Time value and discount rates Personal Finance Problem You just won a lottery that promises to pay you $1,600,000 exactly 10 years from today. Because the $1,600,000 payment is guaranteed by the state in which you live, opportunities 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? (1) 8% (2) 12% (3) 16% b. Rework part a under the assumption that the $1,600,000 payment will be received in 20 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. Click the icon to see the worked Solution (Formula Solution). Click the icon to see the Worked Solution (Financial Calculator Solution). 1 Click the icon to see the Worked Solution (Spreadsheet Solution). a. (1) The least you will sell your calm for if you can eam a rate of return of % during the 10-year period is $. (Round to the nearest cent.) (2) The least you will sell your claim for If you can earn a rate of retum of 12% during the 10-year period is $ (Round to the nearest cent.) (3) The least you will sell your claim for if you can earn a rate of retum of 16% during the 10-year period is $(Round to the nearest cent.) b. (1) The least you will sell your claim for If you can earn a rate of retum of 8% during the 20-year period is $. (Round to the nearest cent.) (2) The least you will sell your claim for If you can earn a rate of retum of 12% during the 20-year period is $ (Round to the nearest cent.) (3) The least you will sell your claim for If you can earn a rate of retum of 16% during the 20-year period is $ (Round to the nearest cent.) (3) The least you will sell your claim for if you can earn a rate of return of 16% during the 20-year period is $ (Round to the nearest cent.) 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. (Select the best answer below.) A. As the discount rate increases, the present value becomes larger. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies. B. As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the greater the present value due to the greater time over which the opportunity cost applies. O C. As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies. OD. As the discount rate increases, the present value becomes smaller. Also, the shorter the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies
