This document discusses various capital budgeting techniques for analyzing investment projects under uncertainty, including sensitivity analysis, scenario analysis, break even analysis, and real options analysis. It provides examples of how to apply these techniques to evaluate projects. Sensitivity analysis involves changing assumptions like sales, costs, and investments to see their impact on NPV. Scenario analysis evaluates projects under different combinations of assumptions. Break even analysis finds the sales level where costs and revenues break even. Real options analysis uses decision trees to value the flexibility inherent in investment opportunities.

1. Chapter 9
Fundamentals of
Corporate
Finance
Fifth Edition
Slides by
Matthew Will
McGraw Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved
Project Analysis

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Topics Covered
How Firms Organize the Investment
Process
Some “What If” Questions
Sensitivity Analysis
Scenario Analysis
Break Even Analysis
Real Options and the Value of Flexibility

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Capital Budgeting Process
Capital Budget - The list of planned investment
projects.
The Decision Process
1 - Develop and rank all investment projects
2 - Authorize projects based on:
• Outlays required by law of company policy
• Maintenance of cost reduction
• Capacity expansion in existing business
• Investment for new products

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Capital Budgeting Process
Capital Budgeting Problems
Consistent forecasts
Conflict of interest
Forecast bias
Selection criteria (NPV and others)

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How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects
of changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a
particular combination of assumptions.
Simulation Analysis - Estimation of the
probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of
sales (or other variable) at which the
company breaks even.

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Sensitivity Analysis
Example
Given the expected cash flow
forecasts listed on the next
slide, determine the NPV of
the project given changes in
the cash flow components
using an 8% cost of capital.
Assume that all variables
remain constant, except the
one you are changing.

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Sensitivity Analysis
780
5,400
-
Flow
Cash
Net
780
flow
cash
Operating
330
after tax
Profit
220
40%
@
.Taxes
550
profit
Pretax
450
on
Depreciati
2,000
Costs
Fixed
13,000
Costs
Variable
16,000
Sales
5,400
-
Investment
12
-
1
Years
0
Year
Example – continued (,000s)
NPV= $478

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Sensitivity Analysis
Example - continued
Possible Outcomes
1,900
2,000
2,100
)
Costs(000s
Fixed
80%
81.25%
83%
sales)
of
(%
Cost
Var
18,000
16,000
14,000
)
Sales(000s
5,000
5,400
6,200
(000s)
Investment
Optimistic
Expected
c
Pessimisti
Variable
Range

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Sensitivity Analysis
Example - continued
NPV Calculations for Pessimistic Investment Scenario
780
6,200
-
Flow
Cash
Net
780
flow
cash
Operating
330
after tax
Profit
220
40%
@
.Taxes
550
profit
Pretax
450
on
Depreciati
2,000
Costs
Fixed
13,000
Costs
Variable
16,000
Sales
6,200
-
Investment
12
-
1
Years
0
Year
NPV= ($121)

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Sensitivity Analysis
Example - continued
NPV Possibilities
930
478
26
)
Costs(000s
Fixed
1,382
478
788
-
sales)
of
(%
Cost
Var
2,174
478
1,218
-
)
Sales(000s
778
478
121
-
(000s)
)
000
(
Investment
Optimistic
Expected
c
Pessimisti
Variable
s
NPV

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Scenario Analysis
Example - continued
Cash Flows (years 1-12)
2,018,000
-
478,000
NPV
3,382,000
5,878,000
flows
cash
of
lue
Present va
448,000
780,000
7)
(4
operations
from
flow
8.Cash
1,200
-
330,000
after tax
Profit
7.
800
-
220,000
6.Taxes
2,000
-
550,000
4)
-
3
-
2
-
(1
profit
Pretax
5.
450,000
450,000
on
Depreciati
4.
2,000,000
2,000,000
costs
3.Fixed
11,152,000
13,000,000
costs
Variable
2.
000
,
600
,
13
000
,
000
,
16
Sales
1.
Scenario.
Store
Competing
Case.
Base


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Break Even Analysis
Example
Given the forecasted data
on the next slide,
determine the number of
planes that the company
must produce in order to
break even, on an NPV
basis. The company’s cost
of capital is 10%.

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Break Even Analysis
12.5
-
Sold)
s
(3.5xPlane
900
-
Flow
Cash
Net
162.5
-
Sold)
s
(3.5xPlane
Profit
Net
162.5
-
Sold)
s
(3.5xPlane
(50%)
Taxes
325
-
Sold)
(7xPlanes
Profit
Pretax
150
=
900/6
on
Depreciati
175
Costs
Fixed
Sold
8.5xPlanes
Cost
Var.
Sold
s
15.5xPlane
Sales
$900
Investment
6
-
1
Years
0
Year

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Break Even Analysis
Answer (Accounting)
The break even point, is the # of
Planes Sold where the fixed costs
and depreciation = $0.
planes
46.4
162.5/3.5
sold
Planes
162.5)
-
Sold
Planes
x
3.5
(
0





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Break Even Analysis
Answer (Finance)
The break even point, is the # of Planes
Sold that generates a NPV=$0.
The present value annuity factor of a 6
year cash flow at 10% is 4.355
Thus,
12.5)
-
Sold
Planes
x
3.5
(
5
35
.
4
900 


NPV

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Answer
Solving for “Planes Sold”
12.5)
-
Sold
Planes
5
.
3
(
355
.
4
900
0 x



63
=
Sold
Planes
Break Even Analysis

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EVA & Break Even
$266,553
-
millions)
$2.45
-
sales
x
(.1875
x
.60
7)
line
-
6
line
(
Added
Value
Economic
8.
$266,553
on
depreciati
allowed
above
and
over
capital
of
Cost
7.
millions)
$2.45
-
sales
x
(.1875
x
.60
profit
accounting
tax
-
After
6.
millions)
$2.45
-
sales
x
(.1875
x
.40
40%)
(as
Tax
5.
million
$2.45
-
sales)
x
(.1875
profit
Pretax
4.
$450,000
on
Depreciati
3.
million
$2
costs
Fixed
2.
sales
of
percent
81.25
costs
Variable
1.


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EVA & Break Even
EVA = accounting profit – additional cost of capital = 0
($3.5 x planes sold - $162.50) - $56.6 = 0
Planes sold = 219.1 / 3.5 = 62.6

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Operating Leverage
Operating Leverage- The degree to which
costs are fixed.
Degree of Operating Leverage (DOL) -
Percentage change in profits given a 1
percent change in sales.
sales
in
change
%
profits
in
change
%

DOL

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Operating Leverage
Example - A company has sales outcomes that range from
$16mil to $19 mil, Depending on the economy. The same
conditions can produce profits in the range from $550,000
to $1,112,000. What is the DOL?
DOL = = 5.45
102.2
18.75

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Flexibility & Real Options
Decision Trees - Diagram of sequential decisions
and possible outcomes.
Decision trees help companies determine their
Options by showing the various choices and
outcomes.
The Option to avoid a loss or produce extra profit
has value.
The ability to create an Option thus has value that
can be bought or sold.

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Decision Trees
NPV=0
Don’t test
Test (Invest
$200,000)
Success
Failure
Pursue project
NPV=$2million
Stop project
NPV=0

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Real Options
1. Option to expand
2. Option to abandon
3. Timing option
4. Flexible production facilities