Ch 12
Cash Flow Estimation and
Risk Analysis
1
Estimating cash flows



NPV, IRR and PI computations are
straightforward.
The difficult part is estimating cash
flows accurately occurring in the future.
Estimating accurate cash flows for a
large capital spending is critical.
2
Timing of project CFs
0
1
2
3
4
Initial
Outlay
OCF1
OCF2
OCF3
OCF4
NCF0
NCF1
+ Terminal
CF
NCF2
NCF3
NCF4
3
Identifying the relevant cash flows

Only cash flows are relevant, not accounting income.





Costs of Fixed Assets
Depreciation
Changes in Net Working Capital
Interest Expense
Focus on incremental cash flows


Incremental cost: cash flows that occur if and only if we
accept the project
(i.e., CF with project – CF without project).
Example: Sunk cost, Opportunity cost, and erosion or
externalities
4
Only cash flows are relevant.

Only cash flows are relevant, not accounting income
(or cost). The accounting income (or cost) ignores
time value of money.
Example: Consider the firm buying a building for
$100,000 today. How much of $100,000 will be
recorded as an accounting expense in the current
year? Assume a straight-line depreciation over 20
years. What is the true capital expense in the current
year?
The entire $100,000 is an immediate cash outflow.
Capital budgeting analysis focuses
on cash inflows and outflows when
they occur.
5
Noncash charge



In calculating net income, accountants
usually subtract depreciation from
revenue.
However, depreciation is noncash
charge. You never write a check made
out to “depreciation”.
Depreciation must be added back when
estimating a project’s cash flow.
6
Working Capital Expenditures

Many capital investments require additions to working
capital


Net working capital (NWC) = current assets minus current
liabilities
Increase in NWC is a cash outflow; decrease a cash inflow
• An example…



We have to buy inventory to support sales although we
haven’t collected cash yet
Thus, usually, in the earlier years of the project life, increase
in NWC is treated as cash outflow.
However, recall that when the project winds down, we enjoy a
return of net working capital.
7
Should CFs include interest expense?
Dividends?


NO. The costs of capital are already
incorporated in the analysis since we
use them in discounting.
If we included them as cash flows, we
would be double counting capital
costs.
8
Forget sunk costs but include
opportunity costs


Forget sunk costs.
Example: The Coca-Cola is launching a new brand in the
beverage market. Previously, the company paid a
consulting firm $300,000 to perform a test-marketing
analysis. Is this expenditure relevant to the decision of
introducing a new brand? NO!
Include opportunity costs.
Example: Lexmark Co. has an empty land that can be used
to build a new factory. Alternatively, Lexmark could sell the
land out. Currently, a real estate appraisal concludes that
the current market price of the land is $1 million. If
Lexmark decides to build new factory on that land, should
Lexmark include $1 millions as a part of initial cash outlay?
9
YES!
Include all incidental or side
effects.

Consider Erosion or externalities (e.g., product
cannibalization).
Example 1: Suppose the Innovative Motors Corporation
(IMC) is determining the NPV of a new convertible sports
car. Some of the customers who would purchase the
new convertibles are owners of IMC’s compact sedan.
Suppose the NPV of the sports car and the NPV of lost
sales due to the transfer from sedan to convertible sports
car is $100 million and -$150 million, respectively. What
is the net NPV of a new convertible sports car project?
Net NPV = $100 million - $150 million = -$50 million.
REJECT!
Example 2: Pepsi One case.
10
Consider after-tax cash flow.


Pay tax (cash outflow) or receive tax credit (cash
inflows)
Taxes = (Market Value – Book Value ) * Tax Rate
Example: Suppose you bought your Mustang for
$15,000 five years ago. Today you decide to sell
Mustang for $9,000 and buy new BMW for $30,000.
Assume you depreciate your Mustang on a straightline basis over 10 years of life with a zero salvage
value. What is the net cash flow? Assume the tax
rate is 30%.
11
Consider after-tax cash flow.
Annual Depreciation $15,000 / 10 = $1,500
Book value
$7,500 ($15,000 – ($1,500* 5 years))
Market value
$9,000
Gain from sale
$1,500
Tax (30%)
$450 ($1,500*30%)
Net cash flow = - $30,000 + $9000 – $450 = -$21,450
12
Depreciation


Modified Accelerated Cost Recovery
System (MACRS)
Depreciable Basis


Purchase Price + Shipping and Installation
Costs
Sale of a Depreciable Asset

Taxes = (Market Value – Book Value ) * Tax
Rate
13
Modified Accelerated Cost
Recovery System (MACRS)
Year
3-year
5-year
7-year
10-year
1
33%
20%
14%
10%
2
45
32
25
18
3
15
19
17
14
4
7
12
13
12
5
11
9
9
6
6
9
7
7
9
7
8
4
7
9
7
10
6
11
3
100%
100%
100%
100% 14
Example: Campbell Co.

