8-1
Fundamentals
of Corporate
Finance
Second Canadian Edition
prepared by:
Carol Edwards
BA, MBA, CFA
Instructor, Finance
British Columbia Institute of Technology
copyright © 2003 McGraw Hill Ryerson Limited
8-2
Chapter 8
Project Analysis
Chapter Outline
How Firms Organize the Investment
Process
 Some “What If” Questions
 Break-Even Analysis
 Flexibility in Capital Budgeting
 Capital Budgeting Practices in Canadian
Firms

copyright © 2003 McGraw Hill Ryerson Limited
8-3
The Investment Decision
• How


Firms Organize the Investment Process
Once a year, a firm’s head office will generally
ask each of its divisions to provide a list of the
investments they would like to make.
A list of planned investments is known as the
capital budget.

This “wish list” must then be examined to determine
which projects should go forward.
How is this done?
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8-4
Some “What If” Questions
• Introduction
Managers want to understand more
than the NPV of a project.
 They also want to predict what events
could happen and how that might affect
NPV.

 Once
they have done this, management
can decide if it is worthwhile investing more
time and effort in understanding the
uncertainty and trying to resolve it.
copyright © 2003 McGraw Hill Ryerson Limited
8-5
Some “What If” Questions
• Introduction

There are five methods managers use
to handle project uncertainty:
 Sensitivity
Analysis
 Scenario Analysis
 Simulation Analysis
 Break-Even Analysis
 Operating Leverage Analysis
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8-6
Some “What If” Questions
• Sensitivity Analysis


A sensitivity analysis calculates the
consequences of incorrectly estimating a
variable in your NPV analysis.
If forces you:
 To
identify the variables underlying your analysis.
 To focus on how changes to these variables could
impact the expected NPV.
 To consider what additional information should be
collected to resolve uncertainties about the
variables.
copyright © 2003 McGraw Hill Ryerson Limited
8-7
Some “What If” Questions
• Sensitivity Analysis

Suppose, as a financial manager, you have
estimated the cash flow forecasts for a new
grocery store.
 These


are shown on on the next slide.
The project has a positive NPV of $478,000.
Before you recommend the project to your
boss, you want to analyze the forecast and
identify the key variables which will determine
whether the project succeeds or fails.
copyright © 2003 McGraw Hill Ryerson Limited
8-8
Some “What If” Questions
Cash Flow Forecasts:
Investment
Sales
Variable Costs (81.25% of Sales)
Fixed Costs
Depreciation (Straight Line)
Pretax Profit
Taxes @ 40%
Profit after Tax
Cash Flow from Operations
Year 0
($5,400)
Net Cash Flow
($5,400)
Years 1-12
$16,000
13,000
2,000
450
550
220
330
780
$780
copyright © 2003 McGraw Hill Ryerson Limited
8-9
Some “What If” Questions
• Sensitivity Analysis
You want to look at how the NPV of the
project may be affected by an incorrect
forecast of sales, costs, etc.
 You develop the optimistic and
pessimistic estimates for the underlying
variables which are shown on the next
slide.

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8-10
Some “What If” Questions
• Sensitivity Analysis

You will use the estimates below, one at time,
to recalculate NPV:
Range in dollars
Variable:
Optimistic
Expected Pessimistic
Investment
Sales
Variable Costs as a % of Sales
Fixed Costs
$6,200
$14,000
83.00%
$2,100
$5,400
$16,000
81.25%
$2,000
$5,000
$18,000
80.00%
$1,900
copyright © 2003 McGraw Hill Ryerson Limited
8-11
Some “What If” Questions
• Sensitivity Analysis

For example, if the initial investment in
the project were $6.2 million, instead of
$5.4 m, you would recalculate NPV as:
NPV = PV of Cash Flows - Investment (C0)
= [$806,667 x 12 year annuity factor] - 6.2 m
= [$806,667 x 7.536] – 6.2 m
= -$120,897 *
* Don’t forget to change the depreciation for the project!
copyright © 2003 McGraw Hill Ryerson Limited
8-12
Some “What If” Questions
• Sensitivity Analysis

After all the recalculations, you would have
the following estimates:
NPV in dollars
Optimistic
Expected
Pessimistic
($121,000)
Investment
($1,218,000)
Sales
($788,000)
Variable Costs as a % of Sales
$26,000
Fixed Costs
$478,000
$478,000
$478,000
$478,000
$778,000
$2,174,000
$1,382,000
$930,000
Variable:
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8-13
Some “What If” Questions
• Sensitivity Analysis


You now know how badly the project could be
thrown off course by changes in certain
variables.
Looking at the table on the previous slide, can
you answer the following questions:
 What
is the least critical variable to the success of
the project?
 What are the two most critical variables to the
success of the project?
copyright © 2003 McGraw Hill Ryerson Limited
8-14
Some “What If” Questions
• Sensitivity Analysis

Did you identify fixed costs as the least critical
variable?
 Even
under the pessimistic assumption about fixed
costs, the project has a positive NPV, so it is
unlikely to give you trouble if you have estimated it
incorrectly.

