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Chapter 6: Q4P (page 307)

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

Expert verified

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

Step by step solution

01

Calculation of Lumpsum Payout

Lumpsumpayout=Amountoflottery-Tax=500,000-500,000脳46%=$270,000

02

Calculation of annuity payments

PresentValueofAnnuitypayment=NetAnnuitypayment脳PVfactor=27,000脳10.60360=$286,297

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

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Most popular questions from this chapter

Adams Inc. will deposit $30,000 in a 6% fund at the end of each year for 8 years beginning December 31, 2017. What amount will be in the fund immediately after the last deposit?

Question: What is the time value of money? Why should accountants have an understanding of compound interest, annuities, and present value concepts?

Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly?

Murphy Mining Company recently purchased a quartz mine that it intends to work for the next 10 years. According to state environmental laws, Murphy must restore the mine site to its original natural prairie state after it ceases mining operations at the site. To properly account for the mine, Murphy must estimate the fair value of this asset retirement obligation. This amount will be recorded as a liability and added to the value of the mine on Murphy鈥檚 books. (You will learn more about these asset retirement obligations in Chapters 10 and 13.) There is no active market for retirement obligations such as these, but Murphy has developed the following cash flow estimates based on its prior experience in mining-site restoration. It will take 3 years to restore the mine site when mining operations cease in 10 years. Each estimated cash outflow reflects an annual payment at the end of each year of the 3-year restoration period.

Restoration Estimated Probability Cash Outflow Assessment $15,000 10% 22,000 30% 25,000 50% 30,000 10%

Instructions (a) What is the estimated fair value of Murphy鈥檚 asset retirement obligation? Murphy determines that the appropriate discount rate for this estimation is 5%. Round calculations to the nearest dollar. (b) Is the estimate developed for part (a) a Level 1 or Level 3 fair value estimate? Explain.

Assuming the same facts as those in E6-18 except that the payments must begin now and be made on the first day of each of the 15 years, what payment method would you recommend?
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