Your financial planner offers you two different investment plans. Plan X is an annual perpetuity of $35,000 per year. Plan Y is an annuity for 15 years with an annual payment of $47,000. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans? (HINT: You will be indifferent when you would pay the same amount for either plan).

 

Indifferent discount rate is computed using the equation given below:

Present value of plan X = Present value of plan Y

Annual perpetual cash flows / r = Periodic payment * [1 - (1 + r)^{-Number of periods}] / r

Annual perpetual cash flows = Annual payment * [1 - (1 + r)^{-Number of periods}]

 $35,000 = $47,000 * [1 - (1 + r)^-15]

[1 - (1 + r)^-15] = $35,000 / $47,000

[1 - (1 + r)^-15] = 0.74468085

(1 + r)^-15 = 1 - 0.74468085

(1 + r)^-15 = 0.25531915

1 + r = 0.25531915^-(1/15)

1 + r = 0.25531915^-0.06666667

1 + r = 1.09528660

r = 1.09528660 - 1

r = 0.09528660 or 9.53%