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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