 2,315,290 46,177,609 20 3,163,916 808,108 2,355,807 43,821,802 21 3,163,916 766,882 2,397,034 41,424,768 22 3,163,916 724,933 2,438,982 38,985,786 23 3,163,916 682,251 2,481,664 36,504,122 24 3,163,916 638,822 2,525,093 33,979,028 25 3,163,916 594,633 2,569,283 31,409,746 26 3,163,916 549,671 2,614,245 28,795,501 27 3,163,916 503,921 2,659,994 26,135,506 28 3,163,916 457,371 2,706,544 23,428,962 29 3,163,916 410,007 2,753,909 20,675,053 30 3,163,916 361,813 2,802,102 17,872,951 31 3,163,916 312,777 2,851,139 15,021,812 32 3,163,916 262,882 2,901,034 12,120,779 33 3,163,916 212,114 2,951,802 9,168,977 34 3,163,916 160,457 3,003,458 6,165,518 35 3,163,916 107,897 3,056,019 3,109,499 36 3,163,916 54,416 3,109,499 0 GRAD. ARITMETICO SISTEMA DE AMORTIZACION GRADIENTE ARITMETICO Vr. Préstamo 224,000,000 Plazo total 180 MESES Gradiente 5,000 Tasa interés 1.02% MV Valor de la primera cuota Gradiente Aritmético Vencido Creciente dado VP Tasa Per. Nper VP Gradiente 1a CUOTA 1.02% 180 224,000,000 5,000 2,412,328 Tabla de amortización gradiente aritmético Cuota Nº Cuota Interés Capital Saldo Capital 0 224,000,000 1 2,412,328 2,293,053 119,275 223,880,725 2 2,417,328 2,291,832 125,496 223,755,230 3 2,422,328 2,290,547 131,780 223,623,450 4 2,427,328 2,289,198 138,129 223,485,321 5 2,432,328 2,287,784 144,543 223,340,777 6 2,437,328 2,286,305 151,023 223,189,754 7 2,442,328 2,284,759 157,569 223,032,186 8 2,447,328 2,283,146 164,182 222,868,004 9 2,452,328 2,281,465 170,863 222,697,141 10 2,457,328 2,279,716 177,612 222,519,529 11 2,462,328 2,277,898 184,430 222,335,100 12 2,467,328 2,276,010 191,318 222,143,782 13 2,472,328 2,274,051 198,276 221,945,505 14 2,477,328 2,272,022 205,306 221,740,199 15 2,482,328 2,269,920 212,408 221,527,792 16 2,487,328 2,267,746 219,582 221,308,210 17 2,492,328 2,265,498 226,830 221,081,380 18 2,497,328 2,263,176 234,152 220,847,228 19 2,502,328 2,260,779 241,549 220,605,679 20 2,507,328 2,258,306 249,022 220,356,657 21 2,512,328 2,255,757 256,571 220,100,086 22 2,517,328 2,253,130 264,197 219,835,889 23 2,522,328 2,250,426 271,902 219,563,987 24 2,527,328 2,247,642 279,685 219,284,302 25 2,532,328 2,244,779 287,548 218,996,753 26 2,537,328 2,241,836 295,492 218,701,261 27 2,542,328 2,238,811 303,517 218,397,744 28 2,547,328 2,235,704 311,624 218,086,120 29 2,552,328 2,232,514 319,814 217,766,306 30 2,557,328 2,229,240 328,088 217,438,219 31 2,562,328 2,225,881 336,446 217,101,772 32 2,567,328 2,222,437 344,891 216,756,882 33 2,572,328 2,218,906 353,421 216,403,460 34 2,577,328 2,215,289 362,039 216,041,421 35 2,582,328 2,211,582 370,745 215,670,676 36 2,587,328 2,207,787 379,541 215,291,135 37 2,592,328 2,203,902 388,426 214,902,710 38 2,597,328 2,199,926 397,402 214,505,308 39 2,602,328 2,195,857 406,470 214,098,837 40 2,607,328 2,191,696 415,631 213,683,206 41 2,612,328 2,187,442 424,886 213,258,320 42 2,617,328 2,183,092 434,235 212,824,085 43 2,622,328 2,178,647 443,681 212,380,404 44 2,627,328 2,174,105 453,223 211,927,182 45 2,632,328 2,169,466 462,862 211,464,320 46 2,637,328 2,164,727 472,600 210,991,719 47 2,642,328 2,159,889 482,438 210,509,281 48 2,647,328 2,154,951 492,377 210,016,904 49 2,652,328 2,149,910 502,417 209,514,487 50 2,657,328 2,144,767 512,560 209,001,926 51 