Question

Howie Long has just learned he has won a $506,300 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 $37,000 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 26%.

Required:

1. Compute the present value of the cash flows for lump sum payout.

2. Assuming Howie can earn an 8% rate of return (compounded annually) on any money invested during this period, compute the present value of the cash flows for annuity payout.

3. Which pay-out option should he choose?

Answer 1

Answer and Explanation:

According to the scenario, computation of the given data are as follow:-

A).Present Value of the Cash Flow for the Lump Sum Payout

= Prize of Lottery Amount × (1 -Tax Rate)

= $506,300 × (1 - 0.46)

= $506,300 × 0.54

= $273,402

B).Present Value of the Cash Flows for Annuity Payout is

= Annuity Payment × (1 - Tax Rate) × PVIFA 8%,20 Years × (1  + Rate of Return)

= $37,000 × (1 - 0.26) × 9.8181 × (1 + .08)

= $37,000 × 0.74 × 9.8181 × 1.08

= $290,325

c). According to the analysis, $290,325 is more than the $273,402, So he should be chooses option (b) $290,325 as a payout option.