# Finance Assignment Problems 11–1 to 11-18

Question

11–1) Investment Outlay

Talbot Industries is considering an expansion project. The necessary equipment

could be purchased for $9 million, and the project would also require an initial

$3 million investment in net operating working capital. The company’s tax rate

is 40%.

a. What is the initial investment outlay?

b. The company spent and expensed $50,000 on research related to the project last

year. Would this change your answer? Explain.

c. The company plans to house the project in a building it owns but is not now

using. The building could be sold for $1 million after taxes and real estate commissions.

How would this affect your answer?

458 Part 4: Projects and Their Valuation

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

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(11–2)

Operating Cash Flow

Cairn Communications is trying to estimate the first-year operating cash flow

(at t = 1) for a proposed project. The financial staff has collected the following

information:

Projected sales $10 million

Operating costs (not including depreciation) $ 7 million

Depreciation $ 2 million

Interest expense $ 2 million

The company faces a 40% tax rate. What is the project’s operating cash flow for the

first year (t = 1)?

(11–3)

Net Salvage Value

Allen Air Lines is now in the terminal year of a project. The equipment originally

cost $20 million, of which 80% has been depreciated. Carter can sell the used equipment

today to another airline for $5 million, and its tax rate is 40%. What is the

equipment’s after-tax net salvage value?

(11–4)

Replacement Analysis

The Chen Company is considering the purchase of a new machine to replace an obsolete

one. The machine being used for the operation has both a book value and a

market value of zero; it is in good working order, however, and will last physically

for at least another 10 years. The proposed replacement machine will perform the

operation so much more efficiently that Chen’s engineers estimate it will produce

after-tax cash flows (labor savings and depreciation) of $9,000 per year. The new machine

will cost $40,000 delivered and installed, and its economic life is estimated to

be 10 years. It has zero salvage value. The firm’s WACC is 10%, and its marginal tax

rate is 35%. Should Chen buy the new machine?

INTERMEDIATE

PROBLEMS 5–11

(11–5)

Depreciation Methods

Wendy is evaluating a capital budgeting project that should last for 4 years. The

project requires $800,000 of equipment. She is unsure what depreciation method to

use in her analysis, straight-line or the 3-year MACRS accelerated method. Under

straight-line depreciation, the cost of the equipment would be depreciated evenly

over its 4-year life (ignore the half-year convention for the straight-line method).

The applicable MACRS depreciation rates are 33%, 45%, 15%, and 7%, as discussed

in Appendix 11A. The company’s WACC is 10%, and its tax rate is 40%.

a. What would the depreciation expense be each year under each method?

b. Which depreciation method would produce the higher NPV, and how much

higher would it be?

(11–6)

New-Project Analysis

The Campbell Company is evaluating the proposed acquisition of a new milling machine.

The machine’s base price is $108,000, and it would cost another $12,500 to

modify it for special use. The machine falls into the MACRS 3-year class, and it

would be sold after 3 years for $65,000. The machine would require an increase in

net working capital (inventory) of $5,500. The milling machine would have no effect

on revenues, but it is expected to save the firm $44,000 per year in before-tax operating

costs, mainly labor. Campbell’s marginal tax rate is 35%.

a. What is the net cost of the machine for capital budgeting purposes?

(That is, what is the Year-0 net cash flow?)

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

Chapter 11: Cash Flow Estimation and Risk Analysis 459

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

ringhtist reeselrvmed. di stkribuutiovn h oeut austhoir izkatiuon

c. What is the additional Year-3 cash flow (i.e., the after-tax salvage and the return

of working capital)?

d. If the project’s cost of capital is 12%, should the machine be purchased?

