Howie Long has just learned he has won a $500,000 prize in the lottery. The lottery has given him two options for receiving payments:(1) If Howie takes all
The money today, the state and the federal governments will deduct taxes at a rate of 46%
Immediately. (2) Alternatively, the lottery offers Howie a payout of 20 equal payments
Of $36,000 with the first payment occurring when Howie turns in the winning ticket.
Howie will be taxed on each of these payments at a rate of 25%
Instructions:
Assuming Howie can earn an 8% rate of return (compounded annually) on any money invested
During this period, which pay-out option should he choose?

For the second option, I'm assuming that the following payments will be made... annually? :confused:

Anyway, get that period well defined, and then work out the net money flow if he chose the first option, then work out the net money flow if he chose the second option. Compare both to be able to give which one is the better.

Option 1 is pretty simple to figure out. Take the prize money times (1- 46%) to get the net cash received. The 46% is your tax rate and this is the easy way to calculate the net amount received or the after tax amount received. Now you will have to calculate the future value of this money and this is a Future Value of money problem. Your known iformation is one payment received calculated earlier, 20 periods, and 8% interest compounded annually, so now you have the information needed to solve this problem.

Option 2 is an annuity problem so you have to figure out what the total cash amount will be after the 20th payment. Your individual net cash received each period will be calculated the same way as option one, just change the amount and the tax rate. Your number of periods or number of payments received is 20, and your annual interest rate is 8%. Now you have the information you need to calculate the total amount of cash received.