Cara owns two investments, A and B, that have a combined total value of 132,764

Question

Cara owns two investments, A and B, that have a combined total value of 132,764 dollars. Investment A is expected to pay 9,193 dollars per year forever; its next payment is expected in 1 year; and its expected return is 11.83 percent per year. Investment B is also expected to make annual payments forever and make its next payment in 1 year. Investment B’s next payment is expected to be 4,498 and all subsequent payments are expected to grow by 2.82 percent per year forever. What is the annual expected return for investment B?  Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Explanation / Answer

Value of Investment A and Investment B = $132,764

Investment A:

Annual Cash Flow = $9,193
Expected Return = 11.83%

Value of Investment A = Annual Cash Flow / Expected Return
Value of Investment A = $9,193 / 0.1183
Value of Investment A = $77,709

Investment B:

Value of Investment B = Value of Investment A and Investment B - Value of Investment A
Value of Investment B = $132,764 - $77,709
Value of Investment B = $55,055

Expected Cash Flow = $4,498
Growth Rate = 2.82%

Value of Investment B = Expected Cash Flow / (Expected Return - Growth Rate)
$55,055 = $4,498 / (Expected Return - 0.0282)
Expected Return - 0.0282 = 0.0817
Expected Return = 0.1099

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