ch12

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.

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.

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.

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.

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

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:

where Unit contribution stands for the per-unit contribution.

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:

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.

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.

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.

o The objective is to identify the bundle or combination of positive-NPV projects

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

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.

II. Suggested and Alternative Approaches to the Material

The focus of Chapter 12 is on the nonfinancially related or operational risks to the firm—that is,

the risks that arise primarily due to the cost structure of the firm rather than the level of debt that

the firm relies on to finance its assets. A large portion of the chapter is allocated to understanding

the effects of operating leverage on a firm’s break-even as well as the concept of variability

within the estimated revenues, costs, and consequently the net cash flows produced by a project

or the firm. The chapter begins with a descriptive understanding of variable and fixed costs. A

more formal understanding of a firm’s cost structure is then discussed within an operating

leverage framework where the impact of revenue changes can be evaluated for EBIT or

EBITDA. That understanding is then used to calculate a firm’s unit break-even from cash, as

well as from an accounting perspective. Those ideas are then used to forecast the impact of input

changes on cash flow by using sensitivity, scenario, and simulation analysis. The chapter then

concludes with a discussion on capital rationing within capital budgeting decisions.

A good portion of the chapter contains material that should be familiar to students who

have completed a managerial accounting course. Therefore the chapter may provide the students

some comfortable ground before they proceed with later chapters, which tend to have a

theoretical basis.

III. Summary of 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.

Because the fixed costs associated with a project do not change as revenue changes,

fluctuations in revenue are magnified so that pretax operating cash flows and accounting

operating profits fluctuate more than revenue in percentage terms. The greater the proportion

of total costs that are fixed, the more the fluctuations in revenue will be magnified. To

demonstrate this, you can perform calculations like those in the hammock-manufacturing

example and in Learning by Doing Applications 12.1 and 12.2.

2. Calculate and distinguish between the degree of pretax cash flow operating leverage

and the degree of accounting operating leverage.

The degree of pretax cash flow operating leverage is a measure of how much pretax operating

cash flow will change in relation to a change in revenue. Similarly, the accounting degree of

operating leverage is a measure of how much accounting operating profits will change in

relation to a change in revenue. The only difference between cash flow operating leverage

and accounting operating leverage is that the accounting measure treats incremental

depreciation and amortization charges as a fixed cost in the calculation. These charges are

excluded from the cash flow operating leverage measure because they do not reflect actual

cash expenses and therefore do not affect pretax cash flows. Equations 12.2 and 12.3 are used

to calculate these two measures.

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.

The pretax operating cash flow break-even point is the number of units that must be sold in a

particular year to break even on a pretax operating cash flow basis. It is calculated using

Equation 12.4.

The accounting operating profit break-even point is the number of units that must be sold

in a particular year to break even on an accounting operating profit basis. A project breaks

even on an accounting operating profit basis when it produces exactly $0 in incremental

operating profits, EBIT. It is calculated using Equation 12.6.

The crossover level of unit sales is the level of unit sales at which the pretax operating

cash flows or accounting operating profits for one project alternative switches from being

lower than that of another alternative to being higher. The EBITDA and EBIT crossover

levels of unit sales are calculated using Equations 12.5 and 12.7, respectively.

4. Define sensitivity analysis, scenario analysis, and simulation analysis and describe

how they are used to evaluate the risks associated with a project.

Sensitivity analysis is concerned with how sensitive the output from a financial analysis, such

as the NPV, is to changes in an individual assumption. It helps identify which assumptions

have the greatest impact on the output and therefore on the value of a project. Knowing this

helps an analyst identify which assumptions are especially important to that analysis.

Scenario analysis is used to examine how the output from a financial analysis changes under

alternative scenarios. This type of analysis recognizes that changing economic and market

conditions affect more than one variable at a time and tries to account for how each of the

different variables will change under alternative scenarios. Simulation analysis is like

scenario analysis except that in simulation analysis a computer is used to examine a large

number of scenarios in a short period of time.

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.

The profitability index (PI) aids in the process of choosing the most valuable bundle of

projects that the firm can afford because it is a measure of value received per dollar invested

that can be used to rank projects in a given period. The major limitation of the PI is that,

while it can be used to rank projects in a given period, it can lead to misleading project

choices in a multiperiod context.

IV. Summary of Key Equations

Equation Description Formula

12.1Op Ex in terms of incremental variable and fixed costs.

Op Ex = VC + FC

12.2Degree of pretax cash flow operating leverage

12.3Degree of accounting operating leverage

12.4Pretax operating cash flow break-even point

12.5Crossover level of unit sales for EBITDA

12.6Accounting operating profit break-even point

12.7 Crossover level of unit sales for EBIT

12.8 Profitability index

V. Before You Go On Questions and Answers

Section 12.1

1. Why do analysts care about how sensitive EBITDA and EBIT are to changes in revenue?

Comparing the sensitivity of EBITDA to changes in revenue can help you better

understand risks and returns associated with alternative options. For example, if we assume that

the sensitivity of EBITDA to changes in revenue is higher for one alternative than for the other.

This means that EBITDA for the more sensitive alternative will decline more when revenue is

lower than expected. A larger decline in EBITDA reduces the value of the project more and has a

greater impact on the amount of cash the firm has available to fund other positive NPV projects.

