As winner of a breakfast cereal competition, you can choose one of the following prizes: a....

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 the discount rate is 12%. i. (20 pts) Write down the discounted cash flow equation for each option.

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Expert Solution

Discounted Cash Flow = CF¹ / (1+dr)¹ + CF² / (1+dr)² + …….. + CFⁿ / (1+dr)ⁿ

Where CF = Cash Flow

dr = Discount Rate

n = total period of cash flows

a. DCF = $ 1,80,000 / (1+ 20%)⁵ = $ 72,337.96

b. Since it is an annual perpetuity, DCF = 11400/20% = $ 57,000

c. DCF = $19000 / (1+20%)¹ + $19000 / (1+20%)² +$19000 / (1+20%)³ + $19000 / (1+20%)⁴ + $19000 / (1+20%)⁵ + $19000 / (1+20%)⁶ + $19000 / (1+20%)⁷ + $19000 / (1+20%)⁸ + $19000 / (1+20%)⁹ + $19000 / (1+20%)¹⁰

= 15833.33333 + 13194.44444 + 10995.37037 + 9162.808642 + 7635.673868 + 6363.061557 + 5302.551297 + 4418.792748 + 3682.32729 + 3068.606075

= $ 79,656.97

d. DCF of a growing perpetuity = Year 1 Cash flow/ (Discount rate – growth rate)

DCF = $ 6,500/ (20% - 5%)

= $ 43,333.33

Therefore, the winner should select the option C of receiving $ 19,000 for ten years.

ekkarill92 answered 2 years ago

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