Your financial planner offers you two different investment p

Your financial planner offers you two different investment plans. Plan X is a $15,000 annual perpetuity. Plan Y is a 14-year, $25,000 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? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Discount rate

Solution

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

=$25000[1-(1+interest rate)^-14]/interest rate

Present value of perpetuity=Annual cash flows/interest rate

=$15000/interest rate

$15000/interest rate =$25000[1-(1+interest rate)^-14]/interest rate

15000=25000[1-(1+interest rate)^-14]

(15000/25000)=1-(1+interest rate)^-14

0.6=1-(1+interest rate)^-14

1-0.6=(1+interest rate)^-14

0.4=(1+interest rate)^-14

[(1/(1+interest rate)]^14=0.4

[(1/(1+interest rate)]=(0.4)^(1/14)

1/(1+interest rate)=(0.4)^(1/14)

1+interest rate=1/[(0.4)^(1/14)]
interest rate=1.067638647-1

=6.76%(Approx).