Did you identify sales and variable costs as
the most critical variables?
A
poor estimate of either of these could lead to a
significantly negative NPV for the project.
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8-15
Some “What If” Questions
• Sensitivity Analysis

Now that you have identified the critical
success/failure factors, you may wish to
focus your attention on them:
 You
might collect additional data on sales
and costs so as to resolve some of the
uncertainty concerning these variables.
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8-16
Some “What If” Questions
• Sensitivity Analysis
Sensitivity analysis is not a “cure-all”.
 It does have its drawbacks:

 The
results are ambiguous since the terms
“optimistic” and “pessimistic” are
completely subjective.
 Variables are often related and it may be
difficult to identify all of the consequences
associated with a change in one of them.
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8-17
Some “What If” Questions
• Scenario Analysis

A scenario analysis involves changing
several variables at once in your NPV
forecast.
 See
Example 8.2
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8-18
Some “What If” Questions
• Simulation
Analysis
A simulation analysis uses a computer
to generate hundreds, or even
thousands, of possible scenarios.
 A probability distribution is assigned to
each combination of variables to create
an entire range of potential outcomes.

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8-19
Break-Even Analysis
• Accounting

vs NPV Break-Even Analysis
A Break-Even analysis shows the level of sales
at which a company “breaks even”.
 An
accounting break-even occurs where total
revenues equal total costs (profits equal zero).
 A NPV break-even occurs when the NPV of the
project equals zero.

Using accounting break-even can lead to poor
decisions.
 You
can avoid this risk by using NPV break-even in
your analysis!
copyright © 2003 McGraw Hill Ryerson Limited
8-20
Break-Even Analysis
• Accounting
Break-Even
An accounting break-even occurs where
total revenues equal total costs, and thus
profits are zero.
 How do we calculate this point?

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8-21
Break-Even Analysis
• Accounting

Break-Even
Go back to the cash flow analysis you did on
Slide #8:
 You
estimated sales to be $16 million.
 Variable costs were 81.25% of sales ($0.8125 of
variable costs per $1 of sales).
 Fixed costs were $2 million and depreciation was
$450,000.

These variables are all you need to calculate
accounting break-even!
copyright © 2003 McGraw Hill Ryerson Limited
8-22
Break-Even Analysis
• Accounting

Break-Even
Accounting break-even is calculated as:
Break-Even Revenues = Fixed Costs + Depreciation
Profit per $1 of Sales
= $2,000 + $450
$1 - $0.8125
= $2,450
$0.1875
= $13.067 million
copyright © 2003 McGraw Hill Ryerson Limited
8-23
Break-Even Analysis
• Accounting

Break-Even
Creating an income statement at $13.067
million of sales shows profit equals zero:
Revenues
Variable Costs
Fixed Costs + Depreciation
$13,067
10,067
2,450
Pretax Profit
0
Taxes
0
Profit after Tax
0
copyright © 2003 McGraw Hill Ryerson Limited
8-24
Break-Even Analysis
• Accounting
Break-Even
If a project breaks even in accounting terms
is it an acceptable investment?
 Clue: This project has a 12 year life …

Would you be happy with an investment
which after 12 years gave you a zero
total rate of return?
copyright © 2003 McGraw Hill Ryerson Limited
8-25
Break-Even Analysis
• Accounting
Break-Even
A project which simply breaks even on an
accounting basis will always have a negative NPV!
Proof:
CFO = profit after tax + depreciation
= $0 + $450,000 = $450,000

NPV = PV of Cash Flows – C0
= [$450,000 * (12 year Annuity Factor)] - $5.4 m
 $0
Note: the 12 year Annuity Factor  12 for all discount rates!
copyright © 2003 McGraw Hill Ryerson Limited
8-26
Break-Even Analysis
• NPV
Break-Even
Asking how bad sales can get before a
project makes an accounting loss is not the
best tool for analysis of a project.
 Instead, it is more useful to focus on the
point at which NPV switches from negative
to positive.
 Let’s develop a method for calculating this
NPV break-even!

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8-27
Break-Even Analysis
• NPV

Break-Even
Going back to our example:
Variable Costs
81.25% of Sales
+ Fixed Costs + Depreciation
 Pretax Profit
$2.45 m
(0.1875 Sales) - 2.45 m
- Tax @ 40%
0.40 x [(0.1875 Sales) - 2.45 m]
 After Tax Profit
0.60 x [(0.1875 Sales) - 2.45 m]
 Cash flow
$0.45 m + 0.60 x [(0.1875 Sales) - 2.45 m]
= 0.1125 * Sales - $1.02 m
Note: Cash flow = Depreciation + After Tax Profit
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8-28
Break-Even Analysis
• NPV

Break-Even
This cash flow will last for 12 years.
 PV(cash flows) = Cash Flows x Annuity Factor
= (0.1125 x Sales - 1.02 m) x 12 year
Annuity Factor
= (0.1125 x Sales - 1.02 m) x 7.536
But: NPV = 0
 NPV = 0
if
if
PV (cash flows) = C0
(0.1125 x Sales – 1.02 m) x 7.536 = 5.4 m
 Sales = $15.4 m
copyright © 2003 McGraw Hill Ryerson Limited
8-29
Break-Even Analysis
• NPV
Break-Even
Using the accounting break-even, the
project had to generate sales of $13.067
million to have zero profit.
 Using the NPV break-even, we find that the
project needs sales of $15.4 million to have
a zero NPV.

