12/16/2001
Chapter 8 Mini Case
Situation
John Crockett Furniture Company is considering adding a new line to its product mix, and the capital budgeting analysis is
being conducted by Joan Samuels, a recently graduated MBA. The production line would be set up in unused space in
Crockett’s main plant. The machinery’s invoice price would be approximately $200,000; another $10,000 in shipping
charges would be required; and it would cost an additional $30,000 to install the equipment. The machinery has an
economic life of 4 years, and Crockett has obtained a special tax ruling which places the equipment in the MACRS 3-year
class. The machinery is expected to have a salvage value of $25,000 after 4 years of use.
The new line would generate incremental sales of 1,250 units per year for four years at an incremental cost of $100 per unit
in the first year, excluding depreciation. Each unit can be sold for $200 in the first year. The sales price and cost are
expected to increase by 3% per year due to inflation. Further, to handle the new line, the firm’s net operating working
capital would have to increase by an amount equal to 12% of sales revenues. The firm’s tax rate is 40 percent, and its
overall weighted average cost of capital is 10 percent.
a. Define “incremental cash flow.” Answer: See Chapter 8 Mini Case Show
(1.) Should you subtract interest expense or dividends when calculating project cash flow? Answer: See Chapter 8 Mini
Case Show
(2.) Suppose the firm had spent $100,000 last year to rehabilitate the production line site. Should this be included in the
analysis? Explain. Answer: See Chapter 8 Mini Case Show
(3.) Now assume that the plant space could be leased out to another firm at $25,000 a year. Should this be included in the
analysis? If so, how? Answer: See Chapter 8 Mini Case Show
(4.) Finally, assume that the new product line is expected to decrease sales of the firm’s other lines by $50,000 per year.
Should this be considered in the analysis? If so, how? Answer:See Chapter 8 Mini Case Show
Analysis of New Expansion Project
Part I: Input Data
Equipment cost $200,000
Shipping charge $10,000
Installation charge $30,000
Economic Life 4
Salvage Value $25,000
Tax Rate 40%
Cost of Capital 10%
Units Sold 1250
Sales Price Per Unit $200
Incremental Cost Per Unit $100
Inventory/sales 12%
Inflation rate 3%
b. Disregard the assumptions in Part a. What is Crockett’s depreciable basis? What are the annual depreciation expenses?
Annual Depreciation Expense
Depreciable Basis = Equipment + freight + installation
Depreciable Basis = $240,000
Year % x Basis = Depr.
1 0.33 $240,000 $79,200
2 0.45 $240,000 $108,000
3 0.15 $240,000 $36,000
4 0.07 $240,000 $16,800
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include inflation when
estimating cash flows?
d. Construct annual incremental operating cash flow statements.
Annual Operating Cash Flows
Year 1 Year 2 Year 3 Year 4
Units 1250 1250 1250 1250
Unit price $200.00 $206.00 $212.18 $218.55
Unit cost $100.00 $103.00 $106.09 $109.27
Sales $250,000 $257,500 $265,225 $273,188
Costs $125,000 $128,750 $132,613 $136,588
Depreciation $79,200 $108,000 $36,000 $16,800
Operating income before taxes (EBIT) $45,800 $20,750 $96,612 $119,800
Taxes (40%) $18,320 $8,300 $38,645 $47,920
Net operating profit after taxes $27,480 $12,450 $57,967 $71,880
Depreciation $79,200 $108,000 $36,000 $16,800
Net Operating CF $106,680 $120,450 $93,967 $88,680
e. Estimate the required net operating working capital for each year, and the cash flow due to investments in net operating
working capital.
Annual Cash Flows due to Investments in Net Operating Working Capital
Year 0 Year 1 Year 2 Year 3 Year 4
Sales $250,000 $257,500 $265,225 $273,188
NOWC (% of sales) $30,000 $30,900 $31,827 $32,783
CF due to investment in NOWC) ($30,000) ($900) ($927) ($956) $32,783
f. Calculate the after-tax salvage cash flow.
After-tax Salvage Value
Salvage Value $25,000
Tax on Salvage Value $10,000
Net Terminal Cash Flow $15,000
g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR, MIRR, and
payback? Do these indicators suggest that the project should be undertaken?
