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 payout option should he choose?

Short answer

The annuity payout should be accepted as it offers a higher present value.

Step-by-step solution

Calculation of Lumpsum Payout

$$\begin{gathered} \mathbf{Lump}\mathbf{}\mathbf{sum}\mathbf{}\mathbf{payout}\mathbf{=}\mathbf{Amount}\mathbf{}\mathbf{of}\mathbf{}\mathbf{lottery}\mathbf{-}\mathbf{Tax} \\ \mathbf{=}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{46}\mathbf{\%} \\ \mathbf{=}\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000} \end{gathered}$$

Calculation of annuity payments

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Annuity}\mathbf{}\mathbf{payment}\mathbf{=}\mathbf{Net}\mathbf{}\mathbf{Annuity}\mathbf{}\mathbf{payment}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{factor} \\ \mathbf{=}\mathbf{27}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{10}\mathbf{.}\mathbf{60360} \\ \mathbf{=}\mathbf{\$}\mathbf{286}\mathbf{,}\mathbf{297} \end{gathered}$$

The annuity payout should be chosen, as its present value is higher.