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 31 annual payments of $250,000, with the first payment being delivered today. The income will be taxed at a rate of 28 percent. Taxes will be withheld when the checks are issued.
b. You will receive $530,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $200,000 each year for 30 years. The cash flows from this annuity will be taxed at 28 percent. Using a discount rate of 6.25 percent, which option should you select?

Answer 1

Answer:

should choose option a

Explanation:

option a)

annuity due, 31 payments of $180,000 per year, 6.25% discount rate

Present value = $180,000 x 14.40432 (PV annuity due factor, 6.25%, 31 periods) = $2,592,726

option b)

$500,000 today + ordinary annuity, 30 periods, 6.25%, $144,000

present value = $500,000 + ($144,000 x 13.40432 [PV annuity factor, 6.25%, 30 periods)] = $2,430,222