Question

Howie Long has just learned he has won a $500,000 prize in the lottery. The lottery has given him two options for receiving the payments: (1) If Howie takes all the money today, the state and 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?

Answer 1

To determine which payout option Howie should choose, we calculate the present value of each option. Option 1 gives him $270,000 after deducting taxes and option 2 gives him a present value of $474,938 for future payments. Therefore, he should choose option 2.

Step-by-step explanation:

To determine which payout option Howie should choose, we need to calculate the present value of each option and compare them. For option 1, if Howie takes all the money today, he will receive $500,000 and the taxes deducted will be 46% of this amount, which is $230,000. So, Howie will be left with $270,000.

For option 2, Howie will receive 20 equal payments of $36,000. To calculate the present value, we need to discount these future cash flows back to the present. Using the formula for the present value of an annuity, we can calculate the present value of the payments to be approximately $474,938.

Now, we compare the present values. The present value of Option 1 is $270,000, while the present value of Option 2 is $474,938. Therefore, Howie should choose option 2, the payout of 20 equal payments of $36,000.