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CHAPTER 12
Cash Flow Estimation and
Risk Analysis
Relevant cash flows
Incorporating inflation
Types of risk
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12 - 2
Proposed Project
Cost: $200,000 + $10,000 shipping
+ $30,000 installation. Depreciable
cost: $240,000.
Inventories will rise by $25,000 and
payables by $5,000.
Economic life = 4 years.
Salvage value = $25,000.
MACRS 3-year class.
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12 - 3
Sales: 100,000 units/year @ $2.
Variable cost = 60% of sales.
Tax rate = 40%.
WACC = 10%.
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12 - 4
Set up, without numbers, a time line
for the project’s cash flows.
0
1
2
3
4
Initial
Costs
(CF0)
OCF1
OCF2
OCF3
OCF4
NCF0
NCF1
+
Terminal
CF
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NCF2
NCF3
NCF4
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Investment at t = 0:
Equipment
-$200
Installation & Shipping
-40
Increase in inventories
-25
Increase in A/P
Net CF0
5
-$260
DNOWC = $25 – $5 = $20.
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12 - 6
What’s the annual depreciation?
Year
Rate
1
2
3
4
0.33
0.45
0.15
0.07
1.00
x
Basis Depreciation
$240
240
240
240
$ 79
108
36
17
$240
Due to 1/2-year convention, a 3-year
asset is depreciated over 4 years.
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12 - 7
Operating cash flows:
1
2
3
4
Revenues
$200 $200 $200 $200
Op. Cost, 60% -120 -120 -120 -120
Depreciation
-79 -108
-36
-17
Oper. inc. (BT)
1
-28
44
63
Tax, 40%
--11
18
25
1
-17
26
38
Oper. inc. (AT)
Add. Depr’n
79
108
36
17
Op. CF
80
91
62
55
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12 - 8
Net Terminal CF at t = 4:
Recovery of NOWC
Salvage Value
Tax on SV (40%)
Net termination CF
$20
25
-10
$35
Q.
Always a tax on SV? Ever a
positive tax number?
Q.
How is NOWC recovered?
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12 - 9
Should CFs include interest expense?
Dividends?
No. The cost of capital is
accounted for by discounting at
the 10% WACC, so deducting
interest and dividends would be
“double counting” financing
costs.
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12 - 10
Suppose $50,000 had been spent last
year to improve the building. Should
this cost be included in the analysis?
No. This is a sunk cost.
Analyze incremental investment.
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12 - 11
Suppose the plant could be leased out
for $25,000 a year. Would this affect
the analysis?
Yes. Accepting the project means
foregoing the $25,000. This is an
opportunity cost, and it should be
charged to the project.
A.T. opportunity cost = $25,000(1 – T)
= $25,000(0.6) = $15,000 annual cost.
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12 - 12
If the new product line would decrease
sales of the firm’s other lines, would
this affect the analysis?
Yes. The effect on other projects’ CFs
is an “externality.”
Net CF loss per year on other lines
would be a cost to this project.
Externalities can be positive or
negative, i.e., complements or
substitutes.
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12 - 13
Here are all the project’s net CFs (in
thousands) on a time line:
0
k = 10%
-260
1
2
79.7
3
91.2
62.4
Terminal CF
4
54.7
35.0
89.7
Enter CFs in CF register, and I = 10%.
NPV = -$4.03
IRR = 9.3%
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12 - 14
What’s the project’s MIRR?
0
1
2
3
4
-260
79.7
91.2
62.4
89.7
68.6
110.4
106.1
374.8
10%
10%
-260
10%
MIRR = ?
Can we solve using a calculator?
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12 - 15
Yes.
CF0
CF1
CF2
CF3
CF4
I
=
=
=
=
=
=
0
79.7
91.2
62.4
89.7
10
NPV = 255.97
INPUTS
4
10
-255.97
0
N
I/YR
PV
PMT
OUTPUT
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FV
TV = FV = 374.8
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Use the FV = TV of inputs to find MIRR
INPUTS
4
N
OUTPUT
I/YR
-260
0
374.8
PV
PMT
FV
9.6
MIRR = 9.6%. Since MIRR < k = 10%,
reject the project.
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12 - 17
What’s the payback period?
0
1
2
3
4
-260
79.7
91.2
62.4
89.7
-89.1
-26.7
63.0
Cumulative:
-260
-180.3
Payback = 3 + 26.7/89.7 = 3.3 years.
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12 - 18
If this were a replacement rather than a
new project, would the analysis change?
Yes. The old equipment would be
sold, and the incremental CFs would
be the changes from the old to the
new situation.
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12 - 19
The relevant depreciation would be
the change with the new equipment.
Also, if the firm sold the old machine
now, it would not receive the SV at
the end of the machine’s life. This is
an opportunity cost for the
replacement project.
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12 - 20
Q. If E(INFL) = 5%, is NPV biased?
CFt
Re v t  Cost t
A. YES. NPV  

.
t
t
1  k 
t  0 1  k 
n
k = k* + IP + DRP + LP + MRP.
Inflation is in denominator but not in
numerator, so downward bias to NPV.
Should build inflation into CF forecasts.
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12 - 21
Consider project with 5% inflation.
Investment remains same, $260.
Terminal CF remains same, $35.
Operating cash flows:
1
Revenues
$210
Op. cost 60% -126
Depr’n
-79
Oper. inc. (BT)
5
Tax, 40%
2
Oper. inc. (AT)
3
Add Depr’n
79
Op. CF
82
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2
$220
-132
-108
-20
-8
-12
108
96
3
$232
-139
-36
57
23
34
36
70
4
$243
-146
-17
80
32
48
17
65
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Here are all the project’s net CFs (in
thousands) when inflation is considered.
0
k = 10%
-260
1
82.1
2
3
96.1
70.0
Terminal CF
4
65.0
35.0
100.0
Enter CFs in CF register, and I = 10%.
NPV = $15.0 Project should be accepted.
IRR = 12.6%
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12 - 23
What are the three types of project risk
that are normally considered?
Stand-alone risk
Corporate risk
Market risk
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What is stand-alone risk?
The project’s total risk if it were
operated independently. Usually
measured by standard deviation (or
coefficient of variation). Though it
ignores the firm’s diversification
among projects and investor’s
diversification among firms.
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12 - 25
What is corporate risk?
The project’s risk giving consideration
to the firm’s other projects, i.e.,
diversification within the firm.
Corporate risk is a function of the
project’s NPV and standard deviation
and its correlation with the returns on
other projects in the firm.
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What is market risk?
The project’s risk to a well-diversified
investor. Theoretically, it is measured
by the project’s beta and it considers
both corporate and stockholder
diversification.
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Which type of risk is most relevant?
Market risk is the most relevant risk
for capital projects, because
management’s primary goal is
shareholder wealth maximization.
However, since total risk affects
creditors, customers, suppliers, and
employees, it should not be
completely ignored.
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12 - 28
Are the three types of risk generally
highly correlated?
Yes. Since most projects the firm
undertakes are in its core business,
stand-alone risk is likely to be highly
correlated with its corporate risk,
which in turn is likely to be highly
correlated with its market risk.
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12 - 29
What is sensitivity analysis?
Sensitivity analysis measures the
effect of changes in a variable on
the project’s NPV. To perform a
sensitivity analysis, all variables are
fixed at their expected values,
except for the variable in question
which is allowed to fluctuate. The
resulting changes in NPV are noted.
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12 - 30
What are the primary advantages and
disadvantages of sensitivity analysis?
ADVANTAGE:
Sensitivity analysis identifies variables
that may have the greatest potential
impact on profitability. This allows
management to focus on those
variables that are most important.
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DISADVANTAGES:
Sensitivity analysis does not reflect
the effects of diversification.
Sensitivity analysis does not
incorporate any information about
the possible magnitudes of the
forecast errors.
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12 - 32
Perform a scenario analysis of the
project, based on changes in the
sales forecast.
Assume that we are confident of all the
variables that affect the cash flows,
except unit sales. We expect unit sales
to adhere to the following profile:
Case
Worst
Base
Best
Probability
0.25
0.50
0.25
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Unit sales
75,000
100,000
125,000
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If cash costs are to remain 60% of
revenues, and all other factors are
constant, we can solve for project
NPV under each scenario.
Case
Worst
Base
Best
Probability
0.25
0.50
0.25
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NPV
($27.8)
$15.0
$57.8
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Use these scenarios, with their given
probabilities, to find the project’s
expected NPV, NPV, and CVNPV.
E(NPV)=.25(-$27.8)+.5($15.0)+.25($57.8)
E(NPV)= $15.0.
NPV = [.25(-$27.8-$15.0)2 + .5($15.0-$15.0)2
+ .25($57.8-$15.0)2]1/2
NPV = $30.3.
CVNPV = $30.3 /$15.0 = 2.0.
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12 - 35
The firm’s average projects have
coefficients of variation ranging from
1.25 to 1.75. Would this project be of
high, average, or low risk?
The project’s CV of 2.0 would
suggest that it would be
classified as high risk.
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12 - 36
Is this project likely to be correlated
with the firm’s business? How would it
contribute to the firm’s overall risk?
We would expect a positive
correlation with the firm’s
aggregate cash flows. As long
as this correlation is not perfectly
positive (i.e., r  1), we would
expect it to contribute to the
lowering of the firm’s total risk.
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12 - 37
If the project had a high correlation
with the economy, how would
corporate and market risk be affected?
The project’s corporate risk would
not be directly affected. However,
when combined with the project’s
high stand-alone risk, correlation
with the economy would suggest
that market risk (beta) is high.
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12 - 38
If the firm uses a +/-3% risk adjustment
for the cost of capital, should the
project be accepted?
Reevaluating this project at a 13%
cost of capital (due to high standalone risk), the NPV of the project
is -$2.2 .
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12 - 39
What is Monte Carlo simulation?
A risk analysis technique in
which probable future events
are simulated on a computer,
generating estimated rates of
return and risk indexes.
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