Chapter 12

Evaluating Project Economics and Capital Rationing

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?

1
 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?

2
 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.

3
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?

4
 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.

Self-Study Problems

5
 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 $2,000,000 per

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

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

Solution:

Revenue $100 × 45,000 = $4,500,000

VC $50 × 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. Management expects to sell 10,000

batteries next year, but 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 Hydrogen Batteries is:

Revenue $85 × 10,000 = $850,000

VC $65 × 10,000 = 650,000

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 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 / 10,000 units = $5 per unit).

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

$90,000 next year, its fixed cost cash expenditures by $100,000, and depreciation and

amortization by $80,000 next year. If the project yields an additional 10 percent in

revenue, what percentage increase in the project’s EBIT will result from the additional

revenue?

Solution:

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

increase in EBIT.

7
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 to 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:

Therefore:

NPV = $2,240,000

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Critical Thinking Questions

12.1 You are involved in the planning process for a firm that is expected to have a

large increase in sales next year. Which type of firm would benefit the most from that

sales increase: a firm with low fixed costs and high variable costs or a 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 range, discuss the safest cost structure alternative for your firm

Solution:

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 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.

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 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
11
subsidies, taxes will always create a difference between EBITDA and FCF for a profitable

firm.

12.6 Describe how the pre-tax operating 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 pre-tax operating 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 point

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:

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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. What is the fundamental difference between a sensitivity analysis and a scenario

analysis?

Solution:

A sensitivity analysis is a form of “what if” analysis that is very useful for identifying key

individual assumptions in models used for financial analysis such as an NPV calculation.

Scenario analysis identifies relationships across several key individual assumptions, and

is therefore a good way of estimating how project values might vary under different

economic scenarios.

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-

13
 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 The profitability index is a tool 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.

Questions and Problems

BASIC

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

each.

LO 1
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 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 in-home technical computer support

business 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.

LO 1

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 firm’s 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.

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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?

LO 1

Solution:

The current EBIT for the firm is:

Revenue $100 × 45,000 = $4,500,000

VC $50 × 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 × 1.5 =

$3,000,000, while the unit variable costs would be 0.5 × $50 = $25.

The new EBIT for the firm would then be:

Revenue $100 × 45,000 = $4,500,000

VC $25 × 45,000 = 1,125,000

FC + D&A 3,000,000
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 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 it 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 instead of 9,500?

LO 1

Solution:

The forecasted EBIT for the firm is:

Revenue $75 × 9,500 = $712,500

VC $50 × 9,500 = 475,000

FC + D&A 100,000

EBIT $137,500

The actual EBIT for the firm is:

Revenue $75 × 11,500 = $862,500

VC $50 × 11,500 = 575,000

FC + D&A 100,000

EBIT $187,500

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 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.

LO 2

Solution:

12.6. Cash Flow DOL: The degree of pretax cash flow operating leverage at Rackit

Corporation is 2.7 when it sells 100,000 units of its new tennis racket and its EBITDA is

$95,000. Ignoring the effects of taxes, what are the fixed costs for Rackit Corporation?

LO 2

Solution:

Cash Flow DOL = 1 + FC/EBITDA

2.7 = 1 + FC / ($95,000)

FC = $161,500

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

LO 2

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.

12.8 Accounting DOL: Caterpillar, Inc. is a manufacturer of large earth-moving and

mining equipment. This firm, and other heavy equipment manufacturers, have

accounting degree of operating leverage that are relatively high. Explain why.

LO 2

Solution:

Caterpillar and other heavy equipment manufacturers are heavily dependent on assets

in place, like manufacturing equipment and facilities, for production. These investments

result in relatively high fixed costs compared to variable costs of production, leading to a

high degree of operating leverage. To illustrate, in 2009, CAT saw a 37% decrease in

revenue and an 88% drop in operating income relative to their 2008 results. However,

for the third quarter of 2010, CAT saw a 53% increase in sales and a 329% jump in

operating profit.

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

analysis?

LO 3

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.

12.10. Break Even: Calculate the accounting operating profit break-even and pretax

operating cash flow break-even for each of the production choices outlined below.

Choice Price Unit VC FC D&A

A $250 $160 $15,000 $3,000
B $55 $10 $1,100 $200
C $10 $1.50 $100 $100

LO 3

Solution:

Choice Unit Unit VC Fixed Depreciation EBIT Pretax

price costs breakeven operating
cash flow

20
 breakeven
A $250 $160 $15,000 $3,000 200 167
B $55 $10 $1,100 $200 29 24
C $10 $1.50 $100 $100 24 12

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

LO 4

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.

