Question

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $9.9 million. Investment A will generate $2.16 million per year? (starting at the end of the first? year) in perpetuity. Investment B will generate $1.49 million at the end of the first? year, and its revenues will grow at 2.8% 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 5.1%??

**c.** In this? case, when does picking the higher
IRR give the correct answer as to which investment is the best?
opportunity?

Answer #1

a. NPV_{A} = 2.16/r - 9.9

To find IRR, we set NPV = 0

0 = 2.16/r - 9.9

r = 2.16/9.9 = 21.82%

NPV_{B} = 1.49/(r - 0.028) - 9.9

To find IRR, we set NPV = 0

0 = 1.49/(r - 0.028) - 9.9

r = 1.49/9.9 + 0.028 = 17.85%

Based on the IRR, you always pick project A

b. At r = 0.055,

NPV_{A} = 2.16/0.055 - 9.9 = 29.37 million

NPV_{B} = 1.49/(0.055 - 0.028) - 9.9 = 45.29

So the NPV says take B.

c. The NPV rule selects A (and so agrees with the IRR rule) for
all discount rates to the right of the crossover point.

Crossover Point:

NPV_{A} = NPV_{B}

2.16/r - 9.9 = 1.49/(r - 0.028) - 9.9

2.16/r = 1.49/(r - 0.028)

2.16r - 2.16 x 0.028 = 1.49r

r = 2.16 x 0.028/(2.16 - 1.49) = 9.03%

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