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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

Question:The Kellys are planning for a retirement home. They estimate they will need $200,000 4 years from now to purchase this home. Assuming an interest rate of 10%, what amount must be deposited at the end of each of the 4 years to fund the home price? (Round to two decimal places.)

What would you pay for a \(100,000 debenture bond that matures in 15 years and pays \)5,000 a year in interest if you wanted to earn a yield of: (a) 4%? (b) 5%? (c) 6%?

Question:What is the nature of interest? Distinguish between 鈥渟imple interest鈥� and 鈥渃ompound interest.鈥�

Using the appropriate interest table, answer each of the following questions. (Each case is independent of the others.) (a) What is the future value of \(7,000 at the end of 5 periods at 8% compounded interest? (b) What is the present value of \)7,000 due 8 periods hence, discounted at 6%? (c) What is the future value of 15 periodic payments of \(7,000 each made at the end of each period and compounded at 10%? (d) What is the present value of \)7,000 to be received at the end of each of 20 periods, discounted at 5% compound interest?

(Analysis of Alternatives) Julia Baker died, leaving to her husband Brent an insurance policy contract that provides that the beneficiary (Brent) can choose any one of the following four options. (a) \(55,000 immediate cash. (b) \)4,000 every 3 months payable at the end of each quarter for 5 years. (c) \(18,000 immediate cash and \)1,800 every 3 months for 10 years, payable at the beginning of each 3-month period. (d) \(4,000 every 3 months for 3 years and \)1,500 each quarter for the following 25 quarters, all payments payable at the end of each quarter.

Instructions If money is worth 2陆% per quarter, compounded quarterly, which option would you recommend that Brent exercise?
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