(11–7)

New-Project Analysis

You have been asked by the president of your company to evaluate the proposed acquisition

of a new spectrometer for the firm’s R&D department. The equipment’s

basic price is $70,000, and it would cost another $15,000 to modify it for special use

by your firm. The spectrometer, which falls into the MACRS 3-year class, would be

sold after 3 years for $30,000. Use of the equipment would require an increase in net

working capital (spare parts inventory) of $4,000. The spectrometer would have no

effect on revenues, but it is expected to save the firm $25,000 per year in before-tax

operating costs, mainly labor. The firm’s marginal federal-plus-state tax rate is 40%.

a. What is the net cost of the spectrometer? (That is, what is the Year-0 net cash

flow?)

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

c. What is the additional (nonoperating) cash flow in Year 3?

d. If the project’s cost of capital is 10%, should the spectrometer be purchased?

(11–8)

Inflation Adjustments

The Rodriguez Company is considering an average-risk investment in a mineral water

spring project that has a cost of $150,000. The project will produce 1,000 cases of

mineral water per year indefinitely. The current sales price is $138 per case, and the

current cost per case is $105. The firm is taxed at a rate of 34%. Both prices and

costs are expected to rise at a rate of 6% per year. The firm uses only equity, and it

has a cost of capital of 15%. Assume that cash flows consist only of after-tax profits,

since the spring has an indefinite life and will not be depreciated.

a. Should the firm accept the project? (Hint: The project is a perpetuity, so you

must use the formula for a perpetuity to find its NPV.)

b. Suppose that total costs consisted of a fixed cost of $10,000 per year plus variable

costs of $95 per unit, and suppose that only the variable costs were expected to

increase with inflation. Would this make the project better or worse? Continue

to assume that the sales price will rise with inflation.

(11–9)

Replacement Analysis

The Taylor Toy Corporation currently uses an injection-molding machine that was

purchased 2 years ago. This machine is being depreciated on a straight-line basis, and

it has 6 years of remaining life. Its current book value is $2,100, and it can be sold for

$2,500 at this time. Thus, the annual depreciation expense is $2,100/6 = $350 per

year. If the old machine is not replaced, it can be sold for $500 at the end of its useful

life.

Taylor is offered a replacement machine that has a cost of $8,000, an estimated

useful life of 6 years, and an estimated salvage value of $800. This

machine falls into the MACRS 5-year class, so the applicable depreciation rates

are 20%, 32%, 19%, 12%, 11%, and 6%. The replacement machine would permit

an output expansion, so sales would rise by $1,000 per year; even so, the new

machine’s much greater efficiency would reduce operating expenses by $1,500

per year. The new machine would require that inventories be increased by

$2,000, but accounts payable would simultaneously increase by $500. Taylor’s

marginal federal-plus-state tax rate is 40%, and its WACC is 15%. Should it

replace the old machine?

460 Part 4: Projects and Their Valuation

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

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(11–10)

Replacement Analysis

St. Johns River Shipyards is considering the replacement of an 8-year-old riveting

machine with a new one that will increase earnings before depreciation from

$27,000 to $54,000 per year. The new machine will cost $82,500, and it will have

an estimated life of 8 years and no salvage value. The new machine will be depreciated

over its 5-year MACRS recovery period, so the applicable depreciation rates are

20%, 32%, 19%, 12%, 11%, and 6%. The applicable corporate tax rate is 40%, and

the firm’s WACC is 12%. The old machine has been fully depreciated and has no

CHALLENGING salvage value. Should the old riveting machine be replaced by the new one?

PROBLEMS 11–17

(11–11)

Scenario Analysis

Shao Industries is considering a proposed project for its capital budget. The company

estimates the project’s NPV is $12 million. This estimate assumes that the economy

and market conditions will be average over the next few years. The company’s CFO,

however, forecasts there is only a 50% chance that the economy will be average. Recognizing

this uncertainty, she has also performed the following scenario analysis:

Economic

Scenario

Probability of

Outcome NPV

Recession 0.05 ?$70 million

Below average 0.20 ?25 million

Average 0.50 12 million

Above average 0.20 20 million

Boom 0.05 30 million

What is the project’s expected NPV, its standard deviation, and its coefficient of

variation?