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

rationing process?

LO 5

21
 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

12.13 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?

LO 1

Solution:

Since depreciation and amortization are noncash items, the manufacturing firm would

have the greatest discrepancy between FCF and EBIT.

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

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

22
 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.

LO 1

Solution:

The forecasted EBIT for the firm is:

Revenue $110 × 15,000 = $1,650,000

VC $80 × 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.

12.15 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
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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?

LO 1

Solution:

The forecasted EBIT for the firm is:

Revenue $15 × 1,000 = $15,000

VC $10 × 1,000 = 10,000

FC 4,000

EBIT $ 1,000

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

bulbs.

12.16. Cash Flow DOL: The pretax operating cash flow of Memphis Motors declined so

much during the recession of 2008 and 2009 that the company almost defaulted on its

debt. The owner of the company wants to change the cost structure of his business so

that this does not happen again. He has been able to reduce fixed costs from $500,000

to $300,000 and, in doing so, reduce the Cash Flow DOL for Memphis Motors from 3.0

to 2.2 with sales of $1,000,000 and pretax operating cash flow of $250,000. If sales

declined by 20 percent from this level, how much more pretax operating cash flow

would Memphis Motors have with the new cost structure than under the old?.
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 LO 2

Solution:

With the old cost structure, pretax operating cash flow would decline by 3.0 × 20% =

60% to $100,000 ($250,000 × (1 – 0.6)).

With the new cost structure, pretax operating cash flow would decline by 2.2 × 20% =

44% to $140,000 ($250,000 × (1 – 0.44)).

Memphis Motors would have $40,000 more pretax operating cash flow under

the cost new structure.

12.17 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?

LO 2

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.

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 Use the following information for Problems 12-18, 12-19, and 12-20:

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 million and a depreciation expense of $300,000 per year, while those expenses

would be $500,000 and $100,000 in the small factory.

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

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

LO 3

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

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

which the accounting operating profits the same, regardless of the factory choice.

LO 3

Solution:

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

CO = 340,000 units

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

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

LO 3

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 = $2,0000,000 / ($10 – $2.5) = 266,667 units

27
 and the cash flow break-even for the small factory is:

CF Break-even = $500,000 / ($10 – $7.5) = 200,000 units

12.21 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 above cash flow break-even.

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

LO 3

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.

12.22 Sensitivity and scenario analyses: Sensitivity analysis and scenario analysis are

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

different scenarios on a project.

LO 4

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

28
 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.

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

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

LO 4

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.

12.24 Scenario analysis: Chip’s Home Brew Whiskey forecasts that if the firm sells each bottle

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

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whereas sales will be 90 percent as high if the price is raised 10 percent. 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 has a 30 percent

marginal tax rate. Management anticipates an increased working capital need of $3,000

for the year. What will be the effect of a price increase on the firm’s FCF for the year?

LO 4

Solution:

If the firm increases its price to $22 per bottle, then it will sell 0.9 × 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 × 13,500)

VC 150,000 135,000 (10 × 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

30
 By increasing the price of a bottle by 10 percent, the FCF increases from $38,000 to

$46,400.

12.25 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?

LO 4

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.

12.26 Profitability index: Suppose that you could invest in the following projects but had only

$30,000 to invest. How would you make your decision and which projects would you

invest in?

31
 Project Cost ($) NPV ($)

A $ 8,000 $4,000

B 11,000 7,000

C 9,000 5,000

D 7,000 4,000

LO 5

Solution:

One would compute the Profitability index for each of the projects as foloows:

The profitability indexes of the projects are:

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

NPV is $16,000.

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12.27 Profitability index: Suppose that you face the same projects as in the previous problem,

but have only $25,000 to invest. Which projects would you chose?

LO 5

Solution:

The profitability indexes of the projects are:

A: 1.50; 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

12.28 Mick’s Soft Lemonade is starting to develop a new product for which the cash fixed

costss are expected to be $80,000. The project’s EBIT is $100,000, and the Accounting

DOL will be 2.0. What is the Cash Flow DOL for the firm?
33
 LO 2

Solution:

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

= 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

12.29 If a firm has a 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.

LO 2

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

34
 zero. Therefore, if depreciation and amortization is positive, then Cash Flow DOL must

be less than Accounting DOL.

