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Nombres Nombres Sección Ismael Araya 4 Pedro José Correa 4 Daniel Correa 4 Tema 1 Suponga usted enfrenta las siguientes alternativas de inversión Flujo esperado en è t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 Proyecto A -1000 120 120 120 120 120 120 1120 B -2000 500 600 0 700 800 0 900 C 200 1000 -1000 -1500 500 400 300 -300 D -5000 2500 3000 0 2500 3000 0 2500 E -1000 1200 1800 -2000 1000 1000 1200 1100 F -500 250 300 0 250 300 0 250 Para cada proyecto se pide calcular: a) El periodo de recuperación de la inversión (payback period) b) La tasa interna de retorno (TIR) c) El VAN (o VPN) suponiendo que los Beta de cada proyecto son los que se indican más abajo, que el premio por riesgo es 0.10 y la tasa libre de riesgo es 0.06 Proyecto Beta Horas hombre Tasa Libre de riesgo 0.06 premio riesgo 0.1 A 0.4 33 B 0.6 17 C 1 25 D 0.9 15 E 0.2 38 F 1.2 12 d) En base a los criterios a), b) y c) haga un ranking de proyectos y explique cuales realizaría si la empresa solo puede llevar a cabo 4 de ellos. Cuando los rankings difieran en su recomendación analice conceptual y gráficamente cuál proyecto usted elegiría y por qué (explique el error de los criterios alternativos) e) Suponga ahora que la empresa cuenta con sólo 100 horas hombre y los proyectos requieren distinto uso de ese recurso para poder implementarlos. ¿Cuáles realizaría y por qué? Respuestas a) Payback Period Flujo acumulado en è t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 Años hasta recuperar inversión Proyecto El color amarillo es el último año en que los flujos acumulados son negativos. A -1000 -880 -760 -640 -520 -400 -280 840 7 El color Rojo es el primer año en que los flujos acumulados son positivos. B -2000 -1500 -900 -900 -200 600 600 1500 5 C 200 1200 200 -1300 -800 -400 -100 -400 - D -5000 -2500 500 500 3000 6000 6000 8500 2 E -1000 200 2000 0 1000 2000 3200 4300 1 F -500 -250 50 50 300 600 600 850 2 b) Tasa Interna de Retorno Flujo esperado en è t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 TIR Proyecto A -1000 120 120 120 120 120 120 1120 12.00% B -2000 500 600 0 700 800 0 900 15.39% C 200 1000 -1000 -1500 500 400 300 -300 30.90% D -5000 2500 3000 0 2500 3000 0 2500 37.33% E -1000 1200 1800 -2000 1000 1000 1200 1100 89.19% F -500 250 300 0 250 300 0 250 37.33% c) VNA o VPN 1/1/2001 1/1/2002 1/1/2003 1/1/2004 1/1/2005 1/1/2006 1/1/2007 1/1/2008 Flujo esperado en è t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 Tasa con Riesgo VNA Proyecto A -1000 120 120 120 120 120 120 1120 10.0% 97.37 B -2000 500 600 0 700 800 0 900 12.0% 230.66 C 200 1000 -1000 -1500 500 400 300 -300 16.0% -158.51 D -5000 2500 3000 0 2500 3000 0 2500 15.0% 3,303.10 E -1000 1200 1800 -2000 1000 1000 1200 1100 8.0% 2,880.31 F -500 250 300 0 250 300 0 250 18.0% 265.88 d) Criterio Periodo de Recuperación de la Inversión Ranking Proyecto 1. E 2. D y F 4. B Criterio TIR Ranking Proyecto 1. E 2. D y F 4. C Criterio VNA Ranking Proyecto 1. D 2. E 3. F 4. B En el caso de la TIR, esta no considera luego el valor presente que depende de la tasa efectiva de cada proyecto ajustado por el riesgo. Es por esto que el proyecto E es más mejor que el proyecto D. La regla del periodo de recuperación no es confiable porque ignora el valor del dinero en el tiempo y no depende del costo de capital. Puede pasar que un proyecto tenga los flujos mayores después de ciertos años, lo que hace que no cumpla con la recuperación que se quiere, pero igual tiene un VPN más alto. Ninguna regla que ignore el conjunto de oportunidades alternativas es óptima. Finalmente, el criterio más correcto sería el del VNA debido a que considera el valor del dinero en el tiempo, ajusta el valor presente de estos según el riesgo de cada uno, considera el costo del capital (la tasa de interés). Tasa 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% 50% 51% 52% 53% 54% 55% 56% 57% 58% 59% 60% 61% 62% 63% 64% 65% 66% 67% 68% 69% 70% 71% 72% 73% 74% 75% 76% 77% 78% 79% 80% 81% 82% 83% 84% 85% 86% 87% 88% 89% 90% 91% 92% 93% 94% 95% 96% 97% 98% 99% 100% VNA E $4,300.00 $4,080.25 $3,874.48 $3,681.62 $3,500.70 $3,330.83 $3,171.20 $3,021.06 $2,879.72 $2,746.56 $2,621.00 $2,502.50 $2,390.59 $2,284.80 $2,184.73 $2,089.99 $2,000.23 $1,915.12 $1,834.36 $1,757.67 $1,684.80 $1,615.49 $1,549.53 $1,486.71 $1,426.85 $1,369.76 $1,315.27 $1,263.23 $1,213.51 $1,165.96 $1,120.45 $1,076.89 $1,035.14 $995.12 $956.73 $919.87 $884.48 $850.46 $817.74 $786.26 $755.96 $726.77 $698.63 $671.50 $645.32 $620.04 $595.63 $572.04 $549.23 $527.16 $505.80 $485.12 $465.09 $445.67 $426.83 $408.57 $390.84 $373.62 $356.89 $340.64 $324.84 $309.47 $294.51 $279.96 $265.78 $251.97 $238.51 $225.39 $212.60 $200.11 $187.93 $176.04 $164.42 $153.08 $141.99 $131.15 $120.55 $110.18 $100.04 $90.11 $80.39 $70.88 $61.55 $52.42 $43.47 $34.69 $26.09 $17.65 $9.37 $1.24 -$6.73 -$14.56 -$22.25 -$29.80 -$37.22 -$44.51 -$51.67 -$58.71 -$65.63 -$72.44 -$79.14 VNA D $8,500.0 $8,004.6 $7,537.3 $7,096.2 $6,679.4 $6,285.3 $5,912.2 $5,558.8 $5,223.8 $4,905.9 $4,604.0 $4,317.1 $4,044.3 $3,784.6 $3,537.3 $3,301.6 $3,076.8 $2,862.2 $2,657.3 $2,461.4 $2,274.1 $2,094.8 $1,923.2 $1,758.7 $1,601.0 $1,449.8 $1,304.6 $1,165.2 $1,031.2 $902.4 $778.5 $659.2 $544.3 $433.7 $327.0 $224.2 $124.9 $29.1 -$63.4 -$152.8 -$239.3 -$322.8 -$403.7 -$482.0 -$557.7 -$631.1 -$702.3 -$771.2 -$838.1 -$903.0 -$965.9 -$1,027.1 -$1,086.4 -$1,144.1 -$1,200.2 -$1,254.7 -$1,307.7 -$1,359.3 -$1,409.5 -$1,458.3 -$1,505.9 -$1,552.2 -$1,597.4 -$1,641.4 -$1,684.3 -$1,726.1 -$1,767.0 -$1,806.8 -$1,845.6 -$1,883.6 -$1,920.6 -$1,956.8 -$1,992.2 -$2,026.7 -$2,060.5 -$2,093.5 -$2,125.8 -$2,157.4 -$2,188.3 -$2,218.5 -$2,248.1 -$2,277.1 -$2,305.5 -$2,333.3 -$2,360.5 -$2,387.2 -$2,413.3 -$2,438.9 -$2,464.0 -$2,488.7 -$2,512.8 -$2,536.5 -$2,559.8 -$2,582.6 -$2,605.0 -$2,626.9 -$2,648.5 -$2,669.7 -$2,690.5 -$2,710.9 -$2,731.0 VNA F $850.0 $800.5 $753.7 $709.6 $667.9 $628.5 $591.2 $555.9 $522.4 $490.6 $460.4 $431.7 $404.4 $378.5 $353.7 $330.2 $307.7 $286.2 $265.7 $246.1 $227.4 $209.5 $192.3 $175.9 $160.1 $145.0 $130.5 $116.5 $103.1 $90.2 $77.8 $65.9 $54.4 $43.4 $32.7 $22.4 $12.5 $2.9 -$6.3 -$15.3 -$23.9 -$32.3 -$40.4 -$48.2 -$55.8 -$63.1 -$70.2 -$77.1 -$83.8 -$90.3 -$96.6 -$102.7 -$108.6 -$114.4 -$120.0 -$125.5 -$130.8 -$135.9 -$140.9 -$145.8 -$150.6 -$155.2 -$159.7 -$164.1 -$168.4 -$172.6 -$176.7 -$180.7 -$184.6 -$188.4 -$192.1 -$195.7 -$199.2 -$202.7 -$206.1 -$209.4 -$212.6 -$215.7 -$218.8 -$221.9 -$224.8 -$227.7 -$230.5 -$233.3 -$236.0 -$238.7 -$241.3 -$243.9 -$246.4 -$248.9 -$251.3 -$253.7 -$256.0 -$258.3 -$260.5 -$262.7 -$264.8 -$267.0 -$269.0 -$271.1 -$273.1 VNA C -$400.0 -$382.2 -$364.9 -$347.9 -$331.3 -$315.1 -$299.2 -$283.7 -$268.5 -$253.7 -$239.2 -$225.0 -$211.2 -$197.6 -$184.3 -$171.4 -$158.7 -$146.3 -$134.2 -$122.3 -$110.8 -$99.4 -$88.4 -$77.5 -$67.0 -$56.6 -$46.5 -$36.6 -$27.0 -$17.5 -$8.3 $0.7 $9.5 $18.1 $26.5 $34.8 $42.8 $50.6 $58.3 $65.8 $73.1 $80.3 $87.3 $94.1 $100.8 $107.3 $113.7 $120.0 $126.1 $132.0 $137.8 $143.5 $149.1 $154.5 $159.8 $165.0 $170.0 $175.0 $179.8 $184.5 $189.2 $193.7 $198.1 $202.4 $206.6 $210.7 $214.7 $218.7 $222.5 $226.3 $229.9 $233.5 $237.0 $240.4 $243.8 $247.0 $250.2 $253.4 $256.4 $259.4 $262.3 $265.2 $267.9 $270.7 $273.3 $275.9 $278.5 $280.9 $283.4 $285.7 $288.1 $290.3 $292.5 $294.7 $296.8 $298.9 $300.9 $302.9 $304.8 $306.7 $308.5 VNA B $1,500.0 $1,356.5 $1,221.7 $1,094.8 $975.3 $862.7 $756.5 $656.2 $561.5 $471.9 $387.1 $306.8 $230.7 $158.5 $89.9 $24.8 -$37.1 -$96.0 -$152.1 -$205.5 -$256.4 -$305.0 -$351.3 -$395.6 -$437.9 -$478.4 -$517.1 -$554.2 -$589.7 -$623.7 -$656.4 -$687.7 -$717.8 -$746.7 -$774.4 -$801.1 -$826.8 -$851.5 -$875.3 -$898.3 -$920.4 -$941.7 -$962.3 -$982.1 -$1,001.3 -$1,019.9 -$1,037.8 -$1,055.1 -$1,071.8 -$1,088.0 -$1,103.7-$1,118.9 -$1,133.6 -$1,147.9 -$1,161.7 -$1,175.1 -$1,188.1 -$1,200.8 -$1,213.0 -$1,224.9 -$1,236.5 -$1,247.7 -$1,258.7 -$1,269.3 -$1,279.6 -$1,289.7 -$1,299.5 -$1,309.0 -$1,318.3 -$1,327.4 -$1,336.2 -$1,344.8 -$1,353.2 -$1,361.3 -$1,369.3 -$1,377.1 -$1,384.7 -$1,392.1 -$1,399.3 -$1,406.4 -$1,413.3 -$1,420.1 -$1,426.7 -$1,433.1 -$1,439.4 -$1,445.6 -$1,451.6 -$1,457.6 -$1,463.3 -$1,469.0 -$1,474.5 -$1,480.0 -$1,485.3 -$1,490.5 -$1,495.6 -$1,500.6 -$1,505.5 -$1,510.3 -$1,515.1 -$1,519.7 -$1,524.2 En el primer gráfico vemos como los VPN no solo dependen de cuando la tasa hace que el retorno sea 0, sino tambien de la tasa ajustada con el riesgo. Tasa VNA E VNA D VNA F VNA C VNA B En el segundo gráfico se ve como sube el flujo acumulado de los proyectos, pudiendo ver cuando comienzan a ser positivos. 