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17 February, 05:57

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?

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  1. 17 February, 06:07
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    Answer: 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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