Question

Your financial planner offers you two different investment plans. Plan X is an annual perpetuity of $15,000. Plan Y is an annuity for 10 years and an annual payment of $20,000. Both plans will make their first payment one year from today.

At what discount rate would you be indifferent between these two plans? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

X:

Present value of perpetuity=Annual cash flows/discount rate

=15000/discount rate

Y:

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

=20,000[1-(1+discount rate)^-10]/discount rate

15000/discount rate=20,000[1-(1+discount rate)^-10]/discount rate

15000=20,000[1-(1+discount rate)^-10]

(15000/20,000)=1-(1+discount rate)^-10

(1+discount rate)^-10=1-(15000/20,000)

(1+discount rate)^-10=0.25

(1/1+discount rate)^10=0.25

(1/1+discount rate)=(0.25)^(1/10)

(1/1+discount rate)=0.870550563

1/0.870550563=1+discount rate

discount rate=(1/0.870550563)-1

=14.87%(Approx).