0% $4,300.00 $8,500.0 $850.0 -$400.0 $1,500.0 1% $4,080.25 $8,004.6 $800.5 -$382.2 $1,356.5 2% $3,874.48 $7,537.3 $753.7 -$364.9 $1,221.7 3% $3,681.62 $7,096.2 $709.6 -$347.9 $1,094.8 4% $3,500.70 $6,679.4 $667.9 -$331.3 $975.3 5% $3,330.83 $6,285.3 $628.5 -$315.1 $862.7 6% $3,171.20 $5,912.2 $591.2 -$299.2 $756.5 7% $3,021.06 $5,558.8 $555.9 -$283.7 $656.2 8% $2,879.72 $5,223.8 $522.4 -$268.5 $561.5 9% $2,746.56 $4,905.9 $490.6 -$253.7 $471.9 10% $2,621.00 $4,604.0 $460.4 -$239.2 $387.1 11% $2,502.50 $4,317.1 $431.7 -$225.0 $306.8 12% $2,390.59 $4,044.3 $404.4 -$211.2 $230.7 13% $2,284.80 $3,784.6 $378.5 -$197.6 $158.5 14% $2,184.73 $3,537.3 $353.7 -$184.3 $89.9 15% $2,089.99 $3,301.6 $330.2 -$171.4 $24.8 16% $2,000.23 $3,076.8 $307.7 -$158.7 -$37.1 17% $1,915.12 $2,862.2 $286.2 -$146.3 -$96.0 18% $1,834.36 $2,657.3 $265.7 -$134.2 -$152.1 19% $1,757.67 $2,461.4 $246.1 -$122.3 -$205.5 20% $1,684.80 $2,274.1 $227.4 -$110.8 -$256.4 e) Flujo esperado en t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 Tasa con Riesgo VNA Horas Hombre Índ. De Rentabilidad Ranking 21% $1,615.49 $2,094.8 $209.5 -$99.4 -$305.0 Proyecto 22% $1,549.53 $1,923.2 $192.3 -$88.4 -$351.3 A -1000 120 120 120 120 120 120 1120 10.0% 97.160 33 $ 2.94 5 23% $1,486.71 $1,758.7 $175.9 -$77.5 -$395.6 B -2000 500 600 0 700 800 0 900 12.0% 230.258 17 $ 13.54 4 24% $1,426.85 $1,601.0 $160.1 -$67.0 -$437.9 C 200 1000 -1000 -1500 500 400 300 -300 16.0% -158.702 25 -$ 6.35 6 25% $1,369.76 $1,449.8 $145.0 -$56.6 -$478.4 D -5000 2500 3000 0 2500 3000 0 2500 15.0% 3301.622 15 $ 220.11 1 26% $1,315.27 $1,304.6 $130.5 -$46.5 -$517.1 E -1000 1200 1800 -2000 1000 1000 1200 1100 8.0% 2879.719 38 $ 75.78 2 27% $1,263.23 $1,165.2 $116.5 -$36.6 -$554.2 F -500 250 300 0 250 300 0 250 18.0% 265.727 12 $ 22.14 3 28% $1,213.51 $1,031.2 $103.1 -$27.0 -$589.7 29% $1,165.96 $902.4 $90.2 -$17.5 -$623.7 Va a ocupar 15 en el proyecto D, luego 38 en E, 12 en F, 17 en B y van a sobrar 18 horas hombre. Los proyectos que realiza son los que tienen un índice de rentabilidad mayor, de mayor a menor. 30% $1,120.45 $778.5 $77.8 -$8.3 -$656.4 31% $1,076.89 $659.2 $65.9 $0.7 -$687.7 32% $1,035.14 $544.3 $54.4 $9.5 -$717.8 33% $995.12 $433.7 $43.4 $18.1 -$746.7 34% $956.73 $327.0 $32.7 $26.5 -$774.4 35% $919.87 $224.2 $22.4 $34.8 -$801.1 36% $884.48 $124.9 $12.5 $42.8 -$826.8 37% $850.46 $29.1 $2.9 $50.6 -$851.5 38% $817.74 -$63.4 -$6.3 $58.3 -$875.3 39% $786.26 -$152.8 -$15.3 $65.8 -$898.3 40% $755.96 -$239.3 -$23.9 $73.1 -$920.4 41% $726.77 -$322.8 -$32.3 $80.3 -$941.7 42% $698.63 -$403.7 -$40.4 $87.3 -$962.3 43% $671.50 -$482.0 -$48.2 $94.1 -$982.1 44% $645.32 -$557.7 -$55.8 $100.8 -$1,001.3 45% $620.04 -$631.1 -$63.1 $107.3 -$1,019.9 46% $595.63 -$702.3 -$70.2 $113.7 -$1,037.8 47% $572.04 -$771.2 -$77.1 $120.0 -$1,055.148% $549.23 -$838.1 -$83.8 $126.1 -$1,071.8 49% $527.16 -$903.0 -$90.3 $132.0 -$1,088.0 50% $505.80 -$965.9 -$96.6 $137.8 -$1,103.7 51% $485.12 -$1,027.1 -$102.7 $143.5 -$1,118.9 52% $465.09 -$1,086.4 -$108.6 $149.1 -$1,133.6 53% $445.67 -$1,144.1 -$114.4 $154.5 -$1,147.9 54% $426.83 -$1,200.2 -$120.0 $159.8 -$1,161.7 55% $408.57 -$1,254.7 -$125.5 $165.0 -$1,175.1 56% $390.84 -$1,307.7 -$130.8 $170.0 -$1,188.1 57% $373.62 -$1,359.3 -$135.9 $175.0 -$1,200.8 58% $356.89 -$1,409.5 -$140.9 $179.8 -$1,213.0 59% $340.64 -$1,458.3 -$145.8 $184.5 -$1,224.9 60% $324.84 -$1,505.9 -$150.6 $189.2 -$1,236.5 61% $309.47 -$1,552.2 -$155.2 $193.7 -$1,247.7 62% $294.51 -$1,597.4 -$159.7 $198.1 -$1,258.7 63% $279.96 -$1,641.4 -$164.1 $202.4 -$1,269.3 64% $265.78 -$1,684.3 -$168.4 $206.6 -$1,279.6 65% $251.97 -$1,726.1 -$172.6 $210.7 -$1,289.7 66% $238.51 -$1,767.0 -$176.7 $214.7 -$1,299.5 67% $225.39 -$1,806.8 -$180.7 $218.7 -$1,309.0 68% $212.60 -$1,845.6 -$184.6 $222.5 -$1,318.3 69% $200.11 -$1,883.6 -$188.4 $226.3 -$1,327.4 70% $187.93 -$1,920.6 -$192.1 $229.9 -$1,336.2 71% $176.04 -$1,956.8 -$195.7 $233.5 -$1,344.8 72% $164.42 -$1,992.2 -$199.2 $237.0 -$1,353.2 73% $153.08 -$2,026.7 -$202.7 $240.4 -$1,361.3 74% $141.99 -$2,060.5 -$206.1 $243.8 -$1,369.3 75% $131.15 -$2,093.5 -$209.4 $247.0 -$1,377.1 76% $120.55 -$2,125.8 -$212.6 $250.2 -$1,384.7 77% $110.18 -$2,157.4 -$215.7 $253.4 -$1,392.1 78% $100.04 -$2,188.3 -$218.8 $256.4 -$1,399.3 79% $90.11 -$2,218.5 -$221.9 $259.4 -$1,406.4 80% $80.39 -$2,248.1 -$224.8 $262.3 -$1,413.3 81% $70.88 -$2,277.1 -$227.7 $265.2 -$1,420.1 82% $61.55 -$2,305.5 -$230.5 $267.9 -$1,426.7 83% $52.42 -$2,333.3 -$233.3 $270.7 -$1,433.1 84% $43.47 -$2,360.5 -$236.0 $273.3 -$1,439.4 85% $34.69 -$2,387.2 -$238.7 $275.9 -$1,445.6 86% $26.09 -$2,413.3 -$241.3 $278.5 -$1,451.6 87% $17.65 -$2,438.9 -$243.9 $280.9 -$1,457.6 88% $9.37 -$2,464.0 -$246.4 $283.4 -$1,463.3 89% $1.24 -$2,488.7 -$248.9 $285.7 -$1,469.0 90% -$6.73 -$2,512.8 -$251.3 $288.1 -$1,474.5 91% -$14.56 -$2,536.5 -$253.7 $290.3 -$1,480.0 92% -$22.25 -$2,559.8 -$256.0 $292.5 -$1,485.3 93% -$29.80 -$2,582.6 -$258.3 $294.7 -$1,490.5 94% -$37.22 -$2,605.0 -$260.5 $296.8 -$1,495.6 95% -$44.51 -$2,626.9 -$262.7 $298.9 -$1,500.6 96% -$51.67 -$2,648.5 -$264.8 $300.9 -$1,505.5 97% -$58.71 -$2,669.7 -$267.0 $302.9 -$1,510.3 98% -$65.63 -$2,690.5 -$269.0 $304.8 -$1,515.1 99% -$72.44 -$2,710.9 -$271.1 $306.7 -$1,519.7 100% -$79.14 -$2,731.0 -$273.1 $308.5 -$1,524.2 TIR y VNA TIR Flujo Acumulado de los Proyectos Flujo acumulado en è Tema 2 Tema II (15 PUNTOS) Suponga la siguiente información de mercado respecto de bonos cero-cupón con valor de caratula $1,000 para los siguientes plazos: MERCADO 1 MERCADO 2 Plazo (años) Precio Plazo (años) Precio 1 990 1 990 2 982 2 980 3 978 3 970 4 970 4 960 Valor Carátula 5 966 5 950 1000 6 958 6 940 7 954 7 930 8 946 8 920 9 942 9 910 10 934 10 900 11 930 11 890 12 922 12 880 13 918 13 870 14 910 14 860 15 906 15 850 16 898 16 840 17 894 17 830 18 886 18 820 19 882 19 810 20 874 20 800 a) En ambos casos encuentre la correspondiente estructura de tasas (yieldcurve) así como las correspondientes tasas forward entre t y t+1 para todos los plazos (para todo t). Grafique y analice sus resultados. (8 puntos) b) Suponga una empresa quiere emitir un bono que paga 200 en t=1, 190 en t=2, 180 en t=3, 170 en t=4 y así sucesivamente hasta t=20. ¿Cuánto estima usted puede recaudar la empresa si hace la emisión de bonos en el mercado 1? ¿Y si hace la emisión en el mercado 2? ¿Qué le recomendaría usted? (3 puntos) c) Si usted tiene acceso a ambos mercados y puede prestar/pedir prestado hasta un máximo de $ 5000 por un plazo máximo de 5 años. ¿Qué estrategia de inversión seguiría? (4 puntos) a) Tasa Spot (YTM) Mercado 1 Tasas Forward Mercado 1 Tasa Spot (YTM) Mercado 2 Tasa Forward Mercado 2 1000=Precio/(1+r)^n r1 1.0101% 1.0101% 1.0101% 1.0101% r=((Precio/1000)^1/n)-1 r2 0.9123% 0.8147% 1.0153% 1.0204% r3 0.7443% 0.4090% 1.0205% 1.0309% r4 0.7644% 0.8247% 1.0258% 1.0417% (1+Rn)^n=(1+Rn-1)^n-1(1+Fn) r5 0.6942% 0.4141% 1.0311% 1.0526% Fn=((1+Rn)^n/(1+Rn-1)^n-1)-1 r6 0.7177% 0.8351% 1.0366% 1.0638% r7 0.6750% 0.4193% 1.0421% 1.0753% r8 0.6963% 0.8457% 1.0477% 1.0870% r9 0.6661% 0.4246% 1.0534% 1.0989% r10 0.6851% 0.8565% 1.0592% 1.1111% r11 0.6619% 0.4301% 1.0650% 1.1236% r12 0.6790% 0.8677% 1.0710% 1.1364% r13 0.6603% 0.4357% 1.0770% 1.1494% r14 0.6759% 0.8791% 1.0831% 1.1628% r15 0.6603% 0.4415% 1.0894% 1.1765% r16 0.6747% 0.8909% 1.0957% 1.1905% r17 0.6613% 0.4474% 1.1021% 1.2048% r18 0.6747% 0.9029% 1.1086% 1.2195% r19 0.6630% 0.4535% 1.1152% 1.2346% r20 0.6756% 0.9153% 1.1220% 1.2500% Respuesta Periodo Pago VP Mercado 1 VP Mercado 2 b) 1 200 198.0 198.0 2 190 186.6 186.2 3 180 176.0 174.6 4 170 164.9 163.2 5 160 154.6 152.0 6 150 143.7 141.0 7 140 133.6 130.2 8 130 123.0 119.6 9 120 113.0 109.2 10 110 102.7 99.0 11 100 93.0 89.0 12 90 83.0 79.2 13 80 73.4 69.6 14 70 63.7 60.2 15 60 54.4 51.0 16 50 44.9 42.0 17 40 35.8 33.2 18 30 26.6 24.6 19 20 17.6 16.2 20 10 8.7 8.0 1997.2 1946.0 Le recomiendo hacerlo emitirlo en el Mercado 1 ya que así recibe un financiamiento mayor (TIENE UN MAYOR VALOR PRESENTE) Respuesta c) t=0 t=1 t=2 t=3 t=4 t=5 Vendo 5 M1 4830 0 0 0 0 -5000 Compro 5 M2 -4750 0 0 0 0 5000 Flujo Neto 80 0 0 0 0 0 Como podemos ver, las tasas son más altas en el mercado dos y menos en el mercado uno, por lo tanto para maximizar mi beneficio me convendría endeudarme en el mercado uno (vendiendo cinco bonos a 5 años plazo) y recibir 4830, luego invierto 4750 en cinco bonos a 5 años plazo en el mercado dos y así logro pagar mi deuda en el año 5 y quedarme con un remanente de 80 en t=0 Tasas Forward Mercado 1 frente a Tasa Spot (YTM) Mercado 1 Plazo (Tiempo) Tasas Tasas Forward Mercado 2 frente a Tasas Spot (YTM) Mercado 2 Plazo (Tiempo) Tasas Tema 3a U(W) = Carl Riqueza (W) Utilidad U(W) Rick Riqueza (W) Utilidad U(W) τ = 15 8,000 4.472 τ = 60 8,000 400.000 8,500 4.518 8,500 416.498 9,000 4.561 9,000 432.675 9,500 4.602 