Año FC( Millones) r VPN0 -100 1% S/. 2,509.841 30 5% S/. 499.972 30 10% S/. 200.003 30 15% S/. 100.004 30 20% S/. 50.005 30 25% S/. 20.006 30 30% S/. 0.007 30 35% S/. -14.298 30 40% S/. -25.009 30 45% S/. -33.33

10 30 50% S/. -40.0011 30 35% S/. -14.2912 30 40% S/. -25.0013 30 45% S/. -33.3314 30 50% S/. -40.0015 30 55% S/. -45.4516 30 60% S/. -50.0017 30 65% S/. -53.8518 30 70% S/. -57.1419 30 75% S/. -60.0020 30 80% S/. -62.5021 30 85% S/. -64.7122 30 90% S/. -66.6723 30 95% S/. -68.4224 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 30

0% 15% 30% 45% 60% 75% 90% 105%

S/. -500.00

S/. 0.00

S/. 500.00

S/. 1,000.00

S/. 1,500.00

S/. 2,000.00

S/. 2,500.00

S/. 3,000.00

VPN

VPN

r(Costo de capital)

44 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 30

92 3093 3094 3095 3096 3097 3098 3099 30

100 30101 30102 30103 30104 30105 30106 30107 30108 30109 30110 30111 30112 30113 30114 30115 30116 30117 30118 30119 30120 30121 30122 30123 30124 30125 30126 30127 30128 30129 30130 30131 30132 30133 30134 30135 30136 30137 30138 30139 30

140 30141 30142 30143 30144 30145 30146 30147 30148 30149 30150 30151 30152 30153 30154 30155 30156 30157 30158 30159 30160 30161 30162 30163 30164 30165 30166 30167 30168 30169 30170 30171 30172 30173 30174 30175 30176 30177 30178 30179 30180 30181 30182 30183 30184 30185 30186 30187 30

188 30189 30190 30191 30192 30193 30194 30195 30196 30197 30198 30199 30200 30201 30202 30203 30204 30205 30

Costo de Capital = 8%

VPN= $275 TIR= 30% ∆(TIR-r)= 22%

Respuesta:El VPN=

0% 15% 30% 45% 60% 75% 90% 105%

S/. -500.00

S/. 0.00

S/. 500.00

S/. 1,000.00

S/. 1,500.00

S/. 2,000.00

S/. 2,500.00

S/. 3,000.00

VPN

VPN

r(Costo de capital)

TIR = 30 %

Año FC( Maillones) r VPN0 10 10.00% S/. -9.891 -8 15.00% S/. -8.272 -8 20.00% S/. -6.853 -8 25.00% S/. -5.62

30.00% S/. -4.5335.00% S/. -3.5740.00% S/. -2.7145.00% S/. -1.9550.00% S/. -1.2655.00% S/. -0.6460.00% S/. -0.0860.74% S/. 0.0070.00% S/. 0.9075.00% S/. 1.3280.00% S/. 1.7185.00% S/. 2.0790.00% S/. 2.4195.00% S/. 2.71

100.00% S/. 3.00

Costo de Capital = 10%

VPN= S/. -9.89TIR= 60.74%

0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

S/. -12.00

S/. -10.00

S/. -8.00

S/. -6.00

S/. -4.00

S/. -2.00

S/. 0.00

S/. 2.00

S/. 4.00

VPN

VPN

r (costo del capital)

0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

S/. -12.00

S/. -10.00

S/. -8.00

S/. -6.00

S/. -4.00

S/. -2.00

S/. 0.00

S/. 2.00

S/. 4.00

VPN

VPN

r (costo del capital)

Libro My Way de Bill Clinton

Año FC (Millones) r VPN(Millones)0 10 1.000% S/. 2.131 -8 1.500% S/. 1.882 -8 2.000% S/. 1.653 -8 2.500% S/. 1.444 5 Decrecimiento 3.000% S/. 1.245 3.5 30% 3.500% S/. 1.056 2.4 4.000% S/. 0.877 1.7 4.500% S/. 0.718 1.2 5.000% S/. 0.559 0.8 5.500% S/. 0.41

10 0.6 6.000% S/. 0.2811 0.4 6.500% S/. 0.1512 0.3 7.165% S/. 0.0013 0.2 7.665% S/. -0.1114 0.1 8.165% S/. -0.2015 0.1 8.665% S/. -0.2916 0.1 9.165% S/. -0.3817 0.0 9.665% S/. -0.4518 0.0 10.165% S/. -0.5319 0.0 10.665% S/. -0.5920 0.0 11.165% S/. -0.6521 0.0 11.665% S/. -0.7122 0.0 12.165% S/. -0.7623 0.0 12.665% S/. -0.8024 0.0 13.165% S/. -0.8425 0.0 13.665% S/. -0.8826 0.0 14.165% S/. -0.9127 0.0 14.665% S/. -0.9428 0.0 15.165% S/. -0.9729 0.0 15.665% S/. -0.9930 0.0 16.165% S/. -1.0131 0.0 16.665% S/. -1.0332 0.0 17.165% S/. -1.0433 0.0 17.665% S/. -1.0534 0.0 18.165% S/. -1.0635 0.0 18.665% S/. -1.0636 0.0 19.165% S/. -1.0637 0.0 19.665% S/. -1.0738 0.0 20.165% S/. -1.0639 0.0 20.665% S/. -1.0640 0.0 21.165% S/. -1.0641 0.0 21.665% S/. -1.0542 0.0 22.165% S/. -1.0443 0.0 22.665% S/. -1.03

44 0.0 23.165% S/. -1.0245 0.0 23.665% S/. -1.0046 0.0 24.165% S/. -0.9947 0.0 24.665% S/. -0.9748 0.0 25.165% S/. -0.9649 0.0 25.665% S/. -0.9450 0.0 26.165% S/. -0.9251 0.0 26.665% S/. -0.9052 0.0 27.165% S/. -0.8853 0.0 27.665% S/. -0.8554 0.0 28.165% S/. -0.8355 0.0 28.665% S/. -0.8056 0.0 29.165% S/. -0.7857 0.0 29.665% S/. -0.7558 0.0 30.165% S/. -0.7359 0.0 30.665% S/. -0.7060 0.0 31.165% S/. -0.6761 0.0 31.665% S/. -0.6462 0.0 32.165% S/. -0.6163 0.0 32.665% S/. -0.5864 0.0 33.165% S/. -0.5565 0.0 33.665% S/. -0.5266 0.0 34.165% S/. -0.4967 0.0 34.665% S/. -0.4668 0.0 35.165% S/. -0.4369 0.0 35.665% S/. -0.4070 0.0 36.165% S/. -0.3771 0.0 36.665% S/. -0.3372 0.0 37.165% S/. -0.3073 0.0 37.665% S/. -0.2774 0.0 38.165% S/. -0.2375 0.0 38.665% S/. -0.2076 0.0 39.165% S/. -0.1777 0.0 39.665% S/. -0.1378 0.0 40.165% S/. -0.1079 0.0 40.665% S/. -0.0680 0.0 41.165% S/. -0.0381 0.0 41.170% S/. -0.0382 0.0 41.220% S/. -0.0283 0.0 41.320% S/. -0.0284 0.0 41.330% S/. -0.0285 0.0 41.430% S/. -0.0186 0.0 41.480% S/. -0.0187 0.0 41.580% S/. 0.0088 0.0 42.080% S/. 0.0489 0.0 42.580% S/. 0.0790 0.0 43.080% S/. 0.1191 0.0 43.580% S/. 0.14

92 0.0 44.080% S/. 0.1893 0.0 44.580% S/. 0.2194 0.0 45.080% S/. 0.2595 0.0 45.580% S/. 0.2896 0.0 46.080% S/. 0.3297 0.0 46.580% S/. 0.3598 0.0 47.080% S/. 0.3999 0.0 47.580% S/. 0.42

100 0.0 48.080% S/. 0.46101 0.0 48.580% S/. 0.49102 0.0 49.080% S/. 0.53103 0.0 49.580% S/. 0.56104 0.0 50.080% S/. 0.60105 0.0 50.580% S/. 0.63106 0.0 51.080% S/. 0.67107 0.0 51.580% S/. 0.70108 0.0 52.080% S/. 0.74109 0.0 52.580% S/. 0.77110 0.0 53.080% S/. 0.81

Costo de Capital = 10%

VPN(US $ Millone)= S/. -0.50TIR 1= 7.165%TIR 2= 41.580%

0.000% 10.000% 20.000% 30.000% 40.000% 50.000% 60.000%

$ -1.5

$ -1.0

$ -0.5

$ 0.0

$ 0.5

$ 1.0

$ 1.5

$ 2.0

$ 2.5

VPN(Millones)

