Question

As winner of a breakfast cereal competition, you can choose one of the following prizes: a. $180,000 at the end of five years. b. $11,400 a year forever. c. $19,000 for each of 10 years. d. $6,500 next year and increasing thereafter by 5% a year forever. Assume that discount rate is 12%. i. (20 pts) Write down the discounted cash flow equation for each option. ii. (10 pts) Decide which prize you should choose and why?

Answer 1

i. Discounted cashflow equations.

a. $180,000 at the end of five years.

This is a lump sum present value/ discounted cashflow which can be calculated as;

Formula = 180,000 / ( 1 + r)^n

= 180,000/ ( 1 + 12%)^5

= $102,136.83

b. $11,400 a year forever

This is a perpetuity. The present value/ discounted cashflow of a perpetuity is calculated as;

Formula = Amount/rate

= 11,400/12%

= $95,000

c. $19,000 for each of 10 years.

This is an annuity. The formula for calculating the Present value/ discounted cashflow of an annuity is;

`Formula = Annuity * [(( 1 - (1 + i)^(-n) ))/(i) ]` where i is interest rate and n is number of periods

`= 19,000 * [(( 1 - (1 + 0.12)^(-10) ))/(0.12) ]`

= $107,354.24

d. $6,500 next year and increasing thereafter by 5% a year forever.

This is a growing perpetuity. The present value/ discounted cashflow formula is;

= Amount / ( discount rate - growth rate)

= 6,500 / ( 12% - 5%)

= $92,857.14

ii. Choose $19,000 for each of 10 years as it has the highest present value.