Conversely, EBITDA will increase more when revenue is greater than expected if the level of

sensitivity is higher.

2. How is the proportion of fixed costs in a project’s cost structure related to the sensitivity

of EBITDA and EBIT to changes in revenue?

The greater the proportion of fixed costs, the more sensitive EBITDA and EBIT will be

to changes in revenue.

Section 12.2

1. How does operating leverage change when there is an increase in the proportion of a

project’s costs that are fixed?

An increase in the proportion of a project’s costs that are fixed increases the operating

leverage of the project.

2. What do the degree of pretax cash flow operating leverage (Cash Flow DOL) and the

degree of accounting operating leverage (Accounting DOL) tell us?

Cash Flow DOL provides us with a measure of how sensitive pretax operating cash flows

are to changes in revenue. Cash Flow DOL changes with the level of revenue. Accounting DOL

is a measure of how sensitive accounting operating profits (EBIT) are to changes in revenue.

Accounting DOL focuses on EBIT, whereas Cash Flow DOL focuses on EBITDA.

Section 12.3

1. How is the per-unit contribution related to the accounting operating profit break-even

point?

The per unit contribution is how much is left from the sale of a single unit after paying

the variable costs associated with that unit. This is the amount that is available to help

cover FC and D&A for the project. When we calculate the accounting operating profit

break-even point, we divide the sum of FC and D&A by the per unit contribution to

determine how many units must be sold to cover FC and D&A.

2. What is the difference between the pretax operating cash flow break-even point and the

accounting operating profit break-even point?

The operating profit cash flow break even point is the number of units that must be sold

in a particular year for cash inflows to exactly equal cash outflows. The accounting

operating profit break-even point is the number of units that must be sold in a particular

year for the project to have operating profits of $0—in other words, to break even on an

accounting operating profit basis.

Section 12.4

1. How is a sensitivity analysis used in project analysis?

Sensitivity analysis is used to examine the sensitivity of a project’s NPV to changes in an

individual assumption.

2. How does a scenario analysis differ from a sensitivity analysis?

Scenario analysis recognizes that variables typically do not change one at a time. A

change in economic or market conditions will usually cause several assumptions to

change. Scenario analysis recognizes this by examining a project under alternative

scenarios in which each assumption can change under each scenario.

3. What is a simulation analysis, and what can it tell us?

Simulation analysis is like scenario analysis in that it enables the analyst to evaluate the

effects of different scenarios. A key difference is that simulation analysis uses computers

to enable the analyst to examine a large number of scenarios in a short period of time.

Section 12.5

1. What decision criteria should managers use in selecting projects when there is not

enough money to invest in all available positive-NPV projects?

When a firm does not have enough money to invest in all available positive-NPV

projects, managers should identify the bundle of positive-NPV projects that creates the

greatest total value for stockholders.

2. What might cause a firm to face capital constraints?

A firm might face capital constraints because it can be difficult for outside investors (new

creditors, bondholders, or stockholders) to accurately assess the risks and returns

associated with the firm’s projects. This might cause the investors to require returns for

their capital that are so high that they make positive-NPV projects unattractive, because

those projects cannot produce the high returns required by investors.

3. How can the PI help in choosing projects when a firm faces capital constraints? What are

its limitations?

The basic principle is to select the projects that yield the largest NPV per dollar invested.

The PI tells us the NPV per dollar invested for an individual project. In a single

period, the PI can be used to identify the bundle of projects that yields the largest NPV

per dollar invested. However, as illustrated in Section 12.5, the PI will not necessarily

help identify the most valuable bundle of projects if investments are being compared

across more than one year and the timing of cash flows from early investments affects the

firm’s ability to make subsequent investments.

VI. Self-Study Problems

12.1 The Yellow Shelf Company sells all of its shelves for $100 per shelf, and incurs $50 in

variable costs to produce each. If the fixed costs for the firm are $2 million per year, then

what will the EBIT be for the firm if it produces and sells 45,000 shelves next year?

Assume that depreciation and amortization is included in the fixed costs.

Solution:

Revenue $100 x 45,000 = $4,500,000

VC $50 x 45,000 = 2,250,000

FC + D&A 2,000,000

EBIT $ 250,000

12.2 Hydrogen Batteries sells its specialty automobile batteries for $85 each, while its current

variable cost per unit is $65. Total fixed costs (including depreciation and amortization

expense) are $150,000 per year. The firm expects to sell 10,000 batteries next yea,r but

the firm is concerned that its variable cost will increase next year due to material cost

increases. What is the maximum variable cost per unit increase that will keep the EBIT

from becoming negative?

Solution:

The forecasted EBIT for the firm is:

Revenue $85 x 10,000 = $850,000

VC $65 x 10,000 = 650,000

FC + D&A 150,000

EBIT $ 50,000

Therefore, total variable cost may increase by $50,000, which means that if the firm

produces and sells 10,000 batteries, then the variable cost per unit may increase by $5

($50,000 / 10,00) units.

12.3 The Vinyl CD Co. is going to take on a project that will increase its EBIT by $90,000

next year. The firm’s fixed cost cash expenditures are expected to increase by $100,000,

and depreciation and amortization will increase by $80,000 next year. If the project just

happens to yield an additional 10 percent in revenue, what percentage increase in the

project’s EBIT will result from the additional revenue?

