Problems

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a. Find the depreciation charge each year.

b. If the sewing machine is sold after 3 years for \$20,000, what will be the after-tax proceeds on the sale if the firm's tax bracket is 35 percent?

12. Proper Cash Flows. Conference Services Inc. has leased a large office building for \$4 million per year. The building is larger than the company needs: two of the building's eight stories are almost empty. A manager wants to expand one of her projects, but this will require using one of the empty floors. In calculating the net present value of the proposed expansion, upper management allocates one-eighth of \$4 million of building rental costs (i.e., \$.5 million) to the project expansion, reasoning that the project will use one-eighth of the building's capacity.

a. Is this a reasonable procedure for purposes of calculating NPV?

b. Can you suggest a better way to assess a cost of the office space used by the project?

Cash Flows and Working Capital. A firm had net income last year of \$1.2 million. Its depreciation expenses were \$.5 million, and its total cash flow was \$1.2 million. What happened to net working capital during the year?

Cash Flows and Working Capital. The only capital investment required for a small project is investment in inventory. Profits this year were \$10,000, and inventory increased from \$4,000 to \$5,000. What was the cash flow from the project?

Cash Flows and Working Capital. A firm's balance sheets for year-end 2000 and 2001 contain the following data. What happened to investment in net working capital during 2001? All items are in millions of dollars.

Accounts receivable 32 35

Inventories 25 30

Accounts payable 12 25

Salvage Value. Quick Computing (from problem 5) installed its previous generation of computer chip manufacturing equipment 3 years ago. Some of that older equipment will become unnecessary when the company goes into production of its new product. The obsolete equipment, which originally cost \$40 million, has been depreciated straight line over an assumed tax life of 5 years, but it can be sold now for \$18 million. The firm's tax rate is 35 percent. What is the after-tax cash flow from the sale of the equipment?

Salvage Value. Your firm purchased machinery with a 7-year MACRS life for \$10 million. The project, however, will end after 5 years. If the equipment can be sold for \$4 million at the completion of the project, and your firm's tax rate is 35 percent, what is the after-tax cash flow from the sale of the machinery?

Depreciation and Project Value. Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for \$6,000 and sell its old washer for \$2,000. The new washer will last for 6 years and save \$1,500 a year in expenses. The opportunity cost of capital is 15 percent, and the firm's tax rate is 40 percent.

a. If the firm uses straight-line depreciation to an assumed salvage value of zero over a 6-year life, what are the cash flows of the project in Years 0-6? The new washer will in fact have zero salvage value after 6 years, and the old washer is fully depreciated.

b. What is project NPV?

c. What will NPV be if the firm uses MACRS depreciation with a 5-year tax life?

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Fundamentals of Corporate Cash-Flow Analysis to Companies, 2001

Finance, Third Edition Make Investment chapter 7 Using Discounted Cash-Flow Analysis to Make Investment Decisions 223

19. Equivalent Annual Cost. What is the equivalent annual cost of the washer in the previous problem if the firm uses straight-line depreciation?

20. Cash Flows and NPV. Johnny's Lunches is considering purchasing a new, energy-efficient grill. The grill will cost \$20,000 and will be depreciated according to the 3-year MACRS schedule. It will be sold for scrap metal after 3 years for \$5,000. The grill will have no effect on revenues but will save Johnny's \$10,000 in energy expenses. The tax rate is 35 percent.

a. What are the operating cash flows in Years 1-3?

b. What are total cash flows in Years 1-3?

c. If the discount rate is 12 percent, should the grill be purchased?

0 21. Project Evaluation. Revenues generated by a new fad product are forecast as follows:

Year Revenues

2 30,000

3 20,000

4 10,000 Thereafter 0

Expenses are expected to be 40 percent of revenues, and working capital required in each year is expected to be 20 percent of revenues in the following year. The product requires an immediate investment of \$50,000 in plant and equipment.

a. What is the initial investment in the product? Remember working capital.

b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm's tax rate is 40 percent, what are the project cash flows in each year?

c. If the opportunity cost of capital is 10 percent, what is project NPV?

d. What is project IRR?

22. Buy versus Lease. You can buy a car for \$25,000 and sell it in 5 years for \$5,000. Or you can lease the car for 5 years for \$5,000 a year. The discount rate is 10 percent per year.

a. Which option do you prefer?

b. What is the maximum amount you should be willing to pay to lease rather than buy the car?

