Clase No. 1 Finanzas
Clase No. 1 Finanzas
Clase No. 1 Finanzas
Flujo de efectivo A B
Ingresos efectivo 2,250 2,750
- Pagos en efectivo 1,833 1,333
- Pago Intereses 120 516
- Pago Impuestos 319 175
= Flujo de efectivo oper -22 725
112.2 61.71
-135 664
Nivel de efectivo
Días de crédito 30
+ Abastecimiento de materia prima 120
+ Periodo de producción 5
+ Inventario productos terminados 30
- Días cuentas por pagar 90
95 días
% de ventas
Apalancamiento operativo
Utilización de los costos fijos para generar una mayor rentabilidad
Conservadora Arriesgada Disminución -25%
A B A B
Ventas 5,000 5,000 3,750 3,750
- Costos variables 3,500 1,250 2,625 938
= Margen de contribución 1,500 3,750 1,125 2,813
- Costos fijos 850 3,100 850 3,100
= UAI 650 650 275 -288
7% -8%
114%
estión de Capital de Trabajo
iclo del negocio o Ciclo del efectivo
Elementos Cálculo Financiero
1.1 Un bono de deuda paga 10 cupones semestrales de US$ 1.200, si el rendimiento requerido de
un inversionista es del 8,33% anual. ¿Cuál es el precio actual del bono?. Si el rendimiento
disminuye a 7,05% anual. ¿A cuánto asciende el valor del bono el día de hoy?.
VA $9,653.62 VA $9,967.36
Precio Precio
1.1 Usted dispone de un bono cero cupón del tesoro americano, que dentro de 20 años tendrá un
valor nominal de US$ 125.000, el rendimiento actual de este bono es del 3,98% anual. ¿A
cuánto asciende el valor del bono el día de hoy?. Si un inversionista quiere compra este bono
y requiere un rendimiento mínimo del 5,75%. ¿Cuánto debería pagar por este bono el día de
hoy?
VA $57,268.23 VA $40,860.39
1.1 Una empresa ha adquirido unos equipos informáticos por un importe de $ 42,071 y ha
decidido financiar la compra mediante un leasing cuyas características son: financiación
100%, plazo 3 años, valor residual $ 2,071, interés 6.1% anual. Amortización del leasing
mediante términos constantes, anuales y prepagables. El valor residual vence al inicio del
cuarto año ¿Cuál es el importe de las anualidades constantes de esta operación de
leasing?.
15474.26 16418.19
TABLA DE AMORTIZACIÓN
Tasa 6.10% anual Pago PagoPrin
Nper 3 años Periodo Cuota Capital
VA 42071 0
VF -2071 1 14,249.22 14,249.22
Tipo 1 2 14,249.22 12,552.09
3 14,249.22 13,317.76
Pago $-14,249.22 Cuota final 4 2,071.00 1,951.93
1.1 Un proyecto de inversión inmobiliario ofrece a sus socios participaciones en las siguientes
condiciones: Inversión anual de $ 5,000 durante 4 años y reembolso de capital y los intereses
al quinto año por $ 24,000 ¿Cuál es el valor actual neto de estas participaciones a una tasa de
descuento anual del 5.45%? y ¿Cuál es el rendimiento de este proyecto de inversión?
0 1 -5,000.00
1 2 -5,000.00
2 3 -5,000.00
3 4 -5,000.00
4 5 24,000.00
1.1 Un seguro de prima única por importe de $125,000 (valor de rescate) devuelve una renta
anual pospagable de $ 12,619 durante 15 años a partir del vencimiento del seguro. ¿Cuál es el
rendimiento anual implícito del seguro?.