Solution:

Accounting DOL = 1 + (FC+ D&A) / (EBIT)

= 1 + ($100,000 + $80,000) / $90,000

= 3

Therefore, a 10 percent additional increase in revenue should result in a 30 percent

increase in EBIT.

12.4 You are considering investing in a business that has monthly fixed costs of $5,500 and

that sells a single product that costs $35 per unit make. This product sells for $90 per

unit. What is the annual pretax operating cash flow break-even point for this business?

Solution:

You can solve for the monthly pretax operating cash flow break-even point using

Equation 12.4:

Therefore, the annual EBITDA break-even point is 100 12 = 1,200 units.

12.5 You are considering a project that has an initial outlay of $1 million. The profitability

index of the project is 2.24. What is the NPV of the project?

Solution:

You can use Equation 12.8 to solve for the NPV:

PI = (NPV + Initial investment) / Initial investment

2.24 = NPV + $1,000,000 / $1,000,000

Therefore:

NPV = $2,240,000

VII.Critical Thinking Questions

12.1 You are planning for a firm that is expected to have a large increase in sales for the next

year. Which type of firm would benefit the most from that sales increase, the firm with

low fixed costs and high variable costs or the firm with high fixed costs and low variable

costs?

Solution:

Under the circumstances described, the firm with the high fixed costs would incur lower

total future costs associated with the increased sales than the firm with the low fixed costs

due to the higher variable cost per unit of sales. Therefore, the firm with the high fixed

costs structure would benefit the most.

12.2 You own a firm with a single new product that is about to be introduced to the public for

the first time. Your marketing analysis suggests that the demand for this product could be

anywhere between 500,000 units and 5,000,000 units. Given such a wide dispersal

concerning the demand forecast, discuss the safest cost structure alternative for your firm

Solution:

Since there is a great deal of variability concerning the demand for the product, then the

safest alternative would be to create a cost structure that limits the variability of the

firm’s EBIT. This means that you would create a cost structure that is composed of high

unit variable costs with low fixed costs. Although this would not enable the firm to

maximize earnings if the 5,000,000 unit forecast occurs, it limits the downside

profitability for the firm in the event that the 500,000 unit forecast occurs.

12.3 Define capital rationing, and explain why it can occur in the real world.

Solution:

Capital rationing is the process of allocating limited capital among the positive-NPV

projects that have been identified in a way that maximizes the overall NPV of the projects

selected. In an ideal world, we should accept all positive NPV projects because we will

always be able to finance them. However, the world is not ideal. It can be difficult for

outside investors to accurately assess the risks and returns associated with a project. With

limited capital available for new projects, we need capital rationing to help us decide how

to allocate capital among all potential investments.

12.4 Discuss the interpretation of the degree of accounting operating leverage and cash flow

degree of operating leverage.

Solution:

While the degree of accounting operating leverage is defined as:

Accounting DOL = 1 + (FC + D&A) / (EBIT)

it is used to interpret the percentage change in EBIT that will be driven by a given

percentage change in net revenue. Similarly, the cash flow degree of operating leverage

is defined as:

Cash Flow DOL = 1 + FC / (EBIT + D&A)

but it is used to interpret the percentage change in EBITDA (or pretax operating cash

flow) that will be driven by a given percentage change in net revenue.

12.5 Explain how EBITDA differs from free cash flows, FCF, and discuss the types of

businesses for which this difference would be especially small or large.

Solution:

Depreciation and amortization, taxes, capital expenditures, and working capital are not

reflected in EBITDA. If any of these is not equal to zero, then EBITDA is likely to differ

from FCF, which is equal to EBIT(1-T) + depreciation—increases in working capital—

capital expenditures. The type of businesses that require large capital expenditures (and

therefore have large depreciation expenses per year) such as heavy manufacturing, are

likely to have substantial differences between EBITDA and FCF. Conversely, smaller

firms that have smaller capital expenditures, such as firms in retail sales, will likely have

small differences between FCF and EBITDA for. Setting aside depreciation and special

tax subsidies, taxes will always create a difference between EBITDA and FCF for a

profitable firm.

12.6 Describe how the cash flow break-even point calculated in this chapter is related to a

break-even point that makes the NPV of a project equal to zero.

Solution:

The cash flow break-even point calculated in this chapter establishes the number of units

that must be sold in a given year to break even for a particular year. The NPV break-even

calculation looks at cash flows over the course of an entire project and tells us how many

units must be sold to achieve an NPV of $0. The NPV calculation is useful when

deciding whether to undertake a project in an economic sense. The cash flow break-even

calculation is useful when considering whether to abandon a project or to make changes

to a project’s cost structure.

12.7 Is it possible to have a crossover point, where the accounting break-even is the same for

two alternatives, that is, above the break-even point for a low-fixed-cost alternative but

below the break-even point for a high-fixed-cost alternative? Explain.

Solution:

No. Above the low fixed cost break-even sales level implies that income is positive.

Below the high fixed cost break-even sales level implies that income is negative.

However, the cross-over point is defined as the sales level at which the income level for

both alternatives is the same. Therefore, it cannot occur.

12.8 In calculus we are able to understand the effect of a change to a single variable, within a

multivariable equation, on the entire equation. We call that effect the partial derivative.

Which is analogous to the partial derivative: sensitivity analysis, scenario analysis, or

simulation analysis?