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

to increase by 10 percent, then 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?

LO 2

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 + ($100,000 + 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.

35
12.31 If a firm’s costs (both variable as well as fixed) are known with certainty, then what are

the only two sources of volatility for a firm’s operating profits or its operating cash

flows?

LO 1

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.

12.32 In most circumstances, given the choice between a higher fixed cost structure and a

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

margin?

LO 1

Solution:

36
 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.

12.33 Using the same logic as with the accounting break-even calculation in Problem 12.19,

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

where the pretax operating cash flow is the same whether the firm chooses the large or

small factory.

LO 3

Solution:

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

follows:

Eliminating D&A, since D&A are non-cash charges, gives us

37
12.34. Scenario Analysis: You are the project manager for Eagle Golf Corporation. You are

considering manufacturing a new golf wedge with a unique groove design. You have put

together the estimates in the following table about the potential demand for the new club, and

the associated selling and manufacturing prices. You expect to sell the club for five years. The

equipment required for the manufacturing process can be depreciated using straight line

depreciation over five years and will have a zero salvage value at the end of the project’s life.

No additional capital expenditures are required. No new working capital is needed for the

project. The required return for projects of this type is 12 percent and the company has a 35

percent marginal tax rate. You estimate that there is a 50 percent chance the project will

achieve the expected sales and a 25 percent chance of achieving either the weak or strong sales

outcomes. Should you recommend the project?

Strong Expecte Weak

Sales d Sales Sales
Units sold 15,000 10,000 7,000
Selling price per unit $130 $120 $110
Variable costs per unit $70 $65 $60
Fixed Costs $1,290 $1,290, $1,29
,000 000 0,000
Initial Investment $1,400 $1,400, $1,40
,000 000 0,000

LO 4

Solution (Excel Model with Solution in Separate File):

Expected unit sales = (0.25 × 15,000) + (0.50 × 10,000) + (0.25 × 7,000) = 10,500
units

38
 Expected unit price = (0.25 × $130) + (0.50 × $120) + (0.25 × $110) = $120

Expected unit variable cost = (0.25 × $70) + (0.50 × $65) + (0.25 × $60) = $65

Based on the expect values outlined below, the NPV of the project is -$279,365.20 so it
should not be accepted.

12.35 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

39
 3 6,000 7,000
4 2,000 7,000

The cost of capital for both projects is 10 percent. Calculate 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?

LO 5

Solution:

The PI calculations are as follows:

The NPV is needed first:

Both methods rank Project X over Project Y. 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 PI at r = 10%, which in this case

is Project X. W.

40
 CFA Problems

12.36 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. 1.00

b. 1.08

c. 1.16

d. 1.25

LO 5

Solution

d is correct.

The present value of future cash flows is”

The profitability index is:

12.37. 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 7. The required rate of return is 10 percent. What is

the investment’s PI?

a. 1.19

41
 b. 1.33

c. 1.56

d. 1.75

LO 5

Solution

c is correct.

=$ 585.53 million

=1.56

12.38. Operating leverage is a measure of the

a. 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.

LO 2

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.

42
 12.39. 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.

LO 1

Solution:

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.

43
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 percent increase in

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

Solution:

The forecasted EBIT for the firm is:

Revenue $15 × 25,000 = $375,000

VC $3 × 25,000 = 75,000

FC + D&A 80,000

EBIT $220,000

The actual EBIT for the firm is:

Revenue $15 × 27,000 = $405,000

VC $3 × 27,000 = 81,000
44
 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. Cash fixed costs are

expected to be $120,000, the projected EBIT for the project is $130,000, and the

Accounting DOL is forecast to be 2.5. What will be the depreciation and amortization for

the firm, as well as Cash Flow DOL?

Solution:

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

= 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

45
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

46
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 the firm sells each bottle of

NitroStrength for $10, then the demand for the product will be 85,000 bottles per year.

Management expects that if it sells NitroStrength for a price that is 10 percent higher,

then it will sell 75 percent as many bottles of the sauce. 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 has a 40 percent marginal tax rate.

Management anticipates an increased working capital need of $2,000 for the year. What

effect would the price increase have 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.

47
 Normal Price Hike

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

VC 340,000 255,000 (4 × 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.

48