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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=500,000-500,000×46%=$270,000

02

Calculation of annuity payments

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

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

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Most popular questions from this chapter

Sosa Excavating Inc. is purchasing a bulldozer. The equipment has a price of \(100,000. The manufacturer has offered a payment plan that would allow Sosa to make 10 equal annual payments of \)16,274.53, with the first payment due one year after the purchase. Instructions (a) How much total interest will Sosa pay on this payment plan? (b) Sosa could borrow $100,000 from its bank to finance the purchase at an annual rate of 9%. Should Sosa borrow from the bank or use the manufacturer’s payment plan to pay for the equipment?

Candice Willis will invest \(30,000 today. She needs \)150,000 in 21 years. What annual interest rate must she earn?

Zach Taylor is settling a \(20,000 loan due today by making 6 equal annual payments of \)4,727.53. Determine the interest rate on this loan, if the payments begin one year after the loan is signed.

Using the appropriate interest table, answer the following questions. (Each case is independent of the others). (a) What is the future value of 20 periodic payments of \(4,000 each made at the beginning of each period and compounded at 8%? (b) What is the present value of \)2,500 to be received at the beginning of each of 30 periods, discounted at 5% compound interest? (c) What is the future value of 15 deposits of \(2,000 each made at the beginning of each period and compounded at 10%? (Future value as of the end of the fifteenth period.) (d) What is the present value of six receipts of \)1,000 each received at the beginning of each period, discounted at 9% compounded interest?

Answer each of these unrelated questions.

(a) On January 1, 2017, Fishbone Corporation sold a building that cost \(250,000 and that had accumulated depreciation of \)100,000 on the date of sale. Fishbone received as consideration a \(240,000 non-interest-bearing note due on January 1, 2020. There was no established exchange price for the building, and the note had no ready market. The prevailing rate of interest for a note of this type on January 1, 2017, was 9%. At what amount should the gain from the sale of the building be reported?

(b) On January 1, 2017, Fishbone Corporation purchased 300 of the \)1,000 face value, 9%, 10-year bonds of Walters Inc. The bonds mature on January 1, 2027, and pay interest annually beginning January 1, 2018. Fishbone purchased the bonds to yield 11%. How much did Fishbone pay for the bonds?

(c) Fishbone Corporation bought a new machine and agreed to pay for it in equal annual installments of \(4,000 at the end of each of the next 10 years. Assuming that a prevailing interest rate of 8% applies to this contract, how much should Fishbone record as the cost of the machine?

(d) Fishbone Corporation purchased a special tractor on December 31, 2017. The purchase agreement stipulated that Fishbone should pay \)20,000 at the time of purchase and \(5,000 at the end of each of the next 8 years. The tractor should be recorded on December 31, 2017, at what amount, assuming an appropriate interest rate of 12%?

(e) Fishbone Corporation wants to withdraw \)120,000 (including principal) from an investment fund at the end of each year for 9 years. What should be the required initial investment at the beginning of the first year if the fund earns 11%?
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