Credit Assignment 4 Mini Case: Kelowna Microchips Inc.

Below is Credit Assignment 4.  Please answer the assignment questions as directed.

Mini Case: Kelowna Microchips Inc.

•          Page 693 in the text. Required: Complete the 5 questions

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MINI CASE
Kelowna Microchips Inc.
Kelowna Microchips Inc. (KMI) is a small company founded 15 years ago by electronics engineers Justin Langer and
Suzanne Maher. KMI manufactures integrated circuits to capitalize on the complex mixed-signal design technology
and has recently entered the market for frequency timing generators, or silicon timing devices, which provide the
timing signals or “clocks” necessary to synchronize electronic systems. Its clock products originally were used in PC
video graphics applications, but the market subsequently expanded to include motherboards, PC peripheral devices,
and other digital consumer electronics, such as digital television boxes and game consoles. KMI also designs and
markets custom application specific integrated circuits (ASICs) for industrial customers. The ASIC’s design combines
analog and digital or mixed-signal technology. In addition to Justin and Suzanne, Andrew Keegan, who provided
capital for the company, is the third primary owner. Each owns 25 percent of the one million shares outstanding. The
company has several other individuals, including current employees, who own the remaining shares.
Recently, the company designed a new computer motherboard. The company’s design is both more efficient and less
expensive to manufacture, and the KMI design is expected to become standard in many personal computers. After
investigating the possibility of manufacturing the new motherboard, KMI determined that the costs involved in building
a new plant would be prohibitive. The owners also decided that they were unwilling to bring in another large outside
owner. Instead, KMI sold the design to an outside firm. The sale of the motherboard design was completed for an
after-tax payment of $30 million.
QUESTIONS
1.
2.
3.
4.
5.
Justin believes the company should use the extra cash to pay a special one-time dividend. How will this
proposal affect the stock price? How will it affect the value of the company?
Suzanne believes the company should use the extra cash to pay off debt and upgrade and expand its
existing manufacturing capability. How would Suzanne’s proposals affect the company?
Andrew favours a share repurchase. He argues that a repurchase will increase the company’s P/E ratio,
return on assets, and return on equity. Are his arguments correct? How will a share repurchase affect the
value of the company?
Another option discussed by Justin, Suzanne, and Andrew would be to begin a regular dividend payment to
shareholders. How would you evaluate this proposal?
One way to value a share of stock is the dividend growth, or growing perpetuity, model. Consider the
following. The dividend payout ratio is 1 minus b, where b is the “retention” or “plowback” ratio. So, the
dividend next year will be the earnings next year, E1, times 1 minus the retention ratio. The most commonly
used equation to calculate the growth rate is the return on equity times the retention ratio. Substituting these
relationships into the dividend growth model, we get the following equation to calculate the price of a share
of stock today:
(Upper P 0 equals, Start-Fraction, Upper E 1, left-parenthesis, 1 minus b, right-parenthesis, Over, Upper R
Subscript s Baseline minus ROE times b, End-Fraction.)
where Rs = Expected rate of return
What are the implications of this result in terms of whether the company should pay a dividend or upgrade
and expand its manufacturing capability? Explain.
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Village Roadshow Pictures Alamy Images
In February 2014, the movie Winter’s Tale, a romantic fantasy film based on Mark Helprin’s famous novel,
was released to negative reviews from both critics and general audiences. One critic wrote, “this is one of
those deals where all the ingredients are Grade A, but the final product is a dud.” Others were even harsher,
saying, “one leaves the film with great relief that it is over,” and, “it would have been better if Winter’s Tale
remained unfilmed.”
Looking at the numbers, Village Roadshow Pictures spent close to $60 million making the movie.
Unfortunately for Village Roadshow, Winter’s Tale crashed and burned, pulling in only $30 million
worldwide. In fact, about four of ten movies lose money at the box office, although DVD sales often help the
final tally. Of course, there are also movies that do quite well. Also in 2014, the Lionsgate movie The Hunger
Games: Mockingjay – Part 1 raked in about $752 million worldwide at a production cost of $125 million.
Obviously, Village Roadshow didn’t plan to lose $30 million or so on Winter’s Tale, but it happened. As the
box office spinout of Winter’s Tale illustrates, projects don’t always go as companies think they will. This
chapter explores how this can happen, and what companies can do to analyze and possibly avoid these
situations.
LEARNING OBJECTIVES
After studying this chapter, you should understand:
1.
2.
3.
4.
5.
LO1 How to perform and interpret a sensitivity analysis for a proposed investment.
LO2 How to perform and interpret a scenario analysis for a proposed investment.
LO3 How to determine and interpret cash, accounting, and financial break-even points.
LO4 How the degree of operating leverage can affect the cash flows of a project.
LO5 How managerial options affect net present value.
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In our previous chapter, we discussed how to identify and organize the relevant cash flows for capital
investment decisions. Our primary interest there was in coming up with a preliminary estimate of the net
present value for a proposed project. In this chapter, we focus on assessing the reliability of such an estimate
and avoiding forecasting risk, the possibility that errors in projected cash flow may lead to incorrect
decisions.
We begin by discussing the need for an evaluation of cash flow and NPV estimates. We go on to develop
some tools that are useful for doing so. We also examine complications and concerns that can arise in project
evaluation.
11.1 | Evaluating NPV Estimates
As we discussed in Chapter 9, an investment has a positive net present value if its market value exceeds its
cost. Such an investment is desirable because it creates value for its owner. The primary problem in
identifying such opportunities is that most of the time we can’t actually observe the relevant market value.
Instead, we estimate it. Having done so, it is only natural to wonder whether our estimates are at least close to
the true values or whether we have fallen prey to forecasting risk. We consider this question next.
The Basic Problem
Suppose we are working on a preliminary DCF analysis along the lines we described in the previous chapter.
We carefully identify the relevant cash flows, avoiding such things as sunk costs, and we remember to
consider working capital requirements. We add back any depreciation, we account for possible erosion, and
we pay attention to opportunity costs. Finally, we double-check our calculations, and, when all is said and
done, the bottom line is that the estimated NPV is positive.
Now what? Do we stop here and move on to the next proposal? Probably not. The fact that the estimated
NPV is positive is definitely a good sign, but, more than anything, this tells us we need to take a closer look.
If you think about it, there are two circumstances under which a discounted cash flow analysis could lead us
to conclude that a project has a positive NPV. The first possibility is that the project really does have a
positive NPV. That’s the good news. The bad news is the second possibility; a project may appear to have a
positive NPV because our estimate is inaccurate.
Notice that we could also err in the opposite way. If we conclude that a project has a negative NPV when the
true NPV is positive, we lose a valuable opportunity.
Projected versus Actual Cash Flows
There is a somewhat subtle point we need to make here. When we say something like, “the projected cash
flow in Year 4 is $700,” what exactly do we mean? Does this mean we think the cash flow will actually be
$700? Not really. It could happen, of course, but we would be surprised to see it turn out exactly that way.
The reason is that the $700 projection is based only on what we know today. Almost anything could happen
between now and then to change that cash flow.
Loosely speaking, we really mean that if we took all the possible cash flows that could occur in four years
and averaged them, the result would be $700. In other words, $700 is the expected cash flow. So, we don’t
really expect a projected cash flow to be exactly right in any one case. What we do expect is that, if we
evaluate a large number of projects, our projections are right on the average.
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Forecasting Risk
The key inputs into a DCF analysis are expected future cash flows. If these projections are seriously in error,
we have a classic GIGO (garbage in, garbage out) system. In this case, no matter how carefully we arrange
the numbers and manipulate them, the resulting answer can still be grossly misleading. This is the danger in
using a relatively sophisticated technique like DCF. It is sometimes easy to get caught up in number
crunching and forget the underlying nuts-and-bolts economic reality.
