Chapter 6 Practice Problems and Solutions PDF

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Chapter 6 Practice Problems FIN 440

Multiple Choice

1. True or False? If debt is to be used to finance a project, then interest payments on the debt should be included in the project’s cash flow estimates. a. True b. False ANS: F

2. True or False? In cash flow estimation, the existence of side effects should be taken into account if those side effects have any effects on the cash flows of the firm’s existing projects. a. True b. False ANS: T 3. True or False? Any investments in current assets should not be included in cash flow estimates. a. True b. False ANS: F 4. True or False? The primary advantage to using accelerated rather than straight-line depreciation is that with accelerated depreciation the present value of the taxes will be lower, other things equal. a. True b. False ANS: T 5. True or False? The opportunity cost is the NPV that would result from the best alternative use of an asset other than using the asset for the project that is being evaluated. a. True b. False ANS: T

6. True or False? Suppose Walker Publishing Company is considering bringing out a new finance text that result in some lost sales of another of Walker's books already in circulation. The expected lost sales on the older book are a sunk cost and as such should not be considered in the analysis of the new book. a. True b. False ANS: F 7. Which of the following statements is true regarding cash flows and accounting income? a. Managers should focus on cash flows instead of accounting earnings when evaluating capital budgeting projects. b. The accounting earnings and cash flow of a project in a given year will usually be the same, although sometimes they can be different. c. Managers should focus on accounting earnings instead of net cash flows when evaluating capital budgeting projects. d. When computing accounting earnings, the cost of a fixed asset is spread throughout the life of the asset as annual depreciation expenses. This is one source of discrepancy between cash flows and accounting earnings. e. Both a and d are true ANS: E 8. Which of the following should not be considered in the analysis of a capital budgeting project? a. b. c. d. e.

Changes in net working capital. Sunk costs. Erosion. Opportunity costs. Costs of equipment.

ANS: B 10.

Which of the following statements is CORRECT? a. b. c. d.

A sunk cost is any cost that must be incurred in order to bring a project into operation. A sunk cost is a cost that was incurred in the past and can be recovered. A sunk cost is a cost that was incurred in the past and cannot be recovered. An example of a sunk cost is a situation where Radio Shack is evaluating a proposal to open a new store in Kansas City, but doing so would cause a decline in sales of one of the firm’s existing stores. e. None of the above ANS: C 11.

Which of the following statements is CORRECT?

a. b. c. d. e.

Erosion occurs when a project decreases the cash flows of an existing project. Erosion occurs when a project increases the cash flows of an existing project. Erosion occurs when the assets used in a project could be used for some alternative use. Erosion occurs when a project has an adverse impact on the environment. None of the above.

ANS: A 12.

A company is considering a new project. The CFO plans to calculate the project’s NPV by estimating the cash flows for each year of the project’s life and then discounting those cash flows at the company’s WACC. Which one of the following factors should the CFO be sure to include in the cash flow estimates? a. A $400,000 consulting fee that the firm paid to a consulting firm last year for advice about whether the project is viable. b. All interest payments on debt that is used to help finance the project. c. The investment or change in net working capital required to operate the project, even if net working capital will be recovered at the end of the project’s life. d. All of the above.

ANS: C 13.

A company is considering a proposed new plant that would increase productive capacity. The firm will use its WACC to discount cash flows. Which of the following statements is CORRECT?

a. In calculating the project's operating cash flows, the firm should not deduct financing costs such as interest expense, because financing costs are accounted for by discounting at the WACC. If interest were deducted when estimating cash flows, this would be “double counting.” b. Since depreciation is a non-cash expense, the firm does not need to deal with depreciation when calculating the operating cash flows. c. When estimating the project’s operating cash flows, it is important to include both opportunity costs and sunk costs, but the firm should ignore the side effects of a project since they are accounted for in the discounting process. d. Capital budgeting decisions should be based on before-tax cash flows. e. The WACC used to discount cash flows in a capital budgeting analysis should be calculated on a before-tax basis. ANS: A 14.

A firm is considering building a widget factory. If built, the firm plans to operate the factory indefinitely (forever). The firm plans to estimate the cash flows in the first ten years of the project’s life. To account for the cash flows expected to occur after Year 10, the firm plans to estimate a terminal value by assuming that cash flows after Year 10 will grow at a constant rate forever. Which of the following statements is true?

a. The terminal value is the present value of all cash flows of the project. b. The WACC should never be used as the discount rate in the terminal value calculation. c. The terminal value treats the cash flows that occur after Year 10 as a growing perpetuity and discounts those cash flows back to Year 10. d. None of the above. ANS: C 15.