VPN(Millones)

r ( tasa de descuento)

TIR 1 = 7.165 %

TIR 2 = 41.580 %

0.000% 10.000% 20.000% 30.000% 40.000% 50.000% 60.000%

$ -1.5

$ -1.0

$ -0.5

$ 0.0

$ 0.5

$ 1.0

$ 1.5

$ 2.0

$ 2.5

VPN(Millones)

VPN(Millones)

r ( tasa de descuento)

TIR 1 = 7.165 %

TIR 2 = 41.580 %

FastTrack Bike, Inc, Bicicleta de carrera

Escenario con desarrollo de planta a 6 años según el enunciadoAño FC (US $) r VPN(Millones)

0 0 1.00% S/. 1,517,623.90Desarrollo 1 -200000 1.50% S/. 1,390,785.63Desarrollo 2 -200000 2.00% S/. 1,272,597.35Desarrollo 3 -200000 2.50% S/. 1,162,438.12Desarrollo 4 -200000 3.00% S/. 1,059,734.89Desarrollo 5 -200000 3.50% S/. 963,958.53Desarrollo 6 -200000 4.00% S/. 874,620.25

7 300000 4.50% S/. 791,268.278 300000 5.00% S/. 713,484.839 300000 5.50% S/. 640,883.46

10 300000 6.00% S/. 573,106.4211 300000 6.50% S/. 509,822.4812 300000 7.00% S/. 450,724.7513 300000 7.50% S/. 395,528.8114 300000 8.00% S/. 343,970.9115 300000 8.50% S/. 295,806.3916 300000 9.00% S/. 250,808.16

9.50% S/. 208,765.4010.00% S/. 169,482.24

Año FC (US $) 10.50% S/. 132,776.710 0 11.00% S/. 98,479.61

Desarrollo 1 -200000 11.50% S/. 66,433.57Desarrollo 2 -200000 12.00% S/. 36,492.18Desarrollo 3 -200000 12.50% S/. 8,519.17Desarrollo 4 -200000 12.66% S/. 0.00Desarrollo 5 -200000 13.00% S/. -17,612.38Desarrollo 6 -200000 13.50% S/. -42,020.67Desarrollo 7 -200000 14.00% S/. -64,815.87

8 300000 14.50% S/. -86,100.689 300000 15.00% S/. -105,970.89

10 300000 15.50% S/. -124,515.8411 300000 16.00% S/. -141,818.9512 300000 16.50% S/. -157,958.0613 300000 17.00% S/. -173,005.9114 300000 17.50% S/. -187,030.4315 300000 18.00% S/. -200,095.1216 300000 18.50% S/. -212,259.3617 300000 19.00% S/. -223,578.66

19.50% S/. -234,104.9720.00% S/. -243,886.9020.50% S/. -252,969.9621.00% S/. -261,396.7821.50% S/. -269,207.26

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

S/. -500,000.00

S/. 0.00

S/. 500,000.00

S/. 1,000,000.00

S/. 1,500,000.00

S/. 2,000,000.00

VPN(US$)

VPN(Millones)

r (Costo de Capital)

Axis Title

22.00% S/. -276,438.8322.50% S/. -283,126.5323.00% S/. -289,303.2523.50% S/. -294,999.8224.00% S/. -300,245.1424.50% S/. -305,066.3825.00% S/. -309,489.0025.50% S/. -313,536.9126.00% S/. -317,232.5926.50% S/. -320,597.1227.00% S/. -323,650.3427.50% S/. -326,410.8828.00% S/. -328,896.2628.50% S/. -331,122.9429.00% S/. -333,106.4129.50% S/. -334,861.2530.00% S/. -336,401.1630.50% S/. -337,739.0631.00% S/. -338,887.0831.50% S/. -339,856.6632.00% S/. -340,658.5732.50% S/. -341,302.9533.00% S/. -341,799.3633.50% S/. -342,156.8034.00% S/. -342,383.7534.50% S/. -342,488.2235.00% S/. -342,477.7235.50% S/. -342,359.3836.00% S/. -342,139.8936.50% S/. -341,825.5837.00% S/. -341,422.3937.50% S/. -340,935.9738.00% S/. -340,371.6038.50% S/. -339,734.3039.00% S/. -339,028.7939.50% S/. -338,259.5340.00% S/. -337,430.7140.50% S/. -336,546.3341.00% S/. -335,610.1141.50% S/. -334,625.6142.00% S/. -333,596.1642.50% S/. -332,524.9143.00% S/. -331,414.8543.50% S/. -330,268.7844.00% S/. -329,089.3744.50% S/. -327,879.1145.00% S/. -326,640.3845.50% S/. -325,375.40

46.00% S/. -324,086.3046.50% S/. -322,775.0647.00% S/. -321,443.5647.50% S/. -320,093.5848.00% S/. -318,726.8048.50% S/. -317,344.7949.00% S/. -315,949.0649.50% S/. -314,541.0150.00% S/. -313,121.9750.50% S/. -311,693.2051.00% S/. -310,255.8851.50% S/. -308,811.1352.00% S/. -307,360.0052.50% S/. -305,903.4853.00% S/. -304,442.5253.50% S/. -302,977.9954.00% S/. -301,510.7354.50% S/. -300,041.5155.00% S/. -298,571.0855.50% S/. -297,100.12

Costo de Capital = 10%

Escenario con desarrallo de planta en 6 años:VPN(US $ Millone)= S/. 169,482.24

TIR= 12.66% ∆(TIR-r)= 2.66%

Escenario con desarrallo de planta en 7 años:VPN(US $ Millone)= S/. -27,743.42

TIR= 9.61%

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

S/. -500,000.00

S/. 0.00

S/. 500,000.00

S/. 1,000,000.00

S/. 1,500,000.00

S/. 2,000,000.00

VPN(US$)

VPN(Millones)

r (Costo de Capital)

Axis Title

FastTrack Bike, Inc, Bicicleta de carrera

Escenario con desarrollo de planta a 6 años según el enunciadoAño FC (US $) r VPN(Millones)

0 0 1.00% S/. 1,517,623.90Desarrollo 1 -200000 1.50% S/. 1,390,785.63Desarrollo 2 -200000 2.00% S/. 1,272,597.35Desarrollo 3 -200000 2.50% S/. 1,162,438.12Desarrollo 4 -200000 3.00% S/. 1,059,734.89Desarrollo 5 -200000 3.50% S/. 963,958.53Desarrollo 6 -200000 4.00% S/. 874,620.25

7 300000 4.50% S/. 791,268.278 300000 5.00% S/. 713,484.839 300000 5.50% S/. 640,883.46

10 300000 6.00% S/. 573,106.4211 300000 6.50% S/. 509,822.4812 300000 7.00% S/. 450,724.7513 300000 7.50% S/. 395,528.8114 300000 8.00% S/. 343,970.9115 300000 8.50% S/. 295,806.3916 300000 9.00% S/. 250,808.16

9.50% S/. 208,765.4010.00% S/. 169,482.24

Año FC (US $) 10.50% S/. 132,776.710 0 11.00% S/. 98,479.61

Desarrollo 1 -200000 11.50% S/. 66,433.57Desarrollo 2 -200000 12.00% S/. 36,492.18Desarrollo 3 -200000 12.50% S/. 8,519.17Desarrollo 4 -200000 12.66% S/. 0.00Desarrollo 5 -200000 13.00% S/. -17,612.38

6 300000 13.50% S/. -42,020.677 300000 14.00% S/. -64,815.878 300000 14.50% S/. -86,100.689 300000 15.00% S/. -105,970.89

10 300000 15.50% S/. -124,515.8411 300000 16.00% S/. -141,818.9512 300000 16.50% S/. -157,958.0613 300000 17.00% S/. -173,005.9114 300000 17.50% S/. -187,030.4315 300000 18.00% S/. -200,095.12

18.50% S/. -212,259.3619.00% S/. -223,578.6619.50% S/. -234,104.9720.00% S/. -243,886.9020.50% S/. -252,969.9621.00% S/. -261,396.7821.50% S/. -269,207.26

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

S/. -500,000.00

S/. 0.00

S/. 500,000.00

S/. 1,000,000.00

S/. 1,500,000.00

S/. 2,000,000.00

VPN(US$)

VPN(Millones)

r (Costo de Capital)