23. Project Evaluation. Kinky Copies may buy a high-volume copier. The machine costs \$100,000 and will be depreciated straight-line over 5 years to a salvage value of \$20,000. Kinky anticipates that the machine actually can be sold in 5 years for \$30,000. The machine will save \$20,000 a year in labor costs but will require an increase in working capital, mainly paper supplies, of \$10,000. The firm's marginal tax rate is 35 percent. Should Kinky buy the machine?

24. Project Evaluation. Blooper Industries must replace its magnoosium purification system. Quick & Dirty Systems sells a relatively cheap purification system for \$10 million. The system will last 5 years. Do-It-Right sells a sturdier but more expensive system for \$12 million; it will last for 8 years. Both systems entail \$1 million in operating costs; both will be depreciated straight line to a final value of zero over their useful lives; neither will have any salvage value at the end of its life. The firm's tax rate is 35 percent, and the discount rate is 12 percent. Which system should Blooper install?

25. Project Evaluation. The following table presents sales forecasts for Golden Gelt Giftware. The unit price is \$40. The unit cost of the giftware is \$25.

Brealey-Myers: I II. Value I 7. Using Discounted I I © The McGraw-Hill

Fundamentals of Corporate Cash-Flow Analysis to Companies, 2001

Finance, Third Edition Make Investment

224 part two Value

Year Unit Sales

1 22,000

2 30,000

3 14,000

4 5,000 Thereafter 0

It is expected that net working capital will amount to 25 percent of sales in the following year. For example, the store will need an initial (Year 0) investment in working capital of .25 x 22,000 x \$40 = \$220,000. Plant and equipment necessary to establish the Giftware business will require an additional investment of \$200,000. This investment will be depreciated using MACRS and a 3-year life. After 4 years, the equipment will have an economic and book value of zero. The firm's tax rate is 35 percent. What is the net present value of the project? The discount rate is 20 percent.

26. Project Evaluation. Ilana Industries, Inc., needs a new lathe. It can buy a new high-speed lathe for \$1 million. The lathe will cost \$35,000 to run, will save the firm \$125,000 in labor costs, and will be useful for 10 years. Suppose that for tax purposes, the lathe will be depreciated on a straight-line basis over its 10-year life to a salvage value of \$100,000. The actual market value of the lathe at that time also will be \$100,000. The discount rate is 10 percent and the corporate tax rate is 35 percent. What is the NPV of buying the new lathe?

Challenge Problems

27. Project Evaluation. The efficiency gains resulting from a just-in-time inventory management system will allow a firm to reduce its level of inventories permanently by \$250,000. What is the most the firm should be willing to pay for installing the system?

28. Project Evaluation. Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of \$6 million. The equipment will be depreciated straight line over 5 years to a value of zero, but in fact it can be sold after 5 years for \$500,000. The firm believes that working capital at each date must be maintained at a level of 10 percent of next year's forecast sales. The firm estimates production costs equal to \$1.50 per trap and believes that the traps can be sold for \$4 each. Sales forecasts are given in the following table. The project will come to an end in 5 years, when the trap becomes technologically obsolete. The firm's tax bracket is 35 percent, and the required rate of return on the project is 12 percent. What is project NPV?

Year:

Thereafter

Sales (millions of traps)

29. Working Capital Management. Return to the previous problem. Suppose the firm can cut its requirements for working capital in half by using better inventory control systems. By how much will this increase project NPV?

30. Project Evaluation. PC Shopping Network may upgrade its modem pool. It last upgraded 2 years ago, when it spent \$115 million on equipment with an assumed life of 5 years and an assumed salvage value of \$15 million for tax purposes. The firm uses straight-line depreciation. The old equipment can be sold today for \$80 million. A new modem pool can be installed today for \$150 million. This will have a 3-year life, and will be depreciated to zero using straight-line depreciation. The new equipment will enable the firm to increase sales by \$25 million per year and decrease operating costs by \$10 million per year. At the end of 3 years, the new equipment will be worthless. Assume the firm's tax rate is 35 percent and the discount rate for projects of this sort is 12 percent.

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Fundamentals of Corporate Cash-Flow Analysis to Companies, 2001

Finance, Third Edition Make Investment chapter 7 Using Discounted Cash-Flow Analysis to Make Investment Decisions 225

a. What is the net cash flow at time 0 if the old equipment is replaced?

b. What are the incremental cash flows in Years 1, 2, and 3?

c. What are the NPV and IRR of the replacement project?

