Fundamentals of Corporate
Finance, 2/e
ROBERT PARRINO, PH.D.
DAVID S. KIDWELL, PH.D.
THOMAS W. BATES, PH.D.
Chapter 12: Evaluating Project
Economics and Capital Rationing
Learning Objectives
1. EXPLAIN AND DEMONSTRATE HOW
VARIABLE COSTS AND FIXED COSTS AFFECT
THE VOLATILITY OF PRETAX OPERATING
CASH FLOWS AND ACCOUNTING OPERATING
PROFITS.
2. CALCULATE AND DISTINGUISH BETWEEN
THE DEGREE OF PRETAX CASH FL OW
OPERATING LEVERAGE AND THE DEGREE OF
ACCOUNTING OPERATING LEVERAGE.
Learning Objectives
3. DEFINE AND CALCULATE THE PRETAX OPERATING
CASH FLOW AND ACCOUNTING OPERATING PROFIT
Break-Even POINTS AND THE CROSSOVER LEVELS
OF UNIT SALES FOR A PROJECT.
4. DEFINE SENSITIVITY ANALYSIS, SCENARIO
ANALYSIS, AND SIMULATION ANALYSIS AND
DESCRIBE HOW THEY ARE USED TO EVALUATE THE
RISKS ASSOCIATED WITH A PROJECT.
Learning Objectives
5. EXPLAIN HOW THE PROFITABILITY INDEX
CAN BE USED TO RANK PROJECTS WHEN A
FIRM FACES CAPITAL RATIONING AND
DESCRIBE THE LIMITATIONS THAT APPLY TO
THE PROFITABILITY INDEX.
Variable Costs, Fixed Costs, And
Project Risk
o Variable costs are costs that vary directly with
the number of units sold.
o Fixed costs, in contrast, do not vary with unit
sales – at least in the short run.
o A project with a higher proportion of fixed
costs will have cash flows and accounting
profits that are more sensitive to changes in
revenues.
EXHIBIT 12.1: Unit and Annual
Costs for Hammock Project
Variable Costs, Fixed Costs, And
Project Risk
o PRETAX OPERATING CASH FLOW
EBITDA = Revenue – Op Ex
where Op Ex = VC + FC
• EBITDA is often called pretax operating cash
flow because it equals the incremental pretax
cash operating profits from a project.
Exhibit 12.2: EBITDA Under Alternative
Production Technologies
Variable Costs, Fixed Costs, And
Project Risk
o COST STRUCTURE AND SENSITIVITY OF EBITDA
TO REVENUE CHANGES
• Comparing the sensitivity of EBITDA to
changes in revenue helps understand the risks
and returns of different decision alternatives.
• Distinguishing between fixed and variable costs
enables us to calculate the sensitivity of
EBITDA to changes in revenue.
Exhibit 12.3: Changes in EBITDA under
Alternative Production Technologies
Variable Costs, Fixed Costs, And
Project Risk
o COST STRUCTURE AND SENSITIVITY OF EBITDA
TO REVENUE CHANGES
• Exhibit 12.3 shows how EBITDA is more
sensitive to changes in revenue with the
automated production process than with the
manual process.
• The reason for the difference is that more of the
total costs are fixed with the automated process,
making it more difficult to adjust costs when
revenue changes.
Exhibit 12.4: EBITDA for Different Levels
of Unit Sales
Variable Costs, Fixed Costs, And
Project Risk
o COST STRUCTURE AND SENSITIVITY OF EBITDA
TO REVENUE CHANGES
• Exhibit 12.4 shows how EBITDA changes as the
number of units sold changes for both the
manual and the automated production process.
• Automated production process produces larger
declines in EBITDA when unit sales are lower
and larger increases in EBITDA when unit sales
are higher.
Variable Costs, Fixed Costs, And
Project Risk
o COST STRUCTURE AND SENSITIVITY OF EBIT
TO REVENUE CHANGES
• The sensitivity of EBIT to changes in revenue
is of concern to managers because EBIT is a
performance measure that is of interest to
investors.
• EBITDA calculation does not include
depreciation and amortization (D&A).
Variable Costs, Fixed Costs, And
Project Risk
o COST STRUCTURE AND SENSITIVITY OF EBIT
TO REVENUE CHANGES
• Depreciation and amortization acts just like a
fixed cost, hence included in the EBIT
calculation to effectively increase the proportion
of costs that are fixed.
• When D&A is greater than zero, the percentage
change in EBIT is greater than the percentage
change in EBITDA.
