Chapter 12: Cash Flow Estimation and Risk Analysis
Learning Objectives
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Chapter 12
Cash Flow Estimation and Risk Analysis
Learning Objectives
After reading this chapter, students should be able to:
◆ Identify “relevant” cash flows that should and should not be included in a capital budgeting analysis.
◆ Estimate a project’s relevant cash flows and put them into a time line format that can be used to
calculate a project’s NPV, IRR, and other capital budgeting metrics.
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Lecture Suggestions
Chapter 12: Cash Flow Estimation and Risk Analysis
Lecture Suggestions
This chapter covers some important but relatively technical topics. Note too that this chapter is more
modular than most, i.e., the major sections are discrete, hence they can be omitted without loss of
DAYS ON CHAPTER: 3 OF 56 DAYS (50-minute periods)
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Answers to End-of-Chapter Questions
12-1 Only cash can be spent or reinvested, and since accounting profits do not represent cash, they
12-2 Capital budgeting analysis should only include those cash flows that will be affected by the
decision. Sunk costs are unrecoverable and cannot be changed, so they have no bearing on the
12-3 When a firm takes on a new capital budgeting project, it typically must increase its investment in
receivables and inventories, over and above the increase in payables and accruals, thus
12-4 The costs associated with financing are reflected in the weighted average cost of capital. To
12-5 Daily cash flows would be theoretically best, but they would be costly to estimate and probably
no more accurate than annual estimates because we simply cannot forecast accurately at a daily
12-6 In replacement projects, the benefits are generally cost savings, although the new machinery
may also permit additional output. The data for replacement analysis are generally easier to
12-7 Stand-alone risk is the project’s risk if it is held as a lone asset. It disregards the fact that it is
but one asset within the firm’s portfolio of assets and that the firm is but one stock in a typical
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12-8 It is often difficult to quantify market risk. On the other hand, we can usually get a good idea of
a project’s stand-alone risk, and that risk is normally correlated with market risk: The higher the
12-9 Simulation analysis involves working with continuous probability distributions, and the output of a
simulation analysis is a distribution of net present values or rates of return. Scenario analysis
12–10 Scenario analyses, and especially simulation analyses, would probably be reserved for very
important “make–or–break” decisions. They would not be used for every project decision because
12-11 The replacement chain approach is a method of comparing projects with unequal lives that
12-12 The equivalent annual annuity method calculates the annual payments a project would provide if it
12-13 Generally, the failure to employ replacement chain analysis or the equivalent annual annuity
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Solutions to End-of-Chapter Problems
12-1 a. Equipment purchase ($ 9,000,000)
12-2 a. Project cash flows: t = 1
Sales revenues $10,000,000
b. The cannibalization of existing sales needs to be considered in this analysis on an after–tax
c. If the tax rate fell to 30%, the project’s cash flow would change to:
EBIT $1,000,000
12-3 Equipment’s original cost $20,000,000
Depreciation (80%) 16,000,000
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Chapter 12: Cash Flow Estimation and Risk Analysis
12-4 Cash outflow = $40,000.
Increase in annual after-tax cash flows: CF = $9,000.
12-5 First, solve for each project’s NPV.
Project A: CF0 = –20000, CF1 = 6000, Nj = 6, I/YR = 10; solve for NPV = $6,131.56.
12-6 a. The applicable depreciation values are as follows for the two scenarios:
Scenario 1 Scenario 2
Year (Straight-Line) (MACRS)
1 $200,000 $264,000
b. To find the difference in net present values under these two methods, we must determine the
difference in incremental cash flows each method provides. The depreciation expenses cannot
simply be subtracted from each other, as there are tax ramifications due to depreciation
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12-7 E(NPV) = 0.05(-$70) + 0.20(-$25) + 0.50($12) + 0.20($20) + 0.05($30)
b.
Project’s operating cash flows:
Year 1 Year 2 Year 3
Savings $50,000 $50,000 $50,000
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Notes:
1. The depreciation expense in each year is the depreciable basis, $170,000, times the MACRS
c. The project has an NPV of ($19,549). Thus, it should not be accepted.
Year Cash Flows PV @ 12%
Alternatively, place the free cash flows on a time line:
12-9 a. The $5,000 spent last year on exploring the feasibility of the project is a sunk cost and should
b. The initial investment outlay at t = 0 is $126,000:
Price ($108,000)
c. The annual project cash flows follow:
Project’s operating cash flows:
Year 1 Year 2 Year 3
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Terminal cash flows at time = 3:
Salvage value $65,000
Tax on salvage value 19,798
AT salvage value $45,202
d. The project has an NPV of $10,841; thus, it should be accepted.