(11–12)

New-Project Analysis

Madison Manufacturing is considering a new machine that costs $250,000 and would

reduce pre-tax manufacturing costs by $90,000 annually. Madison would use the

3-year MACRS method to depreciate the machine, and management thinks the machine

would have a value of $23,000 at the end of its 5-year operating life. The

applicable depreciation rates are 33%, 45%, 15%, and 7%, as discussed in Appendix

11A. Working capital would increase by $25,000 initially, but it would be recovered

at the end of the project’s 5-year life. Madison’s marginal tax rate is 40%, and a 10%

WACC is appropriate for the project.

a. Calculate the project’s NPV, IRR, MIRR, and payback.

b. Assume management is unsure about the $90,000 cost savings—this figure could

deviate by as much as plus or minus 20%. What would the NPV be under each

of these extremes?

c. Suppose the CFO wants you to do a scenario analysis with different values for the

cost savings, the machine’s salvage value, and the working capital (WC) requirement.

She asks you to use the following probabilities and values in the scenario analysis:

Scenario Probability

Cost

Savings

Salvage

Value WC

Worst case 0.35 $ 72,000 $18,000 $30,000

Base case 0.35 90,000 23,000 25,000

Best case 0.30 108,000 28,000 20,000

Calculate the project’s expected NPV, its standard deviation, and its coefficient

of variation. Would you recommend that the project be accepted?

Chapter 11: Cash Flow Estimation and Risk Analysis 461

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

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(11–13)

Replacement Analysis

The Everly Equipment Company purchased a machine 5 years ago at a cost of

$90,000. The machine had an expected life of 10 years at the time of purchase, and

it is being depreciated by the straight-line method by $9,000 per year. If the machine

is not replaced, it can be sold for $10,000 at the end of its useful life.

A new machine can be purchased for $150,000, including installation costs. During

its 5-year life, it will reduce cash operating expenses by $50,000 per year. Sales

are not expected to change. At the end of its useful life, the machine is estimated to

be worthless. MACRS depreciation will be used, and the machine will be depreciated

over its 3-year class life rather than its 5-year economic life, so the applicable depreciation

rates are 33%, 45%, 15%, and 7%.

The old machine can be sold today for $55,000. The firm’s tax rate is 35%, and

the appropriate WACC is 16%.

a. If the new machine is purchased, what is the amount of the initial cash flow at

Year 0?

b. What are the incremental net cash flows that will occur at the end of Years 1

through 5?

c. What is the NPV of this project? Should Everly replace the old machine?

(11–14)

Replacement Analysis

The Balboa Bottling Company is contemplating the replacement of one of its bottling

machines with a newer and more efficient one. The old machine has a book

value of $600,000 and a remaining useful life of 5 years. The firm does not expect

to realize any return from scrapping the old machine in 5 years, but it can sell it

now to another firm in the industry for $265,000. The old machine is being depreciated

by $120,000 per year, using the straight-line method.

The new machine has a purchase price of $1,175,000, an estimated useful life and

MACRS class life of 5 years, and an estimated salvage value of $145,000. The applicable

depreciation rates are 20%, 32%, 19%, 12%, 11%, and 6%. It is expected to

economize on electric power usage, labor, and repair costs, as well as to reduce the

number of defective bottles. In total, an annual savings of $255,000 will be realized if

the new machine is installed. The company’s marginal tax rate is 35%, and it has a

12% WACC.

a. What is the initial net cash flow if the new machine is purchased and the old one

is replaced?

b. Calculate the annual depreciation allowances for both machines, and compute

the change in the annual depreciation expense if the replacement is made.

c. What are the incremental net cash flows in Years 1 through 5?

d. Should the firm purchase the new machine? Support your answer.

e. In general, how would each of the following factors affect the investment

decision, and how should each be treated?

(1) The expected life of the existing machine decreases.

(2) The WACC is not constant but is increasing as Balboa adds more projects

into its capital budget for the year.

