Question

# 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 \$9.9 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?

a. NPVA = 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%

NPVB = 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,
NPVA = 2.16/0.055 - 9.9 = 29.37 million
NPVB = 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:
NPVA = NPVB
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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