2,662,328 2,139,520 522,807 208,479,119 52 2,667,328 2,134,168 533,159 207,945,960 53 2,672,328 2,128,710 543,617 207,402,342 54 2,677,328 2,123,145 554,182 206,848,160 55 2,682,328 2,117,472 564,855 206,283,305 56 2,687,328 2,111,690 575,638 205,707,667 57 2,692,328 2,105,797 586,530 205,121,137 58 2,697,328 2,099,793 597,534 204,523,603 59 2,702,328 2,093,676 608,651 203,914,951 60 2,707,328 2,087,446 619,882 203,295,069 61 2,712,328 2,081,100 631,228 202,663,842 62 2,717,328 2,074,638 642,689 202,021,152 63 2,722,328 2,068,059 654,269 201,366,884 64 2,727,328 2,061,361 665,966 200,700,917 65 2,732,328 2,054,544 677,784 200,023,134 66 2,737,328 2,047,606 689,722 199,333,412 67 2,742,328 2,040,545 701,783 198,631,629 68 2,747,328 2,033,361 713,967 197,917,663 69 2,752,328 2,026,052 726,275 197,191,387 70 2,757,328 2,018,618 738,710 196,452,677 71 2,762,328 2,011,055 751,272 195,701,405 72 2,767,328 2,003,365 763,963 194,937,442 73 2,772,328 1,995,544 776,783 194,160,659 74 2,777,328 1,987,592 789,735 193,370,924 75 2,782,328 1,979,508 802,820 192,568,104 76 2,787,328 1,971,290 816,038 191,752,066 77 2,792,328 1,962,936 829,392 190,922,674 78 2,797,328 1,954,446 842,882 190,079,792 79 2,802,328 1,945,817 856,510 189,223,282 80 2,807,328 1,937,049 870,278 188,353,004 81 2,812,328 1,928,140 884,187 187,468,816 82 2,817,328 1,919,089 898,239 186,570,578 83 2,822,328 1,909,894 912,434 185,658,144 84 2,827,328 1,900,554 926,774 184,731,370 85 2,832,328 1,891,066 941,261 183,790,109 86 2,837,328 1,881,431 955,897 182,834,212 87 2,842,328 1,871,645 970,682 181,863,529 88 2,847,328 1,861,709 985,619 180,877,910 89 2,852,328 1,851,619 1,000,709 179,877,202 90 2,857,328 1,841,375 1,015,953 178,861,249 91 2,862,328 1,830,975 1,031,353 177,829,896 92 2,867,328 1,820,417 1,046,911 176,782,986 93 2,872,328 1,809,700 1,062,628 175,720,358 94 2,877,328 1,798,822 1,078,506 174,641,852 95 2,882,328 1,787,781 1,094,546 173,547,306 96 2,887,328 1,776,577 1,110,751 172,436,555 97 2,892,328 1,765,206 1,127,121 171,309,434 98 2,897,328 1,753,668 1,143,660 170,165,774 99 2,902,328 1,741,961 1,160,367 169,005,407 100 2,907,328 1,730,082 1,177,246 167,828,161 101 2,912,328 1,718,031 1,194,297 166,633,864 102 2,917,328 1,705,805 1,211,523 165,422,342 103 2,922,328 1,693,403 1,228,925 164,193,417 104 2,927,328 1,680,822 1,246,505 162,946,911 105 2,932,328 1,668,062 1,264,265 161,682,646 106 2,937,328 1,655,120 1,282,208 160,400,438 107 2,942,328 1,641,994 1,300,333 159,100,105 108 2,947,328 1,628,683 1,318,645 157,781,460 109 2,952,328 1,615,184 1,337,143 156,444,317 110 2,957,328 1,601,496 1,355,832 155,088,486 111 2,962,328 1,587,617 1,374,711 153,713,775 112 2,967,328 1,573,544 1,393,784 152,319,991 113 2,972,328 1,559,276 1,413,052 150,906,939 114 2,977,328 1,544,811 1,432,517 149,474,422 115 2,982,328 1,530,146 1,452,181 148,022,241 116 2,987,328 1,515,281 1,472,047 146,550,194 117 2,992,328 1,500,212 1,492,116 145,058,078 118 2,997,328 1,484,937 1,512,391 143,545,687 119 3,002,328 1,469,455 1,532,873 142,012,815 120 3,007,328 1,453,763 1,553,565 140,459,250 121 3,012,328 1,437,859 1,574,468 138,884,782 122 3,017,328 1,421,742 1,595,586 137,289,196 123 3,022,328 1,405,408 1,616,920 135,672,277 124 3,027,328 1,388,856 1,638,472 