you are deciding between two mutually exclusive investment opportunities. both require the same initial investment of $20 million. investment a will generate $3 million per year (starting at the end of the first year) in perpetuity. investment b will generate $2 million at the end of the first year and its revenues will grow at 3 percent 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 6 percent? c) which investment has the higher npv when the cost of capital is 12 percent? d) explain why there is a difference in your answers for part (b) and part (c). for what values of the cost of capital does picking the higher irr give the correct answer as to which investment is the best opportunity?

Respuesta :

The IRR is the discount rate that causes the NPV = 0. For Project A: NPV (A) = 2/r − 10 = 0

2/r= 10,

IRR (A)= 20%

For Project B: NPV (B) = 1.5/(r − 0.02) −10 = 0

1.5 = (r − 0.02) × 10

0.15 = r − 0.02

IRR (B) = 17%

Thus, Project A has a higher IRR.

Which investment has the higher NPV when the cost of capital is 7%?

NPV (A) = (2/0.07) − 10 = $18.571 million

NPV (B) = 1.5/(0.07 − 0.02) − 10 = $20 million

The crossover point can be solved by setting the NPVs equal to one another: NPV (A) = NPV (B)

2/r − 10 = 1.5/(r − 0.02) − 10

2(r − 0.02) = 1.5 r

0.5r = 0.04

r = 0.08 = 8%

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