Solution:

Simulation measures the effect of many variables moving at once in order to help with

statistical inference. Scenario analysis also measures the effect of many variables moving

together in a semicoordinated way and it is therefore not analogous to a partial derivative.

Sensitivity analysis measures the effect of a change in a single variable on the income

statement, or even some other financial output, regardless of whether it is even possible

for that variable to move independently without a co-movement in an another variable.

Therefore, sensitivity analysis is most analogous to the partial derivative in calculus.

12.9 High Tech Monopoly Co. has plenty of cash to fund any conceivable positive NPV

project. Can you describe a situation in which capital rationing could still occur?

Solution:

Financial capital is not the only constrainable item within the firm. This might occur, for

example, when human capital is in short supply, as is the case with most high-technology

firms. Even if every positive NPV project could be funded, the firm might not have

enough employees to manage the projects. Therefore, even with ample financial capital,

firms will more than likely still be rationing projects.

12.10 Profitability index is a scaleless attribute for measuring a project’s benefits, relative to the

costs. How might this help to eliminate bias in project selection?

Solution:

Since the profitability index is a modified pure-return-type measure, it offers a method to

maximize the use of capital that is employed by the firm. This could help eliminate some

types of bias if the measure were to be employed universally. However, it does not

necessarily maximize the use of capital that is not employed, which could in some

circumstances be problematic.

VIII. Questions and Problems

BASIC

12.1 Fixed and variable costs: Define variable costs and fixed costs and give an example of

each.

Solution:

Fixed costs are costs that in the short term cannot be changed regardless of how much

output the project produces. One example is the first advertising contract discussed in

Learning by Doing Application 12.1. Regardless of the number of house calls the

technical support firm makes, it will incur the full cost of advertising. Variable costs are

costs that depend on the number of units of output produced by the project. An example

is the gas that the technical support firm uses to make house calls. The cost to keep the

vehicles gassed up is directly related to the number of service calls the firm makes.

12.2 EBIT: Describe the role that the mix of variable versus fixed costs has in the variation of

Earnings before interest and taxes (EBIT) for the firm.

Solution:

By definition, variable costs do not occur unless matching sales or matching revenues

also occur, whereas fixed costs are not a function of the level of sales. Therefore, a large

mix of fixed costs within a firms cost structure will make the firm’s EBIT very reactive to

a change in the level of sales for the firm. The greater the proportion of fixed costs

(compared to variable costs), the greater the variability in EBIT for the firm.

12.3 EBIT: The Generic Publications Text Book Company sells all of its books for $100 per

book, and it currently costs $50 in variable costs to produce each text. The fixed costs,

which include depreciation and amortization for the firm, are currently $2 million per

year. The firm is considering changing its production technology, which will increase the

fixed costs for the firm by 50 percent but decrease the variable costs per unit by 50

percent. If 45,000 books are expected to be sold next year, should the firm switch

technologies?

Solution:

The current EBIT for the firm is:

Revenue $100 x 45,000 = $4,500,000

VC $50 x 45,000 = 2,250,000

FC + D&A 2,000,000

EBIT $ 250,000

If the fixed costs increase by 50 percent, then they will be $2,000,000 x 1.5 = $3,000,000,

while the unit variable costs would be .5 x $50 = $25.

The new EBIT for the firm would then be:

Revenue $100 x 45,000 = $4,500,000

VC $25 x 45,000 = 1,125,000

FC + D&A 3,000,000

EBIT $ 375,000

Since the EBIT after the technology change is $125,000 higher, then the firm should

adopt the new production technology.

12.4 EBIT: WalkAbout Kangaroo Shoe Stores forecasts that they will sell 9,500 pairs of shoes

next year. The firm buys its shoes for $50 per pair from the wholesaler and sells them for

$75 per pair. If the firm will incur fixed costs plus depreciation and amortization of

$100,000, then what is the percentage increase in EBIT if the actual sales next year equal

11,500 pairs of shoes?

Solution:


Revenue $75 x 9,500 = $712,500

VC $50 x 9,500 = 475,000

FC + D&A 100,000

EBIT $137,500

The actual EBIT for the firm is:

Revenue $75 x 11,500 = $862,500

VC $50 x 11,500 = 575,000

FC + D&A 100,000

EBIT $187,500

Therefore, the percent increase in EBIT would be ($187,500 – $137,500) / $137,500 =

0.3636 = 36.36%.

12.5 Cash Flow DOL: The law firm of Dewey, Cheatem, and Howe has monthly fixed

costs of $100,000, EBIT of $250,000, and depreciation charges on its office furniture

and computers of $5,000. Calculate the Cash Flow DOL for this firm.

Solution:

12.6 Accounting DOL: Explain how the value of accounting operating leverage can be used.

Solution:

Accounting operating leverage gives us the ratio by which the firm can convert revenues

into EBIT. That is, if the firm’s operating leverage is 3, then a 15 percent increase will

convert to a 45 percent (15% x 3) increase in EBIT for the firm.

12.7 Break-cven analysis: Why is the per-unit contribution important in a break-even

analysis?

Solution:

Per-unit contribution is critical to break-even analysis in order for a firm to determine how

many units are required to be sold to cover the firm’s fixed costs. The underlying known

variable is the dollar amount of the contribution margin the firm will generate from each

unit sold in order to make the above calculation. Equations 12.4 and 12.6 demonstrate the

calculation for EBITDA and EBIT break-even points. The term in the denominator (Price-

Unit VC) represents the per-unit cash flow contribution.