(11–15)

Risky Cash Flows

The Bartram-Pulley Company (BPC) must decide between two mutually exclusive

investment projects. Each project costs $6,750 and has an expected life of 3 years.

Annual net cash flows from each project begin 1 year after the initial investment is

made and have the following probability distributions:

462 Part 4: Projects and Their Valuation

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

rigehts tivon w itkhoout erxpirlelssi zastioan

Project A Project B

Probability Net Cash Flows Probability Net Cash Flows

0.2 $ 6,000 0.2 $ 0

0.6 6,750 0.6 6,750

0.2 7,500 0.2 18,000

BPC has decided to evaluate the riskier project at a 12% rate and the less risky

project at a 10% rate.

a. What is the expected value of the annual net cash flows from each project? What

is the coefficient of variation (CV)? (Hint: ?B = $5,798 and CVB = 0.76.)

b. What is the risk-adjusted NPV of each project?

c. If it were known that Project B is negatively correlated with other cash flows of

the firm whereas Project A is positively correlated, how would this affect the

decision? If Project B’s cash flows were negatively correlated with gross domestic

product (GDP), would that influence your assessment of its risk?

(11–16)

Simulation

Singleton Supplies Corporation (SSC) manufactures medical products for hospitals,

clinics, and nursing homes. SSC may introduce a new type of X-ray scanner designed to

identify certain types of cancers in their early stages. There are a number of uncertainties

about the proposed project, but the following data are believed to be reasonably accurate.

Probability Developmental Costs Random Numbers

0.3 $2,000,000 00–29

0.4 4,000,000 30–69

0.3 6,000,000 70–99

Probability Project Life Random Numbers

0.2 3 years 00–19

0.6 8 years 20–79

0.2 13 years 80–99

Probability Sales in Units Random Numbers

0.2 100 00–19

0.6 200 20–79

0.2 300 80–99

Probability Sales Price Random Numbers

0.1 $13,000 00–09

0.8 13,500 10–89

0.1 14,000 90–99

Probability

Cost per Unit (Excluding

Developmental Costs) Random Numbers

0.3 $5,000 00–29

0.4 6,000 30–69

0.3 7,000 70–99

SSC uses a cost of capital of 15% to analyze average-risk projects, 12% for low-risk

projects, and 18% for high-risk projects. These risk adjustments primarily reflect the

Chapter 11: Cash Flow Estimation and Risk Analysis 463

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

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uncertainty about each project’s NPV and IRR as measured by their coefficients of

variation. The firm is in the 40% federal-plus-state income tax bracket.

a. What is the expected IRR for the X-ray scanner project? Base your answer on

the expected values of the variables. Also, assume the after-tax “profits” figure

that you develop is equal to annual cash flows. All facilities are leased, so depreciation

may be disregarded. Can you determine the value of ?IRR short of actual

simulation or a fairly complex statistical analysis?

b. Assume that SSC uses a 15% cost of capital for this project. What is the project’s

NPV? Could you estimate ?NPV without either simulation or a complex statistical

analysis?

c. Show the process by which a computer would perform a simulation analysis for

this project. Use the random numbers 44, 17, 16, 58, 1; 79, 83, 86; and 19, 62, 6

to illustrate the process with the first computer run. Actually calculate the firstrun

NPV and IRR. Assume the cash flows for each year are independent of cash

flows for other years. Also, assume the computer operates as follows: (1) A developmental

cost and a project life are estimated for the first run using the first

two random numbers. (2) Next, sales volume, sales price, and cost per unit are

estimated using the next three random numbers and used to derive a cash flow

for the first year. (3) Then, the next three random numbers are used to estimate

sales volume, sales price, and cost per unit for the second year, hence the cash

flow for the second year. (4) Cash flows for other years are developed similarly,

on out to the first run’s estimated life. (5) With the developmental cost and the

cash flow stream established, NPV and IRR for the first run are derived and

stored in the computer’s memory. (6) The process is repeated to generate perhaps

500 other NPVs and IRRs. (7) Frequency distributions for NPV and IRR

are plotted by the computer, and the distributions’ means and standard deviations

are calculated.