 The
project needs to be 18% more successful to
break-even on a NPV basis!
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8-30
Break-Even Analysis
•
Degree of Operating Leverage (DOL)

Let’s say you are predicting a 1% change in
the sales of your firm.

How will that change affect your firm’s profits?
1) A 1% change in sales could lead to a 1%
change in profits.

This would be a very stable situation.
2) Or, it could lead to a 50% change in profits.

This would be a very risky and volatile
situation.
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8-31
Break-Even Analysis
• Degree
of Operating Leverage (DOL)
Operating leverage is a measure of the
percentage of a firm’s costs that are fixed.
 Degree of Operating Leverage (DOL)
measures the percentage change in profits
given a 1% change in sales.

 If
DOL = 1, then a 1% change in sales will
produce a 1% change in profits.
 If DOL = 50, then a 1% change in sales will
produce a 50% change in profits.
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8-32
Break-Even Analysis
• Degree

of Operating Leverage (DOL)
There are two ways of measuring DOL:
DOL = percentage change in profits
percentage change in sales
DOL = 1 + fixed costs
profits
Note that the level of fixed costs in a company will
determine DOL and how volatile its profits are in
response to a change in sales.
copyright © 2003 McGraw Hill Ryerson Limited
8-33
Break-Even Analysis
• Degree

of Operating Leverage (DOL)
If you examine Table 8.4 on page 256, you
will see that the risk of a project is affected
by its DOL.
 If
a large proportion of the project’s costs are
fixed, then DOL will be high.
 If DOL is high, then any shortfall in sales will
have a magnified effect on profits.

In other words, high DOL means high risk
if sales do not work out as forecasted!
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8-34
Flexibility in Capital Budgeting
• The
Value of Having Options
No matter how much analysis you do on
a project, it is impossible to completely
eliminate uncertainty.
 Can you think of any way:

 To
mitigate the effect of unpleasant surprises.
and
 To take advantage of pleasant ones?
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8-35
Flexibility in Capital Budgeting
• The
Value of Having Options
Because the future is uncertain, successful
financial managers seek projects with
flexibility.
 The perfect project would have:

 The
option to expand if things go well.
 The option to bail out or switch production if
things go poorly.
 The option to postpone if future conditions
might improve.
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8-36
Flexibility in Capital Budgeting
• The

Value of Having Options
Options
 to
avoid a loss, switch production or abandon
a project;
 to expand and produce extra profit; or
 to postpone action
have significant value for a firm.
 Good outcomes can be exploited, while poor
outcomes can be avoided or postponed.
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8-37
Flexibility in Capital Budgeting
• The

Value of Having Options
Decision trees are used to diagram the
options in a project.
 You
can then determine the optimal course
of action from a series of potential options.

A decision tree is defined as a diagram
of sequential decisions and their
possible outcomes.
 Figure
8.3 is an example of a decision tree.
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8-38
Flexibility in Capital Budgeting
• The Value of Having Options
 As a general rule, flexibility will be most
valuable to you when the future is most
uncertain.
 The ability to change course as events
develop and new information becomes
available is most valuable when it is
hard to predict with confidence what the
best course of action will be.
copyright © 2003 McGraw Hill Ryerson Limited
8-39
Canadian Practices
• Capital
Budgeting Practices in Canadian
Firms



In Table 8.7 on page 262, you can see how
Canadian firms are actually making capital
budgeting decisions.
Most firms use multiple methods for analyzing
a project’s acceptability.
Note that discounted cash flow techniques
were used by more than 75% of respondents.
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8-40
Summary of Chapter 8



Successful managers know that the
forecasts behind NPV calculations are
imperfect.
Thus, they explore the consequences to
the firm of a poor forecast.
They check whether the project is really
worth pursuing by doing some additional
homework.
 This
consists of asking a series of “what-if”
questions to determine the feasibility of the
project and its risk profile.
copyright © 2003 McGraw Hill Ryerson Limited
8-41
Summary of Chapter 8

The principal tools used by managers in
“what-if” questions are:
 Sensitivity
Analysis
 Scenario Analysis
 Simulation Analysis
 Break-Even Analysis
 Operating Leverage

A desirable characteristic in a project is
flexibility.
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8-42
Summary of Chapter 8
Projects with options to expand,
abandon, switch production, or
postpone actions may have added value
to the firm.
 You can use decision trees to analyze
such flexibility.
 A survey of Canadian firms shows that
most use multiple capital budgeting
methods to assess projects.

copyright © 2003 McGraw Hill Ryerson Limited