12.8 Simulation analysis: What is simulation analysis and how is it used?

Solution:

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. The computer then draws upon the distribution

of each variable in order to generate an observation for a single scenario. After repeating

the number of computer-generated scenarios, a distribution of cash flow outcomes will be

generated, thereby offering the analyst the ability to perform a probability-based analysis

on the cash flow distribution.

12.9 Profitability index: What is the profitability index, and why is it helpful in the capital

rationing process?

Solution:

The profitability index is computed as the ratio of NPV plus initial investment to initial

investment. In the capital rationing process, we can calculate the profitability index for

each potential investment and choose the projects with the largest indexes until we run

out of capital. This follows the basic principle that we need to choose the set of projects

that creates the greatest value given the limited capital available.

INTERMEDIATE

12.10 EBIT: If a manufacturing firm and a service firm have identical cash fixed costs but the

manufacturing firm has much higher depreciation and amortization, then which firm is

more likely to have a large discrepancy between its FCF and its EBIT?

Solution:

Since depreciation and amortization is a noncash item, the manufacturing firm would

have the greatest discrepancy between FCF and EBIT.

12.11 EBIT: Duplicate Baseballs, Inc., expects to sell 15,000 balls this year. The balls sell for

$110 each and have variable cost per unit of $80 per ball. Fixed costs, including

depreciation and amortization, are currently $220,000 per year. How much can either the

fixed costs increase or the variable cost per unit increase in order to keep the company

from having a negative EBIT.

Solution:


Revenue $110 x 15,000 = $1,650,000

VC $80 x 15,000 = 1,200,000

FC + D&A 220,000

EBIT $ 230,000

Therefore, the fixed costs could increase by $230,000 and still keep the EBIT from being

negative. If we focus on the variable costs, we know that total variable costs could

increase by $230,000. If that cost is spread over 15,000 units, then the variable cost per

unit could increase by ($230,000 / 15,000) = $15.33 and still keep the EBIT from being

negative. Note that the analysis assumes that increases in either the fixed cost or the

variable cost per unit will not change the other. This is probably not a realistic

assumption.

12.12 EBIT: Specialty Light Bulbs anticipates selling 3,000 light bulbs this year at a price of

$15 per bulb. It costs Specialty $10 in variable costs to produce each light bulb, and the

fixed costs for the firm are $10,000. Specialty has an opportunity to sell an additional

1,000 bulbs next year at the same price and variable cost, but by doing so the firm will

incur an additional fixed cost of $4,000 if it chooses to sell the additional bulbs. Should

Specialty produce and sell the additional bulbs?

Solution:


Revenue $15 x 1,000 = $15,000

VC $10 x 1,000 = 10,000

FC 4,000

EBIT $ 1,000

Since the EBIT is positive, then Specialty should produce and sell the additional bulbs.

12.13 Cash Flow DOL: For the Vinyl CD Co. in Self-Study Problem 12.3, what percentage

increase in pretax operating cash flow will be driven by the additional revenue?

Solution:

Cash flow DOL = 1 + (FC) / (EBIT + D&A)

=1 + ($100,000) / ($90,000 + $80,000) = 1.59

Therefore, a 10 percent additional increase in revenue should drive a 15.9 percent

increase in pretax operating cash flow.

Use the following information for Problems 12-14, 12-15, and 12-16:

Dandle’s Candles will be producing a new line of dripless candles in the coming years and has

the choice of producing the candles in a large factory with a small number of workers or a small

factory with a large number of workers. Each candle will be sold for $10. If the large factory is

chosen, the cost per unit to produce each candle is $2.50, while it will be $7.50 for the small

factory. The large factory would have fixed cash costs of $2,000,000 and a depreciation expense

of $300,000 per year, while those expenses would be $500,000 and $100,000 in the small factory.

12.14 Accounting operating profit break-even: Calculate the accounting operating profit

break-even point for both factory choices for Dandle’s Candles.

Solution:

The formula for the accounting operating profit break-even is:

EBIT break-even = (FC + D&A) / (Price – Unit VC)

For the large factory:

EBIT break-even = ($2,000,000 $300,000)/ ($10 – $2.50) = 306,667 units

For the small factory:

EBIT break-even = ($500,000 $100,000) / ($10 – $7.50) = 240,000 units

12.15. Crossover level of unit sales: Calculate the number of candles for Dandle’s Candles for

which the Accounting Break-even is the same, regardless of the factory choice.

Solution:

The formula for the crossover level of units sales (CO) is:

CO = 340,000 units

12.16 Pretax operating cash flow break-even: Calculate the pretax operating cash flow

break-even point for both factory choices for Dandle’s Candles.

Solution:

The formula for the pretax operating cash flow break-even is:

CF Break-even = FC / (Price – Unit VC)

and so the cash flow break-even for the large factory is:

CF Break-even = $/ ($10 – $2.5) = 266,667 units

and the cash flow break-even for the small factory is:

CF Break-even = $/ ($10 – $7.5) = 200,000 units

12.17 Accounting and cash flow break-even: Your analysis tells you that at a projected level

of sales, your firm will be below accounting break-even but will be above cash flow

break-even. Explain why this might still be a viable project or firm.