22.00% S/. -276,438.8322.50% S/. -283,126.5323.00% S/. -289,303.2523.50% S/. -294,999.8224.00% S/. -300,245.1424.50% S/. -305,066.3825.00% S/. -309,489.0025.50% S/. -313,536.9126.00% S/. -317,232.5926.50% S/. -320,597.1227.00% S/. -323,650.3427.50% S/. -326,410.8828.00% S/. -328,896.2628.50% S/. -331,122.9429.00% S/. -333,106.4129.50% S/. -334,861.2530.00% S/. -336,401.1630.50% S/. -337,739.0631.00% S/. -338,887.0831.50% S/. -339,856.6632.00% S/. -340,658.5732.50% S/. -341,302.9533.00% S/. -341,799.3633.50% S/. -342,156.8034.00% S/. -342,383.7534.50% S/. -342,488.2235.00% S/. -342,477.7235.50% S/. -342,359.3836.00% S/. -342,139.8936.50% S/. -341,825.5837.00% S/. -341,422.3937.50% S/. -340,935.9738.00% S/. -340,371.6038.50% S/. -339,734.3039.00% S/. -339,028.7939.50% S/. -338,259.5340.00% S/. -337,430.7140.50% S/. -336,546.3341.00% S/. -335,610.1141.50% S/. -334,625.6142.00% S/. -333,596.1642.50% S/. -332,524.9143.00% S/. -331,414.8543.50% S/. -330,268.7844.00% S/. -329,089.3744.50% S/. -327,879.1145.00% S/. -326,640.3845.50% S/. -325,375.40

46.00% S/. -324,086.3046.50% S/. -322,775.0647.00% S/. -321,443.5647.50% S/. -320,093.5848.00% S/. -318,726.8048.50% S/. -317,344.7949.00% S/. -315,949.0649.50% S/. -314,541.0150.00% S/. -313,121.9750.50% S/. -311,693.2051.00% S/. -310,255.8851.50% S/. -308,811.1352.00% S/. -307,360.0052.50% S/. -305,903.4853.00% S/. -304,442.5253.50% S/. -302,977.9954.00% S/. -301,510.7354.50% S/. -300,041.5155.00% S/. -298,571.0855.50% S/. -297,100.12

Costo de Capital(r) = 14%

Escenario con desarrallo de planta en 6 años:VPN(US $ Millone)= S/. -64,815.87

TIR= 12.66% ∆(TIR-r)= 1.34%

Escenario con desarrallo de planta en 5 años:VPN(US $ Millone)= S/. 126,109.91

TIR= 16.93%

El desarrollo de la planta no deberia tomar mas de 5 años para cambiar la decisión de No invertir en el desarrollo de la planta.

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

S/. -500,000.00

S/. 0.00

S/. 500,000.00

S/. 1,000,000.00

S/. 1,500,000.00

S/. 2,000,000.00

VPN(US$)

VPN(Millones)

r (Costo de Capital)

Mes 0 Mes 1 Mes 2 Mes 3 Mes 4 Mes 5Inversión -$5,000Recuperación $500 $500 $500 $500 $500Flujo -$4,500 -$4,000 -$3,500 -$3,000 -$2,500

Mes 6 Mes 7 Mes 8 Mes 9 Mes 10 Mes 11 Mes 12

$500 $500 $500 $500 $500 $500 $500-$2,000 -$1,500 -$1,000 -$500 $0 $500 $1,000

Costo de Capital =

VPN=TIR=

Respuesta:Debido a que el VPN > 0Y el el TIR =30% > r= 30%La regla del TIR está de acuerdo con la del VPN

8%

S/. 275.0030.00%

Debido a que el VPN > 0Y el el TIR =30% > r= 30%La regla del TIR está de acuerdo con la del VPN

Respuesta:El problema tiene dos TIR, el primero es de 7.165% y el segundo es de 41.580 %La regla del TIR no funciona, lo que se puede concluir de la regla del VPN es que si el costo del capital esta por debajo 7.165% o por arriba de 41.580% se debe aceptar la inversión.ya que para esos rangos el VPN es mayor que CERO

0.000% 10.000% 20.000% 30.000% 40.000% 50.000% 60.000%

$ -1.5

$ -1.0

$ -0.5

$ 0.0

$ 0.5

$ 1.0

$ 1.5

$ 2.0

$ 2.5

VPN(Millones)

VPN(Millones)

r ( tasa de descuento)

TIR 1 = 7.165 %

TIR 2 = 41.580 %

VPN(US $ Millone)= S/. -0.50

El problema tiene dos TIR, el primero es de 7.165% y el segundo es de 41.580 %La regla del TIR no funciona, lo que se puede concluir de la regla del VPN es que si el costo del capital esta por debajo 7.165% o por arriba de 41.580% se debe aceptar la inversión.

0.000% 10.000% 20.000% 30.000% 40.000% 50.000% 60.000%

$ -1.5

$ -1.0

$ -0.5

$ 0.0

$ 0.5

$ 1.0

$ 1.5

$ 2.0

$ 2.5

VPN(Millones)

VPN(Millones)

r ( tasa de descuento)

TIR 1 = 7.165 %

TIR 2 = 41.580 %

TEA=(TEM)r=

Año FC (Millones) r VPN(Millones)0 $50,000 1% S/. 99,522.34 VPN=1 $4,400 2% S/. 96,531.50 TIR=2 $4,400 3% S/. 93,797.623 $4,400 4% S/. 91,294.324 $4,400 5% S/. 88,998.315 $4,400 6% S/. 86,888.916 $4,400 7% S/. 84,947.827 $4,400 8% S/. 83,158.748 $4,400 9% S/. 81,507.199 $4,400 10% S/. 79,980.24

10 $4,400 11% S/. 78,566.3711 $4,400 12% S/. 77,255.2512 $4,400 13% S/. 76,037.65

14% S/. 74,905.2915% S/. 73,850.7216% S/. 72,867.2717% S/. 71,948.9018% S/. 71,090.1919% S/. 70,286.2220% S/. 69,532.55

21% S/. 68,825.18 Respuesta:22% S/. 68,160.45 La Regla del TIR no se puede aplicar porque no existe TIR para el problema23% S/. 67,535.06 Nunca intersecta el eje de abcisas para cumplir la condición VPN=024% S/. 66,946.00 La regla de VPN aconseja invertir dado VPN = $ 98,990 que es mayor que CERO25% S/. 66,390.54 y mayor a la inversión incial.26% S/. 65,866.1827% S/. 65,370.6528% S/. 64,901.8829% S/. 64,457.9530% S/. 64,037.1431% S/. 63,637.8532% S/. 63,258.6233% S/. 62,898.1034% S/. 62,555.0635% S/. 62,228.3636% S/. 61,916.9537% S/. 61,619.8738% S/. 61,336.2239% S/. 61,065.1840% S/. 60,805.9841% S/. 60,557.9142% S/. 60,320.3343% S/. 60,092.61

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. 0.00

S/. 20,000.00

S/. 40,000.00

S/. 60,000.00

S/. 80,000.00

S/. 100,000.00

S/. 120,000.00

VPN(US $)

VPN(Millones)

TME(r costo del capital)

44% S/. 59,874.2145% S/. 59,664.5846% S/. 59,463.2547% S/. 59,269.7548% S/. 59,083.6749% S/. 58,904.6050% S/. 58,732.1851% S/. 58,566.0552% S/. 58,405.9153% S/. 58,251.4354% S/. 58,102.3555% S/. 57,958.4056% S/. 57,819.3257% S/. 57,684.8858% S/. 57,554.8659% S/. 57,429.0660% S/. 57,307.2861% S/. 57,189.3362% S/. 57,075.0563% S/. 56,964.2764% S/. 56,856.8465% S/. 56,752.6166% S/. 56,651.4467% S/. 56,553.2168% S/. 56,457.7969% S/. 56,365.0670% S/. 56,274.9371% S/. 56,187.2772% S/. 56,102.0073% S/. 56,019.0174% S/. 55,938.2375% S/. 55,859.5676% S/. 55,782.9277% S/. 55,708.2478% S/. 55,635.4579% S/. 55,564.4780% S/. 55,495.2581% S/. 55,427.7182% S/. 55,361.7983% S/. 55,297.4584% S/. 55,234.62

15.00%1.17%

$98,990Err:523

Respuesta:La Regla del TIR no se puede aplicar porque no existe TIR para el problemaNunca intersecta el eje de abcisas para cumplir la condición VPN=0La regla de VPN aconseja invertir dado VPN = $ 98,990 que es mayor que CEROy mayor a la inversión incial.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. 0.00

S/. 20,000.00

S/. 40,000.00

S/. 60,000.00

S/. 80,000.00

S/. 100,000.00

S/. 120,000.00

VPN(US $)