Nper 15
VA 125000
Pago -12619
minal- anual
ños tendrá un
8% anual. ¿A
pra este bono
ono el día de
42,071 y ha
financiación
ón del leasing
ce al inicio del
ión de
PagoInt
Interes Saldo
42,071.00
0.00 27,821.78
1,697.13 15,269.70
931.45 1,951.93
119.07 -0.00
las siguientes
y los intereses
a una tasa de
sión?
una renta
o. ¿Cuál es el
Alternativa 1
Condiciones: Desembolso en efectivo:
Tasa 14.48% nom. anual Monto operación 50,000.00
Nper 36 meses - Solca 1% 500.00
VA 50,000.00 US$ - Desgravame 0.0015 225.00
VF 0 - Cartera 1.25% 625.00
Tipo 0 vencida - Honorarios 2.50% 1,216.25
Tabla de amortización
(Pago) (Pagoprin) (Pagoint) Flujo de
Periodo Cuota Capital Interes Saldo Caja
0 50,000.00 47,433.75
1 1,720.56 1,117.23 603.33 48,882.77 -1,720.56
2 1,720.56 1,130.71 589.85 47,752.06 -1,720.56
3 1,720.56 1,144.35 576.21 46,607.71 -1,720.56
4 1,720.56 1,158.16 562.40 45,449.55 -1,720.56
5 1,720.56 1,172.14 548.42 44,277.41 -1,720.56
6 1,720.56 1,186.28 534.28 43,091.13 -1,720.56
7 1,720.56 1,200.59 519.97 41,890.54 -1,720.56
8 1,720.56 1,215.08 505.48 40,675.45 -1,720.56
9 1,720.56 1,229.74 490.82 39,445.71 -1,720.56
10 1,720.56 1,244.58 475.98 38,201.13 -1,720.56
11 1,720.56 1,259.60 460.96 36,941.53 -1,720.56
12 1,720.56 1,274.80 445.76 35,666.73 -1,720.56
13 1,720.56 1,290.18 430.38 34,376.54 -1,720.56
14 1,720.56 1,305.75 414.81 33,070.79 -1,720.56
15 1,720.56 1,321.51 399.05 31,749.29 -1,720.56
16 1,720.56 1,337.45 383.11 30,411.83 -1,720.56
17 1,720.56 1,353.59 366.97 29,058.24 -1,720.56
18 1,720.56 1,369.93 350.64 27,688.32 -1,720.56
19 1,720.56 1,386.46 334.11 26,301.86 -1,720.56
20 1,720.56 1,403.19 317.38 24,898.67 -1,720.56
21 1,720.56 1,420.12 300.44 23,478.56 -1,720.56
22 1,720.56 1,437.25 283.31 22,041.30 -1,720.56
23 1,720.56 1,454.60 265.97 20,586.71 -1,720.56
24 1,720.56 1,472.15 248.41 19,114.56 -1,720.56
25 1,720.56 1,489.91 230.65 17,624.65 -1,720.56
26 1,720.56 1,507.89 212.67 16,116.76 -1,720.56
27 1,720.56 1,526.09 194.48 14,590.67 -1,720.56
28 1,720.56 1,544.50 176.06 13,046.17 -1,720.56
29 1,720.56 1,563.14 157.42 11,483.03 -1,720.56
30 1,720.56 1,582.00 138.56 9,901.03 -1,720.56
31 1,720.56 1,601.09 119.47 8,299.95 -1,720.56
32 1,720.56 1,620.41 100.15 6,679.54 -1,720.56
33 1,720.56 1,639.96 80.60 5,039.58 -1,720.56
34 1,720.56 1,659.75 60.81 3,379.83 -1,720.56
35 1,720.56 1,679.78 40.78 1,700.05 -1,720.56
36 1,720.56 1,700.05 20.51 0.00 -1,720.56
Tabla de amortización
(Pago) (Pagoprin) (Pagoint) Flujo de
Periodo Cuota Capital Interes Saldo Caja
0 50,000.00 41,068.13
1 1,660.48 1,160.89 499.58 48,839.11 -1,660.48
2 1,660.48 1,172.49 487.98 47,666.61 -1,660.48
3 1,660.48 1,184.21 476.27 46,482.41 -1,660.48
4 1,660.48 1,196.04 464.44 45,286.37 -1,660.48
5 1,660.48 1,207.99 452.49 44,078.38 -1,660.48
6 1,660.48 1,220.06 440.42 42,858.32 -1,660.48
7 1,660.48 1,232.25 428.23 41,626.06 -1,660.48
