## Problems

Operating Cash Flows. Talia's Tutus bought a new sewing machine for \$40,000 that will be depreciated using the MACRS depreciation schedule for a 5-year recovery period.

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?

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?

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?

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.

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.

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?

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### Responses

• tricia
What is the net cash flow at time 0 if the old equipment is replaced?
2 years ago