Question

Your financial planner offers you two different investment plans. Plan X is a $14,000 annual perpetuity. Plan Y is an annuity lasting 13 years and an annual payment, $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?

Answer 1

X:

Present value of perpetuity=Annual cash flows/discount rate

=14000/discount rate

Y:

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

=20,000[1-(1+discount rate)^-13]/discount rate

14000/discount rate =20,000[1-(1+discount rate)^-13]/discount rate

14000 =20,000[1-(1+discount rate)^-13]

(14000/20,000)=1-(1+discount rate)^-13

1-(14000/20,000)=(1+discount rate)^-13

[1/(1+discount rate)]^13=0.3

1/(1+discount rate)]=(0.3)^(1/13)

1/(1+discount rate)]=0.911545934

(1/0.911545934)=1+discount rate

1+discount rate=1.09703742

discount rate=1.09703742-1

=9.70%(Approx)