Question

You are considering an investment in a clothes distributer. The company needs $ 108,000 today and expects to repay you $ 120,000 in a year from now. What is the IRR of this investment​ opportunity? Given the riskiness of the investment​ opportunity, your cost of capital is 10 %. What does the IRR rule say about whether you should​ invest?

Given the riskiness of the investment​ opportunity, your cost of capital is 10%. What does the IRR rule say about whether you should​ invest?

The IRR rule says that you: (should be indifferent) (should invest) (should not invest)

Answer 1

Present value = $108,000

Future value = $120,000

Time = 1 year

Cost of capital = 10%

Net present value at 10% = Present value of cash inflows - Present value of cash outflows

= 120,000 x PVF(_{10%, 1}) - 108,000

= 120,000 X 0.909 - 108,000

= 109,080 - 108,000

= $1,080

IRR is the rate at which NPV of a product becomes zero.

Since NPV is positive at 10%, hence IRR must be above 10%

We will have to calculate at a higher cost of capital. Let the higher rate be 12%

Net present value at 12% = Present value of cash inflows - Present value of cash outflows

= 120,000 x PVF(_{12%, 1}) - 108,000

= 120,000 X 0.893 - 108,000

= 107,160 - 108,000

= -$840

Since at 12%, NPV is negative, hence IRR must lie below 12%.

%. Exact IRR can be calculated as under:
IRR = Lower rate + {NPV at lower rate/(NPV at lower rate - NPV at higher rate)} x (Higher rate - lower rate)
= 10% + {1,080/(1,080 + 840)} x (12% - 10%)
= 10% + (1,080/1,920) x 2
= 10% + 1.125%
= 11.125%
Hence, IRR of the project is 11.125%
Since IRR is more than cost of capital, investment should be made .

Kindly give a positive rating if you are satisfied with the answer. Feel free to ask if you have any doubt. Thanks.