Posted: September 16th, 2017
Financial Management 460 Problems……………………………
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.
res evrvead. diustritbautio nt whithroiukt exsprie ssk auothosrizkatieon
(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.
s Neo a llpoweedr wuithsoutt euxpire svs auuthoorihzatieon
(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.
. diisttriabut iopn wtiuthonut a utthooriizvatioon
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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