Your financial planner offers you two different investment plans. Plan X is a $2

Question

Your financial planner offers you two different investment plans. Plan X is a $25,000 annual perpetuity. Plan Y is a 15-year, $35,000 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 round your final answer to 2 decimal places. (e.g., 32.16))

Your financial planner offers you two different investment plans. Plan X is a $25,000 annual perpetuity. Plan Y is a 15-year, $35,000 annual annuity. Both plans will make their first payment one year from today.

Explanation / Answer

dAssuming discount rate is "R", for me to be indifferent returns offered by both plans should be equal.

Return of the annual perpetuity = 25000/R

Return of the annual annuity = 35000*(1- (1+R)^-10) /R

Hence

=> 25000/R = 35000*(1-(1+R)^(-10))/R

=> 1-(1+R)^(-10) = 25/35

=> (1+R)^(-10) = 10/35

=> (1+R)^10 = 35/10

=> R = 3.5^1/10 - 1

=> R = 13.35%

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