134,033,805 125 3,032,328 1,372,083 1,660,244 132,373,560 126 3,037,328 1,355,088 1,682,240 130,691,320 127 3,042,328 1,337,867 1,704,461 128,986,859 128 3,047,328 1,320,418 1,726,909 127,259,950 129 3,052,328 1,302,740 1,749,587 125,510,363 130 3,057,328 1,284,830 1,772,498 123,737,865 131 3,062,328 1,266,685 1,795,642 121,942,223 132 3,067,328 1,248,304 1,819,024 120,123,199 133 3,072,328 1,229,682 1,842,645 118,280,554 134 3,077,328 1,210,820 1,866,508 116,414,046 135 3,082,328 1,191,712 1,890,615 114,523,430 136 3,087,328 1,172,359 1,914,969 112,608,461 137 3,092,328 1,152,755 1,939,572 110,668,889 138 3,097,328 1,132,900 1,964,427 108,704,461 139 3,102,328 1,112,791 1,989,537 106,714,924 140 3,107,328 1,092,424 2,014,904 104,700,021 141 3,112,328 1,071,798 2,040,530 102,659,491 142 3,117,328 1,050,909 2,066,418 100,593,073 143 3,122,328 1,029,756 2,092,572 98,500,501 144 3,127,328 1,008,334 2,118,993 96,381,507 145 3,132,328 986,642 2,145,685 94,235,822 146 3,137,328 964,677 2,172,650 92,063,172 147 3,142,328 942,436 2,199,891 89,863,280 148 3,147,328 919,916 2,227,411 87,635,869 149 3,152,328 897,115 2,255,213 85,380,656 150 3,157,328 874,028 2,283,299 83,097,357 151 3,162,328 850,655 2,311,673 80,785,684 152 3,167,328 826,990 2,340,337 78,445,347 153 3,172,328 803,033 2,369,295 76,076,052 154 3,177,328 778,779 2,398,549 73,677,503 155 3,182,328 754,225 2,428,103 71,249,401 156 3,187,328 729,369 2,457,959 68,791,442 157 3,192,328 704,207 2,488,120 66,303,322 158 3,197,328 678,737 2,518,591 63,784,731 159 3,202,328 652,954 2,549,373 61,235,358 160 3,207,328 626,857 2,580,471 58,654,887 161 3,212,328 600,441 2,611,887 56,043,000 162 3,217,328 573,703 2,643,624 53,399,376 163 3,222,328 546,641 2,675,687 50,723,689 164 3,227,328 519,251 2,708,077 48,015,612 165 3,232,328 491,528 2,740,799 45,274,813 166 3,237,328 463,471 2,773,856 42,500,956 167 3,242,328 435,076 2,807,252 39,693,704 168 3,247,328 406,338 2,840,989 36,852,715 169 3,252,328 377,256 2,875,072 33,977,643 170 3,257,328 347,824 2,909,504 31,068,139 171 3,262,328 318,040 2,944,288 28,123,851 172 3,267,328 287,899 2,979,428 25,144,423 173 3,272,328 257,400 3,014,928 22,129,495 174 3,277,328 226,536 3,050,791 19,078,703 175 3,282,328 195,306 3,087,022 15,991,682 176 3,287,328 163,704 3,123,623 12,868,058 177 3,292,328 131,728 3,160,599 9,707,459 178 3,297,328 99,374 3,197,954 6,509,505 179 3,302,328 66,637 3,235,691 3,273,814 180 3,307,328 33,514 3,273,814 0 CUOTA DOS Y SUBSIGUIENTES = Cuota mes anterior (+,-) gradiente GRAD. GEOMETRICO SISTEMA DE AMORTIZACION GRADIENTE GEOMETRICO Vr. Préstamo 350,000,000 Plazo 7 AÑOS Trimestres 28 TRIMESTES Gradiente -3% Tasa 3.02% TV Valor de la primera cuota Gradiente Geomético Vencido Creciente dado VP Tasa Per. Nper VP Gradiente 1a CUOTA 3.02% 28 350,000,000 -3% 25,347,229 Tabla de amortización gradiente geométrico Cuota Nº Cuota Interés Capital Saldo Capital 0 350,000,000 1 25,347,229 10,573,827 14,773,402 335,226,598 2 24,637,507 10,127,509 14,509,998 320,716,600 3 23,947,657 9,689,149 14,258,508 306,458,092 4 23,277,122 9,258,386 14,018,737 292,439,355 5 22,625,363 8,834,867 13,790,496 278,648,859 6 21,991,853 8,418,243 13,573,610 265,075,249 7 21,376,081 8,008,171 13,367,910 251,707,339 8 20,777,551 