Question

In: Finance

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of...

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $ 9.6 million. Investment A will generate $ 2.06 million per year​ (starting at the end of the first​ year) in perpetuity. Investment B will generate $ 1.48 million at the end of the first​ year, and its revenues will grow at 2.2 % per year for every year after that. a. Which investment has the higher IRR​? b. Which investment has the higher NPV when the cost of capital is 5.8 %​? c. In this​ case, when does picking the higher IRR give the correct answer as to which investment is the best​ opportunity?

Solutions

Expert Solution

a]

IRR of Investment A = rate of return on investment = perpetual cash flow / initial investment = $2.06 million / $9.6 million = 0.2146, or 21.46%

IRR of Investment B = (first year cash flow / initial investment) + perpetual growth rate = ($1.48 million / $9.6 million) + 0.022 = 0.1762, or 17.62%

b]

NPV of Investment A = present value of cash inflows - initial investment

present value of cash inflows = perpetual cash flow / cost of capital = $2.06 million / 0.058 = $35,517,241

NPV of Investment A = $35,517,241 - $9,600,000 = $25,917,241

NPV of Investment B = present value of cash inflows - initial investment

present value of cash inflows = perpetual cash flow / (cost of capital - perpetual growth rate) = $1.48 million / (0.058 - 0.022) = $41,111,111

NPV of Investment A = $41,111,111 - $9,600,000 = $31,511,111

c]

Picking the higher IRR would give the correct answer when both investments have a constant perpetual cash flow, or both have a perpetual growth rate in cash flows. In this case, one of them has a constant perpetual cash flow, whereas another has a perpetual growth rate in cash flows. Hence, the IRR would not give the best answer


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