As stated above, the possibility that we can make a bad decision because of errors in the projected cash flows
is called forecasting risk (or estimation risk). Because of forecasting risk, there is the danger that we think a
project has a positive NPV when it really does not. How is this possible? It happens if we are overly
optimistic about the future and, as a result, our projected cash flows don’t realistically reflect the possible
future cash flows.
So far, we have not explicitly considered what to do about the possibility of errors in our forecasts, so one of
our goals in this chapter is to develop some tools that are useful in identifying areas where potential errors
exist and where they might be especially damaging. In one form or another, we try to assess the economic
reasonableness of our estimates. We also consider how much damage can be done by errors in those
estimates.
Sources of Value
The first line of defence against forecasting risk is simply to ask, what is it about this investment that leads to
a positive NPV? We should be able to point to something specific as the source of value. For example, if the
proposal under consideration involved a new product, we might ask questions such as, are we certain that our
new product is significantly better than that of the competition? Can we truly manufacture at lower cost, or
distribute more effectively, or identify undeveloped market niches, or gain control of a market?
These are just a few of the potential sources of value. There are many others. For example, in 2014, Google
Inc. significantly reduced the prices of its Google Drive services. Why? The answer is that the affordable or
even free cloud storage services would not only increase the user base of Google Drive, but also fuel growth
in other Google products that are highly integrated with Google Drive, such as Gmail and Google Docs. A
key factor to keep in mind is the degree of competition in the market. It is a basic principle of economics that
positive NPV investments are rare in a highly competitive environment. Therefore, proposals that appear to
show significant value in the face of stiff competition are particularly troublesome, and the likely reaction of
the competition to any innovations must be closely examined.
Similarly, beware of forecasts that simply extrapolate past trends without taking into account changes in
technology or human behaviour. Forecasts similar to the following fall prey to the forecaster’s trap:
In 1860, several forecasters were secured from the financial community by the city of New York to forecast
the future level of pollution caused by the use of chewing tobacco and horses… . In 1850, the spit level in the
gutter and manure level in the middle of the road had both averaged half an inch (approximately 1 cm). By
1860, each had doubled to a level of one inch. Using this historical growth rate, the forecasters projected
levels of two inches by 1870, four inches by 1880 and 1,024 inches (22.5 metres) by 1960!1
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To avoid the forecaster’s trap, the point to remember is that positive NPV investments are probably not all
that common, and the number of positive NPV projects is almost certainly limited for any given firm. If we
can’t articulate some sound economic basis for thinking ahead of time that we have found something special,
the conclusion that our project has a positive NPV should be viewed with some suspicion.
Concept Questions
1. What is forecasting risk? Why is it a concern for the financial manager?
2. What are some potential sources of value in a new project?
1 This apocryphal example comes from L. Kryzanowski, T. Minh-Chau, and R. Seguin, Business Solvency
Risk Analysis (Montreal: Institute of Canadian Bankers, 1990), chap. 5, p. 10.
11.3 | Break-Even Analysis
It frequently turns out that the crucial variable for a project is sales volume. If we are thinking of a new
product or entering a new market, for example, the hardest thing to forecast accurately is how much we can
sell. For this reason, in order to control forecasting risk, sales volume is usually analyzed more closely than
other variables.
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Break-even analysis is a popular and commonly used tool for analyzing the relationships between sales
volume and profitability. There are a variety of different break-even measures, and we have already seen
several types. All break-even measures have a similar goal. Loosely speaking, we are always asking, how bad
do sales have to get before we actually begin to lose money? Implicitly, we are also asking, is it likely that
things will get that bad? To get started on this subject, we discuss fixed and variable costs.
Fixed and Variable Costs
In discussing break-even, the difference between fixed and variable costs becomes very important. As a
result, we need to be a little more explicit about the difference than we have been so far.
VARIABLE COSTS By definition, variable costs change as the quantity of output changes, and they are
zero when production is zero. For example, direct labour costs and raw material costs are usually considered
variable. This makes sense because, if we shut down operations tomorrow, there will be no future costs for
labour or raw materials.
We assume that variable costs are a constant amount per unit of output. This simply means that total variable
cost is equal to the cost per unit multiplied by the number of units. In other words, the relationship between
total variable cost (VC), cost per unit of output (v), and total quantity of output (Q) can be written simply as:
For example, suppose that v is $2 per unit. If Q is 1000 units, what will VC be?
Similarly, if Q is 5000 units, then VC is 5000 × $2 = $10,000. Figure 11.2 illustrates the relationship between
output level and variable costs in this case. In Figure 11.2, notice that increasing output by one unit results in
variable costs rising by $2, so the “rise over the run” (the slope of the line) is given by $2∕1 = $2.
Click here for a description of Figure 11.2: Output level and total costs.
FIGURE 11.2
FIGURE 11.2Output level and total costs
FIXED COSTS By definition, fixed costs do not change during a specified time period. So, unlike variable
costs, they do not depend on the amount of goods or services produced during a period (at least within some
range of production). For example, the lease payment on a production facility and the company president’s
salary are fixed costs, at least over some period.
Naturally, fixed costs are not fixed forever. They are fixed only during some particular time, say a quarter or a
year. Beyond that time, leases can be terminated and executives retired. More to the point, any fixed cost can
be modified or eliminated given enough time; so, in the long run, all costs are variable.
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Notice that during the time that a cost is fixed, that cost is effectively a sunk cost because we are going to
have to pay it no matter what.
TOTAL COSTS Total costs (TC) for a given level of output are the sum of variable costs (VC) and fixed costs
(FC):
So, for example, if we have a variable cost of $3 per unit and fixed costs of $8,000 per year, our total cost is:
If we produce 6,000 units, our total production cost would be $3 × 6,000 + $8,000 = $26,000. At other
production levels, we have:
Click here for a description of Table: Total Production Cost at Various Production Levels.
By plotting these points in Figure 11.3, we see that the relationship between quantity produced and total cost
is given by a straight line. In Figure 11.3, notice that total costs are equal to fixed costs when sales are zero.
Beyond that point, every one-unit increase in production leads to a $3 increase in total costs, so the slope of
the line is 3. In other words, the marginal cost or incremental cost of producing one more unit is $3.
Click here for a description of Figure 11.3: Output Level and Variable Costs.
FIGURE 11.3
FIGURE 11.3Output level and variable costs
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Accounting Break-Even
The most widely used measure of break-even is accounting break-even. The accounting break-even point is
simply the sales level that results in a zero project net income.
To determine a project’s accounting break-even, we start with some common sense. Suppose we retail oneterabyte Blu-ray discs for $5 a piece. We can buy Blu-ray discs from a wholesale supplier for $3 a piece. We
have accounting expenses of $600 in fixed costs and $300 in depreciation. How many Blu-ray discs do we
have to sell to break even; that is, for net income to be zero?
For every Blu-ray disc we sell, we pick up $5 − 3 = $2 toward covering our other expenses. We have to cover
a total of $600 + 300 = $900 in accounting expenses, so we obviously need to sell $900∕$2 = 450 Blu-ray
discs. We can check this by noting that, at a sales level of 450 units, our revenues are $5 × 450 = $2,250 and
our variable costs are $3 × 450 = $1,350. The income statement is thus:
Click here for a description of Table: Income Statement with a Sales Level of 450 Units.
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Remember, since we are discussing a proposed new project, we do not consider any interest expense in
calculating net income or cash flow from the project. Also, notice that we include depreciation in calculating
expenses here, even though depreciation is not a cash outflow. That is why we call it accounting break-even.
Finally, notice that when net income is zero, so are pre-tax income and, of course, taxes. In accounting terms,
our revenues are equal to our costs, so there is no profit to tax.
