Question

ou are evaluating two investment choices in order to fund an Indiana University endowment. Choice A is a 25 year annuity that pays $25,000 per year, with the first payment paid at the beginning of year 1. Choice B is a growing perpetuity that pays $20,000 per year & grows at 3% per year forever; The first payment is made at the end of year 2. Assume the required rate of return on both products is 10%? How much more will the growing perpetuity cost to purchase compared to the annuity ? Round your answer to the nearest whole dollar.

Answer 1

- Choice A is a 25 year annuity that pays $25,000 per year, with the first payment paid at the beginning of year 1 (or can be said one year from today)

Calculating the Present Value of periodic annuity using ordinary annuity formula:-

Where, C= Periodic Payments = $25,000

r = Periodic Interest rate = 10%

n= no of periods = 25 years

Present Value of Choice A= $226,926

- Choice B is a growing perpetuity that pays $20,000 per year & grows at 3% per year forever; The first payment is made at the end of year 2

As the first payment starts from year end 2 we will calculate the Present value of Growing perpetuity paymnet at year end 1 and then discount it for 1 year to arrive at Present Value today:-

Where, C= First Payments = $20,000

r = Periodic Interest rate = 10%

g = growth rate = 3%

n= no of periods = 1 years

Present Value of Choice B = $259,740.26

The more will the growing perpetuity cost to purchase compared to the annuity = $259,740.26 - $226,926

= $32,814

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