Two mutually exclusive investment opportunities require an initial investment of $7 million. Investment A pays $2.0 million per year in perpetuity, while investment B pays $1.4 million in the first year, with cash flows increasing by 4% per year after that. At what cost of capital would an investor regard both opportunities as being equivalent?
A)3%
B)7%
C)13%
D)15%

Question

Quizplus · Accepted Answer

To determine the cost of capital at which the two investments are equivalent, we need to set their present values equal to each other:
Investment A: 
PV = $2.0 million / 0.03 = $66.67 million
Investment B:
PV = $1.4 million / (0.13 - 0.04) = $17.5 million
PV = $17.5 million * (1.04 / 0.13) = $139.06 million
Therefore, to find the equivalent cost of capital:
$66.67 million = $139.06 million 
/ (1 + r)^1
r = 0.13 or 13%
Since the question asks for the cost of capital at which the two investments are equivalent, the best choice is C) 13%.

Two Mutually Exclusive Investment Opportunities Require an Initial Investment of $7