The Campbell Company is evaluating the proposed
acquisition of a new milling machine. The
machine’s base price is $108,000, and it would
cost another $12,500 to modify it for special use
by your firm. The machine falls into the MACRS 3year class, and it would be sold after 3 years for
$65,000. The machine would require an increase
in net working capital (inventory) of $5,500. The
milling machine would have no effect on revenues,
but it is expected to save the firm $44,000 per
year in before-tax operating costs, mainly labor.
Campbell’s marginal tax rate is 35 percent. The
project’s cost of capital is 12 percent.
15
Timing of project CFs
0
1
2
3
4
Initial
Outlay
OCF1
OCF2
OCF3
OCF4
NCF0
NCF1
+ Terminal
CF
NCF2
NCF3
NCF4
16
Initial Cash Outlay at t=0
Purchase Price
Modification
Increase in NWC
Initial Cash Outlay
$108,000
$ 12,500
$ 5,500
$126,000
17
Operating Cash Flows

Depreciation


Depreciable Basis = Cost + Additional Cost
= $108,000+ 12,500 = $120,500
Depreciation Schedule (MACRS 3-year class)
Year
1
2
3
%
33%
45%
15%
Basis
Depreciation
$120,500
$39,765
$120,500
$54,225
$120,500
$18,075
18
Let’s set up Income Statement to
find Operating Cash Flows
Net Revenue (or Gross
Margin)
- Depreciation
= EBT
Year 1
Year 2
Year 3
$44,000
$44,000
$44,000
($39,765) ($54,225)
($18,075)
$4,235
-$10,225
$25,925
($1,482)
($3,579)
($9,074)
= Net Income
$2,753
-$6,646
$16,851
+ Depreciation
$39,765
$54,225
$18,075
= Net Operating Cash Flow
$42,518
$47,579
$34,926
19
- Taxes (40%)
Terminal Cash Flow
Accumulated Depreciation (t=3)
= Depreciation (t=1) + Depreciation (t=2) + Depreciation (t=3)
= $39,765 + $54,225 + $18,075
= $ 112,065
Book Value = Depreciable basis - Accumulated Depreciation (t=3)
= $120,500 – $112,065
= $8,435
Book value
Market value
Gain from sale
Tax (35%)
$ 8,435
$65,000
$56,565
$19,798 ($56,565*35%)
20
Terminal Cash Flows
Proceeds form sale
Tax on gain
Recovery of NWC
65,000
-19,798
5,500
Terminal Cash Flow
$50,702
21
Timing of project CFs:
Campbell Co.
0
1
2
3
Initial
Outlay
42,518
47,579
34,926
-126,000
42,518
+ 50,702
47,579
85,628
NPV = $10,841 Accept!
IRR = 16.37% > 12% (cost of capital) Accept!
22
Sensitivity and Scenario Analyses

Why sensitivity and scenario analysis?
 In some cases, we may face forecasting risk or
estimation risk.
 Forecasting risk – how sensitive is our NPV to changes
in the cash flow estimates, the more sensitive, the
greater the forecasting risk
 For example, we may miscalculate future cash flows.
We also overestimate or underestimate the required
return or cost of capital (Discussed in Ch 9)
 So we need to conduct “what-if” analysis to see how
sensitive the NPV, IRR and others to varying input
values.
23
Project Risk Analysis

What does “risk” mean in capital
budgeting?


Uncertainty about a project’s future
profitability.
Measured by NPV, IRR, beta.
24
What three types of risk are relevant
in capital budgeting?

Stand-alone risk

Corporate risk

Market (or beta) risk
25
How is each type of risk measured, and
how do they relate to one another?
1. Stand-Alone Risk:
 The project’s risk if it were the firm’s only
asset and there were no shareholders.
 Ignores both firm and shareholder
diversification.

