Question

your financial planner offers you two different investment plans. plan x is a 25000 annual perpetuity. plan y is a 10 year 51000 annual annunity. 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

=$25000/discount rate

Y:

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

=$51000[1-(1+discount rate)^-10]/discount rate

$25000/discount rate =$51000[1-(1+discount rate)^-10]/discount rate

$25000=$51000[1-(1+discount rate)^-10]

($25000/$51000)=[1-(1+discount rate)^-10]

(1+discount rate)^-10]=1-($25000/$51000)

1/(1+discount rate)^10=0.509803921

(1+discount rate)^10=1/0.509803921

(1+discount rate)=(1.961538464)^(1/10)

1+discount rate=1.06969

discount rate=1.06969-1

=6.97%(Approx).