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 18-year, $30,000 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 enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Your financial planner offers you two different investment plans. Plan X is a $17,000 annual perpetuity. Plan Y is a 18-year, $30,000 annual annuity. Both plans will make their first payment one year from today.

Explanation / Answer

Workings:

Let the discount rate be r.

Present value of a perpetity = Perpetuity / r. = $ 17,000 / r.

Present value of an ordinary annuity = Annuity x Present Value Interest Factor of an Annuity = Annuity x [ { 1 - ( 1 / 1+r ) n } / r ] = 30,000 * [ { 1 - ( 1/ 1+ r)18 } / r ]

At indifference point ,

17,000 / r = 30,000 x [ { 1 - ( 1 / 1 + r ) 18 } / r ]

r = 4.75 %.

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