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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

Dunn Inc. owns and operates a number of hardware stores in the New England region. Recently, the company has decided to locate another store in a rapidly growing area of Maryland. The company is trying to decide whether to purchase or lease the building and related facilities.

Purchase: The company can purchase the site, construct the building, and purchase all store fi xtures. The cost would be \(1,850,000. An immediate down payment of \)400,000 is required, and the remaining \(1,450,000 would be paid off over 5 years at \)350,000 per year (including interest payments made at end of year). The property is expected to have a useful life of 12 years, and then it will be sold for \(500,000. As the owner of the property, the company will have the following outof-pocket expenses each period.

Property taxes (to be paid at the end of each year) \)40,000

Insurance (to be paid at the beginning of each year) 27,000

Other (primarily maintenance which occurs at the end of each year) 16,000

\(83,000

Lease: First National Bank has agreed to purchase the site, construct the building, and install the appropriate fi xtures for Dunn Inc. if Dunn will lease the completed facility for 12 years. The annual costs for the lease would be \)270,000. Dunn would have no responsibility related to the facility over the 12 years. The terms of the lease are that Dunn would be required to make 12 annual payments (the fi rst payment to be made at the time the store opens and then each following year). In addition, a deposit of $100,000 is required when the store is opened. This deposit will be returned at the end of the twelfth year, assuming no unusual damage to the building structure or fixtures.

Instructions Which of the two approaches should Dunn Inc. follow? (Currently, the cost of funds for Dunn Inc. is 10%.)

Your client, Keith Moreland Leasing Company, is preparing a contract to lease a machine to Souvenirs Corporation for a period of 25 years. Moreland has an investment cost of $365,755 in the machine, which has a useful life of 25 years and no salvage value at the end of that time. Your client is interested in earning an 11% return on its investment and has agreed to accept 25 equal rental payments at the end of each of the next 25 years.

Instructions You are requested to provide Moreland with the amount of each of the 25 rental payments that will yield an 11% return on investment.

You have been hired as a benefit consultant by Jean Honore, the owner of Attic Angels. She wants to establish a retirement plan for herself and her three employees. Jean has provided the following information. The retirement plan is to be based upon annual salary for the last year before retirement and is to provide 50% of Jean’s last-year annual salary and 40% of the last-year annual salary for each employee. The plan will make annual payments at the beginning of each year for 20 years from the date of retirement. Jean wishes to fund the plan by making 15 annual deposits beginning January 1, 2017. Invested funds will earn 12% compounded annually. Information about plan participants as of January 1, 2017, is as follows.

Jean Honore, owner: Current annual salary of \(48,000; estimated retirement date January 1, 2042.

Colin Davis, flower arranger: Current annual salary of \)36,000; estimated retirement date January 1, 2047.

Anita Baker, sales clerk: Current annual salary of \(18,000; estimated retirement date January 1, 2037.

Gavin Bryars, part-time bookkeeper: Current annual salary of \)15,000; estimated retirement date January 1, 2032.

In the past, Jean has given herself and each employee a year-end salary increase of 4%. Jean plans to continue this policy in the future.

Instructions

(a) Based upon the above information, what will be the annual retirement benefit for each plan participant? (Round to the nearest dollar.) (Hint: Jean will receive raises for 24 years.)

(b) What amount must be on deposit at the end of 15 years to ensure that all benefits will be paid? (Round to the nearest dollar.)

(c) What is the amount of each annual deposit Jean must make to the retirement plan?

(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 2½% per quarter, compounded quarterly, which option would you recommend that Brent exercise?

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?
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