Two mutually exclusive investment opportunities require an initial investment of $10 million. Investment A pays $1.5 million per year in perpetuity, while investment B pays $1.2 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?

15%

Solving this would require finding the rate/cost of capital that gives both investments the same present value.

Investment 1

Investment 1 is a perpetuity which means that it's present value can be calculated as,

= Amount/rate

= 1,500,000/r

Investment 2

Investment 2 pays $1,200,000 in the first year and then grows at a rate of 3% every year afterwards.

The Present Value of such can be calculated with the following equation,

= Amount / ( rate/cost of capital - growth rate)

= 1,200,000 / ( r - 3%)

To find the Rate that gives both figures the same Present Value, simply equate them.

1,500,000/r = 1,200,000 / (r - 3%)

1,500,000(r - 3% ) = 1,200,000r

1,500,000r - 45,000 = 1,200,000r

300,000r = 45,000

r = 45,000/300,000

r= 0.15

r = 15%

At 15% an investor regard both opportunities as being equivalent.

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