Consider two machines, A and B, that do the same job and have the same production capacity. The NPV of Machine A’s costs is equal to the NPV of Machine B’s costs, but machine B has a shorter life. Which of the following statements must be true? Assume that the firm uses the same discount rate for both machines. a. b. c. d.

The EAC of Machine A is equal to the EAC of Machine B. The EAC of the Machine B is more negative than the EAC of Machine A. Machine A costs more to purchase in Year 0 than Machine B. The annual maintenance costs of Machine B are equal to the annual maintenance costs of Machine A. e. None of the above. ANS: B Problems Use the following Information to Answer Problems 1 through 7 Taylor United is considering a new 6-year project that that will require the purchase of new widget making equipment that costs $4 million. The firm will depreciate the equipment using the following MACR depreciate rates: Year 1: 20% Year 2: 32% Year 3: 19.2% Year 4: 11.52% Year 5: 11.52% Year 6: 5.76% The project will require an immediate (Year 0) increase in inventories of $600,000 and an increase in accounts payable of $100,000. In Years 1 through 5, net working capital will not change. In Years 1 through 6, the firm expects to sell 11,000 units per year at a price of $200 per unit, and operating costs are expected to be 35% of sales. In the final year of the project, net working capital will be completely recovered and the equipment is expected to be sold for $500,000. Last year, the firm spent $300,000 on consumer research and testing in order the gauge consumer demand for widgets. The firm is subject to a tax rate of 40% and has a WACC of 10%. P1:

What is the project’s cash flow in Year 0?

A1:

CF0 = - (Investment in FA) – (Change in NWC) = -(4,000,000) – (600,000 – 100,000) = -$4,500,000

P2:

What are the expected annual sales (in $) and expected annual operating costs of Taylor United’s proposed project?

A2:

Sales = (11,000 unites) x ($200/unit) = $2,200,000 Operating Costs = 0.35 x 2,200,000 = $770,000

P3:

What are the annual depreciation expenses of Taylor United’s proposed project? Original Equipment Cost = $4 million

A3:

Year 1 2 3 4 5 6

P4:

Deprec. Rate 20.0% 32.0% 19.2% 11.52% 11.52% 5.76%

Depreciation Expense $ 800,000 1,280,000 768,000 460,800 460,800 230,400

Compute the operating cash flows in Years 1 through 6 of Taylor’s proposed project.

A4: OCF = Sales – Operating Costs - Taxes Year Sales

1 2,200,000

2 3 4 5 6 2,200,000 2,200,000 2,200,000 2,200,000 2,200,000

– Op. Costs

-770,000

-770,000

-770,000

-770,000

-770,000

-770,000

– Depreciation

-800,000

-1,280,000

-768,000

-460,800

-460,800

-230,400

Taxable Income

630,000

150,000

662,000

969,200

-252,000

-60,000

-264,800

-387,680

-387,680

-479,840

1,370,000 1,165,200 1,042,320

1,042,320

950,160

– Taxes (40%) Operating Cash Flow

1,178,000

969,200 1,199,600

P5:

What is the after-tax salvage value (in Year 6) of the equipment that will be used in Taylor’s proposed project?

A5:

The equipment is expected to be sold for $500,000 at the end of Year 6. At the end of year 6, the equipment will have a book value of $0 because it will have been 100% depreciated. Therefore, we have: After-Tax Salvage Value = Sale Value – T*(Salve Value - Book Value) =500,000 – 0.4*(500,000 – 0) = $300,000

P6:

Compute the cash flow in Year 6 of Taylor’s proposed project.

A6:

OCF6 = 950,160 After-Tax Salvage Value = 300,000 Recovery of Net Working Capital = 500,000 Net CF6 = OCF6 + After-Tax Salvage Value + Recovery of NWC CF6 = 950,160 + 300,000 + 500,000 = $1,750,160

P7:

What is the NPV of Taylor’s proposed project if the appropriate discount rate is the firm’s WACC? If this project is independent of any other potential projects, should the firm accept or reject the project?

A7: Year

0

Investment in FA Investment in NWC

1

2

3

4

5

1,165,200

1,042,320

1,042,320

6

-4,000,000 -500,000

Operating Cash Flow

1,178,000

1,370,000

950,160

Recovery of NWC

500,000

After-Tax Salvage Value

300,000

Net CF

-4,500,000

1,178,000

1,370,000

1,165,200

1,042,320

1,042,320

1,750,160

Compute NPV on the Calculator: CF0 = -4,500,000 C01 = 1,178,000 C02 = 1,370,000 C03 = 1,165,200 C04 = 1,042,320 C05 = 1,042,320 C06 = 1,750,160 I = WACC = 10% Solve for NPV = $925,609.49 Since NPV is positive and the project is independent, the firm should accept the project.