9,500 448.555 10,000 4.642 10,000 464.159 10,500 4.679 10,500 479.505 11,000 4.716 11,000 494.609 11,500 4.751 11,500 509.486 12,000 4.785 12,000 524.148 12,500 4.817 12,500 538.609 13,000 4.849 13,000 552.877 13,500 4.880 13,500 566.964 14,000 4.909 14,000 580.879 14,500 4.938 14,500 594.628 15,000 4.966 15,000 608.220 15,500 4.993 15,500 621.662 16,000 5.020 16,000 634.960 16,500 5.046 16,500 648.121 17,000 5.071 17,000 661.149 17,500 5.095 17,500 674.050 18,000 5.119 18,000 686.829 18,500 5.143 18,500 699.489 19,000 5.166 19,000 712.037 19,500 5.188 19,500 724.474 20,000 5.210 20,000 736.806 20,500 5.231 20,500 749.036 21,000 5.253 21,000 761.166 21,500 5.273 21,500 773.201 22,000 5.293 22,000 785.142 22,500 5.313 22,500 796.994 23,000 5.333 23,000 808.758 23,500 5.352 23,500 820.437 24,000 5.371 24,000 832.034 24,500 5.389 24,500 843.550 25,000 5.407 25,000 854.988 25,500 5.425 25,500 866.350 26,000 5.443 26,000 877.638 26,500 5.460 26,500 888.854 27,000 5.477 27,000 900.000 27,500 5.494 27,500 911.077 28,000 5.511 28,000 922.087 28,500 5.527 28,500 933.032 29,000 5.543 29,000 943.913 29,500 5.559 29,500 954.732 30,000 5.574 30,000 965.489 30,500 5.590 30,500 976.187 31,000 5.605 31,000 986.827 31,500 5.620 31,500 997.410 32,000 5.635 32,000 1,007.937 32,500 5.649 32,500 1,018.409 33,000 5.664 33,000 1,028.828 33,500 5.678 33,500 1,039.194 34,000 5.692 34,000 1,049.508 34,500 5.706 34,500 1,059.773 35,000 5.719 35,000 1,069.987 35,500 5.733 35,500 1,080.154 36,000 5.746 36,000 1,090.272 36,500 5.759 36,500 1,100.344 37,000 5.773 37,000 1,110.370 37,500 5.785 37,500 1,120.351 38,000 5.798 38,000 1,130.288 38,500 5.811 38,500 1,140.181 39,000 5.823 39,000 1,150.032 39,500 5.836 39,500 1,159.840 40,000 5.848 40,000 1,169.607 40,500 5.860 40,500 1,179.334 41,000 5.872 41,000 1,189.020 41,500 5.884 41,500 1,198.668 42,000 5.896 42,000 1,208.276 42,500 5.907 42,500 1,217.847 43,000 5.919 43,000 1,227.380 Riqueza vs Utilidad (Carl) Riqueza Utilidad Riqueza vs Utilidad (Rick) Riqueza Utilidad Tema 3b Carl Rick U(W) U(W) τ $ 8,000 $ 43,000 1 1.10501371 1.125856353 2 1.2210553 1.267552528 3 1.349282848 1.427082066 4 1.490976046 1.606689411 5 1.647548972 1.80890148 6 1.820564203 2.036563224 7 2.011748405 2.292877644 8 2.223009569 2.581450862 9 2.456456052 2.906342854 10 2.714417617 3.272124566 11 2.999468682 3.683942231 12 3.314454017 4.147589765 13 3.662517131 4.669590287 14 4.047131645 5.257287891 15 4.472135955 5.918950972 16 4.941771545 6.663888555 17 5.46072531 7.502581266 18 6.034176337 8.446828783 19 6.667847583 9.509915848 20 7.368062997 10.70679918 A medida que va aumentando "τ" (su edad) la utilidad de ambos aumenta ya que producto de la forma de su función de utilidad se aprecia que ambos son aversos alriesgo y que su grado de aversión se determina por sus años. 21 8.141810631 12.05431787 22 8.996812374 13.57143036 23 9.941601023 15.27948109 24 10.98560543 17.20250086 25 12.13924462 19.36754488 26 13.41403174 21.80507345 27 14.82268898 24.54938047 28 16.37927455 27.63907596 29 18.09932294 31.11762927 30 20 35.0339806 31 22.10027421 39.44322964 32 24.421106 44.40741067 33 26.98565695 49.99636543 34 29.81952092 56.28872565 35 32.95097945 63.37301938 36 36.41128406 71.34891648 37 40.2349681 80.32863091 38 44.46019138 90.43849944 39 49.12912104 101.8207592 40 54.28835233 114.6355486 41 59.98937364 129.0631607 42 66.28908035 145.3065794 43 73.25034263 163.5943355 44 80.94263289 184.183722 45 89.4427191 207.3644135 46 98.8354309 233.4625424 47 109.2145062 262.8452865 48 120.6835267 295.9260357 49 133.3569517 333.1702074 50 147.3612599 375.1017946 51 162.8362126 422.3107385 52 179.9362475 475.461228 53 198.8320205 535.3010441 54 219.7121087 602.6720814 55 242.7848924 678.5221916 56 268.2806348 763.9185202 57 296.4537796 860.0625192 58 327.585491 968.3068512 59 361.9864589 1090.17442 60 400 1227.379797 61 442.0054841 1381.853342 62 488.42212 1555.768364 63 539.7131391 1751.571697 64 596.3904183 1972.018123 65 659.019589 2220.209132 66 728.2256812 2499.636556 67 804.699362 2814.231697 68 889.2038277 3168.420635 69 982.5824209 3567.186502 70 1085.767047 4016.139585 71 1199.787473 4521.596267 Utilidad vs τ τ Utilidad Tema 4 Precio S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 Activo 1 587.10 730 950 302 135 845 369 210 470 552 574 Activo 2 395.99 688 403 425 689 395 28 