Two mutually exclusive investment opportunities require an initial investment of $5 million.Investment A then generates $1.5 million per year in perpetuity,while investment B pays $1 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)3%
B)6%
C)9%
D)10%

Question

Quizplus · Accepted Answer

We need to find the cost of capital at which the Present Value (PV) of the perpetuity from Investment A is equal to the PV of the cash flows from Investment B.

PV of perpetuity from Investment A = $1.5 million / 0.09 = $16.67 million
PV of cash flows from Investment B = $1 million / 0.09 + $1.03 million / (0.09)^2 + $1.06 million / (0.09)^3 + ... = $19.44 million

At a cost of capital of 9%, the two investments are equivalent since their present values are equal ($16.67 million = $19.44 million). Therefore, the investor should choose either investment depending on their risk preference. If they prefer a higher initial cash flow and are willing to take on increasing cash flow risk over time, then they should choose Investment B. If they prefer a lower but more stable cash flow over time, then they should choose Investment A.

Two Mutually Exclusive Investment Opportunities Require an Initial Investment of $5