Year Cash Flows PV @ 12%
Alternatively, place the free cash flows on a time line:
12–10 First determine the net cash flow at t = 0:
Purchase price ($8,000)
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Chapter 12: Cash Flow Estimation and Risk Analysis
After-tax revenue increase:
Depreciation:
Year 1 2 3 4 5 6
Newa $1,600 $2,560 $1,520 $960 $880 $480
Finally, place all the cash flows on a time line:
0 1 2 3 4 5 6
| | | | | | |
Net investment (7,160)
After-tax revenue increase 1,500 1,500 1,500 1,500 1,500 1,500
Depreciation tax savings 500 884 468 244 212 52
12-11 1. Net investment at t = 0:
15%
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2. After–tax
Year Earnings T(Dep) Annual CFt
1 $16,200 $ 6,600 $22,800
Notes:
3. Now find the NPV of the replacement machine:
Place the cash flows on a time line:
12-12 a. Expected annual cash flows:
Project A: Probable
Probability × Cash Flow = Cash Flow
0.2 $6,000 $1,200
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Coefficient of variation:
b. Project B is the riskier project because it has the greater variability in its probable cash flows,
whether measured by the standard deviation or the coefficient of variation. Hence, Project B is
evaluated at the 12% cost of capital, while Project A requires only a 10% cost of capital.
12–13 a. Project A: 0 1 2
| | |
-10,000 6,000 8,000
Using a financial calculator, input the following data: CF0 = -10000, CF1 = 6000, CF2 = 8000,
I/YR = 10, and then solve for NPVA = $2,066.12.
Project B: 0 1 2 3 4
| | | | |
-10,000 4,000 4,000 4,000 4,000
Using a financial calculator, input the following data: CF0 = -10000, CF1-4 = 4000, I/YR = 10,
and then solve for NPVB = $2,679.46.
Since neither project can be repeated, Project B should be selected because it has a higher NPV
than Project A.
10%
10%
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b. To determine the answer to Part b, we use the replacement chain (common life) approach to
calculate the extended NPV for Project A. Project B already extends out to 4 years, so its NPV is
$2,679.46.
Project A: 0 1 2 3 4
| | | | |
c. From Part a, NPVA = $2,066.12 and NPVB = $2,679.46. Solving for PMT determines the EAA:
12–14 0 1 2 3
| | | |
-190,000 87,000 87,000 87,000
10%
14%
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12–15 Since Plane A’s renewal investment changes the EAA method cannot be used, so the replacement
12–16 A: 0 1 2 3 4 5 6 7 8
| | | | | | | | |
–10 4 4 4 4
–12 4.2 4.2 4.2 4.2
-8
10%
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12–17 First, solve for each project’s NPV.
Project X: CF0 = -100000, CF1 = 30000, CF2 = 50000, CF3 = 70000, I/YR = 12; solve for NPV =
$16,470.0255.
12–18 If actual life is 5 years:
Using a time line approach:
0 1 2 3 4 5
If actual life is 4 years:
Using a time line approach:
10%
10%
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If actual life is 8 years:
Using a time line approach:
12-19 a. 0 1 2 3 4 5
Capital expenditure ($250,000)
NOWC (25,000)
Cost savings $90,000 $ 90,000 $90,000 $90,000 $90,000
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b. If savings increase by 20%, then savings will be (1.2)($90,000) = $108,000.
(2) Savings decrease by 20%:
0 1 2 3 4 5
Capital expenditure ($250,000)
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c. Worst-case scenario:
0 1 2 3 4 5
Capital expenditure ($250,000)
Base-case scenario:
Best-case scenario:
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12–20 a. Old depreciation = $9,000 per year.
b. Recovery Depreciable Depreciation Depreciation Change in
Year Percentage Basis Allowance, New Allowance, Old Depreciation
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b. Recovery Depreciable Depreciation Depreciation Change in
Year Percentage Basis Allowance, New Allowance, Old Depreciation
1 20% $1,175,000 $235,000 $120,000 $115,000
c. CFt = (Operating expenses)(1 – T) + (Depreciation)(T).
A time line of the cash flows looks like this:
d. From part c input the data into your calculator as follows: CF0 = -792750; CF1 = 206000; CF2
e. 1. If the expected life of the old machine decreases, the new machine will look better as cash