Solution:

While the business may show an accounting loss, our focus should be on the cash flow

gain or loss. The reason that the project will produce an accounting loss but cash flow

income is that the depreciation and amortization charges do not apply to the cash flow

calculations as they are noncash expenses that help to reduce the tax liability. Therefore,

the project is viable if it does not show a cash flow loss.

12.18 Sensitivity and scenario analyses: Sensitivity analysis and scenario analysis are

somewhat similar. Describe which is a more realistic method of analyzing different

scenario impacts on a project.

Solution:

Sensitivity analysis captures the effect of a change in a single item such as unit selling

price or a change in the number of units sold on a specific item such as EBIT. However,

it is unlikely that a change in the selling price of an item will not affect the demand, and

consequently the number of units sold, for the product in question. Scenario analysis

analyzes the multiple effects of a scenario on an item such as EBIT by changing a

number of interrelated variables at the same time to measure the effect of an entire

scenario change. Therefore, scenario analysis is a much more practical tool for stress-

testing a project.

12.19 Sensitivity analysis: Describe the circumstances under which sensitivity analysis might

be a reasonable basis for determining changes to a firm’s EBIT or FCF.

Solution:

Since sensitivity analysis assumes independence among variables (otherwise the analysis

is too superficial), then that is the time when the analysis can yield the most meaningful

results. One time when that might occur is if the sales level and product price are

completely unaffected by movements in the other as with an industry monopoly. In a

competitive market, such an assumption could yield disastrous results if they are

followed without caution.

12.20 Scenario analysis: Chip’s Home Brew Whiskey forecasts that if it sells each bottle of

Snake-Bite for $20, then the demand for the product will be 15,000 bottles per year. If

Chip sells Snake-Bite for a 10 percent higher price, then it believes that it will sell 90

percent of the amount of its pre-hike-priced product. Chip’s variable cost per bottle is

$10, and the total fixed cash cost for the year is $100,000. Depreciation and amortization

charges are $20,000, and the firm is in the 30 percent marginal tax rate. If the firm

anticipates an increased working capital need of $3,000 for the year, then what will be

the effect of a price increase on the firm’s FCF for the year?

Solution:

If the firm increases its price to $22 per bottle, then it will sell 0.9 x 15,000 = 13,500

units next year. We can now find the effect of the change in price.

Normal Price Hike

Revenue $300,000 $297,000 (22 x 13,500)

VC 150,000 135,000 (10 x 13,500)

FC 100,000 100,000

D&A 20,000 20,000

EBIT $ 30,000 $ 42,000

Tax (30%) 9,000 12,600

NOPAT $ 21,000 $ 29,400

D&A 20,000 20,000

Add WC 3,000 3,000

FCF $ 38,000 $ 46,400

By increasing the price of a bottle by 10 percent, the FCF increases from $38,000 to

$46,400.

12.21 Simulation analysis: If you were interested in calculating the probability that your

project will have positive FCF, what type of risk analysis tool would you most likely

use?

Solution:

Sensitivity analysis can only manage a single movement in a modeled variable and can

therefore only show the net impact of that movement. Scenario analysis is much more

flexible and can quantify the impact of moving many interdependent variables at once,

but it cannot produce confidence intervals for a given level of FCF. Simulation analysis

begins with a distribution for the range of possible values for each variable. All of these

modeled variables are then “freed up” to randomly move, all at the same time, within the

modeled range in order to produce an individual observation. If this process is repeated a

large number of times, then a distribution of observations is generated for the FCF value

(or EBIT or a whole host of other calculations) in order to be able to make statistical

inferences about the probability of achieving a given level of FCF.

12.22 Profitability index: Suppose that you faced the following projects but only have $30,000

to invest. How would you make your decision?

Project Cost ($) NPV ($)

A $ 8,000 $4,000

B 11,000 7,000

C 9,000 5,000

D 7,000 4,000

Solution:

The profitability indexes of the projects are:

A: 1.5; B: 1.64; C: 1.56; D: 1.57

With $30,000, you should invest in B, D, and C. The total cost is $27,000, and the total

NPV is $16,000.

12.23 Profitability index: Suppose that you face the same following projects as in the previous

problem, but now only have $25,000 to invest. How would you make your decision?

Solution:

The profitability indexes of the projects are:

A: 1.5; B: 1.64; C: 1.56; D: 1.57

With $25,000, you cannot invest in all of B, D, and C, since the total cost is $27,000. You

may think that you should then invest in only B and D, since they have the highest

profitability indexes. This will yield a total NPV of $11,000, and you are left with $7,000

of idle capital.

If you give up project B, however, which has the highest profitability index and

highest cost, and invest instead in A, C, and D, which require less capital, you will get a

total NPV of $13,000, and you are left with less idle capital ($6,000). From this example

you can see that capital rationing with indivisible projects are sometimes complicated and

require a careful thought of all possibilities (or linear/integer programming).

ADVANCED

12.24 Mick’s Soft Lemonade is starting a new product for which the fixed cash expenditures are

expected to be $80,000. The projected EBIT is $100,000, and the accounting DOL will be

2.0. What is the cash flow DOL for the firm?

Solution:


= 1 + ($80,000 + D&A) / $100,000 = 2 => D&A = $20,000

Cash flow DOL = 1 +(FC) /(EBIT + D&A

= 1 + ($80,000) / ($100,000 + $20,000) = 1.67

12.25 If a firm has any reasonable fixed asset base, meaning that its depreciation and

amortization for any year is positive, discuss the relationship between a firm’s

Accounting DOL and its Cash flow DOL.