VPN(Millones)

TME(r costo del capital)

Año FC( Millones) r VPN0 -$5,000,000 1.0000% S/. -3,281,041.011 $1,000,000 1.5000% S/. -1,207,220.482 $1,000,000 1.6000% S/. -917,768.203 $1,000,000 2.0187966% S/. -0.00 TIR 14 $1,000,000 2.5000% S/. 652,602.215 $1,000,000 2.6000% S/. 751,503.506 $1,000,000 2.745784% S/. 878,310.697 $1,000,000 2.8000% S/. 920,722.528 $1,000,000 2.9000% S/. 992,843.559 $1,000,000 3.0000% S/. 1,057,674.59

10 $1,000,000 3.1000% S/. 1,115,886.2111 -$100,000 3.2000% S/. 1,168,076.6212 -$100,000 3.3000% S/. 1,214,780.5813 -$100,000 3.4000% S/. 1,256,477.0014 -$100,000 3.5000% S/. 1,293,595.6315 -$100,000 3.6000% S/. 1,326,522.8616 -$100,000 3.7000% S/. 1,355,606.6817 -$100,000 3.8000% S/. 1,381,161.1618 -$100,000 3.9000% S/. 1,403,470.2019 -$100,000 4.0000% S/. 1,422,790.9320 -$100,000 4.1000% S/. 1,439,356.6321 -$100,000 4.2000% S/. 1,453,379.3022 -$100,000 4.3000% S/. 1,465,051.9323 -$100,000 4.4000% S/. 1,474,550.4824 -$100,000 4.5000% S/. 1,482,035.6625 -$100,000 4.6000% S/. 1,487,654.4726 -$100,000 4.7000% S/. 1,491,541.5927 -$100,000 4.8000% S/. 1,493,820.5628 -$100,000 4.9000% S/. 1,494,604.9029 -$100,000 5.438761% S/. 1,477,179.0930 -$100,000 6.0000% S/. 1,429,439.9131 -$100,000 7.0000% S/. 1,297,369.6232 -$100,000 8.0000% S/. 1,131,089.7133 -$100,000 9.0000% S/. 948,312.3834 -$100,000 10.0000% S/. 759,023.8235 -$100,000 10.879183% S/. 591,918.6836 -$100,000 11.8792% S/. 404,295.5237 -$100,000 12.8792% S/. 221,353.8538 -$100,000 13.8792% S/. 44,380.4139 -$100,000 14.1359% S/. 0.00 TIR 240 -$100,000 15.1359% S/. -168,518.0441 -$100,000 16.1359% S/. -329,980.8342 -$100,000 17.1359% S/. -484,339.4643 -$100,000 18.1359% S/. -631,684.32

44 -$100,000 19.1359% S/. -772,194.9345 -$100,000 20.1359% S/. -906,106.3046 -$100,000 21.1359% S/. -1,033,686.0847 -$100,000 22.1359% S/. -1,155,219.1348 -$100,000 23.1359% S/. -1,270,996.8549 -$100,000 24.1359% S/. -1,381,310.0650 -$100,000 25.1359% S/. -1,486,444.1451 -$100,000 26.1359% S/. -1,586,675.9152 -$100,000 27.1359% S/. -1,682,271.5353 -$100,000 28.1359% S/. -1,773,485.4254 -$100,000 29.1359% S/. -1,860,559.5755 -$100,000 30.1359% S/. -1,943,723.3956 -$100,000 31.1359% S/. -2,023,193.7257 -$100,000 32.1359% S/. -2,099,175.1858 -$100,000 33.1359% S/. -2,171,860.5059 -$100,000 34.1359% S/. -2,241,431.0360 -$100,000 35.1359% S/. -2,308,057.2861 -$100,000 36.1359% S/. -2,371,899.4462 -$100,000 37.1359% S/. -2,433,107.9963 -$100,000 38.1359% S/. -2,491,824.2164 -$100,00065 -$100,00066 -$100,00067 -$100,00068 -$100,00069 -$100,00070 -$100,00071 -$100,00072 -$100,00073 -$100,00074 -$100,00075 -$100,00076 -$100,00077 -$100,00078 -$100,00079 -$100,00080 -$100,00081 -$100,00082 -$100,00083 -$100,00084 -$100,00085 -$100,00086 -$100,00087 -$100,00088 -$100,00089 -$100,00090 -$100,00091 -$100,000

92 -$100,00093 -$100,00094 -$100,00095 -$100,00096 -$100,00097 -$100,00098 -$100,00099 -$100,000

100 -$100,000101 -$100,000102 -$100,000103 -$100,000104 -$100,000105 -$100,000106 -$100,000107 -$100,000108 -$100,000109 -$100,000110 -$100,000111 -$100,000112 -$100,000113 -$100,000114 -$100,000115 -$100,000116 -$100,000117 -$100,000118 -$100,000119 -$100,000120 -$100,000121 -$100,000122 -$100,000123 -$100,000124 -$100,000125 -$100,000126 -$100,000127 -$100,000128 -$100,000129 -$100,000130 -$100,000131 -$100,000132 -$100,000133 -$100,000134 -$100,000135 -$100,000136 -$100,000137 -$100,000138 -$100,000139 -$100,000

140 -$100,000141 -$100,000142 -$100,000143 -$100,000144 -$100,000145 -$100,000146 -$100,000147 -$100,000148 -$100,000149 -$100,000150 -$100,000151 -$100,000152 -$100,000153 -$100,000154 -$100,000155 -$100,000156 -$100,000157 -$100,000158 -$100,000159 -$100,000160 -$100,000161 -$100,000162 -$100,000163 -$100,000164 -$100,000165 -$100,000166 -$100,000167 -$100,000168 -$100,000169 -$100,000170 -$100,000171 -$100,000172 -$100,000173 -$100,000174 -$100,000175 -$100,000176 -$100,000177 -$100,000178 -$100,000179 -$100,000180 -$100,000181 -$100,000182 -$100,000183 -$100,000184 -$100,000185 -$100,000186 -$100,000187 -$100,000

188 -$100,000189 -$100,000190 -$100,000191 -$100,000192 -$100,000193 -$100,000194 -$100,000195 -$100,000196 -$100,000197 -$100,000198 -$100,000199 -$100,000200 -$100,000201 -$100,000202 -$100,000203 -$100,000204 -$100,000205 -$100,000

Costo de Capital = 5.438761%

VPN( 5.438761%)= $1,477,179TIR 1= 2.0187966%TIR 2= 14.1359%

Respuesta:a.- Para un costo de capital de 5.438761%, el VPN = $ 1´477,179 > 0 se debe emprender el negocioPara las tasa 2.745784% el VPN= $ 878,310 > 0 también se recomienda emprender el proyectoPara las tasa 10.879183% el VPN= $ 591,918> 0 también se recomienda emprender el proyectob.- Esta oportunidad no tiene un TIR unico, tiene dos TIR´s , TIR 1= 2.0187966%y TIR 2= 14.1359%c.- La Regla del TIR indica que las inversiones que se encuentran con VPN del lado positivo de lagráfica son las oportunidades que de inversión que debemos aceptar.La mejor oportunidad para esta inversión entre las tres de la pregunta a sería la que tiene uncosto de capital de 5.438761% porque tiene el mayor VPN entre las tres VPN=$!´477,179

0.0000% 10.0000% 20.0000% 30.0000% 40.0000% 50.0000%

S/. -4,000,000.00

S/. -3,000,000.00

S/. -2,000,000.00

S/. -1,000,000.00

S/. 0.00

S/. 1,000,000.00

S/. 2,000,000.00

VPN

VPN

a.- Para un costo de capital de 5.438761%, el VPN = $ 1´477,179 > 0 se debe emprender el negocio

Minera de Carbón

Año FC( Millones) r VPN0 -$120 1.0000% S/. -85.621 $20 2.0000% S/. -20.662 $20 2.9105% S/. -0.00 TIR 13 $20 3.0000% S/. 1.154 $20 4.0000% S/. 8.465 $20 5.0000% S/. 9.886 $20 6.0000% S/. 8.597 $20 7.0000% S/. 5.958 $20 8.0000% S/. 2.629 $20 8.7226% S/. -0.00 TIR 2

