Chapter 13
Cash Flow Estimation and Risk
Analysis
13-1
Analysis of a New Product Development Project
•
Total depreciable cost
•
Changes in operating working capital
•
– Equipment: $225,000
– Shipping and installation: $40,000
– Inventories will rise by $25,000
– Accounts payable will rise by $5,000
Effect on operations
– New sales: 100,000 units/year @ $2/unit
– Variable cost: 60% of sales
13-2
Proposed Project
•
Life of the project
•
•
Tax rate: 40%
– Economic life: 4 years
– Depreciation method: Straight line method
– Salvage value: $25,000
WACC: 10%
13-3
Determining Project Value
•
Estimate relevant cash flows
– Calculating annual operating cash flows.
– Identifying changes in net operating working capital.
– Calculating terminal cash flows: after-tax salvage
value and return of NOWC.
0
1
2
3
4
Initial
Costs
OCF1
OCF2
OCF3
FCF0
FCF1
FCF2
FCF3
OCF4
+
Terminal
CFs
FCF4
13-4
Initial Year Investment Outlays
•
•
Find NOWC.
–  in inventories of $25,000
– Funded partly by an  in A/P of $5,000
– NOWC = $25,000 – $5,000 = $20,000
Initial year outlays:
Equipment cost
-$225,000
Installation
-$40,000
CAPEX
-$265,000
NOWC
-$20,000
FCF0
-$285,000
13-5
Determining Annual Depreciation Expense
Year
1
2
3
4
Rate
0.25
0.25
0.25
0.25
1.00
x
x
x
x
x
Basis
$240
$240
$240
$240
Deprec.
$60
$60
$60
$60
$240
Basis: $265,000 – $25,000 = $240,000
If the company uses accelerated rate depreciation, the
amount of depreciation and the FCF will be different.
13-6
Project Operating Cash Flows
(Thousands of dollars)
Revenues
– Op. costs
1
200.0
-120.0
2
3
4
200.0 200.0 200.0
-120.0 -120.0 -120.0
– Depreciation
-60.0
-60.0
-60.0
-60.0
EBIT
– Taxes (40%)
20.0
-8.0
20.0
-8.0
20.0
-8.0
20.0
-8.0
EBIT(1 – T)
12.0
12.0
12.0
12.0
+ Depreciation
60.0
60.0
60.0
60.0
EBIT(1 – T) + DEP
72.0
72.0
72.0
72.0
13-7
Terminal Cash Flows
(Thousands of dollars)
Salvage value
– Tax on SV (40%)
AT salvage value
+ NOWC
Terminal CF
$25
10
$15
20
$35
FCF4 = EBIT(1 – T) + DEP + AT SV + NOWC
= $72 + $35
= $107
13-8
Proposed Project’s Cash Flow Time Line
(Thousands of dollars)
0
1
-285
•
72
2
3
72
72
4
107
Calculate the following given the WACC=10.0%:
NPV = -32.9
IRR = 4.87%
MIRR = 6.68%
Payback = 3.645 years
13-9
Questions
Q1. Should financing effects be included in cash flows?
Q2. Should a $50,000 improvement cost from the
previous year be included in the analysis?
Q3. If the facility could be leased out for $25,000 per
year, would this affect the analysis?
Q4. If the new product line decreases the sales of the
firm’s other lines, would this affect the analysis?
13-10
Q1. Should financing effects be included in cash
flows?
•
•
•
No, dividends and interest expense should not be
included in the analysis.
Financing effects have already been taken into
account by discounting cash flows at the WACC of
10%.
Deducting interest expense and dividends would be
“double counting” financing costs.
13-11
Q2. Should a $50,000 improvement cost from
the previous year be included in the analysis?
•
No, the building improvement cost is a sunk cost and
should not be considered.
− A sunk cost is an outlay that was incurred in the
•
past and cannot be recovered in the future
regardless of whether the project under
consideration is accepted.
This analysis should only include incremental
investment.
13-12
Q3. If the facility could be leased out for $25,000
per year, would this affect the analysis?
•
•
Yes, by accepting the project, the firm foregoes a
possible annual cash flow of $25,000, which is an
opportunity cost to be charged to the project.
The relevant cash flow is the annual after-tax
opportunity cost.
A-T opportunity cost:
= $25,000(1 – T)
= $25,000(0.6)
= $15,000
13-13
Q4. If the new product line decreases the 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 (in the case of
complements) or negative (substitutes).
– Negative externality is also called cannibalization.
13-14
Replacement Projects
•
•
•
•
If the project is a replacement project, the analysis
will change.
The incremental CFs would be the changes from the
old to the new situation.
The relevant depreciation expense would be the
change with the new equipment.
If the old machine was sold, the firm would not
receive the SV at the end of the machine’s life. This
is the opportunity cost for the replacement project.
13-15
Example: Cost-Reducing Project
Suppose a firm is considering an investment proposal
to automate its production process to save on labor
costs. It can invest $2 million now in equipment and
thereby save $700,000 per year in pretax labor costs.
