Your financial planner offers you two different investment plans. Plan X is a $14,000 annual perpetuity. Plan Y is an annuity lasting 13 years and an annual payment, $20,000. 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.)

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Business

Isaac Walter

14 October, 22:11

Your financial planner offers you two different investment plans. Plan X is a $14,000 annual perpetuity. Plan Y is an annuity lasting 13 years and an annual payment, $20,000. 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.)

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Toby Davila · Answer 1

At 9.70% discount rate would you be indifferent between these two plans.

Explanation:

Present Value of Perpetuity = P/r

Present Value of Annuity = P/r[1 - (1 + r) ^-n]

$14,000/r = $20,000. / r[1 - (1 + r) ^-13]

(1 + r) ^-13 = 1 - $14,000/$20,000.

(1 + r) ^13 = 10/3

r = 9.70%

Therefore, at 9.70% discount rate would you be indifferent between these two plans.