7,604,314 13,173,236 238,534,103 9 20,195,779 7,206,338 12,989,441 225,544,662 10 19,630,297 6,813,915 12,816,382 212,728,280 11 19,080,649 6,426,720 12,653,929 200,074,351 12 18,546,391 6,044,433 12,501,958 187,572,394 13 18,027,092 5,666,738 12,360,354 175,212,039 14 17,522,333 5,293,320 12,229,014 162,983,026 15 17,031,708 4,923,870 12,107,838 150,875,187 16 16,554,820 4,558,081 11,996,740 138,878,448 17 16,091,285 4,195,648 11,895,637 126,982,810 18 15,640,729 3,836,270 11,804,460 115,178,350 19 15,202,789 3,479,646 11,723,143 103,455,207 20 14,777,111 3,125,479 11,651,632 91,803,575 21 14,363,352 2,773,472 11,589,880 80,213,695 22 13,961,178 2,423,331 11,537,847 68,675,848 23 13,570,265 2,074,762 11,495,503 57,180,345 24 13,190,297 1,727,472 11,462,826 45,717,519 25 12,820,969 1,381,169 11,439,800 34,277,719 26 12,461,982 1,035,562 11,426,420 22,851,299 27 12,113,046 690,359 11,422,687 11,428,612 28 11,773,881 345,269 11,428,612 0 CUOTA DOS Y SUBSIGUIENTES = Cuota mes anterior x (1+G) IND.CONVENIENCIA INDICADORES DE CONVENIENCIA Año Ingresos Egresos Flujo Neto VP Egresos VF Ingresos ANALISIS SENSIBILIDAD 0 20,000,000 (20,000,000) (20,000,000) TIO 3,025,506 1 2,350,000 500,000 1,850,000 2,440,417 2.0% 4,840,708 2 2,350,000 500,000 1,850,000 2,379,734 2.5% 3,909,505 3 2,350,000 1,250,000 1,100,000 1,379,792 3.0% 3,025,506 4 2,350,000 650,000 1,700,000 2,079,382 3.5% 2,185,943 5 3,300,000 650,000 2,650,000 3,160,789 4.0% 1,388,228 6 3,300,000 4,500,000 (1,200,000) (1,117,116) 4.5% 629,940 7 3,300,000 750,000 2,550,000 2,892,135 5.0% (91,188) 8 4,350,000 750,000 3,600,000 3,981,486 5.5% (777,277) 9 4,350,000 2,500,000 1,850,000 1,995,165 6.0% (1,430,313) 10 3,850,000 850,000 3,000,000 3,154,951 6.5% (2,052,160) 11 1,000,000 850,000 150,000 153,825 7.0% (2,644,561) 12 10,000,000 10,000,000 10,000,000 TOTALES 21,117,116 33,617,675 Tasa descuento 3% Tasa de financiación 1.20% Tasa de Reinversión 2.55% INDICADORES SIGLA RESULTADO FORMULA VPN 3,025,506 +VNA(D18;D3:$D$14)+$D$2 TIR 4.94% +TIR(D2:D14) TIRM 3.95% +TIRM(D2:D14;$D$19;$D$20) TIRM 3.95% +(F15/E15)^(1/A14)-1 CAUE 303,949 +PAGO($D$18;A14;-D24) B/C 1.10 +(VNA($D$25;B8:B19)+B7)/(VNA($D$25;C8:C18)+C7) Sensibilidad del VPN ante variaciones en la TIO VPN 0.02 2.5000000000000001E-2 0.03 3.5000000000000003E-2 0.04 4.4999999999999998E-2 0.05 5.5E-2 0.06 6.5000000000000002E-2 7.0000000000000007E-2 4840707.6600793377 3909504.99953923 3025506.2044957541 2185943.4232856221 1388228.4337594174 629939.99490896985 -91187.846340715885 -777276.56992878392 -1430313.1892759465 -2052159.5140096657 -2644560.7276749425 TIO Valor VPN image1.emf =VP (1+ i) n -1 i * (1+ i) n A image2.emf =VFA (1+ i) n -1 i image3.emf AVP i(1+ i) n (1+ i) n -1 = image4.emf AVF i (1+ i) n -1 = image5.emf (1+i) VP=A (1+ i) n -1 i(1+ i) n image6.emf (1+ i) n -1 (1+i) i VF=A image7.emf VP i (1+ i) n (1+i) A= (1+ i) n -1 image8.emf VF i (1+i) A= (1+ i) n -1 image9.emf A (1+i) s -1 (1+i) r VP= i (1+i) s image10.emf i (1+i) s A= P (1+i) r (1+i) s -1 image11.emf A i VP= image12.png image21.png image13.png image14.png image15.png image16.png image17.png image18.png image19.png image20.png image22.png image30.png image31.png image23.png image24.png image25.png image26.png image27.png image28.png image29.png