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 30 annual payments of $210,000, with the first payment being delivered today. The income will be taxed at a rate of 30 percent. Taxes will be withheld when the checks are issued. b. You will receive $625,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $160,000 each year for 29 years. The cash flows from this annuity will be taxed at 30 percent

Answer 1

Note: Interest rate is not mentioned. The same is assumes as 10% for calculation purpose.

Option (a):

The income stream constitutes an annuity due with cash flow as follows:

Annual payments= $210,000. Tax rate= 30%

Net yearly payment =$210,000*(1-30%) = $147,000.

Present value of this cash flow= $1,524,332.07 calculated as PV of annuity as follows:

Option (b):

The income stream comprise of the following:

(i)   Single payment of $625,000 now (PV= $625,000)

(ii) Ordinary annuity of 29 cash flow as follows:

Annual payments= $160,000. Tax rate= 30%

Net yearly payment =$160,000*(1-30%) = $112,000.

Present value of this cash flow= $1,049,395.86 calculated as PV of annuity as follows:

Total present value of option (b)= $625,000 + $1,049,395.86 = $1,674,395.86

The PV of option (b) is higher and hence the same is recommended.