Projected Net Cash Flows
Year 0 Year 1 Year 2 Year 3
Investment Outlay: Long Term Assets ($240,000)
Operating Cash Flows $106,680 $120,450 $93,967
CF due to investment in NOWC ($30,000) ($900) ($927) ($956)
Salvage Cash Flows
Net Cash Flows ($270,000) $105,780 $119,523 $93,011
NPV $88,030
IRR 23.9%
$358,030 $524,191
Years
Find MIRR 0 1 2 3
Net Cash Flows ($270,000) $105,780 $119,523 $93,011
PV= ($270,000) TV =
To find MIRR, we could now find the discount rate that equates the PV and TV. But it is easier to use the MIRR function.
MIRR = 18.0%
Find Payback Years
0 1 2 3
Cumulative Cash Flow for Payback ($270,000) ($164,220) ($44,697) $48,314
Cum. CF > 0, hence Payback Year: FALSE FALSE FALSE TRUE
Payback found with Excel function = 0 0 0 2.5
Payback = 2.5
h. What does the term ”risk” mean in the context of capital budgeting, to what extent can risk be quantified, and when risk
is quantified, is the quantification based primarily on statistical analysis of historical data or on subjective, judgmental
estimates?
Risk in capital budgeting really means the probability that the actual outcome will be worse than the expected outcome. For
example, if there were a high probability that the expected NPV as calculated above will actually turn out to be negative,
then the project would be classified as relatively risky. The reason for a worse-than-expected outcome is, typically, because
sales were lower than expected, costs were higher than expected, or the project turned out to have a higher than expected
initial cost. In other words, if the assumed inputs turn out to be worse than expected then the output will likewise be worse
than expected. We use Excel to examine the project's sensitivity to changes in the input variables.
i. (1.) What are the three types of risk that are relevant in capital budgeting? Answer: See Chapter 8 Mini Case Show
(2.) How is each of these risk types measured, and how do they relate to one another? Answer: See Chapter 8 Mini Case
Show
(3.) How is each type of risk used in the capital budgeting process? Answer: See Chapter 8 Mini Case Show
Evaluating Risk: Sensitivity Analysis
Sensitivity of NPV and to Variations in Unit Sales.
j. (1.) What is sensitivity analysis? Answer:See Chapter 8 Mini Case Show
(2.) Perform a sensitivity analysis on the unit sales, salvage value, and cost of capital for the project. Assume that each of
these variables can vary from its base case, or expected, value by plus and minus 10, 20, and 30 percent. Include a
sensitivity diagram, and discuss the results.
Here we use an Excel "Data Table" to find NPV different unit sales, holding other thing constant. For example, after
inputting the values for WACC in cells B205:B209 and the formula =C105 for NPV in cell C204, select the range
B204:C209. Then choose from the menu Data, Table, and enter D31 (which is the input for WACC) as the Column input.
This produces the sensitivity analysis for WACC as shown below.
We summarize the data tables, arranged by sensitivity, and graphed the most sensitive items in the following chart:
% Deviation WACC % Deviation 1st YEAR UNIT SALES % Deviation SALVAGE
from NPV from Units NPV from Variable
Base Case WACC 88,030 Base Case Sold $88,030 Base Case Cost
-30% 7.0% $113,288 -30% 875 $16,668 -30% $17,500.00
-15% 8.5% $100,310 -15% 1,063 $52,348 -15% $21,250.00
0% 10.0% $88,030 0% 1,250 $88,030 0% $25,000.00
15% 11.5% $76,398 15% 1,438 $123,711 15% $28,750.00
30% 13.0% $65,371 30% 1,625 $159,392 30% $32,500.00
Evaluating Risk: Sensitivity Analysis
Sensitivity Analysis
$180,000
$160,000
$140,000
$120,000 WACC
$100,000
NPV
Units Sold
$80,000
Salvage
$60,000
$40,000
$20,000
$0
-40% -20% 0% 20% 40%
Deviation from Base-Case Value
Deviation NPV Deviation from Base Case -30% $113
from Units -15% $100
Base Case WACC Sold Salvage 0% $88
-30% $113,288 $16,668 $84,956 15% $76
-15% $100,310 $52,348 $86,493 30% $65
0% $88,030 $88,030 $88,030
15% $76,398 $123,711 $89,567
30% $65,371 $159,392 $91,103
Range 47,916 176,060 6,147
(3.) What is the primary weakness of sensitivity analysis? What is its primary usefulness? Answer: See Chapter 8 Mini
Case Show
k. Assume that Joan Samuels is confident of her estimates of all the variables that affect the project’s cash flows except unit
sales and sales price: If product acceptance is poor, unit sales would be only 900 units a year and the unit price would only
be $160; a strong consumer response would produce sales of 1,600 units and a unit price of $240. Joan believes that there is
a 25 percent chance of poor acceptance, a 25 percent chance of excellent acceptance, and a 50 percent chance of average
acceptance (the base case).
