Question

A proposal for investing 10.5 million has been made. The investment would return end of period payments of 1.15 million for 14 periods at which time the investment could be sold for 2.4 million. What is the internal rate of return for this proposal?  

Answer 1

Initial investment = 10.5 million

End of the period returns (benefits) = 1.15 million

Time period = 14 years

Investment can be sold for 2.4 million (salvage value)

What is the internal rate of return?

Using the trial and error method for calculating the IRR

Let the rate of interest is 10%

First, calculate the NPV of the cash flows at 10%

NPV = -10.5 million + 1.15 million (P/A, 10%, 14) + 2.4 million (P/F, 10%, 14)

NPV = -10.5 million + 1.15 million (7.3667) + 2.4 million (0.2633)

NPV = -1.396375 million

The NPV is negative. We have to calculate a positive NPV. To do so we have to decrease the rate of interest.

Let the rate of interest is 7%

Calculate the NPV of the cash flows at 10%

NPV = -10.5 million + 1.15 million (P/A, 7%, 14) + 2.4 million (P/F, 7%, 14)

NPV = -10.5 million + 1.15 million (8.7455) + 2.4 million (0.3878)

NPV = 0.488045 million

After calculating the positive and negative NPV, use interpolation and calculate the IRR

IRR = 7% + [0.488045 million – 0 ÷ 0.488045 million – (-1.396375 million)]*3%

IRR = 7.7%

Internal rate of return for this proposal is 7.7%.