If the equipment has an expected life of five years and
if the firm pays income tax at the rate of 33.3%, is this
a worthwhile investment?
1. What are the incremental cash flows due to the
investment?
2. What is the NPV of this project?
16
What are the 3 types of project risk?
•
•
•
Stand-alone risk
Corporate risk
Market risk
13-17
Stand-alone risk
•
•
•
•
•
The project’s total risk, if it were operated independently.
Usually measured by standard deviation (or coefficient of
variation).
However, it ignores the firm’s diversification among
projects and investors’ diversification among firms.
Stand-alone risk is the easiest to measure. Firms often
focus on stand-alone risk when making capital budgeting
decisions.
Focusing on stand-alone risk is not theoretically correct,
but it does not necessarily lead to poor decisions.
13-18
Corporate risk
•
•
•
•
The project’s risk when considering 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 firm projects.
Since most projects the firm undertakes are in its
core business, stand-alone risk is likely to be highly
correlated with its corporate risk.
In addition, corporate risk is likely to be highly
correlated with its market risk.
13-19
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.
Market risk is the most relevant risk for capital
projects, because management’s primary goal is
shareholder wealth maximization.
However, since corporate risk affects creditors,
customers, suppliers, and employees, it should not
be completely ignored.
13-20
Measuring stand-alone risk
•
•
Three techniques used to assess stand-alone risk:
− Sensitivity analysis
− Scenario analysis
− Monte Carlo simulation
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.
− Resulting changes in NPV are noted.
13-21
What are the advantages and disadvantages of
sensitivity analysis?
•
•
Advantage
– Identifies variables that may have the greatest
potential impact on profitability and allows
management to focus on these variables.
Disadvantages
– Does not reflect the effects of diversification.
– Does not incorporate any information about the
possible magnitude of the forecast errors.
12-22
Scenario analysis and Monte Carlo simulation
•
Scenario analysis
– A risk analysis technique in which bad and good
sets of financial circumstances are compared
with a most likely, or base-case, situation.
•
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.
12-23
Perform a Scenario Analysis of the Project, Based on
Changes in the Sales Forecast
•
Suppose we are confident of all the variable
estimates, except unit sales. The actual unit sales
are expected to follow the following probability
distribution:
Case
Worst
Base
Best
Probability
0.25
0.50
0.25
Unit Sales
75,000
100,000
125,000
13-24
Scenario Analysis
•
All other factors shall remain constant and the NPV
under each scenario can be determined.
Case
Worst
Base
Best
Probability
0.25
0.50
0.25
NPV
($27.8)
15.0
57.8
13-25
Determining Expected NPV, NPV, and CVNPV from the
Scenario Analysis
E(NPV)  0.25(-$27.8)  0.5($15.0)  0.25($57.8)
 $15.0
NPV  [0.25(-$27.8  $15.0)2  0.5($15.0  $15.0)2
 0.25($57.8  $15.0)2 ]1/2
 $30.3
CVNPV  $30.3/$15.0  2.0
13-26
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 correlation is not perfectly positive (i.e.,
ρ  1), we would expect it to contribute to the
lowering of the firm’s overall risk.
13-27
Evaluating Projects with Unequal Lives
•
Machines A and B are mutually exclusive, and will be
repurchased. If WACC = 10%, which is better?
Year
0
1
2
3
4
Expected Net CFs
Machine A
Machine B
($50,000)
($50,000)
17,500
34,000
17,500
27,500
17,500
–
17,500
–
13-28
Solving for NPV with No Repetition
•
Calculate the two projects’ NPV with I/YR = 10%.
•
Is Machine A better?
– NPVA = $5,472.65
– NPVB = $3,636.36
– Need replacement chain and/or equivalent annual
annuity analysis.
13-29
Replacement Chain
•
•
Use the replacement chain to calculate an extended
NPVB to a common life.
Since Machine B has a 2-year life and Machine A has a
4-year life, the common life is 4 years.
0
10%
-50,000
1
2
3
27,500
-50,000
34,000
-22,500
NPVB = $6,641.62 (on extended basis)
4
34,000
27,500
13-30
Equivalent Annual Annuity
•
•
•
•
Using the previously solved project NPVs, the EAA is the
annual payment that the project would provide if it
were an annuity.
Machine A
– Enter N = 4, I/YR = 10, PV = -5472.65, FV = 0; solve for
PMT = EAAA = $1,726.46.
Machine B
– Enter N = 2, I/YR = 10, PV = -3636.36, FV = 0; solve for
PMT = EAAB = $2,095.24.
Machine B is better!
13-31
Inflation and Capital Budgeting
There are two correct ways of computing NPV:
1. Use the nominal cost of capital to discount nominal
cash flows.
2. Use the real cost of capital to discount real cash flows.
Ex: Consider an investment that requires an initial outlay of
$2 million. In the absence of inflation it is expected to
produce an annual after-tax cash flow of $600,000 for
five years and the cost of capital is 10% per year. The NPV
of this project is $274,472. What is this project’s NPV if
the inflation rate is 6%?
32