   Chapter 14, Problem 14.4CP

Chapter
Section
Textbook Problem

Present valuesAlex Kelton recently won the jackpot in the Colorado lottery while he was visiting his parents. When he arrived at the lottery office to collect his winnings, he was offered the following three payout options:a. Receive $100,000,000 in cash today.b. Receive$25,000,000 today and $9,000,000 per year for eight years, with the first payment being received one year from today.c. Receive$15,000,000 per year for 10 years, with the first payment being received one year from today.Assuming that the effective rate of interest is 7%, which payout option should Alex select? Use the present value tables in Appendix A. Explain your answer and provide any necessary supporting calculations.

To determine

Present Value: The value of today’s amount expected to be paid or received in the future at a compound interest rate is called as present value.

To determine: the payout option that Mr. A would select.

Explanation

Payout Option 1: Receive $100,000,000 in cash today. The present value of$100,000,000 today is $100,000,000. Payout Option 2: Receive$25,000,000 today and $9,000,000 per year for eight years. Calculate the total value of the payout. Present value of$25,000,000 today = $25,000,000 Present value of$9,000,000 =$53,741,700 (1) Totalvalue=(Presentvalueof$25,000,000)+(Presentvalueof$9,000,000)=$25,000,000+$53,741,700=$78,741,700

Working notes:

Calculate the present value of \$9,000,000

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