Question

Two mutually exclusive investment opportunities require an initial investment of $ 8million. Investment A then generates $ 1.50 million per year in? perpetuity, while investment B pays $1.10 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?

Answer 1

Present Value of Perpetuity = Annual Cash Flow / (Cost of Capital - Growth Rate)

Let cost of capital be i%

Investment A:

Initial Investment = $8 million
Annual Cash Flows = $1.50 million

Net Present Value = -$8,000,000 + $1,500,000 / i

Investment B:

Initial Investment = $8 million
Cash Flows in Year 1 = $1.10 million
Growth Rate = 3%

Net Present Value = -$8,000,000 + $1,100,000 / (i - 0.03)

NPV of Project A = NPV of Project B
-$8,000,000 + $1,500,000 / i = -$8,000,000 + $1,100,000 / (i - 0.03)
$1,500,000 * i - $45,000 = $1,100,000 * i
$400,000 * i = $45,000
i = 0.1125
i = 11.25%

So, Investor will be indifferent for both investment at 11.25% cost of capital