Question

Submitted Problem 4-54 Calculating Annuities 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. 12 points awarded a. You will receive 31 annual payments of $200,000, 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 Scored b. You will receive $615,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $150,000 each year for 30 years. The cash flows from this annuity will be taxed at 28 percent. Book Using a discount rate of 7 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.) Present value of Option A Present value of Option B S S 1,930,901 93 1.782 976 45

Answer 1

Given,

Discount rate (r) = 7% or 0.07

Tax rate (t) = 28% or 0.28

Solution :-

Annual payments = $200000 Tax rate (t) = 28% ag 0.28 After-tax annual payments (A) - Annual payments (1 – t) = $200000 (1-0.28) 3 $ 200000 (0.72) = $144000 since the first payment being delivered to day, we would calculate pu of 30 payments and add the Pu of 30 payments with the first payment. so no. of payment (n) = 30 7 Pu of 30 = 4 [- ton] payments uuooo 0.07

Fotoga [ 2.62455] $144000 6.612255 0.07 27.612255 - $1786901.93 Present value of option o - Pu of 30 payments + First payment atter tax 9 $1286901.93 + $144000 = $1930901.93 (6) First payment = $615000 No. of years (n) = 30 years. Annual Payments = $150000 After-tax annual Payments (A) - Annual Payments (1-t) $150000 (1-0.28) - $ 150000 (0.72) = $ 108000

payments - rl - Titaal $ 90sovo 0.07 7.612255 $ 108000 [6.612255 0.07 7.612255 - $1340176.45 Present value of option B = PV of annual Payments + First payment - $1340176.45 + $ 615000 = $1955 176.45