8 1,660.48 1,244.56 415.91 40,381.50 -1,660.48
9 1,660.48 1,257.00 403.48 39,124.50 -1,660.48
10 1,660.48 1,269.56 390.92 37,854.95 -1,660.48
11 1,660.48 1,282.24 378.23 36,572.70 -1,660.48
12 1,660.48 1,295.05 365.42 35,277.65 -1,660.48
13 1,660.48 1,307.99 352.48 33,969.65 -1,660.48
14 1,660.48 1,321.06 339.41 32,648.59 -1,660.48
15 1,660.48 1,334.26 326.21 31,314.33 -1,660.48
16 1,660.48 1,347.59 312.88 29,966.73 -1,660.48
17 1,660.48 1,361.06 299.42 28,605.68 -1,660.48
18 1,660.48 1,374.66 285.82 27,231.02 -1,660.48
19 1,660.48 1,388.39 272.08 25,842.62 -1,660.48
20 1,660.48 1,402.27 258.21 24,440.36 -1,660.48
21 1,660.48 1,416.28 244.20 23,024.08 -1,660.48
22 1,660.48 1,430.43 230.05 21,593.65 -1,660.48
23 1,660.48 1,444.72 215.76 20,148.93 -1,660.48
24 1,660.48 1,459.16 201.32 18,689.78 -1,660.48
25 1,660.48 1,473.73 186.74 17,216.04 -1,660.48
26 1,660.48 1,488.46 172.02 15,727.58 -1,660.48
27 1,660.48 1,503.33 157.14 14,224.25 -1,660.48
28 1,660.48 1,518.35 142.12 12,705.90 -1,660.48
29 1,660.48 1,533.52 126.95 11,172.38 -1,660.48
30 1,660.48 1,548.85 111.63 9,623.53 -1,660.48
31 1,660.48 1,564.32 96.16 8,059.21 -1,660.48
32 1,660.48 1,579.95 80.52 6,479.26 -1,660.48
33 1,660.48 1,595.74 64.74 4,883.52 -1,660.48
34 1,660.48 1,611.68 48.79 3,271.84 -1,660.48
35 1,660.48 1,627.79 32.69 1,644.05 -1,660.48
36 1,660.48 1,644.05 16.43 0.00 6,000.00 4,339.52
Flujo de
Rendimiento Saldo Caja
0 500.00 47,055.63
2.50 558.00 -1,769.24
2.79 616.28 -1,769.24
3.08 674.86 -1,769.24
3.37 733.73 -1,769.24
3.66 792.89 -1,769.24
3.96 852.35 -1,769.24
4.25 912.10 -1,769.24
4.55 972.15 -1,769.24
4.85 1,032.51 -1,769.24
5.15 1,093.16 -1,769.24
5.46 1,154.12 -1,769.24
5.76 1,215.38 -1,769.24
6.07 1,276.95 -1,769.24
6.37 1,338.82 -1,769.24
6.68 1,401.00 -1,769.24
6.99 1,463.50 -1,769.24
7.31 1,526.30 -1,769.24
7.62 1,589.42 -1,769.24
7.93 1,652.85 -1,769.24
8.25 1,716.60 -1,769.24
8.57 1,780.67 -1,769.24
8.89 1,845.06 -1,769.24
9.21 1,909.77 -1,769.24
9.53 1,974.80 -1,769.24
9.86 2,040.16 -1,769.24
10.18 2,105.85 -1,769.24
10.51 2,171.86 -1,769.24
10.84 2,238.20 -1,769.24
11.17 2,304.87 -1,769.24
11.51 2,371.88 -1,769.24
11.84 2,439.22 -1,769.24
12.18 2,506.89 -1,769.24
12.51 2,574.90 -1,769.24
12.85 2,643.26 -1,769.24
13.19 2,711.95 -1,769.24
13.54 2,780.99 1,011.75
pensiones mensuales
Interes Saldo
318,736.52
1,322.76 317,959.27
1,319.53 317,178.81
1,316.29 316,395.10
1,313.04 315,608.14
1,309.77 314,817.91
1,306.49 314,024.41
1,303.20 313,227.61
1,299.89 312,427.50
1,296.57 311,624.08
1,293.24 310,817.31
1,289.89 310,007.21
1,286.53 309,193.74
1,283.15 308,376.89
1,279.76 307,556.65
1,276.36 306,733.01
1,272.94 305,905.96
1,269.51 305,075.47
1,266.06 304,241.53
1,262.60 303,404.13
1,259.13 302,563.26
1,255.64 301,718.90
1,252.13 300,871.03
1,248.61 300,019.65
1,245.08 299,164.73
1,241.53 298,306.26
1,237.97 297,444.23