Figure 11.4 is another way to see what is happening. This figure looks like Figure 11.3 except that we add a
line for revenues. As indicated, total revenues are zero when output is zero. Beyond that, each unit sold
brings in another $5, so the slope of the revenue line is 5.
Click here for a description of Figure 11.4: Accounting break-even.
FIGURE 11.4
FIGURE 11.4Accounting break-even
From our preceding discussion, we break even when revenues are equal to total costs. The line for revenues
and the line for total cost cross right where output is 450 units. As illustrated, at any level below 450, our
accounting profit is negative and, at any level above 450, we have a positive net income.
Accounting Break-Even: A Closer Look
In our numerical example, notice that the break-even level is equal to the sum of fixed costs and depreciation
divided by price per unit less variable costs per unit. This is always true. To see why, we recall the following
set of abbreviations for the different variables:
P = Selling price per unit
v = Variable cost per unit
Q = Total units sold
FC = Fixed costs
D = Depreciation
t = Tax rate
VC = Variable cost in dollars
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Project net income is given by:
Click here for a description of Equation: Project Net Income.
From here, it is not difficult to calculate the break-even point. If we set this net income equal to zero, we get:
Divide both sides by (1 − t) to get:
As we have seen, this says, when net income is zero, so is pre-tax income. If we recall that S = P × Q and VC
= v × Q, we can rearrange this to solve for the break-even level:
[11.1]
Click here for a description of Formula 11.1.
This is the same result we described earlier.
Uses for the Accounting Break-Even
Why would anyone be interested in knowing the accounting break-even point? To illustrate how it can be
useful, suppose we are a small specialty ice cream manufacturer in Vancouver with a strictly local
distribution. We are thinking about expanding into new markets. Based on the estimated cash flow, we find
that the expansion has a positive NPV.
Going back to our discussion of forecasting risk, it is likely that what makes or breaks our expansion is sales
volume. The reason is that, in this case at least, we probably have a fairly good idea of what we can charge
for the ice cream. Further, we know relevant production and distribution costs with a fair degree of accuracy
because we are already in the business. What we do not know with any real precision is how much ice cream
we can sell.
Given the costs and selling price, however, we can immediately calculate the break-even point. Once we have
done so, we might find that we need to get 30 percent of the market just to break even. If we think that this is
unlikely to occur because, for example, we only have 10 percent of our current market, we know that our
forecast is questionable and there is a real possibility that the true NPV is negative.
On the other hand, we might find that we already have firm commitments from buyers for about the breakeven amount, so we are almost certain that we can sell more. Because the forecasting risk is much lower, we
have greater confidence in our estimates. If we need outside financing for our expansion, this break-even
analysis would be useful in presenting our proposal to our banker.
COMPLICATIONS IN APPLYING BREAK-EVEN ANALYSIS Our discussion ignored several
complications you may encounter in applying this useful tool. To begin, it is only in the short run that
revenues and variable costs fall along straight lines. For large increases in sales, price may decrease with
volume discounts while variable costs increase as production runs up against capacity limits. If you have
sufficient data, you can redraw cost and revenue as curves. Otherwise, remember that the analysis is most
accurate in the short run.
Further, while our examples classified costs as fixed or variable, in practice some costs are semivariable (i.e.,
partly fixed and partly variable). A common example is telephone expense, which breaks down into a fixed
charge plus a variable cost depending on the volume of calls. In applying break-even analysis, you have to
make judgments on the breakdown.
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Concept Questions
1. How are fixed costs similar to sunk costs?
2. What is net income at the accounting break-even point? What about taxes?
3. Why might a financial manager be interested in the accounting break-even point?
11.4 | Operating Cash Flow, Sales Volume, and Break-Even
Accounting break-even is one tool that is useful for project analysis. Ultimately, however, we are more
interested in cash flow than accounting income. So, for example, if sales volume is the critical variable in
avoiding forecasting risk, we need to know more about the relationship between sales volume and cash flow
than just the accounting break-even.
Our goal in this section is to illustrate the relationship between operating cash flow and sales volume. We also
discuss some other break-even measures. To simplify matters somewhat, we ignore the effect of taxes.6 We
start by looking at the relationship between accounting break-even and cash flow.
Accounting Break-Even and Cash Flow
Now that we know how to find the accounting break-even, it is natural to wonder what happens with cash
flow. To illustrate, suppose that Victoria Sailboats Limited is considering whether to launch its new Monaclass sailboat. The selling price would be $40,000 per boat. The variable costs would be about half that, or
$20,000 per boat, and fixed costs will be $500,000 per year.
THE BASE CASE The total investment needed to undertake the project is $3.5 million for leasehold
improvements to the company’s factory. This amount will be depreciated straight-line to zero over the fiveyear life of the equipment. The salvage value is zero, and there are no working capital consequences. Victoria
has a 20 percent required return on new projects.
Based on market surveys and historical experience, Victoria projects total sales for the five years at 425 boats,
or about 85 boats per year. Should this project be launched?
To begin (ignoring taxes), the operating cash flow at 85 boats per year is:
Click here for a description of Equation: Operating Cash Flow.
At 20 percent, the five-year annuity factor is 2.9906, so the NPV is:
Click here for a description of Equation: NPV if Five-Year Annuity Factor is 2.9906.
In the absence of additional information, the project should be launched.
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CALCULATING THE ACCOUNTING BREAK-EVEN LEVEL To begin looking a little more closely at
this project, you might ask a series of questions. For example, how many new boats does Victoria need to sell
for the project to break even on an accounting basis? If Victoria does break even, what would be the annual
cash flow from the project? What would be the return on the investment?
Before fixed costs and depreciation are considered, Victoria generates $40,000 − 20,000 = $20,000 per boat
(this is revenue less variable cost). Depreciation is $3,500,000∕5 = $700,000 per year. Fixed costs and
depreciation together total $1.2 million, so Victoria needs to sell (FC + D)∕(P − v) = $1.2 million∕$20,000 =
60 boats per year to break even on an accounting basis. This is 25 boats fewer than projected sales; so,
assuming that Victoria is confident that its projection is accurate to within, say, 15 boats, it appears unlikely
that the new investment will fail to at least break even on an accounting basis.
To calculate Victoria’s cash flow, we note that if 60 boats are sold, net income is exactly zero. Recalling from
our previous chapter that operating cash flow for a project can be written as net income plus depreciation (the
bottom-up definition), the operating cash flow is obviously equal to the depreciation, or $700,000 in this case.
The internal rate of return would be exactly zero (why?).
The bad news is that a project that just breaks even on an accounting basis has a negative NPV and a zero
return. For our sailboat project, the fact that we would almost surely break even on an accounting basis is
partially comforting since our downside risk (our potential loss) is limited, but we still don’t know if the
project is truly profitable. More work is needed.
SALES VOLUME AND OPERATING CASH FLOW At this point, we can generalize our example and
introduce some other break-even measures. As we just discussed, we know that, ignoring taxes, a project’s
operating cash flow (OCF) can be written simply as EBIT plus depreciation:7
[11.2]
Click here for a description of Formula 11.2.
For the Victoria Sailboats project, the general relationship between operating cash flow and sales volume is
thus:
Click here for a description of Equation: Operating Cash Flow and Sales Volume Relationship.
What this tells us is that the relationship between operating cash flow and sales volume is given by a straight
line with a slope of $20,000 and a y-intercept of −$500,000. If we calculate some different values, we get:
Click here for a description of Table: Operating Cash Flow and Sales Volume Relationship with Different
Values.
These points are plotted in Figure 11.5. In Figure 11.5, we have indicated three different break-even points.
We already covered the accounting break-even. We discuss the other two next.
Click here for a description of Figure 11.5: Operating Cash Flow and Sales Volume.