Measured by the  of NPV, IRR, or MIRR.
26
Probability Density
0
E(NPV)
NPV
Flatter distribution, larger ,
larger stand-alone risk.
27
2. Corporate Risk:
 Reflects the project’s marginal effect on
corporate earnings stability.
 Considers firm’s other assets (diversification
within firm).
 Depends on:
project’s , and
 its correlation with returns on firm’s other
assets.


Measured by the project’s corporate beta.
28
Profitability
Project X
Total Firm
Rest of Firm
0
Years
1. Project X is negatively correlated to
firm’s other assets.
2. If correlation < 1.0, some diversification benefits.
3. If correlation = 1.0, no diversification effects.
29
3. Market Risk:




Reflects the project’s effect on a welldiversified stock portfolio.
Takes account of stockholders’ other assets.
Depends on project’s  and correlation with
the stock market.
Measured by the project’s market beta.
30
How is each type of risk used?



Stand-alone risk is easiest to measure,
more intuitive.
Core projects are highly correlated with
other assets, so stand-alone risk
generally reflects corporate risk.
If the project is highly correlated with
the economy, stand-alone risk also
reflects market risk.
31
Measuring Stand-Alone Risk

Three techniques



Sensitivity Analysis
Scenario Analysis
Monte Carlo Simulation
32
What is sensitivity analysis?



Shows how changes in a variable
such as unit sales affect NPV or IRR.
Each variable is fixed except one.
Change this one variable to see the
effect on NPV or IRR.
Answers “what if” questions, e.g.
“What if sales decline by 30%?”
33
Illustration
Change from
Base Level
-30%
-20
-10
0
+10
+20
+30
Resulting NPV (000s)
Unit Sales
Salvage WACC
$ 10
35
58
82
105
129
153
$78
80
81
82
83
84
85
$105
97
89
82
74
67
61 34
NPV
(000s)
Unit Sales
Salvage
82
k
-30
-20
-10 Base 10
Value
20
30
35
Results of Sensitivity Analysis


Steeper sensitivity lines show greater
risk. Small changes result in large
declines in NPV.
Unit sales line is steeper than
salvage value or WACC, so for this
project, should worry most about
accuracy of sales forecast.
36
Pros and Cons of Sensitivity Analysis


Pros

Gives some idea of stand-alone risk.

Identifies dangerous variables.

Gives some breakeven information.
Cons



Does not reflect diversification.
Says nothing about the likelihood of change in a
variable, i.e. a steep sales line is not a problem if
sales won’t fall.
Ignores relationships among variables.
37
What is scenario analysis?


Examines several possible situations,
usually worst case, most likely case,
and best case.
Provides a probability, likelihood of
each case occurrence
38
Assume we know with certainty all
variables except unit sales, which could
range from 900 to 1,600.
Scenario
Probability NPV(000)
Worst
Base
0.25
0.50
Best
0.25
$ 15
82
148
E(NPV) = $ 82
(NPV) = 47
39
Are there any problems with scenario
analysis?

Only considers a few possible out-comes.
 Assumes that inputs are perfectly correlated--all
“bad” values occur together and all “good”
values occur together.
 Focuses on stand-alone risk, although
subjective adjustments can be made.
40
What is a simulation analysis?


A computerized version of scenario analysis
which uses continuous probability distributions.
Computer selects values for each variable based
on given probability distributions.

NPV and IRR are calculated.

Process is repeated many times (1,000 or more).


End result: Probability distribution of NPV and
IRR based on sample of simulated values.
Computer-intensive
41
Probability Density
xxxx
xxxxxxx
xx xxxxxxx
xxx xxxxxxxx
xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxx
0
E(NPV)
NPV
42
Pros and Cons of Simulation Analysis


Reflects the probability distributions of each
input.
Shows range of NPVs, the expected NPV and
NPV.

Difficult to specify probability distributions
and correlations.

If inputs are bad, output will be bad:
“Garbage in, garbage out.”
43


Sensitivity, scenario, and simulation
analyses do not provide a decision rule.
They do not indicate whether a
project’s expected return is sufficient to
compensate for its risk.
Sensitivity, scenario, and simulation
analyses all ignore diversification. Thus
they measure only stand-alone risk,
which may not be the most relevant risk
in capital budgeting.
44