Question

1. A project that provides annual cash flows of $12,500 for 8 years costs $65,000 today. At what discount rate would you be indifferent between accepting the project or rejecting it? If the required rate of return is 9%, what is the profitability index of this project?   

Answer 1

a)

The discount rate that you should be different is the internal rate of return

IRR is the rate of return that makes initial investment equal to preset value of cash inflows

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

65,000 = 12,500 * [1 - 1 / (1 + r)^8] / R

Using trial and method, i.e, after trying various values for R, lets try R as 10.71%

65,000 = 12,500 * [1 - 1 / (1 + 0.1071)^8] / 0.1071

65,000 = 12,500 * [1 - 0.443104] / 0.1071

65,000 = 12,500 * 5.19978

65,000 = 65,000

Therefore, indifferent rate is 10.71%

2)

Profitability index = Present value / initial investment

Present value = 12,500 * [1 - 1 / (1 + 0.09)^8] / 0.09

Present value = 12,500 * [1 - 0.501866] / 0.09

Present value = 12,500 * 5.534819

Present value = 69,185.23893

Profitability index = 69,185.23893 / 65,000

Profitability index = 1.06