Solutions to Spreadsheet Model Questions

 A B C D E F G H Year: 0 1 2 3 4 5 6 Capital investment 10,000 Working capital 1 ,500 4,075 4,279 4,493 4,717 3,039 0 Change in Wk Capital 1 ,500 2,575 204 214 225 -1 ,679 -3,039 Revenues 15,000 15,750 16,538 17,364 18,233 Expenses 10,000 10,500 11,025 1 1 ,576 12,155 Depreciation 3,333 4.445 1.481 741 0 Pretax profit 1 ,667 805 4,032 5,047 6,078 Tax 583 282 1.411 1 ,766 2,127 Profit after tax 1 ,084 523 2,620 3,281 3,950 Cash flow -1 1 ,500 1 ,842 4,765 3,888 3,797 5,629 3,039 PV of Cash flow -1 1 ,500 1 ,644 3,798 2,767 2,413 3,194 1,540 Net present value 3,856
 A B c D E F G H Year: 0 1 2 3 4 5 6 Capital investment 10,000 Working capital 1 ,500 4,000 4,000 4,000 4,000 2,500 0 Change In Wk Capital 1 ,500 2,500 0 0 0 -1,500 -2,500 Revenues 15,000 15,000 15,000 15,000 15,000 Expenses 10,000 10,000 10,000 10,000 10,000 Depreciation 2.000 2.000 2.000 2.000 2.000 Pretax profit 3,000 3,000 3,000 3,000 3,000 Tax 1.050 1.050 1.050 1.050 1.050 Profit after tax 1,950 1,950 1,950 1,950 1,950 Cash flow -1 1 ,500 1,450 3,950 3,950 3,950 5,450 2,500 PV of Cash flow -1 1 ,500 1,355 3,450 3,224 3,013 3,886 1 ,666 Net present value 5,095 Although the real discount rate is barely affected by the change in inflation, the real value of depreciation and the present value of the depreciation tax shield increase, which increases project NPV.

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Fundamentals of Corporate Cash-Flow Analysis to Companies, 2001

Finance, Third Edition Make Investment

226 part two Value

Solutions to

Self-Test

Questions

7.1 Remember, discount cash flows, not profits. Each tewgit machine costs \$250,000 right away. Recognize that outlay, but forget accounting depreciation. Cash flows per machine are:

Year:

Year:

 Investment (outflow) -250,000 Sales 250,000 300,000 300,000 250,000 250,000 Operating expenses -200,000 -200,000 -200,000 -200,000 -200,000 Cash flow -250,000 + 50,000 +100,000 +100,000 + 50,000 + 50,000

Each machine is forecast to generate \$50,000 of cash flow in Years 4 and 5. Thus it makes sense to keep operating for 5 years.

7.2 a,b. The site and buildings could have been sold or put to another use. Their values are op portunity costs, which should be treated as incremental cash outflows.

c. Demolition costs are incremental cash outflows.

d. The cost of the access road is sunk and not incremental.

e. Lost cash flows from other projects are incremental cash outflows.

f. Depreciation is not a cash expense and should not be included, except as it affects taxes. (Taxes are discussed later in this chapter.)

7.3 Actual health costs will be increasing at about 7 percent a year.

Year

The present value at 10 percent is \$9,214 if the first payment is made immediately. If it is delayed a year, present value falls to \$8,377. 7.4 The tax rate is T = 35 percent. Taxes paid will be

T x (revenue - expenses - depreciation) = .35 x (600 - 300 - 200) = \$35 Operating cash flow can be calculated as follows.

a. Revenue - expenses - taxes = 600 - 300 - 35 = \$265

b. Net profit + depreciation = (600 - 300 - 200 - 35) + 200

c. (Revenues - cash expenses) x (1 - tax rate) + (depreciation x tax rate) = (600 - 300) x (1 - .35) + (200 x .35) = 265

Year

MACRS 3-Year Depreciation

Tax Shield

PV Tax Shield at 12%

Year

MACRS 3-Year Depreciation

Tax Shield

PV Tax Shield at 12%

 1 3,333 1,167 1,042 2 4,445 1,556 1,240 3 1,481 518 369 4 741 259 165 Totals 10,000 3,500 2,816

The present value increases to 2,816, or \$2,816,000.

The present value increases to 2,816, or \$2,816,000.

Brealey-Myers: I II. Value I 7. Using Discounted I I © The McGraw-Hill

Fundamentals of Corporate Cash-Flow Analysis to Companies, 2001

Finance, Third Edition Make Investment chapter 7 Using Discounted Cash-Flow Analysis to Make Investment Decisions 227

Jack Tar, CFO of Sheetbend & Halyard, Inc., opened the company-confidential envelope. It contained a draft of a competitive bid for a contract to supply duffel canvas to the U.S. Navy. The cover memo from Sheetbend's CEO asked Mr. Tar to review the bid before it was submitted.

