Question

Alan Long has just learned he has won a $511,700 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Alan takes all the money today, the state and federal governments will deduct taxes at a rate of 47% immediately. (2) Alternatively, the lottery offers Alan a payout of 20 equal payments of $42,100 with the first payment occurring when Alan turns in the winning ticket. Alan will be taxed on each of these payments at a rate of 26%.

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Compute the present value of the cash flows for lump sum payout. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Lump sum payout

$

Assuming Alan can earn an 11% rate of return (compounded annually) on any money invested during this period, compute the present value of the cash flows for annuity payout. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Present value of annuity payout

Answer 1

The answer has been presented in the supporting sheet. For detailed answer refer to the supporting sheet.

D A B C Answer Part 1) Present value of lumsum payment = Lottery Price *(1- Tax Rate) = 511700*(1-47%) = $ 271201 Thus the correct answer is $ 271201 2 B 2 5 Part 2) Present value of annuity payment = annual inflow after tax * ((Present value annuity (11%,19))+1) = (42100*(1-26%))*((1-(1.11)^-19)/.11)+1) = 31154*8.83929 = $ 275379 3 Thus the correct answer is $275379 Thank You