You just won a lottery that promises to pay you $1 million exactly 10 years from

Question

You just won a lottery that promises to pay you $1 million exactly 10 years from today. Because the $1 million payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate lump-sum cash payment.
a. What is the least you will sell your claim for if you could earn the following rates of return on similar-risk investments during the 10-year period?
1. 6 percent
2. 9 percent
3. 12 percent
b. Rework part (a) under the assumption that the $1 million payment will be received in 15 rather than 10 years.
c. Based on your findings in parts (a) and (b), discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

Explanation / Answer

a) 1. 1000000/(1.06)^10 = 558394 2. 1000000/(1.09)^10 = $422411 and 3. 1000000/(1.12)^10 = $321973 b) 1. $ 417265 2. $ 274538 3. $ 182696 c) As time period increases, the expected minimum present value decreases As interest rate increases, the expected minimum present value decreases

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