Question

Two mutually exclusive investment opportunities require an initial investment of $5 million. Investment A then generates $2.00 million per year in​ perpetuity, while investment B pays $1.50 million in the first​ year, with cash flows increasing by 3% per year after that. At what cost of capital would an investor regard both opportunities as being​ equivalent?

A.13​%

B.3​%

C.12​%

D.6​%

Answer 1

Suppose the cost of capital so that the investor would regard both opportunities as equivalent = r

Investment A

Initial investment = -$5 million

The present value of cash flows of A = C/r = 2/r

The present value of investment A = PVA = Initial investment + Present values of cash flows of A = -5 + (2/r)

Investment B

Initial investment = -$5 million

Cash flows of B = 1.5

Growth rate of the cash flows = g = 3%

Present value of cash flows of B  = C/(r-g) = 1.5/(r - 3%)

Present value of investment A = PVA = Initial investment + Present values of cash flows of A = -5 + 1.5/(r-3%)

For the investments A and B to be equivalent, PVA = PVB

-5 + (2/r) = -5 + 1.5/(r-3%)

2/r = 1.5/(r - 0.03)

2r - 0.06 = 1.5r

0.5r = 0.06

r = 0.06/0.5 = 0.12 = 12%

Answer -> 12% (Option C)