The bid and its supporting documents had been prepared by Sheetbend's sales staff. It called for Sheetbend to supply 100,000 yards of duffel canvas per year for 5 years. The proposed selling price was fixed at \$30 per yard.

Mr. Tar was not usually involved in sales, but this bid was unusual in at least two respects. First, if accepted by the navy, it would commit Sheetbend to a fixed price, long-term contract. Second, producing the duffel canvas would require an investment of \$1.5 million to purchase machinery and to refurbish Sheetbend's plant in Pleasantboro, Maine.

Mr. Tar set to work and by the end of the week had collected the following facts and assumptions:

• The plant in Pleasantboro had been built in the early 1900s and is now idle. The plant was fully depreciated on Sheet-bend's books, except for the purchase cost of the land (in 1947) of \$10,000.

• Now that the land was valuable shorefront property, Mr. Tar thought the land and the idle plant could be sold, immediately or in the future, for \$600,000.

• Refurbishing the plant would cost \$500,000. This investment would be depreciated for tax purposes on the 10-year MACRS schedule.

• The new machinery would cost \$1 million. This investment could be depreciated on the 5-year MACRS schedule.

• The refurbished plant and new machinery would last for many years. However, the remaining market for duffel canvas was small, and it was not clear that additional orders could be obtained once the navy contract was finished. The machinery was custom built and could be used only for duffel canvas. Its second-hand value at the end of 5 years was probably zero.

• Table 7.6 shows the sales staff's forecasts of income from the navy contract. Mr. Tar reviewed this forecast and decided that its assumptions were reasonable, except that the forecast used book, not tax, depreciation.

• But the forecast income statement contained no mention of working capital. Mr. Tar thought that working capital would average about 10 percent of sales.

Armed with this information, Mr. Tar constructed a spreadsheet to calculate the NPV of the duffel canvas project, assuming that Sheetbend's bid would be accepted by the navy.

He had just finished debugging the spreadsheet when another confidential envelope arrived from Sheetbend's CEO. It contained a firm offer from a Maine real estate developer to purchase Sheetbend's Pleasantboro land and plant for \$1.5 million in cash.

Should Mr. Tar recommend submitting the bid to the navy at the proposed price of \$30 per yard? The discount rate for this project is 12 percent.

table 7.6

Forecasted income statement for the navy duffel canvas project (dollarfigures in thousands, except price per yard)

 Year 1 2 3 4 5 1. Yards sold 100.00 100.00 100.00 100.00 100.00 2. Price per yard 30.00 30.00 30.00 30.00 30.00 3. Revenue (1 x 2) 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 4. Cost of goods sold 2,100.00 2,184.00 2,271.36 2,362.21 2,456.70 5. Operating cash flow (3 - 4) 900.00 816.00 728.64 637.79 543.30 6. Depreciation 250.00 250.00 250.00 250.00 250.00 7. Income (5 - 6) 650.00 566.00 478.64 387.79 293.30 8. Tax at 35% 227.50 198.10 167.52 135.72 102.65 9. Net income (7 - 8) \$422.50 \$367.90 \$311.12 \$252.06 1. Yards sold and price per yard would be fixed by contract. 2. Cost of goods includes fixed cost of \$300,000 per year plus variable costs of \$18 per yard. Costs are expected to increase at the inflation rate of 4 percent per year. 3. Depreciation: A \$1 million investment in machinery is depreciated straight-line over 5 years (\$200,000 per year). The \$500,000 cost of refurbishing the Pleasantboro plant is depreciated straight-line over 10 years (\$50,000 per year). Notes: 1. Yards sold and price per yard would be fixed by contract. 2. Cost of goods includes fixed cost of \$300,000 per year plus variable costs of \$18 per yard. Costs are expected to increase at the inflation rate of 4 percent per year. 3. Depreciation: A \$1 million investment in machinery is depreciated straight-line over 5 years (\$200,000 per year). The \$500,000 cost of refurbishing the Pleasantboro plant is depreciated straight-line over 10 years (\$50,000 per year).

0 0

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Responses

• anna
What is the equivalent annual cost of the washer, if the firm uses straightline depreciation?
8 years ago
• Dexter
Is this a reasonable procedure for purposes of calculating npv?
3 years ago