398 270 806 547 Activo 3 539.99 779 744 372 348 487 976 458 855 236 291 Activo 4 471.60 35 527 398 471 411 605 380 700 649 596 Activo 5 494.06 305 144 197 380 935 706 171 748 600 399 Activo 6 316.90 955 459 418 881 133 274 614 212 333 145 Activo 7 570.89 739 810 483 248 932 170 612 332 869 360 Activo 8 545.43 299 400 664 156 713 903 69 716 959 398 Activo 9 630.17 812 154 443 730 900 788 153 868 188 917 Activo 10 676.23 519 654 991 430 608 730 776 994 22 855 t1 Inversion Inicial S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 Proyecto A 500 164 83 347 487 922 734 421 157 598 34 Proyecto B 500 748 142 766 273 766 999 131 453 695 80 Proyecto C 500 83 472 402 867 141 650 510 159 467 989 A) Para encontrar los precios, ocupamos solver para solucionar el sistema de ecuaciones. Proyecto A Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 S1 730 688 779 35 305 955 739 299 812 519 S2 950 403 744 527 144 459 810 400 154 654 S3 302 425 372 398 197 418 483 664 443 991 S4 135 689 348 471 380 881 248 156 730 430 S5 845 395 487 411 935 133 932 713 900 608 S6 369 28 976 605 706 274 170 903 788 730 S7 210 398 458 380 171 614 612 69 153 776 S8 470 270 855 700 748 212 332 716 868 994 S9 552 806 236 649 600 333 869 959 188 22 S10 574 547 291 596 399 145 360 398 917 855 Suma - F en Si Pagos Proyecto A S1 -1193.724178 -2293.060543 -678.8535512 70.60203161 -499.4823015 1095.743927 2317.493523 174.6886702 1844.826206 -674.2337855 0.000E+00 164 S2 -1553.47667 -1343.173545 -648.3530708 1063.064876 -235.8211522 526.6455106 2540.148517 233.6972177 349.8808322 -849.6125159 0.000E+00 83 S3 -493.8420572 -1416.498155 -324.1765354 802.8459595 -322.6164373 479.6031011 1514.681153 387.9373814 1006.475381 -1287.409791 0.000E+00 347 S4 -220.757211 -2296.393479 -303.2619202 950.1016254 -622.3058182 1010.838115 777.7244842 91.14191491 1658.526023 -558.6137337 0.000E+00 487 S5 -1381.776617 -1316.51005 -424.3923998 829.0695712 -1531.199842 152.6009867 2922.738787 416.5652906 2044.75811 -789.8538374 0.000E+00 922 S6 -603.4030434 -93.32223139 -850.5276842 1220.406546 -1156.178704 314.3809802 533.11759 527.571469 1790.299323 -948.3442455 0.000E+00 734 S7 -343.400106 -1326.50886 -399.1205731 766.5363432 -280.0376182 704.4887658 1919.223324 40.31277005 347.6088788 -1008.102924 0.000E+00 421 S8 -768.5621421 -899.8929455 -745.083166 1412.040632 -1224.959874 243.2436781 1041.147293 418.3180197 1972.0556 -1291.307096 0.000E+00 157 S9 -902.6517073 -2686.347089 -205.6603827 1309.163386 -982.588134 382.0761547 2725.171681 560.2890795 427.1272497 -28.58023754 0.000E+00 598 S10 -938.6269565 -1823.116449 -253.5897091 1202.251738 -653.4211091 166.3694968 1128.954896 232.5287316 2083.381319 -1110.731959 0.000E+00 34 Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 0.000E+00 Variables Proyecto A -1.6352386001 -3.3329368352 -0.8714422994 2.0172009032 -1.63764689 1.1473758401 3.1359858234 0.5842430443 2.2719534561 -1.2991017062 Precio 587.10 395.99 539.99 471.60 494.06 316.90 570.89 545.43 630.17 676.23 Precio Portafolio imitador 417.5894231 VPN -82.41057692 Proyecto B Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 S1 730 688 779 35 305 955 739 299 812 519 S2 950 403 744 527 144 459 810 400 154 654 S3 302 425 372 398 197 418 483 664 443 991 S4 135 689 348 471 380 881 248 156 730 430 S5 845 395 487 411 935 133 932 713 900 608 S6 369 28 976 605 706 274 170 903 788 730 S7 210 398 458 380 171 614 612 69 153 776 S8 470 270 855 700 748 212 332 716 868 994 S9 552 806 236 649 600 333 869 959 188 22 S10 574 547 291 596 399 145 360 398 917 855 Sumaproducto - F en Si Pagos Proyecto B S1 -616.8369126 -819.1541136 -60.79458058 -4.569452271 -277.3617171 574.9677659 894.6696642 412.8474157 876.9199269 -232.6879967 0.000E+00 748 S2 -802.7329684 -479.8242846 -58.06311676 -68.80289562 -130.9511058 276.3457639 980.6257484 552.3042351 166.3123999 -293.2137762 0.000E+00 142 S3 -255.1845857 -506.0181661 -29.03155838 -51.96120011 -179.1483878 251.6612839 584.7435018 916.8250303 478.4181375 -444.3040554 0.000E+00 766 S4 -114.0725797 -820.3447446 -27.15855461 -61.49177199 -345.5654181 530.4152898 300.2409699 215.3986517 788.3639737 -192.7858162 0.000E+00 273 S5 -714.0098509 -470.2992367 -38.00636809 -53.65842524 -850.272805 80.07404489 1128.324935 984.4822991 971.955584 -272.5901773 0.000E+00 766 S6 -311.7983846 -33.33766741 -76.16881983 -78.9862464 -642.0241715 164.9645737 205.8103422 1246.826811 851.0011113 -327.2875484 9.998E-09 999 S7 -177.4462351 -473.8711297 -35.74315521 -49.61119608 -155.5044381 369.6651396 740.9172321 95.27248056 165.2324493 -347.9111473 0.000E+00 131 S8 -397.1415738 -321.4703643 -66.72575918 -91.38904542 -680.218244 127.6368234 401.9354919 988.6245808 937.3971633 -445.6490727 0.000E+00 453 S9 -466.4301038 -959.6485691 -18.41787037 -84.73070068 -545.6296075 200.4861425 1052.054044 1324.149404 203.030722 -9.863460361 0.000E+00 695 S10 -485.0197093 -651.2751455 -22.71017067 -77.81124439 -362.843689 87.29877075 435.8336659 549.5427139 990.3147451 -383.3299368 0.000E+00 80 Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 1.000E-08 Variables Proyecto B -0.844982072 -1.1906309791 -0.0780418236 -0.1305557792 -0.9093826791 0.6020604879 1.210649072 1.3807605878 1.0799506489 -0.4483391073 Precio 587.10 395.99 539.99 471.60 494.06 316.90 570.89 545.43 630.17 676.23 Precio Portafolio imitador 491.8538462 VPN -8.14615 Proyecto C Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 S1 730 688 779 35 305 955 739 299 812 519 S2 950 403 744 527 144 459 810 400 154 654 S3 302 425 372 398 197 418 483 664 443 991 S4 135 689 348 471 380 881 248 156 730 430 S5 845 395 487 411 935 133 932 713 900 608 S6 369 28 976 605 706 274 170 903 788 730 S7 210 398 458 380 171 614 612 69 153 776 S8 470 270 855 700 748 212 332 716 868 994 S9 552 806 236 649 600 333 869 959 188 22 S10 574 547 291 596 399 145 360 398 917 855 Sumaproducto- F en Si Pagos Proyecto C S1 -2423.158071 -2276.877012 312.0395328 167.5636391 -1817.211398 -337.7663918 3744.647977 52.81602604 4082.170925 -1421.225227 0.000E+00 83 S2 -3153.424887 -1333.693948 298.0197848 2523.029652 -857.9621026 -162.3400773 4104.417945 70.65689103 774.2048305 -1790.908089 0.000E+00 472 S3 -1002.457175 -1406.501061 149.0098924 1905.437954 -1173.739821 -147.8391118 2447.449219 117.2904391 2227.095714 -2713.746049 0.000E+00 402 S4 -448.1182734 -2280.186426 139.396351 2254.927829 -2264.06666 -311.5939174 1256.661297 27.5561875 3669.931989 -1177.508377 0.000E+00 867 S5 -2804.888452 -1307.218633 195.0747785 1967.675877 -5570.795597 -47.03971739 4722.614228 125.9459083 4524.573685 -1664.942077 0.000E+00 141 S6 -1224.856614 -92.66359933 390.9506855 2896.457191 -4206.397531 -96.90889146 861.4210502 159.5079315 3961.515626 -1999.025849 0.000E+00 650 S7 -697.0728697 -1317.146876 183.4584159 1819.262368 -1018.829997 -217.1608006 3101.115781 12.1883137 769.1775264 -2124.991861 0.000E+00 510 S10 -1560.11547 -893.5418507 342.482414 3351.272783 -4456.636477 -74.98060215 1682.304639 126.4758349 4363.699954 -2721.961224 0.000E+00 159 S9 -1832.305829 -2667.387895 94.53315755 3107.108623 -3574.842094 -117.7761345 4403.381721 169.3998962 945.1331697 -60.24461462 0.000E+00 467 -1905.332511 -1810.249601 116.56419 2853.369398 -2377.269993 -51.28390241 1824.185753 70.30360657 4610.037854 -2341.324795 0.000E+00 989 Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 0.000E+00 Variables Proyecto C -3.3193946177 -3.3094142619 0.4005642269 4.7875325466 -5.9580701569 -0.3536820856 5.067182648 0.1766422276 5.0273040943 -2.7383915734 Precio 587.10 395.99 539.99 471.60 494.06 316.90 570.89 545.43 630.17 676.23 Proyecto libre de riesgo Variables Proyecto C Precio Portafolio imitador Libre de Riesgo Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 Precio Precio Portafolio imitador S1 730 688 779 35 305 955 739 299 812 519 -0.0011186884 Activo 1 587.10 0.9615384615 464.5259615 S2 950 403 744 527 144 459 810 400 154 654 -0.0007147588 Activo 2 395.99 Tasa libre de riesgo S3 302 425 372 398 197 418 483 664 443 991 0.0003506491 Activo 3 539.99 4% VPN -35.47403846 S4 135 689 348 471 380 881 248 156 730 430 0.0014493831 Activo 4 471.60 S5 845 395 487 411 935 133 932 713 900 608 -0.0015422323 Activo 5 494.06 S6 369 28 976 605 706 274 170 903 788 730 0.0000904114 Activo 6 316.90 S7 210 398 458 380 171 614 612 69 153 776 0.0018752599 Activo 7 570.89 S8 470 270 855 700 748 212 332 716 868 994 0.0001822431 Activo 8 545.43 S9 552 806 236 649 600 333 869 959 188 22 0.0014436889 Activo 9 630.17 B) Para encontrar los activos puros para cadas estado es necesario tener la matriz inversa de los pagos de los activos. Esta matriz nos dice cuanto de cada activo hay que comprar o vender para hacer una activo