Chapter 12
Evaluating Project Economics and Capital Rationing
Learning Objectives
1. Explain and be able to 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 flow operating leverage
and the degree of accounting operating leverage.
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.
5. Explain how the profitability index can be used to rank projects when a firm faces
capital rationing, and describe limitations that apply to the profitability index.
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I.
Chapter Outline
12.1
Variable Costs, Fixed Costs, and Project Risk

Variable costs (VC) are costs that vary directly with the number of units sold.

Fixed costs (FC), in contrast, do not vary with unit sales in the short run.

The cash flows and accounting profits for a project are sensitive to the proportion of
its costs that are variable and the proportion that are fixed.
 A project with a higher proportion of fixed costs will have cash flows and
accounting profits that are more sensitive to changes in revenues than an
otherwise identical project with a lower proportion of fixed costs.

EBITDA is often called pretax operating cash flow because it equals the
incremental pretax cash operating profits from a project.
 EBITDA = Revenue – VC – FC
 Op Ex = VC + FC

By comparing the sensitivity of EBITDA to changes in revenue between two project
alternatives, it may help to better understand the risks and returns for each of the
alternatives.
 Distinguishing between fixed and variable costs will then enable us to calculate
the sensitivity of EBITDA to changes in revenue.

The greater the proportion that total costs are fixed will make it more
difficult to adjust costs when revenue changes.
 EBIT is more sensitive to changes in revenue than EBITDA because the EBITDA
does not include depreciation and amortization.
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
Depreciation and amortization acts just like a fixed cost because it is based
on the amount that was invested in the project.
12.2
Calculating Operating Leverage

Operating leverage is a measure of the sensitivity of EBITDA or EBIT to changes
in revenue.

Two measures of operating leverage are often used by analysts: the degree of
pretax cash flow operating leverage and the degree of accounting operating
leverage.
A.
Degree of Pretax Cash Flow Operating Leverage

The degree of pretax cash flow operating leverage (Cash Flow DOL)
provides us with a measure of how sensitive pretax operating cash flows are to
changes in revenue.
Fixed Costs
FC
= 1+
.
Pretax Operating Cash Flows
EBITDA

Cash Flow DOL = 1 +

Cash Flow DOL changes with the level of revenue; the sensitivity of
operating cash flows is not the same for all levels of revenue.
B.
Degree of Accounting Operating Leverage

The degree of accounting operating leverage (Accounting DOL) is a
measure of how sensitive accounting operating profits, EBIT, are to changes
in revenue.
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Accounting DOL = 1 +

Fixed Charges
Accounting Operating Profits
1
FC + D&A
EBITDA - D&A
=1+
FC + D&A
.
EBIT
o D&A is treated as a fixed cost and is added to FC to obtain the total of
the cash and noncash fixed costs that would be reflected in the income
statement if the project were adopted.
12.3

Break-Even Analysis
Break-even analysis tells us how many units must be sold in order for a project to break
even on a cash flow or accounting profit basis.
A.
Cash Flow Break-Even
The pretax operating cash flow (EBITDA) break-even point is calculated as follows:
o
EBITDA Break-Even =

FC
Price - Unit VC
Simply divide the fixed costs, FC, by the per-unit contribution (Price –
Unit VC).
o The cross-over level of unit sales (CO) is calculated as follows:
COEBITDA =
FCAlternative1 - FC Alternative2
Unit Contribution Alternative1 - Unit Contribution Alternative2
where Unit contribution stands for the per-unit contribution.
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
When using the above formula, make sure that the smaller value of FC is
in the second term in the numerator since putting the smaller number first
will usually give you a negative answer.
B.
Accounting Break-Even

The accounting operating profit (EBIT) break-even point is calculated as:
EBIT Break-Even =
FC + D&A
.
Price - Unit VC
o When we calculate the accounting operating profit break-even point, we
are calculating how many units must be sold to avoid an accounting
operating loss.
12.4
Risk Analysis
A.
Sensitivity analysis involves examining the sensitivity of the output from an
analysis, such as the NPV estimate, to changes in individual assumptions.

In a sensitivity analysis, 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.
B.
Scenario analysis will be performed if one wants to examine how the results from
a financial analysis will change under alternative scenarios.

A scenario might describe how a set of project inputs might be different
under different economic conditions.
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
By comparing the range of NPVs provided by the different scenarios, it is
possible to understand how much uncertainty is associated with an NPV
estimate.
C.
Simulation analysis is like scenario analysis except that in simulation analysis, an
analyst typically uses a computer to examine a large number of scenarios in a
short period of time.

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.

A computer program then calculates the cash flows associated with a large
number of scenarios by repeatedly drawing numbers for the distributions
for various assumptions, plugging them into the cash flow model, and
computing the annual cash flows and then the NPV.

In addition to providing an estimate of the expected cash flows, simulation
analysis gives information on the distribution of the cash flows that the
project is likely to produce in each year.
12.5

Investment Decisions with Capital Rationing
What does a firm do when it does not have enough money to invest in all available
positive-NPV projects?
o 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.
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o
In an ideal world, the firm could accept all positive-NPV projects, because it
would be able to finance them.

However, the world is not ideal, and so the firm must determine the most
efficient method of allocating its capital.
A.
Capital rationing in a single period involves choosing the set of projects that
creates the greatest value in a given period. The goal is to select the projects that
yield the largest value per dollar invested.
o The profitability index (PI) is computed for each project, and the firm then
chooses the projects with the largest profitability indexes until it runs out of
money.
Benefits Present Value of Future Cash Flows NPV + Initial Investment
PI objective isto identify the bundle or combination of positive-NPV projects
o The
Costs
Initial Investment
Initial Investment
that creates the greatest total value for stockholders.
o The following steps should be taken:

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
our way down (to the project with the lowest PI), select the projects that
the firm can afford.

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.
B.
Capital Rationing Across Multiple Periods
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
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 to reinvest some or all of the cash
flows generated by the projects you invest in this year.

A limitation of the profitability index is that it does not tell us enough to
make informed decisions over multiple periods.
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