You are deciding between two mutually exclusive investment opportunities. Both r

Question

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $ 10.3 million. Investment A will generate $ 2.06 million per year? (starting at the end of the first? year) in perpetuity. Investment B will generate $ 1.42 million at the end of the first? year, and its revenues will grow at 2.9 % 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 7.6 %?? c. In this? case, when does picking the higher IRR give the correct answer as to which investment is the best? opportunity?

Explanation / Answer

Answer a.

Investment A:

Let IRR be i%

NPV of Investment = -$10,300,000 + $2,060,000 / i
0 = -$10,300,000 + $2,060,000 / i
i = 20%

IRR = 20%

Investment B:

Let IRR be i%

NPV of Investment = -$10,300,000 + $1,420,000 / (i - 0.029)
0 = -$10,300,000 + $1,420,000 / (i - 0.029)
i - 0.029 = 0.1379
i = 0.1669 or 16.69%

IRR = 16.69%

So, Investment A has higher IRR.

Answer b.

Investment A:

NPV of Investment = -$10,300,000 + $2,060,000 / 0.076
NPV of Investment = $16,805,263.16

Investment B:

NPV of Investment = -$10,300,000 + $1,420,000 / (0.076 - 0.029)
NPV of Investment = $19,912,765.96

So, Investment B has higher NPV at 7.6%.

Answer c.

Let crossover rate be i%

NPV of Investment A at i% = NPV of Investment B at i%
-$10,300,000 + $2,060,000 / i = -$10,300,000 + $1,420,000 / (i - 0.029)
206 / i = 142 / (i - 0.029)
103 / i = 71 / (i - 0.029)
103*i - 2.987 = 71*i
32*i = 2.987
i = 0.0933 or 9.33%

IRR will provide correct answer if cost of capital is higher than 9.33%

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