Solution:

By comparing the equations for the Accounting DOL and Cash Flow DOL:

Accounting DOL = 1 +(FC + D&A) / (EBIT)

Cash flow DOL = 1 +(FC) / (EBIT + D&A)

We find that the denominator of the Cash Flow DOL will always be greater than the

denominator of the Accounting DOL if depreciation and amortization is greater than

zero. In addition, the numerator of the Cash Flow DOL will always be less than the

denominator of the Accounting DOL if depreciation and amortization is greater than

zero. Therefore, if depreciation and amortization is positive, then Cash Flow DOL must

be less than Accounting DOL.

12.26 DOL and Cash Flow DOL: Silver Polygon, Inc., has determined that if its revenues

were to increase by 10 percent, then its change in EBIT would increase by 25 percent to

$100,000. The fixed costs (cash only) for the firm are $100,000. Given the same 10

percent increase in revenues, what would be the corresponding change in EBITDA?

Solution:

Since a 10 percent increase in revenue will drive a 25 percent corresponding increase in

EBIT, then we know that Accounting DOL = 2.5. The new EBIT would be 100,000, after

the 25 percent increase, so the original EBIT was 100,000 / (1 + 0.25) = $80,000.

Therefore,

Accounting DOL = 1 + (FC + D&A) / (EBIT) = 2.5

= 1 +($100,00 + D&A) / ($80,000) = 2.5 ==> D&A = $20,000

Cash Flow DOL = 1 + (FC) / (EBIT + D&A) =

= 1 + ($100,000) / ($80,000 + $20,000) = 1.20

A 10 percent increase in revenue will drive a 12 percent increase in EBITDA.

12.27 If a firm’s costs are absolutely known (variable as well as fixed), then what are the only

two sources of volatility for a firm’s accounting profits or its cash flows?

Solution:

If the cost structure is known, then costs will only vary according to the firm’s unit sales.

Therefore, one source of volatility would be net revenue uncertainty. The second source

of volatility is based on the mix of variable and fixed costs within the firm’s cost

structure. A higher mix of fixed costs would increase the operating leverage for a firm

(both accounting and cash flow) and therefore increase the accounting profit and cash

flow volatility for the firm.

12.28 In most circumstances, if a firm were given the choice of a higher fixed cost structure

versus a lower fixed cost structure, which of the two would generate a larger contribution

margin?

Solution:

The firm with the higher fixed cost should have a lower variable cost per unit, assuming

that there is a trade-off. A lower variable cost per unit would then create a higher

contribution margin for that firm.

12.29 Using the same logic as with the accounting break-even calculation in Problem 12.15,

adapt the formula for cross-over level of unit sales to find the number of units sold where

the free cash flow is the same whether the firm chooses the large or small factory.

Solution:

The formula for the cross-over level of unit sales, based on accounting EBIT, is as

follows:

.

Since depreciation and amortization are noncash items, we could adapt the above formula

by omitting the depreciation and amortization from the numerator of the above formula

as below:

The formula for FCF in terms of unit contribution is given by:

By setting FCF1 = FCF2 and solving for the common number of units, we get:

12.30 You are analyzing two proposed capital investments with the following cash flows:

Year Project X ($) Project Y ($)

0 $(20,000) $(20,000)

1 13,000 7,000

2 6,000 7,000

3 6,000 7,000

4 2,000 7,000

The cost of capital for both projects is 10 percent. Calculate the NPV and the profitability

index (PI) for each project. Which project, or projects, should be accepted if you have

unlimited funds to invest? Which project should be accepted if they are mutually

exclusive?

Solution:

The NPV and PI calculations are as follows:

Both methods rank Project X over Project Y. However, both projects should be accepted

under the NPV criteria. Therefore, both should be accepted if they are independent and

sufficient resources are available. If the projects are mutually exclusive, we should

choose the project with the higher NPV or PI at r = 10%, which in this case is Project X.

We can directly compare the NPVs because both projects have four-year lives.

CFA Problems

12.31 An investment of $20,000 will create a perpetual after-tax cash flow of $2,000. The required rate of return is 8 percent. What is the investment’s profitability index?

A. 1.00B. 1.08C. 1.16D. 1.25

SolutionD is correct.

The present value of future cash flows is PV = 08.0

000,2

= 25,000.

The profitability index is PI =

PV 25,000

Investment 20,000

=1.25.

12.32. Hermann Corporation is considering an investment of €375 million with expected after-tax cash inflows of €115 million per year for seven years and an additional after-tax salvage value of €50 million in Year seven. The required rate of return is 10 percent. What is the investment’s PI?

A. 1.19B. 1.33C. 1.56

D. 1.75

SolutionC is correct.

7

71

115 50PV

1.10 1.10tt

= 585.53 million euros

585.53PI

375

=1.56

12.33. Operating leverage is a measure of theA. sensitivity of net earnings to changes in operating earnings.B. sensitivity of net earnings to changes in sales.C. sensitivity of fixed operating costs to changes in variable costs.D. sensitivity of earnings before interest and taxes to changes in the number of

units produced and sold.