(11–17)

Decision Tree

The Yoran Yacht Company (YYC), a prominent sailboat builder in Newport, may

design a new 30-foot sailboat based on the “winged” keels first introduced on the

12-meter yachts that raced for the America’s Cup.

First, YYC would have to invest $10,000 at t = 0 for the design and model tank

testing of the new boat. YYC’s managers believe there is a 60% probability that this

phase will be successful and the project will continue. If Stage 1 is not successful, the

project will be abandoned with zero salvage value.

The next stage, if undertaken, would consist of making the molds and producing

two prototype boats. This would cost $500,000 at t = 1. If the boats test well, YYC

would go into production. If they do not, the molds and prototypes could be sold for

$100,000. The managers estimate the probability is 80% that the boats will pass testing

and that Stage 3 will be undertaken.

Stage 3 consists of converting an unused production line to produce the new design.

This would cost $1 million at t = 2. If the economy is strong at this point, the

net value of sales would be $3 million; if the economy is weak, the net value would be

$1.5 million. Both net values occur at t = 3, and each state of the economy has a

probability of 0.5. YYC’s corporate cost of capital is 12%.

a. Assume this project has average risk. Construct a decision tree and determine the

project’s expected NPV.

b. Find the project’s standard deviation of NPV and coefficient of variation of

NPV. If YYC’s average project had a CV of between 1.0 and 2.0, would this

project be of high, low, or average stand-alone risk?

464 Part 4: Projects and Their Valuation

9781133665007, Financial Management: Theory and Practice, Michael C. Ehrhardt – © Cengage Learning.

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SPREADSHEET PROBLEM

(11-18)

Build a Model: Issues in

Capital Budgeting

Start with the partial model in the file Ch11 P18 Build a Model.xls on the textbook’s

Web site. Webmasters.com has developed a powerful new server that would be used

for corporations’ Internet activities. It would cost $10 million at Year 0 to buy the equipment

necessary to manufacture the server. The project would require net working capital

at the beginning of a year in an amount equal to 10% of the year’s projected sales:

NOWC0 = 10%(Sales1). The servers would sell for $24,000 per unit, and Webmasters

believes that variable costs would amount to $17,500 per unit. After Year 1, the sales

price and variable costs will increase at the inflation rate of 3%. The company’s nonvariable

costs would be $1 million at Year 1 and would increase with inflation.

The server project would have a life of 4 years. If the project is undertaken, it

must be continued for the entire 4 years. Also, the project’s returns are expected to

be highly correlated with returns on the firm’s other assets. The firm believes it

could sell 1,000 units per year.

The equipment would be depreciated over a 5-year period, using MACRS rates. The

estimated market value of the equipment at the end of the project’s 4-year life is $500,000.

Webmasters’ federal-plus-state tax rate is 40%. Its cost of capital is 10% for average-risk

projects, defined as projects with an NPV coefficient of variation between 0.8 and 1.2.

Low-risk projects are evaluated with aWACC of 8% and high-risk projects at 13%.

a. Develop a spreadsheet model, and use it to find the project’s NPV, IRR, and

payback.

b. Now conduct a sensitivity analysis to determine the sensitivity of NPV to changes in

the sales price, variable costs per unit, and number of units sold. Set these variables’

values at 10% and 20% above and below their base-case values. Include a graph in

your analysis.

c. Now conduct a scenario analysis. Assume that there is a 25% probability that best-case

conditions, with each of the variables discussed in part b being 20% better than its

base-case value, will occur. There is a 25% probability of worst-case conditions, with

the variables 20% worse than base, and a 50% probability of base-case conditions.

d. If the project appears to be more or less risky than an average project, find its riskadjusted

NPV, IRR, and payback.

e. On the basis of information in the problem, would you recommend that the project be

accepted?

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