Exhibit 12.5: Changes in EBITDA and
EBIT
Calculating Operating Leverage
o OPERATING LEVERAGE
• Is a measure of the relative amounts of fixed
and variable costs in a project’s cost structure; it
will be higher with more fixed costs.
• Two measures of operating Leverage:
Degree of pretax cash flow operating leverage
Degree of accounting operating leverage
Calculating Operating Leverage
o DEGREE OF PRETAX CASH FLOW OPERATING
LEVERAGE
• Measures the sensitivity of pretax operating
cash flows to changes in revenue.
Cash Flow DOL  1 
Fixed Costs
FC
 1
(12.2)
Pretax operating cash flows
EBITDA
• It changes with the level of revenue; the
sensitivity of operating cash flows are not the
same for all levels of revenue.
Calculating Operating Leverage
o DEGREE OF PRETAX CASH FLOW OPERATING
LEVERAGE
• Calculate the Cash Flow DOL for the automated
production alternative in Exhibit 12.2.
$35,000
Cash Flow DOL = 1+
= 1.64
$55,000
• EBITDA in the denominator of equation 12.2
varies directly with revenue and will be larger for
larger amounts of revenue. The Cash Flow
DOL will be smaller as revenue increases.
Exhibit 12.6: EBITDA with Unit Sales
Calculating Operating Leverage
o DEGREE OF ACCOUNTING OPERATING
LEVERAGE
• Measures the sensitivity of accounting
operating profits, EBIT, to changes in revenue.
Fixed Charges
Accounting operating profits
FC  D & A
 1
EBITDA  D & A
FC  D & A
 1
(12.3)
EBIT
Accounting DOL  1 
Calculating Operating Leverage
o DEGREE OF ACCOUNTING OPERATING
LEVERAGE EXAMPLE
• Calculate the Accounting DOL for the
automated production alternative in Exhibit 12.5
for expected demand.
$35,000 + $10,000
Accounting DOL = 1+
$45,000
= 2.00
Break-Even Analysis
o Break-Even ANALYSIS
• Analysis that tells us how many units must be
sold in order for a project to Break-Even on a
cash flow or accounting profit basis
• Helps to understand the sensitivity of cash
flows and accounting profits to changes in the
number of units that will be sold
Break-Even Analysis
o PRETAX OPERATING CASH FLOW Break-Even
• Number of units that must be sold for pretax
operating cash flow to equal $0
FC
EBITDA Break-even =
Price - Unit VC
(12.4)
Break-Even Analysis
o CASH FLOW Break-Even EXAMPLE
• Calculate the EBITDA Break-Even points for
the automated and manual production
alternatives in Exhibit 12.2.
$35,000
= 3,889 units
$25-$16
$4,000
=
= 800 units
$25-$20
EBITDA Break-even Automated =
EBITDA Break-evenManual
Exhibit 12.7: EBITDA Break-Even Points
Break-Even Analysis
o PER-UNIT CONTRIBUTION
• Dollar amount that is left over from the sale of a
single unit after all the variable costs associated
with that unit have been paid
• Amount that is available to help cover fixed
costs for the project
Break-Even Analysis
o CROSSOVER LEVEL OF UNIT SALES (CO)
• Level of unit sales at which cash flows or
profitability for one project alternative switches
from being lower than that of another
alternative to being higher
COEBITDA 
FCAlternative1  FCAlternative2
(12.5)
Unit contribution Alt.1  Unit contribution Alt.2
Break-Even Analysis
o THE CROSSOVER LEVEL OF UNIT SALES
EXAMPLE
• Calculate the Crossover level of unit sales for
the automated and manual production
alternatives in Exhibit 12.2.
COEBITDA
$35,000 - $4,000
=
$9 - $5
= 7,750 units
Break-Even analysis
o ACCOUNTING BREAK-EVEN
• Number of units that must be sold for
accounting operating profit to equal $0
FC+D & A
EBITBreak - Even =
.
Price-Unit VC
Break-Even Analysis
o ACCOUNTING Break-Even
• In addition to the accounting operating profit
Break-even points, we can also calculate the
crossover level of unit sales for EBIT.
COEBIT 
(FC  D & A)Alt.1  (FC  D & A)Alt.2
(12.7)
Unit contributionAlt.1  Unit contribution Alt.1
Break-Even Analysis
o ACCOUNTING BREAK-EVEN EXAMPLE
• Calculate the accounting operating profit Breakeven point and the crossover level of unit sales
for the automated and manual production
alternatives in Exhibits 12.1 and 12.2.