(1.) What is scenario analysis?
Scenario analysis extends risk analysis in two ways: (1) It allows us to change more than one variable at a time, hence to see
the combined effects of changes in several variables on NPV, and (2) It allows us to bring in the probabilities of to see the
combined effects of changes in several variables on NPV, and (2) It allows us to bring in the probabilities of changes in the
key variables.
(2.) What is the worst-case NPV? The best-case NPV?
(3.) Use the worst-, most likely, and best-case NPVs and probabilities of occurrence to find the project’s expected NPV,
standard deviation, and coefficient of variation.
Evaluating Risk: Scenario Analysis
We could find the NPV by entering the value of unit sales and price for each scenario and then recording the NPV (this is
what we did for the table below). Alternatively, we could use Tools, Scenarios to define the inputs for each scenario, which
we did. In fact, you could even use Tools, Scenarios, and then click the Summary button on the dialog box, and it will
automatically create a table similar to the one below. This is a powerful feature of Excel, and we encourage you to explore
Scenario Analysis
Squared Deviation
Scenario Probability Unit Sales Unit Price NPV times probability
Best Case 25% 1600 $240 $278,965 $7,862,111,358.79
Base Case 50% 1250 $200 $88,030 $92,450,542.34
Worst Case 25% 900 $160 ($48,514) $5,635,612,088.43
Expected NPV = $101,628
Standard Deviation = $75,684
Coefficient of Variation = Std Dev / Expected NPV = 0.74
l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and
disadvantages. Answer: See Chapter 8 Mini Case Show
Monte Carlo Simulation
Monte Carlo simulation is similar to scenario analysis in that different values of key inputs are input. Unlike scenario
analysis, Monte Carlo simulation draws the input values from a specified probability distribution and then computes the
NPV. It repeats this process hundred, or even thousands, of times. It then averages the NPVs from each repetition. See the
file Ch 08 Mini Case Simulation.xls for a detailed example. To use this spreadsheet, you will need to install the Excel Add-In
Simtools.xla . See the file Explanation of Simulation.doc for an explanation of how to install the Add-In.
Risk Adjusted Cost of Capital
m. (1.) Assume that Crockett’s average project has a coefficient of variation in the range of 0.2 – 0.4. Would the new
furniture line be classified as high risk, average risk, or low risk? What type of risk is being measured here? Answer: See
Chapter 8 Mini Case Show
(2.) Crockett typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk. This project
is riskier than the firm's average project, so he adds 3 points. Should the new furniture line be accepted?
Cost of capital for average projects: 10%
Adjustment for risky projects: 3%
Risk adjusted cost of capital: 13%
NPV with risk adjusted cost of capital: $65,371 (See the +30% WACC in the sensitivity analysis above.)
(3.) Are there any subjective risk factors that should be considered before the final decision is made? Answer: See
Chapter 8 Mini Case Show
pital budgeting analysis is
up in unused space in
$10,000 in shipping
machinery has an
t in the MACRS 3-year
ental cost of $100 per unit
s price and cost are
et operating working
s 40 percent, and its
wer: See Chapter 8 Mini
d this be included in the
uld this be included in the
es by $50,000 per year.
ual depreciation expenses?
include inflation when
estments in net operating
PV, IRR, MIRR, and
Year 4
$88,680
$32,783
$15,000
$136,463
4
$136,463
$102,312
$144,623
$140,793
$524,191
o use the MIRR function.
4
$184,777
FALSE
0
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er 8 Mini Case Show
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ni Case Show
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For example, after
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e following chart:
SALVAGE
NPV
$88,030
$84,956
$86,493
$88,030
$89,567
$91,103
WACC
Units Sold
Salvage
$17 ##
$52 ##
$88 ##
$124 ##
$159 ##
wer: See Chapter 8 Mini
ct’s cash flows except unit
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Joan believes that there is
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for each scenario, which
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to install the Excel Add-In
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just for risk. This project
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Scenario Summary
Current Values: Base Case Best Case Worst Case
Changing Cells:
$D$31 1250 1250 1600 900
$D$32 $200 $200 $240 $160
Result Cells:
$C$109 $88,030 $88,030 $278,965 ($48,514)
$C$110 23.9% 23.9% 48.3% 1.0%
Notes: Current Values column represents values of changing cells at
time Scenario Summary Report was created. Changing cells for each
scenario are highlighted in gray.