# Ejercicios capitulos 4 y 5 libro de ross

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4.1 calcular el valor futuro de \$1000 anualmente capitalizables en 10 anos al 5%. 10 anos al 7% c. 20 anos a 5%

a. Future Value = C0 (1+r)T = \$1,000 (1.05)10 = \$1,628.89
b. Future Value = \$1,000 (1.07)10 = \$1,967.15
c. Future Value = \$1,000 (1.05)20 = \$2,653.30
d. Because interest compounds on interest already earned, the interest earned in part (c), \$1,653.30 (=\$2,653.30 - \$1,000) ismore than double the amount earned in part (a), \$628.89 (=\$1,628.89).
4.3 Preferiria usted recibir \$1000 el dia de ho o \$2000 dentro de l10 anos si la tasa de descuento fuera de 8%
The decision involves comparing the present value, PV, of each option. Choose the option with the highest PV. Since the first cash flow occurs 0 years in the future, or today, it does not need to be adjusted.PV(C0) = \$1,000
Since the second cash flow occurs 10 years in the future, it must be discounted back 10 years at eight percent.

PV(C10) = C10 / (1+r)10 = \$2,000 / (1.08)10 = \$926.39
Since the present value of the cash flow occurring today is higher than the present value of the cash flow occurring in year 10, you should take the \$1,000 now.
4.4 Una empresa tiene una pension en elpasivo de su balance general por \$1/5 millones, que sera pagadera despues de 27 anos contados a partir de hoy. Si la empresa puede invertir en un instrumento libre de riesgo que tenga una tasa de einteres de 8%. ¿Qué cantidad de dinero deberá invertir la empresa hoy para estar en condiciones de hacer el pago de \$ 1.5 millones?
The future value, FV, of the firm’s investment must equal the \$1.5million pension liability.
FV = C0 (1+r)27
To solve for the initial investment, C0, discount the future pension liability (\$1,500,000) back 27 years at eight percent, (1.08)27.
\$1,500,000 / (1.08)27 = C0 = \$187,780.23
The firm must invest \$187,708.23 today to be able to make the \$1.5 million payment.
4.5 Suponga que esta vendiendo su casa. Los Smith le han ofrecido \$115.000, perole pagarían inmediatamente. Los Jones le han pfrecido S150.00, pero no podrán pagarle, sino hasta después de tres años contados a partir del dia de hoy. La tasa de interés es de 10%. Que oferta eleigiria.
The decision involves comparing the present value, PV, of each offer. Choose the offer with the highest PV.
Since the Smiths’ payment occurs immediately, its present value does not need tobe adjusted.
PV(Smith) = \$115,000
The Joneses’ offer occurs three years from today. Therefore, the payment must be discounted back three periods at 10 percent.
PV(Jones) = C3 / (1+r)3
= \$150,000 / (1.10)3
= \$112,697.22

Since the PV of the Joneses’ offer, \$112,697.22, is less than the Smiths’ offer, \$115,000, you should choose the Smiths’ offer.
4.15. Suponga que deposita\$1000 al final de cada uno de los cuatro anos. Si la cuenta deja 12% anual ¿Cuánto habrá en su cuenta después de siete años?.
The deposit at the end of the first year will earn interest for six years, from the end of year 1 to the end of year 7.
FV = \$1,000 (1.12)6 = \$1,973.82
The deposit at the end of the second year will earn interest for five years.
FV = \$1,000 (1.12)5 = \$1,762.34The deposit at the end of the third year will earn interest for four years.
FV = \$1,000 (1.12)4 = \$1,573.52
The deposit at the end of the fourth year will earn interest for three years.
FV = \$1,000 (1.12)3 = \$1,404.93
Combine the values found above to calculate the total value of the account at the end of the seventh year:
FV = \$1,973.82 + \$1,762.34 + \$1,573.52 + \$1,404.93 =\$6,714.61
The value of the account at the end of seven years will be \$6,714.61.

4.23. Harris inc. pago un dividendo de \$ 3 ayer. Si la empresa aumenta su dividendo 5% cada ano y la tasa de descuento apropiada es de 12% ¿Cuál es el precio de las acciones de Harris?
Use the growing perpetuity formula. Since Harris Inc.’s last dividend was \$3, the next dividend (occurring one year from today)...