10 $20 9.0000% S/. -1.0311 -$2 10.0000% S/. -4.8212 -$2 11.0000% S/. -8.6213 -$2 12.0000% S/. -12.3614 -$2 13.0000% S/. -16.0115 -$2 14.0000% S/. -19.5316 -$2 15.0000% S/. -22.9217 -$2 16.0000% S/. -26.1718 -$2 17.0000% S/. -29.2819 -$2 18.0000% S/. -32.2420 -$2 19.0000% S/. -35.0721 -$2 20.0000% S/. -37.7722 -$2 21.0000% S/. -40.3323 -$2 22.0000% S/. -42.7824 -$2 23.0000% S/. -45.1125 -$2 24.0000% S/. -47.3326 -$2 25.0000% S/. -49.4527 -$2 26.0000% S/. -51.4728 -$2 27.0000% S/. -53.3929 -$2 28.0000% S/. -55.2330 -$2 29.0000% S/. -56.9831 -$2 30.0000% S/. -58.6532 -$2 31.0000% S/. -60.2533 -$2 32.0000% S/. -61.7834 -$2 33.0000% S/. -63.2435 -$2 34.0000% S/. -64.6436 -$2 35.0000% S/. -65.9837 -$2 36.0000% S/. -67.2738 -$2 37.0000% S/. -68.5039 -$2 38.0000% S/. -69.6840 -$2 39.0000% S/. -70.8141 -$2 40.0000% S/. -71.9042 -$243 -$2

44 -$245 -$246 -$247 -$248 -$249 -$250 -$251 -$252 -$253 -$254 -$255 -$256 -$257 -$258 -$259 -$260 -$261 -$262 -$263 -$264 -$265 -$266 -$267 -$268 -$269 -$270 -$271 -$272 -$273 -$274 -$275 -$276 -$277 -$278 -$279 -$280 -$281 -$282 -$283 -$284 -$285 -$286 -$287 -$288 -$289 -$290 -$291 -$2

92 -$293 -$294 -$295 -$296 -$297 -$298 -$299 -$2

100 -$2101 -$2102 -$2103 -$2104 -$2105 -$2106 -$2107 -$2108 -$2109 -$2110 -$2111 -$2112 -$2113 -$2114 -$2115 -$2116 -$2117 -$2118 -$2119 -$2120 -$2121 -$2122 -$2123 -$2124 -$2125 -$2126 -$2127 -$2128 -$2129 -$2130 -$2131 -$2132 -$2133 -$2134 -$2135 -$2136 -$2137 -$2138 -$2139 -$2

140 -$2141 -$2142 -$2143 -$2144 -$2145 -$2146 -$2147 -$2148 -$2149 -$2150 -$2151 -$2152 -$2153 -$2154 -$2155 -$2156 -$2157 -$2158 -$2159 -$2160 -$2161 -$2162 -$2163 -$2164 -$2165 -$2166 -$2167 -$2168 -$2169 -$2170 -$2171 -$2172 -$2173 -$2174 -$2175 -$2176 -$2177 -$2178 -$2179 -$2180 -$2181 -$2182 -$2183 -$2184 -$2185 -$2186 -$2187 -$2

188 -$2189 -$2190 -$2191 -$2192 -$2193 -$2194 -$2195 -$2196 -$2197 -$2198 -$2199 -$2200 -$2201 -$2202 -$2203 -$2204 -$2205 -$2

Costo de Capital = 8.00%

VPN= $2.622

TIR 2= 8.7226%

Respuesta:a.- Como tiene TIR multiples, el rango que nos aconseja el TIR es de costos de capital de2.9105 < r < 8.7226 entre esos valores el VPN el positivo, y esta regla nos aconseja invertir en ese rangomientras la regla de VPN nos aconseja invertir entre los valores de VPN´s entre 8% < r < 8.7226% para cumplir con que la inversión rinda mas que el costo del dinero(8%)

0.0000% 10.0000% 20.0000% 30.0000% 40.0000% 50.0000%

S/. -100.00

S/. -80.00

S/. -60.00

S/. -40.00

S/. -20.00

S/. 0.00

S/. 20.00

VPN

VPN

Zona en la cual el VPN >0 y tasa de retorno > costo del dinero, zon recomendable de inver-tir

2.9105 < r < 8.7226 entre esos valores el VPN el positivo, y esta regla nos aconseja invertir en ese rangomientras la regla de VPN nos aconseja invertir entre los valores de VPN´s entre 8% < r < 8.7226%

0.0000% 10.0000% 20.0000% 30.0000% 40.0000% 50.0000%

S/. -100.00

S/. -80.00

S/. -60.00

S/. -40.00

S/. -20.00

S/. 0.00

S/. 20.00

VPN

VPN

Zona en la cual el VPN >0 y tasa de retorno > costo del dinero, zon recomendable de inver-tir

Mina de Oro en Sudafrica

Año FC( Millones) r VPN0 -$250 1% S/. -233.831 $20 2% S/. -86.902 $20 3% S/. -44.343 $20 4% S/. -35.204 $20 5% S/. -38.445 $20 6% S/. -46.586 $20 7% S/. -56.587 $20 8% S/. -67.058 $20 9% S/. -77.349 $20 10% S/. -87.16

10 $20 11% S/. -96.3711 $20 12% S/. -104.9312 $20 13% S/. -112.8413 $20 14% S/. -120.1414 $20 15% S/. -126.8515 $20 16% S/. -133.0316 $20 17% S/. -138.7217 $20 18% S/. -143.9618 $20 19% S/. -148.7919 $20 20% S/. -153.2620 $20 21% S/. -157.3921 -$5 22% S/. -161.2222 -$5 23% S/. -164.7723 -$5 24% S/. -168.0824 -$5 25% S/. -171.1525 -$5 26% S/. -174.0226 -$5 27% S/. -176.7027 -$5 28% S/. -179.2128 -$5 29% S/. -181.5629 -$5 30% S/. -183.7730 -$5 31% S/. -185.8531 -$5 32% S/. -187.8032 -$5 33% S/. -189.6533 -$5 34% S/. -191.3934 -$5 35% S/. -193.0335 -$5 36% S/. -194.5936 -$5 37% S/. -196.0737 -$5 38% S/. -197.4738 -$5 39% S/. -198.8139 -$5 40% S/. -200.0740 -$5 41% S/. -201.2841 -$5 42% S/. -202.4342 -$5 43% S/. -203.5343 -$5 44% S/. -204.58

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

S/. -250.00

S/. -200.00

S/. -150.00

S/. -100.00

S/. -50.00

S/. 0.00

VPN

VPN

r (Costo de Capital)

44 -$5 45% S/. -205.5945 -$5 46% S/. -206.5546 -$5 47% S/. -207.4747 -$5 48% S/. -208.3548 -$5 49% S/. -209.2049 -$5 50% S/. -210.0250 -$5 51% S/. -210.8051 -$5 52% S/. -211.5552 -$5 53% S/. -212.2753 -$5 54% S/. -212.9754 -$5 55% S/. -213.6455 -$5 56% S/. -214.2956 -$5 57% S/. -214.9257 -$5 58% S/. -215.5258 -$5 59% S/. -216.1159 -$5 60% S/. -216.6760 -$5 61% S/. -217.2261 -$5 62% S/. -217.7462 -$5 63% S/. -218.2663 -$5 64% S/. -218.7564 -$5 65% S/. -219.2365 -$5 66% S/. -219.7066 -$5 67% S/. -220.1567 -$5 68% S/. -220.5968 -$5 69% S/. -221.0269 -$5 70% S/. -221.4370 -$5 71% S/. -221.8371 -$5 72% S/. -222.2272 -$5 73% S/. -222.6073 -$5 74% S/. -222.9774 -$5 75% S/. -223.3375 -$5 76% S/. -223.6876 -$5 77% S/. -224.0377 -$578 -$579 -$580 -$581 -$582 -$583 -$584 -$585 -$586 -$587 -$588 -$589 -$590 -$591 -$5

92 -$593 -$594 -$595 -$596 -$597 -$598 -$599 -$5

100 -$5101 -$5102 -$5103 -$5104 -$5105 -$5106 -$5107 -$5108 -$5109 -$5110 -$5111 -$5112 -$5113 -$5114 -$5115 -$5116 -$5117 -$5118 -$5119 -$5120 -$5121 -$5122 -$5123 -$5124 -$5125 -$5126 -$5127 -$5128 -$5129 -$5130 -$5131 -$5132 -$5133 -$5134 -$5135 -$5136 -$5137 -$5138 -$5139 -$5

140 -$5141 -$5142 -$5143 -$5144 -$5145 -$5146 -$5147 -$5148 -$5149 -$5150 -$5151 -$5152 -$5153 -$5154 -$5155 -$5156 -$5157 -$5158 -$5159 -$5160 -$5161 -$5162 -$5163 -$5164 -$5165 -$5166 -$5167 -$5168 -$5169 -$5170 -$5171 -$5172 -$5173 -$5174 -$5175 -$5176 -$5177 -$5178 -$5179 -$5180 -$5181 -$5182 -$5183 -$5184 -$5185 -$5186 -$5187 -$5

