Question

You have recently won the super jackpot in the Washington State Lottery. On reading the fine print, you discover that you have the following two options: a. You will receive 32 annual payments of $220,000, with the first payment being delivered today. The income will be taxed at a rate of 25 percent. Taxes will be withheld when the checks are issued. b. You will receive $635,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $170,000 each year for 31 years. The cash flows from this annuity will be taxed at 25 percent. Using a discount rate of 8 percent, what is the present value of your winnings for each option? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) a. P Present value of Option A b. Present value of Option B

Answer 1

a). Present value of option A:

PMT = 220,000*(1-25%) = 165,000; FV = 0; N = 32; rate = 8%; Mode (or type) =1, solve for PV.

PV = 2,037,716.90

b). Present value of option B:

PMT = 170,000*(1-25%) = 127,500; FV = 0; N = 31; rate = 8%, Mode (or type) = 0, solve for PV.

PV = 1,447,099.42

Total value = 1,447,099.42 + 635,000 = 2,082,099.42