1,234.39 296,578.62
1,230.80 295,709.43
1,227.19 294,836.62
1,223.57 293,960.19
1,219.93 293,080.13
1,216.28 292,196.41
1,212.62 291,309.02
1,208.93 290,417.96
1,205.23 289,523.19
1,201.52 288,624.71
1,197.79 287,722.51
1,194.05 286,816.55
1,190.29 285,906.84
1,186.51 284,993.36
1,182.72 284,076.08
1,178.92 283,154.99
1,175.09 282,230.09
1,171.25 281,301.34
1,167.40 280,368.74
1,163.53 279,432.27
1,159.64 278,491.92
1,155.74 277,547.66
1,151.82 276,599.48
1,147.89 275,647.37
1,143.94 274,691.31
1,139.97 273,731.27
1,135.98 272,767.26
1,131.98 271,799.24
1,127.97 270,827.21
1,123.93 269,851.14
1,119.88 268,871.03
1,115.81 267,886.84
1,111.73 266,898.57
1,107.63 265,906.20
1,103.51 264,909.71
1,099.38 263,909.09
1,095.22 262,904.31
1,091.05 261,895.36
1,086.87 260,882.23
1,082.66 259,864.89
1,078.44 258,843.33
1,074.20 257,817.53
1,069.94 256,787.47
1,065.67 255,753.14
1,061.38 254,714.51
1,057.07 253,671.58
1,052.74 252,624.32
1,048.39 251,572.71
1,044.03 250,516.73
1,039.64 249,456.38
1,035.24 248,391.62
1,030.83 247,322.45
1,026.39 246,248.84
1,021.93 245,170.77
1,017.46 244,088.23
1,012.97 243,001.19
1,008.45 241,909.65
1,003.93 240,813.57
999.38 239,712.95
994.81 238,607.76
990.22 237,497.98
985.62 236,383.60
980.99 235,264.59
976.35 234,140.94
971.68 233,012.62
967.00 231,879.62
962.30 230,741.92
957.58 229,599.50
952.84 228,452.34
948.08 227,300.42
943.30 226,143.72
938.50 224,982.21
933.68 223,815.89
928.84 222,644.72
923.98 221,468.70
919.10 220,287.79
914.19 219,101.99
909.27 217,911.26
904.33 216,715.59
899.37 215,514.96
894.39 214,309.35
889.38 213,098.73
884.36 211,883.09
879.31 210,662.41
874.25 209,436.66
869.16 208,205.82
864.05 206,969.87
858.92 205,728.80
853.77 204,482.57
848.60 203,231.18
843.41 201,974.59
838.19 200,712.78
832.96 199,445.74
827.70 198,173.44
822.42 196,895.86
817.12 195,612.98
811.79 194,324.77
806.45 193,031.22
801.08 191,732.30
795.69 190,427.99
790.28 189,118.26
784.84 187,803.10
779.38 186,482.49
773.90 185,156.39
768.40 183,824.79
762.87 182,487.66
757.32 181,144.98
751.75 179,796.74
746.16 178,442.89
740.54 177,083.43
734.90 175,718.33
729.23 174,347.56
723.54 172,971.10
717.83 171,588.93
712.09 170,201.02
706.33 168,807.36
700.55 167,407.91
694.74 166,002.65
688.91 164,591.56
683.05 163,174.62
677.17 161,751.79
671.27 160,323.06
665.34 158,888.40
659.39 157,447.79
653.41 156,001.20
647.40 154,548.60
641.38 153,089.98
635.32 151,625.30
629.25 150,154.55
623.14 148,677.69
617.01 147,194.70
610.86 145,705.56
604.68 144,210.24
598.47 142,708.71
592.24 141,200.95
585.98 139,686.94
579.70 138,166.64
573.39 136,640.03
567.06 135,107.08
560.69 133,567.78
554.31 132,022.08
547.89 130,469.98
541.45 128,911.43
534.98 127,346.41
528.49 125,774.90
521.97 124,196.86
515.42 122,612.28
508.84 121,021.12
502.24 119,423.36
495.61 117,818.96
488.95 116,207.91
482.26 114,590.18
475.55 112,965.73
468.81 111,334.53
462.04 109,696.57
455.24 108,051.81
448.42 106,400.23
441.56 104,741.79
434.68 103,076.47
427.77 101,404.23
420.83 99,725.06
413.86 98,038.92
406.86 96,345.78
399.83 94,645.62
392.78 92,938.40
385.69 91,224.09
378.58 89,502.67
371.44 87,774.11
364.26 86,038.37
357.06 84,295.43
349.83 82,545.25
342.56 80,787.82
335.27 79,023.09
327.95 77,251.03
320.59 75,471.62
313.21 73,684.83
305.79 71,890.62
298.35 70,088.97
290.87 68,279.84
283.36 66,463.20
275.82 64,639.02
268.25 62,807.27
260.65 60,967.93
253.02 59,120.94
245.35 57,266.29
237.66 55,403.95
229.93 53,533.88
222.17 51,656.04
214.37 49,770.41
206.55 47,876.96
198.69 45,975.65
190.80 44,066.45
182.88 42,149.32
174.92 40,224.24
166.93 38,291.18
158.91 36,350.08
150.85 34,400.94
142.76 32,443.70
134.64 30,478.34
126.49 28,504.83
118.30 26,523.12
110.07 24,533.19
101.81 22,535.01
93.52 20,528.53
85.19 18,513.72
76.83 16,490.55
68.44 14,458.99
60.00 12,418.99
51.54 10,370.53
43.04 8,313.57
34.50 6,248.07
25.93 4,174.00
17.32 2,091.32
8.68 0.00
Fase productiva Fase de retiro
pensiones mensuales
Interes Saldo
455,337.88
1,889.65 454,227.53
1,885.04 453,112.58
1,880.42 451,993.00
1,875.77 450,868.77
1,871.11 449,739.87
1,866.42 448,606.29
1,861.72 447,468.01
1,856.99 446,325.00
1,852.25 445,177.25
1,847.49 444,024.74
1,842.70 442,867.44
1,837.90 441,705.34
1,833.08 440,538.42
1,828.23 439,366.65
1,823.37 438,190.02
1,818.49 437,008.51
1,813.59 435,822.10
1,808.66 434,630.76
1,803.72 433,434.47
1,798.75 432,233.23
1,793.77 431,027.00
1,788.76 429,815.76
1,783.74 428,599.49
1,778.69 427,378.18
1,773.62 426,151.80
1,768.53 424,920.33
1,763.42 423,683.75
1,758.29 422,442.04
1,753.13 421,195.17
1,747.96 419,943.13
1,742.76 418,685.90
1,737.55 417,423.44
1,732.31 416,155.75
1,727.05 414,882.80
1,721.76 413,604.56
1,716.46 412,321.02
1,711.13 411,032.15
1,705.78 409,737.93
1,700.41 408,438.35
1,695.02 407,133.37
1,689.60 405,822.97
1,684.17 404,507.13
1,678.70 403,185.84
1,673.22 401,859.06
1,667.72 400,526.78
1,662.19 399,188.96
1,656.63 397,845.60
1,651.06 396,496.65
1,645.46 395,142.12
1,639.84 393,781.96
1,634.20 392,416.15
1,628.53 391,044.68
1,622.84 389,667.51
1,617.12 388,284.63
1,611.38 386,896.01
1,605.62 385,501.63
1,599.83 384,101.46
1,594.02 382,695.49
1,588.19 381,283.67
1,582.33 379,866.00
1,576.44 378,442.44
1,570.54 377,012.98
1,564.60 375,577.58
1,558.65 374,136.23
1,552.67 372,688.90
1,546.66 371,235.55
1,540.63 369,776.18
1,534.57 368,310.75
1,528.49 366,839.24
1,522.38 365,361.63
1,516.25 363,877.88
1,510.09 362,387.97
1,503.91 360,891.88
1,497.70 359,389.58
1,491.47 357,881.05
1,485.21 356,366.25
1,478.92 354,845.17
1,472.61 353,317.78
1,466.27 351,784.05
1,459.90 350,243.95
1,453.51 348,697.47
1,447.09 347,144.56
1,440.65 345,585.21
1,434.18 344,019.39
1,427.68 342,447.07
1,421.16 340,868.23
1,414.60 339,282.83