188 -$5189 -$5190 -$5191 -$5192 -$5193 -$5194 -$5195 -$5196 -$5197 -$5198 -$5199 -$5200 -$5201 -$5202 -$5203 -$5204 -$5205 -$5

TIR = Err:523

Respuesta:La inversión no tiene TIR, la curva nunca intersecta el eje de abcisas (r costo de capital)Los VPN siempre son negativos, la inversión no es rentable.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

S/. -250.00

S/. -200.00

S/. -150.00

S/. -100.00

S/. -50.00

S/. 0.00

VPN

VPN

r (Costo de Capital)

La inversión no tiene TIR, los valores de VPN nunca superan a CERO

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

S/. -250.00

S/. -200.00

S/. -150.00

S/. -100.00

S/. -50.00

S/. 0.00

VPN

VPN

r (Costo de Capital)

Inversion Inicial $100 millonesBeneficio periodico $30 millones

8%

VP(VEA)= $275

Respuesta:Este valor coincide con el cálculo anterior del VPN del proyecto del problema 1La empresa debería realizar la inversión si el costo del capital es menor a 8%

r(tasa de descuento para el periodo)

Este valor coincide con el cálculo anterior del VPN del proyecto del problema 1La empresa debería realizar la inversión si el costo del capital es menor a 8%

Planta producto novedoso Costo de Capital 12%

Año FC( Millones) VPN= $14.11500 -$1001 $15 TIR = 14.1350%2 $153 $154 $155 $15 Año 0 16 $15 Capital 100 957 $15 Flujo de efectivo 158 $15 Cargo Capital -129 $15 Depreciación -5

10 $15 Valor de Rescate11 $15 VEA -212 $15 VEAn -1.7857142913 $15 VP(VEA)= Σ VEAn= $14.115014 $1515 $15

16 $15 Respuesta:17 $15 Se comprueba que los valores de VPN y VP(VEA) son iguales18 $1519 $1520 $35

r VPN1% Err:5222% Err:5223% Err:5224% Err:5225% Err:5226% Err:5227% Err:5228% Err:5229% Err:522

10% Err:52211% Err:52212% Err:52213% Err:52214% Err:522

14.1350% Err:52215% Err:52216% Err:52217% Err:52218% Err:52219% Err:522

VPN = VP(VEA)

20% Err:52221% Err:52222% Err:52223% Err:52224% Err:52225% Err:52226% Err:52227% Err:52228% Err:52229% Err:52230% Err:52231% Err:52232% Err:52233% Err:52234% Err:52235% Err:52236% Err:52237% Err:52238% Err:52239% Err:52240% Err:52241% Err:52242% Err:52243% Err:52244% Err:52245% Err:52246% Err:52247% Err:52248% Err:52249% Err:52250% Err:52251% Err:52252% Err:52253% Err:52254% Err:52255% Err:52256% Err:52257% Err:52258% Err:52259% Err:52260% Err:522

depreciación 5

2 3 4 5 6 7 890 85 80 75 70 65 6015 15 15 15 15 15 15

-11.4 -10.8 -10.2 -9.6 -9 -8.4 -7.8-5 -5 -5 -5 -5 -5 -5

-1.4 -0.8 -0.2 0.4 1 1.6 2.2-1.116071429 -0.5694242 -0.12710362 0.22697074 0.50663112 0.72375874 0.8885431

Se comprueba que los valores de VPN y VP(VEA) son iguales

VPN = VP(VEA)

9 10 11 12 13 14 15 1655 50 45 40 35 30 25 2015 15 15 15 15 15 15 15

-7.2 -6.6 -6 -5.4 -4.8 -4.2 -3.6 -3-5 -5 -5 -5 -5 -5 -5 -5

2.8 3.4 4 4.6 5.2 5.8 6.4 71.00970807 1.094709 1.14990442 1.18070543 1.19170579 1.18679491 1.16925607 1.14185163

17 18 19 2015 10 5 015 15 15 15

-2.4 -1.8 -1.2 -0.6-5 -5 -5 -5

207.6 8.2 8.8 29.4

1.10689699 1.06632464 1.02173964 3.04780289 14.1150

Periodo 0 Periodo 1 Periodo 2

FC (US Millones) -10 5 2-10 -5 -3

+

3 +

3.5 años

VPN = $0.31 Millones

Respuesta:Si se requiere u periodo de recuperación de 2 años no se debe hacer la inversión ya que el periodo de recuperación cálculado es de 3.5 añosSin embargo la regla del VPN nos aconseja realizare la pelicula dado que VPN = US 310,000 que cumple la regla VPN > 0

Periodo de

Recuperación =

Año anterior a la

recuperación

total

Periodo de Recuperación =

Periodo de Recuperación =

Periodo 3 Periodo 4 Periodo 5

2 2 2-1 1 3

/

1 / 2

Si se requiere u periodo de recuperación de 2 años no se debe hacer la inversión ya que el periodo de recuperación cálculado es de 3.5 añosSin embargo la regla del VPN nos aconseja realizare la pelicula dado que VPN = US 310,000 que

Costo no

recuperado al

inicio del año

Flujo de efectivo

durante el año recupación

Respuesta:

Sabiendo que es importante evaluar primero La regla del Valor Presente Neto sea Mayor que CERO, y mas aun un valor aceptable Que permita ganancias a la compañía, nosotros buscariamos una tasa de referencia de mercado que haya conseguido la empresao que corresponda al riesgo del sector, calculariamos el VPN y si cumple ( VPN > 0) y el TIR que se encuentre sea mayor a la tasa de descuento correspondiente al sector y un rango de seguridad recomendaría invertir en el proyecto, de lo contrario alertariamosen no invertir en ese proyecto.

Sabiendo que es importante evaluar primero La regla del Valor Presente Neto sea Mayor que CERO, y mas aun un valor aceptable Que permita ganancias a la compañía, nosotros buscariamos una tasa de referencia de mercado que haya conseguido la empresao que corresponda al riesgo del sector, calculariamos el VPN y si cumple ( VPN > 0) y el TIR que se encuentre sea mayor a la tasa de descuento correspondiente al sector y un rango de seguridad recomendaría invertir en el proyecto, de lo contrario alertariamos

Inversión A Inversión B rA VPNA rB-10 -10 1% S/. 163.99 1%2 1.5 3% S/. 56.51 3%2 1.53 5% S/. 30.00 5%2 1.5606 6% S/. 23.33 6%2 1.591812 7% S/. 18.57 7%2 1.62364824 8% S/. 15.00 8%2 1.656121205 9% S/. 12.22 9%2 1.689243629 10% S/. 10.00 10%2 1.723028501 11% S/. 8.18 11%2 1.757489072 12% S/. 6.67 12%2 1.792638853 13% S/. 5.38 13%2 1.82849163 14% S/. 4.29 14%2 1.865061463 15% S/. 3.33 15%2 1.902362692 16% S/. 2.50 16%2 1.940409946 17% S/. 1.76 17%2 1.979218145 18% S/. 1.11 18%2 2.018802507 19% S/. 0.53 19%2 2.059178558 20% S/. 0.00 20%2 2.100362129 21% S/. -0.48 21%2 2.142369371 22% S/. -0.91 22%2 2.185216759 23% S/. -1.30 23%2 2.228921094 24% S/. -1.67 24%2 2.273499516 25% S/. -2.00 25%2 2.318969506 26% S/. -2.31 26%2 2.365348896 27% S/. -2.59 27%2 2.412655874 28% S/. -2.86 28%2 2.460908992 29% S/. -3.10 29%2 2.510127172 30% S/. -3.33 30%2 2.560329715 31% S/. -3.55 31%2 2.611536309 32% S/. -3.75 32%2 2.663767035 33% S/. -3.94 33%2 2.717042376 34% S/. -4.12 34%2 2.771383224 35% S/. -4.29 35%2 2.826810888 36% S/. -4.44 36%2 2.883347106 37% S/. -4.59 37%2 2.941014048 38% S/. -4.74 38%2 2.999834329 39% S/. -4.87 39%2 3.059831016 40% S/. -5.00 40%2 3.121027636 41% S/. -5.12 41%2 3.183448189 42% S/. -5.24 42%2 3.247117152 43% S/. -5.35 43%2 3.312059495 44% S/. -5.45 44%2 3.378300685 45% S/. -5.56 45%2 3.445866699 46% S/. -5.65 46%

