Question

2. An investment costs $23,958 and will generate cash flow of $6,000 annually for five years. The firm’s cost of capital is 6 percent. a. What is the investment’s internal rate of return? Based on the internal rate of return, should the firm make the investment? b. What is the investment’s net present value? Based on the net present value, should the firm make the investment? c. Compare the answers to Problems 1 and 2. Do the net present values and the internal rates of return suggest the same courses of action in each problem?

Answer 1

a)

Internal rate of return is the rate that makes initial investment equal to present value of cash inflows

Initial investment = Annuity * [ 1 - 1 / ( 1 + r)ⁿ] / r

23,958 = 6,000 * [ 1 - 1 / ( 1 + r)⁵] / r

Using trial and error method i.e after trying various values for R, let's try R as 8%

23,958 = 6,000 * [ 1 - 1 / ( 1 + 0.08)⁵] / 0.08

23,958 = 6,000 * 3.99271

23,958 = 23,958

Therefore, IRR is 8%

b)

Company should make the investment as the IRR is greater than the cost of capital of 6%.

c)

Net present value = Present value of cash inflows - present value of cash outflows

Net present value = Annuity * [ 1 - 1 / ( 1 + r)ⁿ] / r - Initial investment

Net present value = 6,000 * [ 1 - 1 / ( 1 + 0.06)⁵] / 0.06 - 23,958

Net present value = 6,000 * 4.212364 - 23,958

Net present value = $1,316.18

d)

Firm should make the investment as it has a positive NPV.

e)

net present values and the internal rates of return will suggest the same course of action.