FIGURE 11.5
FIGURE 11.5Operating cash flow and sales volume
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Cash Flow and Financial Break-Even Points
We know that the relationship between operating cash flow and sales volume (ignoring taxes) is:
If we rearrange this and solve it for Q, we get:
[11.3]
This tells us what sales volume (Q) is necessary to achieve any given OCF, so this result is more general than
the accounting break-even. We use it to find the various break-even points in Figure 11.5.
CASH BREAK-EVEN We have seen that our sailboat project that breaks even on an accounting basis has a
net income of zero, but it still has a positive cash flow. At some sales level below the accounting break-even,
the operating cash flow actually goes negative. This is a particularly unpleasant occurrence. If it happens, we
actually have to supply additional cash to the project just to keep it afloat.
To calculate the cash break-even (the point where operating cash flow is equal to zero), we put in a zero for
OCF:
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Victoria must therefore sell 25 boats to cover the $500,000 in fixed costs. As we show in Figure 11.5, this
point occurs right where the operating cash flow line crosses the horizontal axis.
In this example, cash break-even is lower than accounting break-even. Equation 11.3 shows why; when we
calculated accounting break-even we substituted depreciation of $700,000 for OCF. The formula for cash
break-even sets OCF equal to zero. Figure 11.5 shows that accounting break-even is 60 boats and cash breakeven, 25 boats. Accounting break-even is 35 boats higher. Since Victoria generates a $20,000 contribution per
boat, the difference exactly covers the depreciation of $700,000 = 35 × $20,000.
This analysis also shows that cash break-even does not always have to be lower than accounting break-even.
To see why, suppose that Victoria had to make a cash outlay of $1 million for working capital in Year 1.
Accounting break-even remains at 60 boats. The new cash break-even is 75 boats:
Click here for a description of Equation: New Cash Break-Even is 75 Boats.
In general, retail firms and other companies that experience substantial needs for working capital relative to
depreciation expenses have cash break-evens greater than accounting break-evens.
Regardless of whether the cash break-even point is more or less than the accounting break-even, a project that
just breaks even on a cash flow basis can cover its own fixed operating costs, but that is all. It never pays back
anything, so the original investment is a complete loss (the IRR is −100 percent).
FINANCIAL BREAK-EVEN The last case we consider is financial break-even, the sales level that results
in a zero NPV. To the financial manager, this is the most interesting case. What we do is first determine what
operating cash flow has to be for the NPV to be zero. We then use this amount to determine the sales volume.
To illustrate, recall that Victoria requires a 20 percent return on its $3,500,000 investment. How many
sailboats does Victoria have to sell to break even once we account for the 20 percent per year opportunity
cost?
The sailboat project has a five-year life. The project has a zero NPV when the present value of the operating
cash flow equals the $3,500,000 investment. Since the cash flow is the same each year, we can solve for the
unknown amount by viewing it as an ordinary annuity. The five-year annuity factor at 20 percent is 2.9906,
and the OCF can be determined as follows:
Click here for a description of Equation: OCF where the Five-Year Annuity Factor at 20% equaling 2.9906.
Victoria thus needs an operating cash flow of $1,170,000 each year to break even. We can now plug this OCF
into the equation for sales volume:
So Victoria needs to sell about 84 boats per year. This is not good news.
As indicated in Figure 11.5, the financial break-even is substantially higher than the accounting break-even
point. This is often the case. Moreover, what we have discovered is that the sailboat project has a substantial
degree of forecasting risk. We project sales of 85 boats per year, but it takes 84 just to earn our required
return.
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CONCLUSION Overall, it seems unlikely that the Victoria Sailboats project would fail to break even on an
accounting basis. However, there appears to be a very good chance that the true NPV is negative. This
illustrates the danger in just looking at the accounting break-even.
Victoria can learn this lesson from the U.S. government. In the early 1970s, the U.S. Congress voted a
guarantee for Lockheed Corporation, the airplane manufacturer, based on analysis that showed the L1011TriStar would break even on an accounting basis. It subsequently turned out that the financial break-even
point was much higher.
What should Victoria Sailboats do? Is the new project “all wet”? The decision at this point is essentially a
managerial issue—a judgment call. The crucial questions are as follows:
1. How much confidence do we have in our projections? Do we think that forecasting risk is too high?
2. How important is the project to the future of the company?
3. How badly will the company be hurt if sales do turn out low?
What options are available to the company?
We consider questions such as these in a later section. For future reference, our discussion of different breakeven measures is summarized in Table 11.2.
TABLE 11.2
Summary of break-even measures
Click here for a description of Table 11.2: Summary of Break-Even Measures.
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Concept Questions
1. If a project breaks even on an accounting basis, what is its operating cash flow?
2. If a project breaks even on a cash basis, what is its operating cash flow?
3. If a project breaks even on a financial basis, what do you know about its discounted payback?
6 This is a minor simplification because the firm pays no taxes when it just breaks even in the accounting
sense. We also use straight-line depreciation, realistic in this case for leasehold improvements, for simplicity.
7 With no taxes, depreciation drops out of cash flow because there is no tax shield.
11.5 | Operating Leverage
We have discussed how to calculate and interpret various measures of break-even for a proposed project.
What we have not explicitly discussed is what determines these points and how they might be changed. We
now turn to this subject.
The Basic Idea
Operating leverage is the degree to which a project or firm is committed to fixed production costs. A firm
with low operating leverage has low fixed costs (as a proportion of total costs) compared to a firm with high
operating leverage. Generally, projects with a relatively heavy investment in plant and equipment have a
relatively high degree of operating leverage. Such projects are said to be capital intensive. Airlines and hotels
are two industries that have high operating leverage.
Any time we are thinking about a new venture, there are normally alternative ways of producing and
delivering the product. For example, Victoria Sailboats can purchase the necessary equipment and build all
the components for its sailboats in-house. Alternatively, some of the work could be farmed out to other firms.
The first option involves a greater investment in plant and equipment, greater fixed costs and depreciation,
and, as a result, a higher degree of operating leverage.
Implications of Operating Leverage
Regardless of how it is measured, operating leverage has important implications for project evaluation. Fixed
costs act like a lever in the sense that a small percentage change in operating revenue can be magnified into a
large percentage change in operating cash flow and NPV. This explains why we call it operating leverage.
The higher the degree of operating leverage, the greater is the potential danger from forecasting risk. The
reason is that relatively small errors in forecasting sales volume can get magnified or “levered up” into large
errors in cash flow projections.
From a managerial perspective, one way of coping with highly uncertain projects is to keep the degree of
operating leverage as low as possible.8 This generally has the effect of keeping the break-even point
(however measured) at its minimum level. We illustrate this point after discussing how to measure operating
leverage.
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Measuring Operating Leverage
One way of measuring operating leverage is to ask, if the quantity sold rises by 5 percent what will be the
percentage change in operating cash flow? In other words, the degree of operating leverage (DOL) is
defined such that
Based on the relationship between OCF and Q, DOL can be written as:9
Also, based on our definition of OCF:
Thus, DOL can be written as:10
The ratio FC∕OCF simply measures fixed costs as a percentage of total operating cash flow. Notice that zero
fixed costs would result in a DOL of 1, implying that changes in quantity sold would show up one for one in
operating cash flow. In other words, no magnification or leverage effect would exist.
To illustrate this measure of operating leverage, we go back to the Victoria Sailboats project. Fixed costs were
$500 and (P − v) was $20, so OCF was:
Suppose Q is currently 50 boats. At this level of output, OCF is −$500 + 1,000 = $500.
