Question

What discount rate would make you indifferent between receiving $3,765.00 per year forever and $5,455.00 per year for 28.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Answer 1

Present value of perpetuity=Perpetual cash flows/discount rate

=3,765/discount rate

Present value of annuity=Annuity[1-(1+discount rate)^-time period]/rate

=5,455[1-(1+discount rate)^-28]/discount rate

3,765/discount rate=5,455[1-(1+discount rate)^-28]/discount rate

3,765=5,455[1-(1+discount rate)^-28]

(3,765/5,455)=[1-(1+discount rate)^-28]

1-(3,765/5,455)=(1+discount rate)^-28

0.309807516=(1+discount rate)^-28

0.309807516=(1/1+discount rate)^28

(0.309807516)^(1/28)=(1/1+discount rate)

(1/1+discount rate)=0.959013482

1+discount rate=(1/0.959013482)

discount rate=(1/0.959013482)-1

=4.27%(Approx)