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12/10/2012
Chapter 11 Mini Case
Situation
Analysis of New Expansion Project
Part I: Input Data
Equipment cost $200,000 Key Output: NPV = $88,010
Shipping charge $10,000
Installation charge $30,000
Economic Life 4
Salvage Value $25,000
Annual Depreciation Expense
Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting
analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would be set
up in unused space in Shrieves' 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 Shrieves has obtained a special tax ruling
that 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 4 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 working capital would have to increase by an amount equal to 12% of sales revenues. The firm’s
tax rate is 40%, and its overall weighted average cost of capital is 10%.
a. Define “incremental cash flow.” Answer: See Chapter 11 Mini Case Show
Show
b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual
depreciation expenses?
Annual Operating Cash Flows
Year 1 Year 2 Year 3 Year 4
Units 1,250 1,250 1,250 1,250
Unit price $200.00 $206.00 $212.18 $218.55
Unit cost $100.00 $103.00 $106.09 $109.27
Annual Cash Flows due to Investments in Net Working Capital
d. Construct annual incremental operating cash flow statements.
e. Estimate the required net working capital for each year, and the cash flow due to investments in net
working capital.
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include
inflation when estimating cash flows? See answer to part d.
f. Calculate the after-tax salvage cash flow.
After-tax Salvage Value
Based on
facts in
Projected Net Cash Flows
Year 0 Year 1 Year 2 Year 3 Year 4
MIRR = 18.0%
Find Payback
0 1 2 3 4
Cash Flow ($270,000) $106,097 $118,995 $92,830 $136,850
Cumulative Cash Flow for Payback ($270,000) ($163,903) ($44,908) $47,922 $184,772
Payback = 2.5
Hypothetical: If sold
after 3 years for
Years
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 the project should be undertaken?
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.
Evaluating Risk: Sensitivity Analysis
Sensitivity of NPV and to Variations in Input Variables
i. (1.) What are the three types of risk that are relevant in capital budgeting? Answer: See Chapter 11 Mini
Case Show
(3.) How is each type of risk used in the capital budgeting process? Answer: See Chapter 11 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%. Include a sensitivity diagram, and discuss the results.
(2.) How is each of these risk types measured, and how do they relate to one another? Answer: See
Chapter 11 Mini Case Show
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
examine the project's sensitivity to changes in the input variables.
j. (1.) What is sensitivity analysis? Answer: See Chapter 11 Mini Case Show
Evaluating Risk: Sensitivity Analysis
Deviation NPV Deviation from Base Case
from Units
Base Case WACC Sold Salvage
-30% $113,270 $16,649 $84,936
-15% 100,291 52,329 86,473
0% 88,010 88,010 88,010
15% 76,378 123,690 89,546
30% 65,350 159,371 91,083
Range $47,920 $176,020 $6,147
Evaluating Risk: Scenario Analysis
Scenario Analysis
(3.) What is the primary weakness of sensitivity analysis? What is its primary usefulness? Answer: See
Chapter 11 Mini Case Show
k. Assume that Sidney Johnson is confident of her estimates of all the variables that affect the project’s cash
(1.) What is scenario analysis?
(2.) What is the worst-case NPV? The best-case NPV?
(3.) Use the worst-, most likely, and best-case NPVs and probabilities of occurrence to find the project’s
expected NPV, standard deviation, and coefficient of variation.
Scenario analysis extends risk analysis in two ways: (1) It allows us to change more than one variable at a
time, hence to see the combined effects of changes in several variables on NPV, and (2) it allows us to bring
in the probabilities of changes in the key variables.
140,000
160,000
180,000
NPV ($)
Sensitivity Analysis
Units Sold
Probability Unit Sales Unit Price NPV
Monte Carlo Simulation
Risk Adjusted Cost of Capital
(2.) Shrieves typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk.
Should the new line be accepted?
(3.) Are there any subjective risk factors that should be considered before the final decision is made?
Answer: See Chapter 11 Mini Case Show
Squared Deviation
times Probability
m. (1.) Assume that Shrieves' average project has a coefficient of variation in the range of 0.2 to 0.4. Would
the new line be classified as high risk, average risk, or low risk? What type of risk is being measured here?
Answer: See Chapter 11 Mini Case Show
Monte Carlo simulation is similar to scenario analysis in that different values of key input variables are used.
Unlike scenario analysis, Monte Carlo simulation draws the input values from specified probability
distributions and then computes the NPV. It repeats this process hundreds, or even thousands, of times. It
then averages the NPVs from each repetition.
Scenario
l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal
advantages and disadvantages. Answer: See Chapter 11 Mini Case Show
Scenario Summary
Current Values: Base Case Best Case Worst Case Base-but forget inflation
Changing Cells:
$D$36 $200,000 $200,000 $200,000 $200,000 $200,000
$D$37 $10,000 $10,000 $10,000 $10,000 $10,000
$D$38 $30,000 $30,000 $30,000 $30,000 $30,000
$D$39 4 4 4 4 4
$D$40 $25,000 $25,000 $25,000 $25,000 $25,000
12/10/2012
Analysis of New Expansion Project
Part I: Input Data
Equipment cost $200,000 Key Output: NPV = $25,263
Shipping charge $10,000
Installation charge $30,000
Economic Life 4
Salvage Value $25,000
Annual Depreciation Expense
Depreciable Basis = Equipment + Freight + Installation
Depreciable Basis = $240,000
Year % x Basis = Depr.