2 3.514784033 47% S/. -5.74 47%2 3.585079714 48% S/. -5.83 48%2 3.656781308 49% S/. -5.92 49%2 3.729916934 50% S/. -6.00 50%2 3.804515273 51% S/. -6.08 51%2 3.880605578 52% S/. -6.15 52%2 3.95821769 53% S/. -6.23 53%2 4.037382044 54% S/. -6.30 54%2 4.118129684 55% S/. -6.36 55%2 4.200492278 56% S/. -6.43 56%2 4.284502124 57% S/. -6.49 57%2 4.370192166 58% S/. -6.55 58%2 4.45759601 59% S/. -6.61 59%2 4.54674793 60% S/. -6.67 60%2 4.637682888 61% S/. -6.72 61%2 4.730436546 62% S/. -6.77 62%2 4.825045277 63% S/. -6.83 63%2 4.921546183 64% S/. -6.88 64%2 5.019977106 65% S/. -6.92 65%2 5.120376648 66% S/. -6.97 66%2 5.222784181 67% S/. -7.01 67%2 5.327239865 68% S/. -7.06 68%2 5.433784662 69% S/. -7.10 69%2 5.542460355 70% S/. -7.14 70%2 5.653309563 71% S/. -7.18 71%2 5.766375754 72% S/. -7.22 72%2 5.881703269 73% S/. -7.26 73%2 5.999337334 74% S/. -7.30 74%2 6.119324081 75% S/. -7.33 75%2 6.241710563 76% S/. -7.37 76%2 6.366544774 77% S/. -7.40 77%2 6.493875669 78% S/. -7.44 78%2 6.623753183 79% S/. -7.47 79%2 6.756228246 80% S/. -7.50 80%2 6.891352811 81% S/. -7.53 81%2 7.029179867 82% S/. -8.13 82%2 7.1697634652 7.3131587342 7.4594219092 7.6086103472 7.7607825542 7.9159982052 8.0743181692 8.2358045332 8.4005206232 8.5685310362 8.7399016562 8.914699689

2 9.0929936832 9.2748535572 9.4603506282 9.6495576412 9.8425487932 10.039399772 10.240187762 10.444991522 10.653891352 10.866969182 11.084308562 11.305994732 11.532114632 11.762756922 11.998012062 12.23797232 12.482731742 12.732386382 12.987034112 13.246774792 13.511710292 13.781944492 14.057583382 14.338735052 14.625509752 14.918019942 15.216380342 15.520707952 15.831122112 16.147744552 16.470699442 16.800113432 17.13611572 17.478838012 17.828414772 18.184983072 18.548682732 18.919656392 19.298049512 19.68401052 20.077690712 20.479244532 20.888829422 21.306606012 21.732738132 22.167392892 22.610740752 23.06295556

2 23.524214672 23.994698972 24.474592952 24.964084812 25.46336652 25.972633832 26.492086512 27.021928242 27.56236682 28.113614142 28.675886422 29.249404152 29.834392232 30.431080082 31.039701682 31.660495712 32.293705632 32.939579742 33.598371332 34.270338762 34.955745542 35.654860452 36.367957662 37.095316812 37.837223152 38.593967612 39.365846962 40.15316392 40.956227182 41.775351722 42.610858762 43.463075932 44.332337452 45.21898422 46.123363882 47.045831162 47.986747782 48.946482742 49.925412392 50.923920642 51.942399052 52.981247042 54.040871982 55.121689422 56.22412322 57.348605672 58.495577782 59.66548934

2 60.858799122 62.075975112 63.317494612 64.58384452 65.875521392 67.193031822 68.536892452 69.90763032 71.305782912 72.731898572 74.186536542 75.670267272 77.183672622 78.727346072 80.301892992 81.907930852 83.546089472 85.217011262 86.921351482 88.659778512 90.432974082 92.241633562 94.086466232 95.968195562 97.887559472 99.845310662 101.84221692 103.8790612

VPNBS/. 970.43 a)S/. 119.70 TIR A = 20%

S/. 39.87 TIR B = 17%S/. 27.49 B)S/. 20.00 Costo de Capital= 7%S/. 15.00S/. 11.43 VAN A = S/. 18.57

S/. 8.75 VAN B = S/. 20.00S/. 6.67S/. 5.00 Respuesta:S/. 3.64 a).- La Inversión A tiene mayor TIRS/. 2.50 TIR A = 20% > TIR B = 17%S/. 1.54 b).- Le VPN B(Inversión B) es la mas elevadaS/. 0.71 VPN B = US 20 Millo> VPN A = US 18.57Millo.

S/. -0.00 VPN B > VPN AS/. -0.63 c) La TIR mas elevada lleva a la respuesta S/. -1.18 correcta, cuando ocurre primero que la S/. -1.67 VPN es mayor. El criterio de la VPN prima.S/. -2.11S/. -2.50S/. -2.86S/. -3.18S/. -3.48S/. -3.75S/. -4.00S/. -4.23S/. -4.44S/. -4.64S/. -4.83S/. -5.00S/. -5.16S/. -5.31S/. -5.45S/. -5.59S/. -5.71S/. -5.83S/. -5.95S/. -6.05S/. -6.15S/. -6.25S/. -6.34S/. -6.43S/. -6.51S/. -6.59

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. -20.00

S/. 0.00

S/. 20.00

S/. 40.00

S/. 60.00

S/. 80.00

S/. 100.00

S/. 120.00

S/. 140.00

S/. 160.00

S/. 180.00

VPNA

VPNA

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. -200.00

S/. 0.00

S/. 200.00

S/. 400.00

S/. 600.00

S/. 800.00

S/. 1,000.00

S/. 1,200.00

VPNB

VPNB

S/. -6.67S/. -6.74S/. -6.81S/. -6.88S/. -6.94S/. -7.00S/. -7.06S/. -7.12S/. -7.17S/. -7.22S/. -7.27S/. -7.32S/. -7.37S/. -7.41S/. -7.46S/. -7.50S/. -7.54S/. -7.58S/. -7.62S/. -7.66S/. -7.69S/. -7.73S/. -7.76S/. -7.79S/. -7.83S/. -7.86S/. -7.89S/. -7.92S/. -7.95S/. -7.97S/. -8.00S/. -8.03S/. -8.05S/. -8.08S/. -8.10S/. -8.13

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. -200.00

S/. 0.00

S/. 200.00

S/. 400.00

S/. 600.00

S/. 800.00

S/. 1,000.00

S/. 1,200.00

VPNB

VPNB

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. -20.00

S/. 0.00

S/. 20.00

S/. 40.00

S/. 60.00

S/. 80.00

S/. 100.00

S/. 120.00

S/. 140.00

S/. 160.00

S/. 180.00

VPNA

VPNA

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. -200.00

S/. 0.00

S/. 200.00

S/. 400.00

S/. 600.00

S/. 800.00

S/. 1,000.00

S/. 1,200.00

VPNB

VPNB

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%S/. -200.00

S/. 0.00

S/. 200.00

S/. 400.00

S/. 600.00

S/. 800.00

S/. 1,000.00

S/. 1,200.00

VPNB

VPNB

Inversión A Inversión B rA VPNA rB VPNB-10 -10 1% S/. 163.99 1% S/. 970.432 1.5 3% S/. 56.51 3% S/. 119.702 1.53 5% S/. 30.00 5% S/. 39.872 1.5606 6% S/. 23.33 6% S/. 27.49