If Q rises by 1 unit to 51, then the percentage change in Q is (51 − 50)∕50 = .02, or 2%. OCF rises to $520, a
change of (P − v) = $20. The percentage change in OCF is ($520 − 500)∕500 = .04, or 4%. So a 2 percent
increase in the number of boats sold leads to a 4 percent increase in operating cash flow. The degree of
operating leverage must be exactly 2.00. We can check this by noting that:
Click here for a description of Equation: Upper D Upper O Upper L equals 2.00. Upper D Upper O Upper L
equals 1 plus upper F upper C slash Upper O Upper C Upper F equals 1 plus $500 slash $500 equals 2
This verifies our previous calculations.
Our formulation of DOL depends on the current output level, Q. However, it can handle changes from the
current level of any size, not just one unit. For example, suppose Q rises from 50 to 75, a 50 percent increase.
With DOL equal to 2, operating cash flow should increase by 100 percent, or exactly double. Does it? The
answer is yes, because, at a Q of 75, OCF is:
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Notice that operating leverage declines as output (Q) rises. For example, at an output level of 75, we have:
The reason DOL declines is that fixed costs, considered as a percentage of operating cash flow, get smaller
and smaller, so the leverage effect diminishes.11
What do you think DOL works out to at the cash break-even point, an output level of 25 boats? At the cash
break-even point, OCF is zero. Since you cannot divide by zero, DOL is undefined.
EXAMPLE 11.1 Operating Leverage
The Huskies Corporation currently sells gourmet dog food for $1.20 per can. The variable cost is 80 cents per
can, and the packaging and marketing operation has fixed costs of $360,000 per year. Depreciation is $60,000
per year. What is the accounting break-even? Ignoring taxes, what will be the increase in operating cash flow
if the quantity sold rises to 10 percent more than the break-even point?
The accounting break-even is $420,000∕.40 = 1,050,000 cans. As we know, the operating cash flow is equal
to the $60,000 depreciation at this level of production, so the degree of operating leverage is:
Given this, a 10 percent increase in the number of cans of dog food sold increases operating cash flow by a
substantial 70 percent.
To check this answer, we note that if sales rise by 10 percent, the quantity sold rises to 1,050,000 × 1.1 =
1,155,000. Ignoring taxes, the operating cash flow is 1,155,000 × .40 − $360,000 = $102,000. Compared to
the $60,000 cash flow we had, this is exactly 70 percent more: $102,000∕60,000 = 1.70.
Operating Leverage and Break-Even
We illustrate why operating leverage is an important consideration by examining the Victoria Sailboats
project under an alternative scenario. At a Q of 85 boats, the degree of operating leverage for the sailboat
project under the original scenario is:
Also, recall that the NPV at a sales level of 85 boats was $88,720, and that the accounting break-even was 60
boats.
An option available to Victoria is to subcontract production of the boat hull assemblies. If it does, the
necessary investment falls to $3.2 million, and the fixed operating costs fall to $180,000. However, variable
costs rise to $25,000 per boat since subcontracting is more expensive than doing it in-house. Ignoring taxes,
evaluate this option.
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For practice, see if you don’t agree with the following:
Click here for a description of Equations: NPV, Accounting Break-Even, and DOL.
What has happened? This option results in slightly lower estimated net present value, and the accounting
break-even point falls to 55 boats from 60 boats. As shown above, the higher the DOL, the higher is the
break-even point of a project.
Given that this alternative has the lower NPV, is there any reason to consider it further? Maybe there is. The
degree of operating leverage is substantially lower in the second case. If we are worried about the possibility
of an overly optimistic projection, we might prefer to subcontract.
There is another reason we might consider the second arrangement. If sales turned out better than expected,
we always have the option of starting to produce in-house later. As a practical matter, it is much easier to
increase operating leverage (by purchasing equipment) than to decrease it (by selling equipment).12 As we
discuss later, one of the drawbacks to discounted cash flow is that it is difficult to explicitly include options of
this sort, even though they may be quite important.
Concept Questions
1. What is operating leverage?
2. How is operating leverage measured?
3. What are the implications of operating leverage for the financial manager?
8 Another response is to keep the amount of debt low. We cover financial leverage in Chapter 16.
9 To see this, note that, if Q goes up by 1 unit, OCF goes up by (P − v). The percentage change in Q is 1∕Q,
and the percentage change in OCF is (P − v)∕OCF. Given this, we have:
Click here for a description of Equation: Footnote 9.
10 An alternative formula for calculating DOL is: DOL = (Sales − VC)∕(Sales − VC − FC)
11 Students who have studied economics will recognize DOL as an elasticity. Recall that elasticities vary
with quantity along demand and supply curves. For the same reason, DOL varies with unit sales, Q.
12 In the extreme case, if firms were able to readjust the ratio of variable and fixed costs continually, there
would be no increased risk associated with greater operating leverage.
11.6 | Managerial Options
In our capital budgeting analysis thus far, we have more or less ignored the possibility of future managerial
actions. Implicitly, we assumed that once a project is launched, its basic features cannot be changed. For this
reason, we say that our analysis is static (as opposed to dynamic).
In reality, depending on what actually happens in the future, there are always ways to modify a project. We
call these opportunities managerial options or real options. As we will see, in many cases managerial
options can improve project cash flows, making the best case better while placing a floor under the worst
case. As a result, ignoring such options would lead to forecasting risk in underestimating NPV. There are a
great number of these options. The way a product is priced, manufactured, advertised, and produced can all
be changed, and these are just a few of the possibilities.13
For example, at the time of writing, demand for oil storage in Alberta was strong due to the low oil price. A
Canadian firm which utilized real options in this situation was Gibson Energy Inc., a midstream service
provider to the energy industry. In 2015, Gibson initiated a project to expand its crude storage capacity by
900,000 barrels.14 Despite uncertain industry conditions, the company had confidence it could to capture the
growing demand through diversified service offerings. As this example suggests, the possibility of future
actions is important. We discuss some of the most common types of managerial actions in the next few
sections.
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CONTINGENCY PLANNING The various what-if procedures, particularly the break-even measures, in this
chapter have another use. We can also view them as primitive ways of exploring the dynamics of a project
and investigating managerial options. What we think about are some of the possible futures that could come
about and what actions we might take if they do.
For example, we might find that a project fails to break even when sales drop below 10,000 units. This is a
fact that is interesting to know, but the more important thing is to go on and ask, what actions are we going to
take if this actually occurs? This is called contingency planning, and it amounts to an investigation of some
of the managerial options implicit in a project.
There is no limit to the number of possible futures or contingencies that we could investigate. However, there
are some broad classes, and we consider these next.
THE OPTION TO EXPAND One particularly important option that we have not explicitly addressed is the
option to expand. If we truly find a positive NPV project, there is an obvious consideration. Can we expand
the project or repeat it to get an even larger NPV? Our static analysis implicitly assumes that the scale of the
project is fixed.
For example, if the sales demand for a particular product were to greatly exceed expectations, we might
investigate increasing production. If this is not feasible for some reason, we could always increase cash flow
by raising the price. Either way, the potential cash flow is higher than we have indicated because we have
implicitly assumed that no expansion or price increase is possible. Overall, because we ignore the option to
expand in our analysis, we underestimate NPV (all other things being equal).
THE OPTION TO ABANDON At the other extreme, the option to scale back or even abandon a project is
also quite valuable. For example, if a project does not break even on a cash flow basis, it can’t even cover its
own expenses. We would be better off if we just abandoned it. Our DCF analysis implicitly assumes that we
would keep operating even in this case.
Sometimes the best thing to do is to reverse direction. For example, Merrill Lynch Canada has done this three
times. First, it built up a retail brokerage operation in the 1980s and sold it to CIBC Wood Gundy in 1990.