1,408.02 337,690.85
1,401.42 336,092.27
1,394.78 334,487.05
1,388.12 332,875.17
1,381.43 331,256.61
1,374.71 329,631.32
1,367.97 327,999.29
1,361.20 326,360.49
1,354.40 324,714.88
1,347.57 323,062.45
1,340.71 321,403.16
1,333.82 319,736.98
1,326.91 318,063.89
1,319.97 316,383.86
1,312.99 314,696.85
1,305.99 313,002.84
1,298.96 311,301.80
1,291.90 309,593.71
1,284.81 307,878.52
1,277.70 306,156.22
1,270.55 304,426.76
1,263.37 302,690.13
1,256.16 300,946.30
1,248.93 299,195.23
1,241.66 297,436.89
1,234.36 295,671.25
1,227.04 293,898.28
1,219.68 292,117.96
1,212.29 290,330.25
1,204.87 288,535.12
1,197.42 286,732.54
1,189.94 284,922.48
1,182.43 283,104.91
1,174.89 281,279.80
1,167.31 279,447.11
1,159.71 277,606.81
1,152.07 275,758.88
1,144.40 273,903.28
1,136.70 272,039.98
1,128.97 270,168.95
1,121.20 268,290.15
1,113.40 266,403.55
1,105.57 264,509.13
1,097.71 262,606.84
1,089.82 260,696.66
1,081.89 258,778.55
1,073.93 256,852.48
1,065.94 254,918.42
1,057.91 252,976.33
1,049.85 251,026.18
1,041.76 249,067.94
1,033.63 247,101.57
1,025.47 245,127.04
1,017.28 243,144.32
1,009.05 241,153.37
1,000.79 239,154.15
992.49 237,146.64
984.16 235,130.80
975.79 233,106.60
967.39 231,073.99
958.96 229,032.95
950.49 226,983.43
941.98 224,925.41
933.44 222,858.85
924.86 220,783.72
916.25 218,699.97
907.60 216,607.58
898.92 214,506.50
890.20 212,396.70
881.45 210,278.15
872.65 208,150.80
863.83 206,014.63
854.96 203,869.59
846.06 201,715.64
837.12 199,552.76
828.14 197,380.91
819.13 195,200.04
810.08 193,010.12
800.99 190,811.11
791.87 188,602.98
782.70 186,385.68
773.50 184,159.18
764.26 181,923.44
754.98 179,678.42
745.67 177,424.09
736.31 175,160.40
726.92 172,887.31
717.48 170,604.80
708.01 168,312.81
698.50 166,011.31
688.95 163,700.25
679.36 161,379.61
669.73 159,049.33
660.05 156,709.39
650.34 154,359.73
640.59 152,000.32
630.80 149,631.13
620.97 147,252.10
611.10 144,863.19
601.18 142,464.37
591.23 140,055.60
581.23 137,636.83
571.19 135,208.02
561.11 132,769.14
550.99 130,320.13
540.83 127,860.96
530.62 125,391.58
520.38 122,911.96
510.08 120,422.04
499.75 117,921.79
489.38 115,411.17
478.96 112,890.12
468.49 110,358.62
457.99 107,816.61
447.44 105,264.05
436.85 102,700.89
426.21 100,127.10
415.53 97,542.63
404.80 94,947.43
394.03 92,341.46
383.22 89,724.68
372.36 87,097.04
361.45 84,458.49
350.50 81,808.99
339.51 79,148.50
328.47 76,476.96
317.38 73,794.34
306.25 71,100.59
295.07 68,395.66
283.84 65,679.50
272.57 62,952.07
261.25 60,213.32
249.89 57,463.21
238.47 54,701.68
227.01 51,928.69
215.50 49,144.19
203.95 46,348.14
192.34 43,540.49
180.69 40,721.18
168.99 37,890.17
157.24 35,047.42
145.45 32,192.86
133.60 29,326.47
121.70 26,448.17
109.76 23,557.93
97.77 20,655.70
85.72 17,741.42
73.63 14,815.04
61.48 11,876.53
49.29 8,925.81
37.04 5,962.86
24.75 2,987.60
12.40 -0.00
Fase productiva Fase de retiro
pensiones mensuales