Question

Your financial planner offers you two different investment plans. Plan X is a $10,000 annual perpetuity. Plan Y is a 12-year, $20,000 annual perpetuity. Both plans will make their first payment from one year 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

=10,000/discount rate

Y:

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

=20,000[1-(1+discount rate)^-12]/discount rate

Hence

20,000[1-(1+discount rate)^-12]/discount rate=10,000/discount rate

20,000[1-(1+discount rate)^-12]=10,000

(10,000/20,000)=1-(1+discount rate)^-12

0.5=1-(1+discount rate)^-12

1-0.5=(1+discount rate)^-12

(1+discount rate)^-12=0.5

[(1/(1+discount rate)]^12=0.5

(1/(1+discount rate)=(0.5)^(1/12)

(1/(1+discount rate)=0.943874313

(1/0.943874313)=1+discount rate

Hence discount rate=(1/0.943874313)-1

=5.95%(Approx).