2 1.591812 7% S/. 18.57 7% S/. 20.002 1.62364824 8% S/. 15.00 8% S/. 15.002 1.656121205 9% S/. 12.22 9% S/. 11.432 1.689243629 10% S/. 10.00 10% S/. 8.752 1.723028501 11% S/. 8.18 11% S/. 6.672 1.757489072 12% S/. 6.67 12% S/. 5.002 1.792638853 13% S/. 5.38 13% S/. 3.642 1.82849163 14% S/. 4.29 14% S/. 2.502 1.865061463 15% S/. 3.33 15% S/. 1.542 1.902362692 16% S/. 2.50 16% S/. 0.712 1.940409946 17% S/. 1.76 17% S/. -0.002 1.979218145 18% S/. 1.11 18% S/. -0.632 2.018802507 19% S/. 0.53 19% S/. -1.182 2.059178558 20% S/. 0.00 20% S/. -1.672 2.100362129 21% S/. -0.48 21% S/. -2.112 2.142369371 22% S/. -0.91 22% S/. -2.502 2.185216759 23% S/. -1.30 23% S/. -2.862 2.228921094 24% S/. -1.67 24% S/. -3.182 2.273499516 25% S/. -2.00 25% S/. -3.482 2.318969506 26% S/. -2.31 26% S/. -3.752 2.365348896 27% S/. -2.59 27% S/. -4.002 2.412655874 28% S/. -2.86 28% S/. -4.232 2.460908992 29% S/. -3.10 29% S/. -4.442 2.510127172 30% S/. -3.33 30% S/. -4.642 2.560329715 31% S/. -3.55 31% S/. -4.832 2.611536309 32% S/. -3.75 32% S/. -5.002 2.663767035 33% S/. -3.94 33% S/. -5.162 2.717042376 34% S/. -4.12 34% S/. -5.312 2.771383224 35% S/. -4.29 35% S/. -5.452 2.826810888 36% S/. -4.44 36% S/. -5.592 2.883347106 37% S/. -4.59 37% S/. -5.712 2.941014048 38% S/. -4.74 38% S/. -5.832 2.999834329 39% S/. -4.87 39% S/. -5.952 3.059831016 40% S/. -5.00 40% S/. -6.052 3.121027636 41% S/. -5.12 41% S/. -6.152 3.183448189 42% S/. -5.24 42% S/. -6.252 3.247117152 43% S/. -5.35 43% S/. -6.342 3.312059495 44% S/. -5.45 44% S/. -6.432 3.378300685 45% S/. -5.56 45% S/. -6.512 3.445866699 46% S/. -5.65 46% S/. -6.59

2 3.514784033 47% S/. -5.74 47% S/. -6.672 3.585079714 48% S/. -5.83 48% S/. -6.742 3.656781308 49% S/. -5.92 49% S/. -6.812 3.729916934 50% S/. -6.00 50% S/. -6.882 3.804515273 51% S/. -6.08 51% S/. -6.942 3.880605578 52% S/. -6.15 52% S/. -7.002 3.95821769 53% S/. -6.23 53% S/. -7.062 4.037382044 54% S/. -6.30 54% S/. -7.122 4.118129684 55% S/. -6.36 55% S/. -7.172 4.200492278 56% S/. -6.43 56% S/. -7.222 4.284502124 57% S/. -6.49 57% S/. -7.272 4.370192166 58% S/. -6.55 58% S/. -7.322 4.45759601 59% S/. -6.61 59% S/. -7.372 4.54674793 60% S/. -6.67 60% S/. -7.412 4.637682888 61% S/. -6.72 61% S/. -7.462 4.730436546 62% S/. -6.77 62% S/. -7.502 4.825045277 63% S/. -6.83 63% S/. -7.542 4.921546183 64% S/. -6.88 64% S/. -7.582 5.019977106 65% S/. -6.92 65% S/. -7.622 5.120376648 66% S/. -6.97 66% S/. -7.662 5.222784181 67% S/. -7.01 67% S/. -7.692 5.327239865 68% S/. -7.06 68% S/. -7.732 5.433784662 69% S/. -7.10 69% S/. -7.762 5.542460355 70% S/. -7.14 70% S/. -7.792 5.653309563 71% S/. -7.18 71% S/. -7.832 5.766375754 72% S/. -7.22 72% S/. -7.862 5.881703269 73% S/. -7.26 73% S/. -7.892 5.999337334 74% S/. -7.30 74% S/. -7.922 6.119324081 75% S/. -7.33 75% S/. -7.952 6.241710563 76% S/. -7.37 76% S/. -7.972 6.366544774 77% S/. -7.40 77% S/. -8.002 6.493875669 78% S/. -7.44 78% S/. -8.032 6.623753183 79% S/. -7.47 79% S/. -8.052 6.756228246 80% S/. -7.50 80% S/. -8.082 6.891352811 81% S/. -7.53 81% S/. -8.102 7.029179867 82% S/. -7.56 82% S/. -8.132 7.1697634652 7.3131587342 7.4594219092 7.6086103472 7.7607825542 7.9159982052 8.0743181692 8.2358045332 8.4005206232 8.5685310362 8.7399016562 8.914699689

2 9.0929936832 9.2748535572 9.4603506282 9.6495576412 9.8425487932 10.039399772 10.240187762 10.444991522 10.653891352 10.866969182 11.084308562 11.305994732 11.532114632 11.762756922 11.998012062 12.23797232 12.482731742 12.732386382 12.987034112 13.246774792 13.511710292 13.781944492 14.057583382 14.338735052 14.625509752 14.918019942 15.216380342 15.520707952 15.831122112 16.147744552 16.470699442 16.800113432 17.13611572 17.478838012 17.828414772 18.184983072 18.548682732 18.919656392 19.298049512 19.68401052 20.077690712 20.479244532 20.888829422 21.306606012 21.732738132 22.167392892 22.610740752 23.06295556

2 23.524214672 23.994698972 24.474592952 24.964084812 25.46336652 25.972633832 26.492086512 27.021928242 27.56236682 28.113614142 28.675886422 29.249404152 29.834392232 30.431080082 31.039701682 31.660495712 32.293705632 32.939579742 33.598371332 34.270338762 34.955745542 35.654860452 36.367957662 37.095316812 37.837223152 38.593967612 39.365846962 40.15316392 40.956227182 41.775351722 42.610858762 43.463075932 44.332337452 45.21898422 46.123363882 47.045831162 47.986747782 48.946482742 49.925412392 50.923920642 51.942399052 52.981247042 54.040871982 55.121689422 56.22412322 57.348605672 58.495577782 59.66548934

2 60.858799122 62.075975112 63.317494612 64.58384452 65.875521392 67.193031822 68.536892452 69.90763032 71.305782912 72.731898572 74.186536542 75.670267272 77.183672622 78.727346072 80.301892992 81.907930852 83.546089472 85.217011262 86.921351482 88.659778512 90.432974082 92.241633562 94.086466232 95.968195562 97.887559472 99.845310662 101.84221692 103.8790612

VPN = 1.5 - 2r + 0.02 R

El TIR Incremental se da cuando VPN de la diferencia es igual a CERO

0 = 1.5 - 2r + 0.02 R

TIR Incremental = 8%

Respuesta:Se deberia aceptar las inversiones que tengan menor tasa o costo del capital menor a 8 %

0% 5% 10% 15% 20% 25% 30%S/. -10.00

S/. 0.00

S/. 10.00

S/. 20.00

S/. 30.00

S/. 40.00

S/. 50.00

S/. 60.00

S/. 70.00

S/. 80.00

VPNA

rB

VPNB

TIR Incremental = 8 %

Flujos de efectivo al final del año(miles de $)

Proyecto 0 1 2 TIRCasita -30 15 20 10.4%Fuente -80 39 52 8.6%

-50 24 32 7.52%

r VPN Casita r VPN Fuente1% $4.46 1% $9.59 2% $3.93 2% $8.22 3% $3.42 3% $6.88 4% $2.91 4% $5.58 5% $2.43 5% $4.31 6% $1.95 6% $3.07

7.52% $1.25 7.52% $1.25 8% $1.04 8.6% $0.00 9% $0.60 10% -$1.13

10.0% $0.17 11% -$2.23 10.4% $0.00 12% -$3.30 11% -$0.42 13% -$4.35 12% -$0.82 14% -$5.38 13% -$1.22 15% -$6.38 14% -$1.60 16% -$7.35 15% -$1.98 17% -$8.31 16% -$2.35 18% -$9.24 17% -$2.71 19% -$10.15 18% -$3.06 20% -$11.04 19% -$3.41 21% -$11.91 20% -$3.74 22% -$12.76 21% -$4.07 23% -$13.59 22% -$4.39 24% -$14.41 23% -$4.71 25% -$15.21 24% -$5.02 26% -$15.99 25% -$5.32 27% -$16.75 26% -$5.61 28% -$17.50

Flujos de Efectivo incrementales

Repuesta:Si el costo de capital es del 8% se recomienda escoger a partir del TIR incrementalque es del 7.52% la curva del proyecto Casita, debido que es el que tiene mayor VPNel gráfico muestra que la línea azul corresponde al "proyecto casita" tiene un TIR = 10.4% y sus valores de VPN son mayores en el rango del costo del capital de 8%

0% 5% 10% 15% 20% 25% 30%

-$15.00

-$10.00

-$5.00

$0.00

$5.00

$10.00

$15.00

VPN CasitaVPN Fuente

r(Costo de Capital)

VPN ($ miles)

TIR Incremental 7.52%

TIR Fuente= 8.6%TIR Fuente= 8.6%

TIR Casita= 10.4%TIR Casita= 10.4%