Solution:D is correct. Operating leverage is the sensitivity of earnings before interest and taxes to changes

in the number of units produced and sold. The degree of operating leverage is the

elasticity of operating earnings with respect to the number of units produced and sold.

12.34. The Fulcrum Company produces decorative swivel platforms for home televisions. If Fulcrum produces 40 million units, it estimates that it can sell them for $100 each. The variable production costs are $65 per unit, whereas the fixed production costs are $1.05 billion. Which of the following statements is true?

A. The Fulcrum Company produces a positive operating income if it produces and sells more than 25 million swivel platforms.

B. The Fulcrum Company’s degree of operating leverage is 1.333.C. If the Fulcrum Company increases production and sales by 5 percent, its

operating earnings are expected to increase by 20 percent.D. Increasing the fixed production costs by 10 percent will result in a lower

sensitivity of operating earnings to changes in units produced and sold.

Solution:

C is correct.

Fulcrum produces positive operating income if it produces more than 30 million units. If it produces and sells fewer than 30 million, it will generate a loss.

The DOL is 4.If unit sales increase by 5 percent, Fulcrum’s operating earnings are expected to increase

by 4 × 5% = 20%.Increasing fixed production costs will increase the sensitivity of Fulcrum’s operating

earnings to changes in sales.

Sample Test Problems

12.1. Steven’s Hats forecasts that it will sell 25,000 baseball caps next year. The firm buys its

caps for $3 from the wholesaler and sells them for $15 each. If the firm will incur fixed

costs plus depreciation and amortization of $80,000, then what is the percentage increase

in EBIT if the actual sales next year equal 27,000 caps?

Solution:


Revenue $15 x 25,000 = $375,000

VC $3 x 25,000 = 75,000

FC + D&A 80,000

EBIT $220,000

The actual EBIT for the firm is:

Revenue $15 x 27,000 = $405,000

VC $3 x 27,000 = 81,000

FC + D&A 80,000

EBIT $244,000

Therefore, the percent increase in EBIT would be ($244,000 – $220,000) / $220,000 =

0.1091 = 10.91%.

12.2 Alan’s Fine Furniture will be creating custom bed frames, and the fixed cash

expenditures are expected to be $120,000. The projected EBIT for the project is

$130,000, and the accounting DOL will be 2.5. What is the depreciation and amortization

for the firm as well as Cash Flow DOL?

Solution:


= 1 + ($120,000 + D&A) / $130,000 = 2.5 => D&A = $75,000

Cash Flow DOL = 1 + (FC) / (EBIT + D&A)

= 1 + ($120,000) / ($130,000 + $75,000) = 1.59

12.3 Red Cat Firecrackers is considering whether to build a large or small factory to produce

its firecrackers. Regardless of the production method, each bundle of firecrackers sells for

$4.00. If the large factory is chosen, then the variable cost per bundle of firecrackers will

be $0.50, while the fixed costs will be $300,000 and the annual depreciation and

amortization amount will be $100,000. If the small factory is chosen, then the variable

cost per bundle of firecrackers will be $1.75 while the fixed costs will be $100,000 and

the annual depreciation and amortization amount will be $10,000. Calculate the number

of firecracker bundles for Red Cat such that the accounting operating profit is the same,

regardless of the factory choice.

Solution:

The formula for the cross-over level of unit sales (CO) is:

, and so

12.4 You are chairperson of the investment committee at your firm. Five projects have been

submitted to your committee for approval this month. The investment required and the

project profitability index for each of these projects are presented in the following table:

Project Investment ($) PI ($)

A $20,000 2.500

B 50,000 2.000

C 70,000 1.750

D 10,000 1.000

E 80,000 0.800

If you have $500,000 available for investments, which of these projects would you

approve? Assume that you do not have to worry about having enough resources for future

investments when making this decision.

Solution:

Definitely accept projects A, B, and C. They all have a positive NPV. Project D just

returns the opportunity cost of capital, so you would be indifferent with regards to

accepting this project. Do not accept project E; it has a negative NPV.

12.5 Ibrahim’s Habanero Sauce Products forecasts that if it sells each bottle of NitroStrength

for $10, then the demand for the product will be 85,000 bottles per year. If it sells Snake-

Bite for a 10 percent higher price, then it believes that it will sell 75 percent of the

amount of its pre-hike-priced product. Ibrahim’s variable cost per bottle is $4, and the

total fixed cash cost for the year is $20,000. Depreciation and amortization charges are

$3,000, and the firm is in the 40 percent marginal tax rate. If the firm anticipates an

increased working capital need of $2,000 for the year, then find the effect of a price

increase on the firm’s FCF for the year.

Solution:

If the firm increases its price to $11 per bottle, then it will sell 0.75 x 85,000 = 63,750

units next year. We can now find the effect of the change in price.

Normal Price Hike

Revenue $850,000 $701,250 (11 x 63,750)

VC 340,000 255,000 (4 x 63,750)

FC 20,000 20,000

D&A 3,000 3,000

EBIT $487,000 $423,250

Tax (40%) 194,800 169,300

NOPAT $292,200 $253,950

D&A 3,000 3,000

Add WC 2,000 2,000

FCF $293,200 $254,950

By increasing the price of a bottle by 10 percent, the FCF decreases from $293,200 to

$254,950.

ch12

Documents

Transcript of ch12