que pague 1 en el estado Si y 0 en el resto. S10 574 547 291 596 399 145 360 398 917 855 -0.0004701977 Activo 10 676.23 Libre de Riesgo Matris Inversa S1 -0.8166425158 -0.4917540474 0.2731556336 0.0507284095 -0.4703808563 0.0863428795 1.38581703 0.0544906964 1.172275353 -0.2440325824 0.00000E+00 1 Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 Precio S2 -1.062753959 -0.2880477923 0.2608829158 0.7638249091 -0.2220814535 0.041498829 1.51896048 0.0728972527 0.2223280841 -0.3075092657 0.00000E+00 1 S1 -0.0011195598 0.0014283016 0.0018251524 -0.0010597593 -0.0011830872 -0.0012665493 0.0008198101 -0.0000066862 0.0008581244 -0.0005401468 Ac. Puro S1 0.04808 S3 -0.3378438901 -0.3037724856 0.1304414579 0.5768544855 -0.3038197662 0.0377919619 0.9057505083 0.1210094394 0.6395541641 -0.4659658751 0.00000E+00 1 S2 0.0032348266 -0.0005960172 -0.0015052603 -0.000089222 0.0017892851 0.0018047604 -0.0024885065 -0.000039907 -0.0020526715 0.0009109568 Ac. Puro S2 0.14423 S4 -0.151022931 -0.4924688061 0.12202588 0.6826594539 -0.58604828 0.0796524364 0.4650644432 0.0284299285 1.053892866 -0.2021849912 0.00000E+00 1 S3 0.0021722337 0.0000069703 -0.0023133342 -0.0018173492 0.0020373372 0.0019078508 -0.0025982677 0.0013258776 -0.0021051048 0.0020516582 Ac. Puro S3 0.08365 S5 -0.9452916793 -0.282329722 0.1707661021 0.5956964661 -1.441987215 0.0120247152 1.747742182 0.1299393529 1.299319972 -0.2858801736 0.00000E+00 1 S4 0.0030234858 -0.0006335763 -0.0027417811 -0.0003142171 0.0033504747 0.0031240871 -0.0033713645 -0.0000581984 -0.0021153521 0.0011497276 Ac. Puro S4 0.02885 S6 -0.4127960114 -0.0200132461 0.3422335025 0.8768767932 -1.088816015 0.0247727214 0.3187941748 0.1645655479 1.13762682 -0.3432442874 0.00000E+00 1 S5 0.0013224929 -0.0016712878 -0.0019192681 -0.0003254761 0.0017656609 0.0014037979 -0.0001670044 -0.0000405917 -0.0003864499 0.0005031305 Ac. Puro S5 0.22115 S7 -0.2349245594 -0.2844739983 0.1605972788 0.5507655891 -0.263721726 0.0555125947 1.147659029 0.0125747761 0.2208843953 -0.3648733795 0.00000E+00 1 S6 -0.0037755774 -0.0036591288 0.0014265938 0.0034896521 -0.0056342913 -0.0006769902 0.0051797819 0.0007284866 0.004805718 -0.0029725185 Ac. Puro S6 0.12500 S8 -0.5257835376 -0.1929848732 0.2998049637 1.01456819 -1.153589772 0.0191672151 0.6225862707 0.1304860823 1.253121929 -0.4673764681 0.00000E+00 1 S7 -0.0047906855 -0.001093284 0.0024718377 0.0024658188 -0.0041352527 -0.0021913425 0.0055612867 -0.0009029258 0.0033320696 -0.001838069 Ac. Puro S7 0.05385 S9 -0.6175159846 -0.5760955845 0.082753183 0.9406496509 -0.9253393895 0.0301069936 1.629600811 0.1747711633 0.2714135053 -0.0103443484 0.00000E+00 1 S8 0.0037369128 0.0051368811 0.0001461246 -0.004280335 0.0071060323 -0.0001279877 -0.0067355971 -0.0008149911 -0.0059679251 0.003460486 Ac. Puro S8 0.04808 S10 -0.6421271289 -0.390973058 0.1020388824 0.8638323451 -0.615350694 0.0131096518 0.6750935465 0.0725327664 1.323862683 -0.4020189942 0.00000E+00 1 S9 -0.0014128185 0.0011639668 0.0011530922 0.0004250156 -0.0010144296 -0.0012424398 0.0011113253 0.0002979017 0.000448145 -0.0008880362 Ac. Puro S9 0.03846 S10 -0.0035099989 -0.0007975844 0.0018074923 0.0029552554 -0.0056239617 -0.0026447752 0.004563796 -0.0003067227 0.0046271352 -0.0023073862 Ac. Puro S10 0.17019 0.0000E+00 Activo 1 Activo 2 Activo 3 Activo 4 Activo 5 Activo 6 Activo 7 Activo 8 Activo 9 Activo 10 Precio 587.10 395.99 539.99 471.60 494.06 316.90 570.89 545.43 630.17 676.23 Teniendo el precio de los activos puros hay que multipilcarlos por el pago que hace el proyecto en cada estado. Restandole la inversión inicial, queda el VPN del proyecto. Ac. Puro S1 Ac. Puro S2 Ac. Puro S3 Ac. Puro S4 Ac. Puro S5 Ac. Puro S6 Ac. Puro S7 Ac. Puro S8 Ac. Puro S9 Ac. Puro S10 Precio 0.0480769231 0.1442307692 0.0836538462 0.0288461538 0.2211538462 0.125 0.0538461538 0.0480769231 0.0384615385 0.1701923077 Proyecto A Inversion Inicial S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 500 164 83 347 487 922 734 421 157 598 34 VPN -82.41057692 Proyecto B Inversion Inicial S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 500 748 142 766 273 766 999 131 453 695 80 VPN -8.146153846 Proyecto C Inversion Inicial S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 500 83 472 402 867 141 650 510 159 467 989 VPN -35.47403846
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