Your financial planner offers you two different investment plans. Plan X is a $1

Question

Your financial planner offers you two different investment plans. Plan X is a $17,000 annual perpetuity. Plan Y is a 17-year, $24,000 annual annuity. Both plans will make their first payment one year from today. 1. At what discount rate would you be indifferent between these two plans? 2. For this part of the question, assume that Plan Y is a $18,000 annual perpetuity with the first payment two years from today. At what discount rate would you be indifferent between Plan X and Plan Y? 3. For this part of the question assume that Plan Y is a $27,000 annual perpetuity with the first payment three years from today? At what discount rate would you be indifferent between Plan X and Plan Y? Are you expecting a discount rate higher or smaller than the one you found in part (1) and (2)? If you cannot find the discount rate, provide at least your intuition regarding the magnitude of this discount rate.

Explanation / Answer

Let r be the discount rate
1.
PV of Plan X=17000/r
PV of Plan Y=24000/r*(1-1/1(1+r)^17)
Hence,
17000/r=24000/r*(1-1/1(1+r)^17)
=>r=7.51702689614526%

2.
PV of Plan X=17000/r
PV of Plan Y=18000/(r*(1+r))
Hence,
17000/r=18000/(r*(1+r))
=>r=5.88235295137626%

3.
PV of Plan X=17000/r
PV of Plan Y=27000/(r*(1+r)^2)
Hence,
17000/r=27000/(r*(1+r)^2)
=>r=26.0252075608245%

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