Problem 6-4 Tony Long has just learned he has won a $508,300 prize in the lotter
ID: 2541625 • Letter: P
Question
Problem 6-4 Tony Long has just learned he has won a $508,300 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Tony takes all the money today, the state and federal governments will deduct taxes at a rate of 46% immediately. (2) Alternatively, the lottery offers Tony a payout of 20 equal payments of $39,600 with the first payment occurring when Tony turns in the winning ticket. Tony will be taxed on each of these payments at a rate of 25%. Click here to view factor tables 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 o decimal places, e.g. 458,581.) Lump sum payout $ Assuming Tony can earn an 10% 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 $ Which pay-out option should he choose? Click if you would like to Show Work for this question: Open Show Work SHOW SOLUTION SHOW ANSWER LINK TO TEXTExplanation / Answer
PV of lump sum pay-out = 508300 * (1 - .46) { tax arte = 46%}
= 508300 * 0.54
= $274482
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Annual pay in = 39600 * (1 - .25)
= 39600 * .75
= $29700
Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is
PV of annuity = P[1- (1+ r)^-n]/ r
Where,
Periodic deposit (P) = $29700
Interest rate = 10%
Time (n) = 20
Let's put all the values in the formula to find PV o annuity
= 29700[1- (1+ 0.1)^-20]/ 0.1
= 29700[1- (1.1)^-20]/ 0.1
= 29700[1- 0.148643628024143]/ 0.1
= 29700[0.851356371975857/ 0.1]
= 29700[8.51356371975857]
= $252852.84
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First option has greater present value so first option should be selected.
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