Your financial planner offers you two different investment plans. Plan X is an a

Question

Your financial planner offers you two different investment plans. Plan X is an annual perpetuity of $24,000. Plan Y is an annuity for 12 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? Show how to calculate with financial calculator

Your financial planner offers you two different investment plans. Plan X is an annual perpetuity of $24,000. Plan Y is an annuity for 12 years and an annual payment of $35,000. Both plans will make their first payment one year from today.

Explanation / Answer

Let r be the discount rate

Present Value of perpetuity = Annual Cashflow /  discount rate

= 24000/r

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

Where                                                                                            

A - Annuity payment = 35000

r - rate per period = ?

n - no. of periods = 12

Present value of Annuity = 35000* [(1-(1+r)-12)/r]

24000/r = 35000* [(1-(1+r)-12)/r]

[(1-(1+r)-12)/r]*r= 24000/35000 = 0.68571428571

1-(1+r)-12) = 0.68571428571

(1+r)^-12 = 1-0.68571428571 = 0.31428571429

1+r = (0.31428571429)^(-1/12) = 1.10125936153

r = 1.10125936153-1

= .10125936153

r = 10.13%

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