Later, in 1998, Merrill Lynch made headlines by paying $1.26 billion for Midland Walwyn, the last
independently owned retail brokerage firm in Canada. The reason? Merrill Lynch wanted to continue its
globalization drive and get back into the business it had earlier abandoned. However, in November 2001,
Merrill Lynch Canada once again sold its retail brokerage and mutual fund and securities services businesses
to CIBC Wood Gundy. This sale was part of an effort to cut back expenses on its international operations.
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In reality, if sales demand were significantly below expectations, we might be able to sell some capacity or
put it to another use. Maybe the product or service could be redesigned or otherwise improved. Regardless of
the specifics, we once again underestimate NPV if we assume the project must last for some fixed number of
years, no matter what happens in the future. For example, TransCanada’s Energy East pipeline project
proposes to convert an existing under-used natural gas pipeline to an oil transportation pipeline.
THE OPTION TO WAIT Implicitly, we have treated proposed investments as if they were go or no-go
decisions. Actually, there is a third possibility. The project can be postponed, perhaps in hope of more
favourable conditions. We call this the option to wait.
For example, suppose an investment costs $120 and has a perpetual cash flow of $10 per year. If the discount
rate is 10 percent, the NPV is $10∕.10 − 120 = −$20, so the project should not be undertaken now. However,
this does not mean we should forget about the project forever, because in the next period the appropriate
discount rate could be different. If it fell to, say, 5 percent, the NPV would be $10∕.05 − 120 = $80, and we
would take it.
More generally, as long as there is some possible future scenario under which a project has a positive NPV,
the option to wait is valuable. Related to the option to wait is the option to suspend operations. For example,
in early 2015, Aural Minerals Inc., a Canadian mid-tier gold and copper producer, temporarily suspended all
operations at its Aranzazu mine due to lack of cash and the unfavourable market conditions.
THE TAX OPTION Investment decisions may trigger favourable or unfavourable tax treatment of existing
assets. This can occur because, as you recall from Chapter 2, capital cost allowance calculations are usually
based on assets in a pooled class. Tax liabilities for recaptured CCA and tax shelters from terminal losses
occur only when an asset class is liquidated either by selling all the assets or writing the undepreciated capital
cost below zero. As a result, management has a potentially valuable tax option.
For example, suppose your firm is planning to replace all its company delivery vans at the end of the year.
Because of unfavourable conditions in the used vehicle market, prices are depressed and you expect to realize
a loss. Since you are replacing the vehicles, as opposed to closing out the class, no immediate tax shelter
results from the loss. If your company is profitable and the potential tax shelter sizable, you could exercise
your tax option by closing out Class 12. To do this, you could lease the new vehicles or set up a separate firm
to purchase the vehicles.
OPTIONS IN CAPITAL BUDGETING: AN EXAMPLE Suppose we are examining a new project. To keep
things relatively simple, we expect to sell 100 units per year at $1 net cash flow apiece into perpetuity. We
thus expect the cash flow to be $100 per year.
In one year, we will know more about the project. In particular, we will have a better idea of whether it is
successful or not. If it looks like a long-run success, the expected sales could be revised upward to 150 units
per year. If it does not, the expected sales could be revised downward to 50 units per year.
Success and failure are equally likely. Notice that with an even chance of selling 50 or 150 units, the expected
sales are still 100 units as we originally projected.
The cost is $550, and the discount rate is 20 percent. The project can be dismantled and sold in one year for
$400, if we decide to abandon it. Should we take it?
A standard DCF analysis is not difficult. The expected cash flow is $100 per year forever and the discount
rate is 20 percent. The PV of the cash flows is $100∕.20 = $500, so the NPV is $500 − 550 = −$50. We
shouldn’t take it.
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This analysis is static, however. In one year, we can sell out for $400. How can we account for this? What we
have to do is to decide what we are going to do one year from now. In this simple case, there are only two
contingencies that we need to evaluate, an upward revision and a downward revision, so the extra work is not
great.
In one year, if the expected cash flows are revised to $50, the PV of the cash flows is revised downward to
$50∕.20 = $250. We get $400 by abandoning the project, so that is what we will do (the NPV of keeping the
project in one year is $250 − 400 = −$150).
If the demand is revised upward, the PV of the future cash flows at Year 1 is $150∕.20 = $750. This exceeds
the $400 abandonment value, so we would keep the project.
We now have a project that costs $550 today. In one year, we expect a cash flow of $100 from the project. In
addition, this project would either be worth $400 (if we abandon it because it is a failure) or $750 (if we keep
it because it succeeds). These outcomes are equally likely, so we expect it to be worth ($400 + 750)∕2, or
$575.
Summing up, in one year, we expect to have $100 in cash plus a project worth $575, or $675 total. At a 20
percent discount rate, this $675 is worth $562.50 today, so the NPV is $562.50 − 550 = $12.50. We should
take it.
The NPV of our project has increased by $62.50. Where did this come from? Our original analysis implicitly
assumed we would keep the project even if it was a failure. At Year 1, however, we saw that we were $150
better off ($400 versus $250) if we abandoned. There was a 50 percent chance of this happening, so the
expected gain from abandoning is $75. The PV of the amount is the value of the option to abandon, $75∕1.20
= $62.50.
STRATEGIC OPTIONS Companies sometimes undertake new projects just to explore possibilities and
evaluate potential future business strategies. This is a little like testing the water by sticking a toe in before
diving. When Microsoft decided to buy Skype for US$8.5 billion in 2011, strategic considerations likely
dominated immediate cash flow analysis.
Such projects are difficult to analyze using conventional DCF because most of the benefits come in the form
of strategic options; that is, options for future, related business moves. Projects that create such options may
be very valuable, but that value is difficult to measure. Research and development, for example, is an
important and valuable activity for many firms precisely because it creates options for new products and
procedures.
To give another example, a large manufacturer might decide to open a retail outlet as a pilot study. The
primary goal is to gain some market insight. Because of the high start-up costs, this one operation won’t break
even. However, based on the sales experience from the pilot, we can then evaluate whether or not to open
more outlets, to change the product mix, to enter new markets, and so on. The information gained and the
resulting options for actions are all valuable, but coming up with a reliable dollar figure is probably not
feasible.
Strategic options can also include political issues. For example, in 2013, the government of Canada rejected
Accelero Capital Holding’s proposed acquisition of Manitoba Telecom Services Inc. because of national
security concerns.
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CONCLUSION We have seen that incorporating options into capital budgeting analysis is not easy. What can
we do about them in practice? The answer is that we can only keep them in the back of our minds as we work
with the projected cash flows. We tend to underestimate NPV by ignoring options. The damage might be
small for a highly structured, very specific proposal, but it might be great for an exploratory one such as a
gold mine. The value of a gold mine depends on management’s ability to shut it down if the price of gold falls
below a certain point, and the ability to reopen it subsequently if conditions are right.15 The most commonly
used real options in Canada are the option to expand and the option to wait. Managers also report that a lack
of expertise prevents them from realizing the full potential of real options.16
13 We introduce managerial options here and return to the topic in more depth in Chapter 25.
14 Source: business.financialpost.com/news/energy/gibson-energy-plans-to-expand-oil-storage-capacity-asdemand-in-alberta-soars?__lsa=6c07-2601
15 M. J. Brennan and E. S. Schwartz, “A New Approach to Evaluating Natural Resource Investments,”
Midland Corporate Financial Journal 3 (Spring 1985).
16 H. K. Baker, S. Dutta, and S. Saadi, “Management Views on Real Options in Capital Budgeting?” Journal
of Applied Finance 21(1) (2011), pp. 18–29.
11.7 | Summary and Conclusions
In this chapter, we looked at some ways of evaluating the results of a discounted cash flow analysis. We also
touched on some problems that can come up in practice. We saw the following:
1. Net present value estimates depend on projected future cash flows. If there are errors in those
projections, our estimated NPVs can be misleading. We called this forecasting risk.
