CHAPTER 12 Cash Flow Estimation and Risk Analysis

1
CHAPTER 12Cash Flow Estimation andRisk Analysis

• Relevant cash flows
• Incorporating inflation
• Types of risk

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.

3

• Sales 100,000 units/year _at_ 2.
• Variable cost 60 of sales.
• Tax rate 40.
• WACC 10.

4
Set up, without numbers, a time line for the
projects cash flows.
0
1
2
3
4
OCF1
OCF2
OCF3
OCF4
Initial Costs

(CF0)
Terminal CF
NCF0
NCF1
NCF2
NCF3
NCF4
5
Investment at t 0
Equipment
-200
Installation Shipping
-40
Increase in inventories
-25
Increase in A/P
5
Net CF0
-260
DNOWC 25 5 20.
6
Whats the annual depreciation?
Year
Rate
x
Basis
Depreciation
1
0.33
240
79
2
0.45
240
108
3
0.15
240
36
4
0.07
240
17
1.00
240
Due to 1/2-year convention, a 3-year asset is
depreciated over 4 years.
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. Deprn
79
108
36
17
Op. CF
80
91
62
55
8
Net Terminal CF at t 4
Recovery of NOWC
20
Salvage Value
25
Tax on SV (40)
-10
Net termination CF
35
Q. Always a tax on SV? Ever a positive tax
number? Q. How is NOWC recovered?
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.

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.

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.

12
If the new product line would decrease sales of
the firms 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.

13
Here are all the projects net CFs (in thousands)
on a time line
0
1
2
3
4
k 10
79.7
91.2
62.4
54.7
-260
Terminal CF
35.0 89.7
Enter CFs in CF register, and I 10.
NPV -4.03 IRR 9.3
14
Whats the projects MIRR?
0
1
2
3
4
79.7
91.2
62.4
89.7
-260
10
68.6
10
110.4
10
106.1
MIRR ?
374.8
-260
Can we solve using a calculator?
15
Yes.
CF0 0 CF1 79.7 CF2 91.2 CF3
62.4 CF4 89.7 I 10
NPV 255.97
INPUTS
4 10 -255.97 0
TV FV 374.8
N
I/YR
PV
PMT
FV
OUTPUT
16
Use the FV TV of inputs to find MIRR
INPUTS
4 -260 0 374.8
9.6
N
I/YR
PV
PMT
FV
OUTPUT
MIRR 9.6. Since MIRR lt k 10, reject the
project.
17
Whats the payback period?
0
1
2
3
4
79.7
91.2
62.4
89.7
-260
Cumulative
-26.7
-260
-89.1
-180.3
63.0
Payback 3 26.7/89.7 3.3 years.
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.
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
  machines life. This is an opportunity cost for
  the replacement project.

20
Q. If E(INFL) 5, is NPV biased?
A. YES.
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.
21
Consider project with 5 inflation. Investment
remains same, 260. Terminal CF remains same,
35.
Operating cash flows 1 2 3 4
Revenues 210 220 232 243 Op. cost
60 -126 -132 -139 -146 Deprn -79 -108
-36 -17 Oper. inc. (BT) 5 -20 57 80 Tax, 40
2 -8 23 32 Oper. inc.
(AT) 3 -12 34 48 Add Deprn 79 108 36
17 Op. CF 82 96 70 65
22
Here are all the projects net CFs (in thousands)
when inflation is considered.
0
1
2
3
4
k 10
82.1
96.1
70.0
65.0
-260
35.0 100.0
Terminal CF
Enter CFs in CF register, and I 10.
NPV 15.0 IRR 12.6
Project should be accepted.
23
What are the three types of project risk that are
normally considered?

• Stand-alone risk
• Corporate risk
• Market risk

24
What is stand-alone risk?
The projects total risk if it were operated
independently. Usually measured by standard
deviation (or coefficient of variation). Though
it ignores the firms diversification among
projects and investors diversification among
firms.
25
What is corporate risk?
The projects risk giving consideration to the
firms other projects, i.e., diversification
within the firm. Corporate risk is a function of
the projects NPV and standard deviation and its
correlation with the returns on other projects in
the firm.
26
What is market risk?
The projects risk to a well-diversified
investor. Theoretically, it is measured by the
projects beta and it considers both corporate
and stockholder diversification.
27
Which type of risk is most relevant?
Market risk is the most relevant risk for capital
projects, because managements primary goal is
shareholder wealth maximization. However, since
total risk affects creditors, customers,
suppliers, and employees, it should not be
completely ignored.
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.
29
What is sensitivity analysis?
Sensitivity analysis measures the effect of
changes in a variable on the projects 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.
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.
31
DISADVANTAGES Sensitivity analysis does not
reflect the effects of diversification. Sensitivit
y analysis does not incorporate any information
about the possible magnitudes of the forecast
errors.
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 Probability Unit sales
Worst 0.25 75,000
Base 0.50 100,000
Best 0.25 125,000
33
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 Probability NPV
Worst 0.25 (27.8)
Base 0.50 15.0
Best 0.25 57.8
34
Use these scenarios, with their given
probabilities, to find the projects 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)21/2 ?NPV 30.3.
CVNPV 30.3 /15.0 2.0.
35
The firms average projects have coefficients of
variation ranging from 1.25 to 1.75. Would this
project be of high, average, or low risk?
The projects CV of 2.0 would suggest that it
would be classified as high risk.
36
Is this project likely to be correlated with the
firms business? How would it contribute to the
firms overall risk?
We would expect a positive correlation with the
firms 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 firms total risk.
37
If the project had a high correlation with the
economy, how would corporate and market risk be
affected?
The projects corporate risk would not be
directly affected. However, when combined with
the projects high stand-alone risk, correlation
with the economy would suggest that market risk
(beta) is high.
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 stand-alone risk), the NPV
of the project is -2.2 .
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.