Question

# 14. You own two investments, A and B, that have a combined total value of 63,418...

14. You own two investments, A and B, that have a combined total value of 63,418 dollars. Investment A is expected to make its next payment in 1 month. A’s next payment is expected to be 266 dollars and subsequent payments are expected to grow by 0.78 percent per month forever. The expected return for investment A is 1.25 percent per month. Investment B is expected to pay 219 dollars each quarter forever and the next payment is expected in 3 months. What is the quarterly 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.

Solution

Present value of growing perpetuity (monthly)=Payment next month/(r-g)

where

r= discount rate/month

g=growth rate per month

For investment A

Present value =266/(.0125-.0078)

=56595.74468

Total value of investment A and B= 63,418

Thus present value of investment B=63,418-56595.74468

=6822.25532

Now B is a normal perpetuity making payments per quarter

PV of perpetuity=Periodic payment/rate of return per period

6822.25532=219/rate of return per quarter

Rate of return per quarter=219/6822.25532

=0.032101

Thus quaterly expected return of B=0.032101

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