Question

Your financial planner offers you two different investment plans. Plan X is a $20,000 annual perpetuity. Plan Y is a 10-year, $34,000 annual annuity. 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

=$20000/discount rate

Y:

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

=34000[1-(1+discount rate)^-10]/discount rate

$20000/discount rate =34000[1-(1+discount rate)^-10]/discount rate

$20000=34000[1-(1+discount rate)^-10]

($20000/34000)=[1-(1+discount rate)^-10]

(1+discount rate)^-10=1-($20000/34000)

1/(1+discount rate)^10=0.411764705

1/(1+discount rate)^10=0.411764705

(1/0.411764705)=(1+discount rate)^10

(1+discount rate)=(2.428571434)^(1/10)

discount rate=1.0928-1

=9.28%(Approx).