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Chapter 6: Q14Q (page 301)
Question:Explain how the present value of an ordinary annuity interest table is converted to the present value of an annuity due interest table.
It is converted by multiplying by the factors by one plus the interest rate
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During the past year, Stacy McGill planted a new vineyard on 150 acres of land that she leases for \(30,000 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation.
The vineyard will bear no grapes for the first 5 years (1鈥�5). In the next 5 years (6鈥�10), Stacy estimates that the vines will bear grapes that can be sold for \)60,000 each year. For the next 20 years (11鈥�30), she expects the harvest will provide annual revenues of \(110,000. But during the last 10 years (31鈥�40) of the vineyard鈥檚 life, she estimates that revenues will decline to \)80,000 per year.
During the first 5 years, the annual cost of pruning, fertilizing, and caring for the vineyard is estimated at \(9,000; during the years of production, 6鈥�40, these costs will rise to \)12,000 per year. The relevant market rate of interest for the entire period is 6%. Assume that all receipts and payments are made at the end of each year.
Instructions Dick Button has offered to buy Stacy鈥檚 vineyard business by assuming the 40-year lease. On the basis of the current value of the business, what is the minimum price Stacy should accept?
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?
Amy Monroe wants to create a fund today that will enable her to withdraw $25,000 per year for 8 years, with the first withdrawal to take place 5 years from today. If the fund earns 8% interest, how much must Amy invest today?
Assume that Wal-Mart Stores, Inc. has decided to surface and maintain for 10 years a vacant lot next to one of its stores to serve as a parking lot for customers. Management is considering the following bids involving two different qualities of surfacing for a parking area of 12,000 square yards.
Bid A: A surface that costs \(5.75 per square yard to install. This surface will have to be replaced at the end of 5 years. The annual maintenance cost on this surface is estimated at 25 cents per square yard for each year except the last year of its service. The replacement surface will be similar to the initial surface.
Bid B: A surface that costs \)10.50 per square yard to install. This surface has a probable useful life of 10 years and will require annual maintenance in each year except the last year, at an estimated cost of 9 cents per square yard.
Instructions Prepare computations showing which bid should be accepted by Wal-Mart. You may assume that the cost of capital is 9%, that the annual maintenance expenditures are incurred at the end of each year, and that prices are not expected to change during the next 10 years.
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?
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