$35,000+$10,000
=5,000 units
$25-$16
$4,000+$1,000
EBIT break-evenManual =
=1,000 units
$25-$20
($35,000+$10,000)-($4,000+$1,000)
COEBIT =
=10,000 units
$9-$5
EBIT break-even Automated =
Risk Analysis
o Financial analysts must often resort to
different types of risk analysis to obtain a
better understanding of how errors in
forecasting these factors affect the
attractiveness of a project.
Risk Analysis
o SENSITIVITY ANALYSIS
• Involves examination of the sensitivity of the
results from a financial analysis to changes in
individual assumptions
• An analyst might examine how a project’s NPV
changes if there is a decrease in the value of
individual cash inflow assumptions or an
increase in the value of individual cash outflow
assumptions.
Using Excel – Sensitivity Analysis
Exhibit 12.8: Incremental Free Cash
Flows and NPV
Risk Analysis
o SCENARIO ANALYSIS
• An analytical method concerned with how the
results from a financial analysis will change
under alternative scenarios
• An analyst who wants to examine how the
results from a financial analysis will change
under alternative scenarios performs a scenario
analysis.
Exhibit 12.9: NPV Values for
Automated Hammock Production
Risk Analysis
o SIMULATION ANALYSIS
• An analytical method that uses a computer to
quickly examine a large number of scenarios
and obtain probability estimates for various
values in a financial analysis
• Rather than selecting individual values for each
of the assumptions–such as unit sales, unit
price, and unit variable costs–the analyst
assumes that those assumptions can be
represented by statistical distributions.
Risk Analysis
o SIMULATION ANALYSIS
• A computer program repeatedly draws numbers
for the distributions for various assumptions,
plugs them into the cash flow model, and
computes the annual cash flows and NPV.
• In addition to providing an estimate of the
expected cash flows, it also provides
information on the distribution of the cash
flows that the project is likely to produce in each
year.
Investment Decisions With Capital
Rationing
o SELECTING THE BEST PROJECTS
• What does a firm do when it does not have
enough money to invest in all available positiveNPV projects?
• The process of identifying the bundle of
projects that creates the greatest total value and
allocating the available capital to these projects
is known as capital rationing.
Exhibit 12.10: Positive NPV
Investments for a Single Year
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING IN A SINGLE PERIOD
• Involves choosing the set of projects that
creates the greatest value in a given period
• Goal is to select the projects that yield the
largest value per dollar invested
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING IN A SINGLE PERIOD
• Profitability index (PI) is computed for each
project
• Firm chooses the project(s) with the largest
profitability indices until it runs out of money.
Profitability Index is a measure of the value a project
generates for each dollar invested in that project.
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING IN A SINGLE PERIOD
• Objective is to identify the bundle or
combination of positive-NPV projects that
creates the greatest total value for stockholders.
Benefits Present Value of Future Cash Flows
PI 

Costs
Initial Investment
NPV  Initial Investment

(12.8)
Initial Investment
Investment Decisions With Capital
Rationing
o PROFITABILITY INDEX EXAMPLE
• Calculate the profitability index for the lawn
mower problem in Chapter 11. The new mower
costs $2,000 and brings in net cash flows of
$7,000. The discount rate is 10 percent and the
NPV is $20,189.
$20,189 + $2,000
PI =
= 11.09
$2,000
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING IN A SINGLE PERIOD
• Using PI to choose project(s) that create the
most value per dollar invested (4 step
procedure):
Calculate the PI for each project.
Rank the projects from highest PI to lowest PI.
Starting at the top of the list (the project with the
highest PI) and working your way down (to the project
with the lowest PI), select the projects that the firm can
afford.
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING IN A SINGLE PERIOD
Repeat the third step by starting with the second
project on the list, the third project on the list, and so
on, to make sure that a more valuable bundle cannot
be identified.
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING ACROSS MULTIPLE
PERIODS
• If you are planning to make investments over
several years, the investments you choose this
year can affect your ability to make investments
in future years.
• This can happen if you plan on reinvesting
some or all of the cash flows generated by the
projects you invest in this year.
Investment Decisions With Capital
Rationing
o CAPITAL RATIONING ACROSS MULTIPLE
PERIODS
• PI can only be relied upon to identify the
projects that the firm should invest in the
current year.
• A limitation of the profitability index is that it
does not tell us enough to make informed
decisions over multiple periods.
Exhibit 12.11: Positive NPV Investments for
Two Years
Exhibit 12.11: Positive NPV Investments