Question

Your financial planner offers you two different investment plans. Plan X is an annual perpetuity of $20,000. Plan Y is an annuity for 15 years and an annual payment of $35,000. 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.)

Answer 1

To  be indifferent between these two plans, The prsent value of both plans should be equal.

Let r be the discount rate

Present Value of perpetuity = Annual Cashflow /  discount rate

= 20000/r

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where                                                                                            

A - Annuity payment = 35000

r - rate per period = ?

n - no. of periods = 15

Present value of Annuity = 35000* [(1-(1+r)^-15)/r]

20000/r = 35000* [(1-(1+r)^-15)/r]

[(1-(1+r)^-15)/r]*r= 20000/35000 = 0.57142857142

1-(1+r)^-15) = 0.57142857142

(1+r)^-15 = 1-0.57142857142 = 0.42857142858

1+r = 0.42857142858^(-1/15) = 1.05811235561

r = 1.05811235561-1

= .05811235561

r = 5.81%