Remainin
g Book
Value
Annual Operating Cash Flows
Year 1 Year 2 Year 3 Year 4
Units 1,279 1,279 1,279 1,279
Annual Cash Flows due to Investments in Net Working Capital
e. Estimate the required net working capital for each year, and the cash flow due to investments in net working
capital.
Section 11.7 Scenario Analysis
Monte Carlo simulation is similar to scenario analysis in that different values of key inputs are used Unlike scenario
analysis, Monte Carlo simulation draws a trial set of input values from specified probability distributions and then computes
the NPV for this trial. This process is repeated for hundreds, or even thousands, of trials, with key results (like NPV) saved
from each trial. After running the number of desired trials, the NPVs from the trials can be averaged to estimate the project's
expected NPV; the trial results can also be used to provide a histogram showing the project's possible outcomes.
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include
inflation when estimating cash flows? See answer to part d.
b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual
d. Construct annual incremental operating cash flow statements.
Year 0 Year 1 Year 2 Year 3 Year 4
Sales $220,638 $227,257 $234,072 $241,093
NWC (% of sales) 26,477 27,271 28,089 28,931
CF due to investment in NOWC) (26,477) (794) (818) (842) 28,931
f. Calculate the after-tax salvage cash flow.
Projected Net Cash Flows
Year 0 Year 1 Year 2 Year 3 Year 4
Investment Outlay: Long Term Assets
($240,000)
Operating Cash Flows
$87,331 $100,520 $73,438 $67,531
CF due to investment in NWC
(26,477) (794) (818) (842) 28,931
Salvage Cash Flows 15,000
Net Cash Flows ($266,477) $86,537 $99,702 $72,596 $111,462
NPV $25,263
IRR 14.2%
PV of Inflows
TV of Inflows
How the Simulation Works
Column input cell to "trick" Excel into updating random variables in Data Table: 1Don't change the the red cell.
You don't need to change anything in this section. It will be updated automatically if you do a simulation. The summary of
the simulation results and the histogram are based on the simulation trials n the Data Table below and are updated
automatically when you do a simulation. You can do an updated simulation by hitting the F9 key.
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 the project should be undertaken?
We use a Data Table to perform the simulation (the Data Table is below, shaded bright yellow). When the Data Table is
updated, it will insert new random variables for each of the inputs we allow to change in Panel A above, run the analysis is
Table, all the random values will be updated.
Number of Trials = 100
Scratch work for chart: see comments.
Count
Range bottom 0Percent
-$306,270 0 0%
-$284,393 0 0%
-$262,517 0 0%
-$240,640 0 0%
-$218,764 0 0%
-$196,888 0 0%
Output of Simulation in Data Table
Trial Number Units Sold
Sales
Price Per
Unit
NPV
1,279 $173 $25,263
1 1549.2439 180.2574 85565.0196
2 1129.057 179.04317 19050.6786
3 1368.9238 217.06253 156031.855
4 1200.4633 169.08357 6501.97329
5 1450.8464 189.49232 96629.5009
6 1615.3433 231.87061 257558.829
7 1374.3042 233.06231 199956.285
8 1346.0799 179.36168 52339.3347
9 1253.4387 237.49918 179987.48
Figure 11-27 Summary of Simulation Results (Thousands of Dollars)
Sales
Price Per
Simulated Input Variables and Key Results
Key Results:
Probability
26 1089.8577 168.87897 -8340.68356
35 1457.0543 236.69662 231295.079
36 839.81992 205.21054 18473.7454
37 1255.1591 183.29047 48262.2957
38 1439.4991 183.68336 78464.0382
39 1631.8013 202.99668 170182.963
40 1209.3076 142.71423 -54288.6856
41 1300.2693 181.3835 50568.53
42 1334.3627 173.10723 34372.7179
43 1255.085 212.75838 120106.707
44 1248.0614 203.11229 95200.7859
45 1313.894 162.64423 4843.02397
59 1178.7318 207.88691 92529.7312
60 1157.4502 186.23583 39471.0865
61 1292.4625 196.49043 87298.8929
62 1349.0912 198.34679 102555.175
63 1403.2338 241.40022 230038.457
64 1083.5914 117.69926 -116876.905
65 964.58781 188.72092 12577.1982
66 1182.9824 219.51536 120120.093
75 1374.1586 227.40936 184825.811
76 1326.809 168.43704 21285.9497
77 898.88534 192.19184 7580.74606
78 1684.7558 189.52012 136457.391
79 1475.9078 200.646 132877.43
80 959.45861 221.37248 72572.4393
81 1347.2946 163.46753 10923.7853
82 1761.5787 235.32555 306269.661
83 1405.7894 187.88447 84592.1369
84 1514.2106 196.10571 126851.781
85 1308.3114 253.48184 235052.125
86 1151.9958 214.15883 101063.259
87 1148.4777 227.99731 131170.839
88 1099.4388 237.74523 139989.164