2. Scenario and sensitivity analyses are useful tools for identifying which variables are critical to a project
and where forecasting problems can do the most damage.
3. Break-even analysis in its various forms is a particularly common type of scenario analysis that is
useful for identifying critical levels of sales.
4. Operating leverage is a key determinant of break-even levels. It reflects the degree to which a project or
a firm is committed to fixed costs. The degree of operating leverage tells us the sensitivity of operating
cash flow to changes in sales volume.
5. Projects usually have future managerial options associated with them. These options may be very
important, but standard discounted cash flow analysis tends to ignore them.
The most important thing to carry away from reading this chapter is that estimated NPVs or returns should
not be taken at face value. They depend critically on projected cash flows. If there is room for significant
disagreement about those projected cash flows, the results from the analysis have to be taken with a grain of
salt.
Despite the problems we have discussed, discounted cash flow is still the way of attacking problems, because
it forces us to ask the right questions. What we learn in this chapter is that knowing the questions to ask does
not guarantee that we get all the answers.
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KEY TERMS
accounting break-even
cash break-even
contingency planning
degree of operating leverage
financial break-even
fixed costs
forecasting risk
managerial options or real options
marginal cost or incremental cost
operating leverage
scenario analysis
sensitivity analysis
simulation analysis
strategic options
variable costs
CHAPTER REVIEW PROBLEMS AND SELF-TEST
Use the following base-case information to work the self-test problems.
A project under consideration costs $750,000, has a five-year life, and has no salvage value. Depreciation is
straight-line to zero. The required return is 17 percent, and the tax rate is 34 percent. Sales are projected at
500 units per year. Price per unit is $2,500, variable cost per unit is $1,500, and fixed costs are $200,000 per
year.
11.1 Scenario Analysis Suppose you think that the unit sales, price, variable cost, and fixed cost
projections given here are accurate to within 5 percent. What are the upper and lower bounds for these
projections? What is the base-case NPV? What are the best- and worst-case scenario NPVs?
11.2 Break-Even Analysis Given the base-case projections in the previous problem, what are the cash,
accounting, and financial break-even sales levels for this project? Ignore taxes in answering.
ANSWERS TO SELF-TEST PROBLEMS
11.1 We can summarize the relevant information as follows:
Click here for a description of Table: Answers to Self-Test Problems 11.1; Summary of Relevant
Information.
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Depreciation is $150,000 per year; knowing this, we can calculate the cash flows under each scenario.
Remember that we assign high costs and low prices and volume for the worst-case and just the
opposite for the best-case scenario.
Click here for a description of Table: Answers to Self-Test Problems 11.1; Worst-Case and Best-Case
Scenarios.
At 17 percent, the five-year annuity factor is 3.19935, so the NPVs are:
Click here for a description of Equations: Answers to Self-Test Problems 11.1.
11.2 In this case, we have $200,000 in cash fixed costs to cover. Each unit contributes $2,500 − 1,500 =
$1,000 toward covering fixed costs. The cash break-even is thus $200,000∕$1,000 = 200 units. We
have another $150,000 in depreciation, so the accounting break-even is ($200,000 + 150,000)∕$1,000
= 350 units.
To get the financial break-even, we need to find the OCF such that the project has a zero NPV. As we
have seen, the five-year annuity factor is 3.19935 and the project costs $750,000, so the OCF must be
such that:
So, for the project to break even on a financial basis, the project’s cash flow must be
$750,000∕3.19935, or $234,423 per year. If we add this to the $200,000 in cash fixed costs, we get a
total of $434,423 that we have to cover. At $1,000 per unit, we need to sell $434,423∕$1,000 = 435
units.
CONCEPTS REVIEW AND CRITICAL THINKING QUESTIONS
1. (LO1) What is forecasting risk? In general, would the degree of forecasting risk be greater for a new
product or a cost-cutting proposal? Why?
2. (LO2) What is the essential difference between sensitivity analysis and scenario analysis?
3. (LO3) If you were to include the effect of taxes in break-even analysis, what do you think would
happen to the cash, accounting, and financial break-even points?
4. (LO3) A co-worker claims that looking at all this marginal this and incremental that is just a bunch of
nonsense, and states, “Listen, if our average revenue doesn’t exceed our average cost, then we will have
a negative cash flow, and we will go broke!” How do you respond?
5. (LO5) What is the option to abandon? Explain why we underestimate NPV if we ignore this option.
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6. (LO5) In this chapter, we discussed TransCanada’s Energy East pipeline project. Suppose demand for
crude oil transportation went extremely high and TransCanada was forced to expand capacity to meet
demand. TransCanada’s action in this case would be an example of exploiting what kind of option?
7. (LO4) At one time at least, many Japanese companies had a “no layoff” policy (for that matter, so did
IBM). What are the implications of such a policy for the degree of operating leverage a company
faces?
8. (LO4) Airlines offer an example of an industry in which the degree of operating leverage is fairly high.
Why?
9. (LO5) Natural resource extraction facilities (e.g., oil wells or gold mines) provide a good example of
the value of the option to suspend operations. Why?
10. (LO1, 2) In looking at Euro Disney and its “Mickey Mouse” financial performance early on, note that
the subsequent actions taken amount to a product reformulation. Is this a marketing issue, a finance
issue, or both? What does Euro Disney’s experience suggest about the importance of coordination
between marketing and finance?
QUESTIONS AND PROBLEMS
Basic (Questions 1–15)
1. Calculating Costs and Break-Even (LO3) Thunder Bay Inc. (TBI) manufactures biotech sunglasses.
The variable materials cost is $9.64 per unit, and the variable labour cost is $8.63 per unit.
1. What is the variable cost per unit?
2. Suppose TBI incurs fixed costs of $915,000 during a year in which total production is 215,000
units. What are the total costs for the year?
3. If the selling price is $39.99 per unit, does TBI break even on a cash basis? If depreciation is
$465,000 per year, what is the accounting break-even point?
2. Computing Average Cost (LO3) Vickers Everwear Corporation can manufacture mountain climbing
shoes for $35.85 per pair in variable raw material costs and $26.45 per pair in variable labour expense.
The shoes sell for $165 per pair. Last year, production was 145,000 pairs. Fixed costs were $1,750,000.
What were total production costs? What is the marginal cost per pair? What is the average cost? If the
company is considering a one-time order for an extra 5000 pairs, what is the minimum acceptable total
revenue from the order? Explain.
3. Scenario Analysis (LO2) Whitewater Transmissions Inc. has the following estimates for its new gear
assembly project: price = $1,700 per unit; variable costs = $480 per unit; fixed costs = $4.1 million;
quantity = 95,000 units. Suppose the company believes all of its estimates are accurate only to within
±15 percent. What values should the company use for the four variables given here when it performs its
best-case scenario analysis? What about the worst-case scenario?
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4. Sensitivity Analysis (LO1) For the company in the previous problem, suppose management is most
concerned about the impact of its price estimate on the project’s profitability. How could you address
this concern? Describe how you would calculate your answer. What values would you use for the other
forecast variables?
5. Sensitivity Analysis and Break-Even (LO1, 3) We are evaluating a project that costs $864,000, has an
eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life
of the project. Sales are projected at 71,000 units per year. Price per unit is $49, variable cost per unit is
$33, and fixed costs are $765,000 per year. The tax rate is 35 percent, and we require a 10 percent
return on this project.
1. Calculate the accounting break-even point. What is the degree of operating leverage at the
accounting break-even point?
2. Calculate the base-case cash flow and NPV. What is the sensitivity of NPV to changes in the
sales figure? Explain what your answer tells you about a 500-unit decrease in projected sales.
3. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer
tells you about a $1 decrease in estimated variable costs.
