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# You just won the lottery that promises to pay \$1,000,000 10 years from today, what would you sell your claim for?

You just won the lottery that promises to pay you \$1,000,000 exactly 10 years from today. Because the \$1,000,000 payment is guaranteed by the state in which you live, opportunitites exist to sell the claim today for an immediate single cash payment.

A. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10 year period?
A. 6%
B. 9%
C. 12%

B. Rework part a under the assumption that the \$1,000,000 payment will be received in 15 rather than 10 years.

C. On the basis of 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.

#### Solution Preview

A. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10 year period?

The least one will sell the claim for is the present value of the amount that is to be received in 10 years. The PV is calculated as FV/(1+r)^n
Here we have to calculate the PV under different r and n= 10 years

A. 6%

PV = ...

#### Solution Summary

The solution calculates the amounts a lottery winner could expect to receive in a sale of a state-guaranteed annuity payment plan for an immediate single cash payment today. The calculations are made at various interest rates and the solution contains comment about those calculations.

\$2.19