Answer: 15%
Solving this would require finding the rate/cost of capital that gives both investments the same present value.
<u>Investment</u> <u>1</u>
Investment 1 is a perpetuity which means that it's present value can be calculated as,
= Amount/rate
= 1,500,000/r
<u>Investment</u> <u>2</u>
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.