P8:

A firm is considering a 3-year project that requires the purchase of a piece of equipment for $10.5 million. At the end of the project (end of Year 3) the firm expects to sell the equipment for $3 million. Under the MACRS (Modified Accelerated Cost Recovery System) the firm is required to depreciate the equipment over 4 years using the rates listed below. The firm is subject to a tax rate of 40%. What is the after-tax salvage value of the equipment at the end of Year 3? Depreciation Rates Year 1: 33% Year 2: 45% Year 3: 15% Year 4: 7%

A8:

The after-tax salvage value is defined as follows: A-T Salvage Value = Sale Value – T*(Sale Value - Book Value) By the end of Year 3, the equipment has only been 93% (33%+45%+15%) depreciated. This means that 7% (100% - 93%) of the equipment’s initial cost still remains on the books. Therefore, the book value of the equipment at the end of Year 3 is: Book Value = (10,500,000) x (1-0.93) = $735,000 Plug this book value into the formula for the after tax salvage value: A-T Salvage Value = 3,000,000 – 0.4* (3,000,000 - 735,000) = 2,094,000

P9.

A manufacturing firm is considering building a factory that will last forever. The project generates the following sequence of cash flows in the first six years of its life. The WACC is 11%. Year 0 1 2 3 4 5 6

Cash Flow ($ in millions) −59.00 4.00 5.00 6.00 7.33 8.00 8.25

a. Assume that cash flows after Year 6 will continue to be $8.25 million per year forever. Calculate the terminal value (at the end of year 6) and the project’s NPV. b. Assume that cash flows after Year 6 will grow at a rate of 2% per year, forever. Calculate the terminal value (at the end of year 6) and the project’s NPV. A9.

$8.25 million = $75 million. 0.11 NPV on the calculator:

a. TV6 =CF7 / r =

CF0: -59 C01: 4 C02: 5 C03: 6 C04: 7.33 C05: 8 C06: 8.25 + TV6 = 8.25+ 75 = 83.25 I = 11 NPV = 7.13 million b. TV6 =CF7 / ( r – g) =

8.25 million 1.02 = $93.50 million. 0.11  0.02

NPV on the Calculator: CF0: -59 C01: 4 C02: 5 C03: 6 C04: 7.33 C05: 8 C06: 8.25 + TV6 = 8.25+ 93.5 = 101.75 I = 11 NPV = 17.02 million

P10.

A firm is evaluating a machine that costs $20,000 upfront and that will last for three years. Annual maintenance costs will be $5,000 at the end of the first year, $6,000 at the end of the second year, and $1,000 at the end of the third year. After three years, the machine will be worthless (no salvage value). Calculate the equivalent annual cost (EAC) of this machine if the firm uses a discount rate of 15%.

A10.

To find EAC, you have to calculate PV(costs) and find the payment of an annuity with a present value equal to PV(costs). Here is how to do it on the calculator. Step 1 Calculate PV(costs) using the CF and NPV registers on the calculator CF0 = -20,000 C01 = -5,000 C02 = -6,000 C03 = -1,000 I = 15 Solve for NPV (present value of costs) è = -29,542.20 Step 2 Calculate EAC using the PMT button on the calculator. N=3 I/Y = 15 PV = 29,542.20

FV = 0 Solve for PMT è EAC = -$12,938.80

P11.

Seattle Manufacturing is considering the purchase of two mutually exclusive machines for improving its assembly line. Machine Y will last for two years. Machine X will last for four years but will cost more upfront and have higher operating and maintenance costs than Machine Y. Both machines will need to be replaced at the end of their lives and both will have no salvage value. The annual costs associated with each machine are presented below.

Initial Cost (Year 0) Year 1 2 3 4

Machine X

Machine Y

-$156,000

-$104,000

Annual Maintenance and Operating Costs -$34,000 -$56,000 -$50,000 -$56,000 -$66,000 — -$82,000 —

a. Calculate the equivalent annual cost (EAC) of each machine if the firm uses a 14% discount rate. b. Which machine should the firm choose based on EAC? A11.

a. Machine X Year: Costs

0 -$156,000

1 -$34,000

2 3 4 -$50,000 -$66,000 -$82,000

PV(costs) = -$317,396.64 (you can compute this by hand or with the CF and NPV registers on the calculator) Using the calculator to solve for EAC: N=4 I/Y=14 PV = 317,396.64 Solve for PMT = -$108,932.05 = EAC

Machine Y

Year: Costs

0 -$104,000

1 -$56,000

2 -$56,000

PV(Costs) = -$196,212.98 Using the calculator to solve for EAC: N=2 I/Y=14 PV = 196,212.98 Solve for PMT = -119,158.13= EAC EAC = -$119,158.13 b. According to EAC, Machine X is less costly (on an annual basis). Therefore, the firm should choose Machine X....