Question

Using the tables in Exhibits 26-3 and 26-4, determine the present value of the following cash flows, discounted at an annual rate of 15 percent. (Round "PV factors" to 3 decimal places. Do not round intermediate calculations and round your final answers to the nearest whole dollar amount.)

a) $9,400 to be received 20 years from today.

b) $14,000 to be received annually for 10 years.

c) $9,300 to be received annually for five years, with an additional $12,000 salvage value expected at the end of the fifth year.

d) $29,000 to be received annually for the first three years, followed by $20,000 received annually for the next two years (total of five years in which cash is received).

Answer 1

a)

Present value = Future value / (1 + r)ⁿ

Present value = 9,400 / (1 + 0.15)²⁰

Present value = 9,400 / 16.367

Present value = $574

b)

Present value = annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = 14,000 * [1 - 1 / (1 + 0.15)¹⁰] / 0.15

Present value = 14,000 * 5.018769

Present value = $70,263

c)

Present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Present value = 9,300 * [1 - 1 / (1 + 0.15)⁵] / 0.15 + 12,000 / (1 + 0.15)⁵

Present value = 9,300 * 3.352 + 5,966.1208

Present value = $37,141

d)

Present value = 29,000 / (1 + 0.15)¹ + 29,000 / (1 + 0.15)² + 29,000 / (1 + 0.15)³ + 20,000 / (1 + 0.15)⁴ + 20,000 / (1 + 0.15)⁵

Present value = $87,592