Question

What discount rate would make you indifferent between receiving $3,117.00 per year forever and $5,819.00 per year for 24.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

Present value of perpetuity=Annual cash flows/discount rate

=3,117/discount rate

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

=5,819[1-(1+discount rate)^-24]/discount rate

3,117/discount rate=5,819[1-(1+discount rate)^-24]/discount rate

3,117=5,819[1-(1+discount rate)^-24]

(3,117/5,819)=1-(1+discount rate)^-24

1-(3,117/5,819)=(1+discount rate)^-24

[1/(1+discount rate)]^24=0.464340952

1/0.464340952=(1+discount rate)^24

(1+discount rate)^24=2.15358993

1+discount rate=(2.15358993)^(1/24)

discount rate=1.03248034-1

=3.25%(Approx)