6. Scenario Analysis (LO2) In the previous problem, suppose the projections given for price, quantity,
variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worstcase NPV figures.
7. Calculating Break-Even (LO3) In each of the following cases, calculate the accounting break-even and
the cash break-even points. Ignore any tax effects in calculating the cash break-even.
Click here for a description of Table: Questions and Problems 7.
8. Calculating Break-Even (LO3) In each of the following cases, find the unknown variable:
Click here for a description of Table: Questions and Problems 8.
9. Calculating Break-Even (LO3) A project has the following estimated data: price = $54 per unit;
variable costs = $36 per unit; fixed costs = $19,300; required return = 12 percent; initial investment =
$26,800; life = four years. Ignoring the effect of taxes, what is the accounting break-even quantity? The
cash break-even quantity? The financial break-even quantity? What is the degree of operating leverage
at the financial break-even level of output?
10. Using Break-Even Analysis (LO3) Consider a project with the following data: accounting break-even
quantity = 14,200 units; cash break-even quantity = 10,300 units; life = five years; fixed costs =
$170,000; variable costs = $27 per unit; required return = 12 percent. Ignoring the effect of taxes, find
the financial break-even quantity.
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11. Calculating Operating Leverage (LO4) At an output level of 53,000 units, you calculate that the degree
of operating leverage is 3.21. If output rises to 57,000 units, what will the percentage change in
operating cash flow be? Will the new level of operating leverage be higher or lower? Explain.
12. Leverage (LO4) In the previous problem, suppose fixed costs are $175,000. What is the operating cash
flow at 46,000 units? The degree of operating leverage?
13. Operating Cash Flow and Leverage (LO4) A proposed project has fixed costs of $84,000 per year. The
operating cash flow at 7,500 units is $93,200. Ignoring the effect of taxes, what is the degree of
operating leverage? If units sold rise from 7,500 to 8,000, what will be the increase in operating cash
flow? What is the new degree of operating leverage?
14. Cash Flow and Leverage (LO4) At an output level of 17,500 units, you have calculated that the degree
of operating leverage is 3.42. The operating cash flow is $64,000 in this case. Ignoring the effect of
taxes, what are fixed costs? What will be the operating cash flow if output rises to 18,500 units? If
output falls to 16,500 units?
15. Leverage (LO4) In the previous problem, what will be the new degree of operating leverage in each
case?
Intermediate (Questions 16–27)
16. Break-Even Intuition (LO3) Consider a project with a required return of R% that costs $I and will last
for N years. The project uses straight-line depreciation to zero over the N-year life; there is no salvage
value or net working capital requirements.
1. At the accounting break-even level of output, what is the IRR of this project? The payback
period? The NPV?
2. At the cash break-even level of output, what is the IRR of this project? The payback period? The
NPV?
3. At the financial break-even level of output, what is the IRR of this project? The payback period?
The NPV?
17.
Sensitivity Analysis (LO1) Consider a four-year project with the following information: initial fixed
asset investment = $475,000; straight-line depreciation to zero over the four-year life; zero salvage
value; price = $26; variable costs = $18; fixed costs = $195,000; quantity sold = 84,000 units; tax rate =
34 percent. How sensitive is OCF to changes in quantity sold?
18. Operating Leverage (LO4) In the previous problem, what is the degree of operating leverage at the
given level of output? What is the degree of operating leverage at the accounting break-even level of
output?
19. Project Analysis (LO1, 2, 3, 4) You are considering a new product launch. The project will cost
$1,400,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales
are projected at 180 units per year; price per unit will be $16,000; variable cost per unit will be $9,800;
and fixed costs will be $430,000 per year. The required return on the project is 12 percent, and the
relevant tax rate is 35 percent.
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1. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given
here are probably accurate to within ±10 percent. What are the upper and lower bounds for these
projections? What is the base-case NPV? What are the best-case and worst-case scenarios?
2. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.
3. What is the cash break-even level of output for this project (ignoring taxes)?
4. What is the accounting break-even level of output for this project? What is the degree of
operating leverage at the accounting break-even point? How do you interpret this number?
20. Abandonment Value (LO5) We are examining a new project. We expect to sell 8,750 units per year at
$189 net cash flow apiece (including CCA) for the next 16 years. In other words, the annual operating
cash flow is projected to be $189 × 8,750 = $1,653,750. The relevant discount rate is 14 percent, and
the initial investment required is $5,500,000.
1. What is the base-case NPV?
2. After the first year, the project can be dismantled and sold for $2,800,000. If expected sales are
revised based on the first year’s performance, when would it make sense to abandon the
investment? In other words, at what level of expected sales would it make sense to abandon the
project?
3. Explain how the $2,800,000 abandonment value can be viewed as the opportunity cost of
keeping the project one year.
21. Abandonment (LO5) In the previous problem, suppose you think it is likely that expected sales will be
revised upwards to 9,500 units if the first year is a success and revised downwards to 4,300 units if the
first year is not a success.
1. If success and failure are equally likely, what is the NPV of the project? Consider the possibility
of abandonment in answering.
2. What is the value of the option to abandon?
22. Abandonment and Expansion (LO5) In the previous problem, supposed the scale of the project can be
doubled in one year in the sense that twice as many units can be produced and sold. Naturally,
expansion would only be desirable if the project is a success. This implies that if the project is a
success, projected sales after expansion will be 17,600. Again, assuming that success and failure are
equally likely, what is the NPV of the project? Note that abandonment is still an option if the project is
a failure. What is the value of the option to expand?
23. Project Analysis (LO1, 2) Baird Golf has decided to sell a new line of golf clubs. The clubs will sell for
$715 per set and have a variable cost of $385 per set. The company has spent $150,000 for a marketing
study that determined the company will sell 75,000 sets per year for seven years. The marketing study
also determined that the company will lose sales of 10,000 sets of its high-priced clubs. The highpriced clubs sell at $1,150 and have variable costs of $620. The company will also increase sales of its
cheap clubs by 12,000 sets. The cheap clubs sell for $425 and have variable costs of $195 per set. The
fixed costs each year will be $9,400,000. The company has also spent $1,000,000 on research and
development for the new clubs. The plant and equipment required will cost $30,100,000 and will be
depreciated on a straight-line basis. The new clubs will also require an increase in net working capital
of $1,400,000 that will be returned at the end of the project. The tax rate is 40 percent, and the cost of
capital is 10 percent. Calculate the payback period, the NPV, and the IRR.
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24. Scenario Analysis (LO2) In the previous problem, you feel that the values are accurate to within only
±10 percent. What are the best-case and worst-case NPVs? (Hint: The price and variable costs for the
two existing sets of clubs are known with certainty; only the sales gained or lost are uncertain.)
25. Sensitivity Analysis (LO1) Baird Golf would like to know the sensitivity of NPV to changes in the
price of the new clubs and the quantity of new clubs sold. What is the sensitivity of the NPV to each of
these variables?
26. Break-Even Analysis (LO3) Hybrid cars are touted as a “green” alternative; however, the financial
aspects of hybrid ownership are not as clear. Consider a 2015 Lexus RX 450h, which had a list price of
$5,565 (including tax consequences) more than a Lexus RX 350. Additionally, the annual ownership
costs (other than fuel) for the hybrid were expected to be $300 more than the traditional sedan. The
mileage estimate was 5 litre/100 km for the hybrid and 6.7 for the traditional sedan.
1. Assume that gasoline costs $1.35 per litre and you plan to keep either car for six years. How
many kilometres per year would you need to drive to make the decision to buy the hybrid
worthwhile, ignoring the time value of money?
2. If you drive 15,000 km per year and keep either car for six years, what price per litre would
make the decision to buy the hybrid worthwhile, ignoring the time value of money?
3. Rework parts (a) and (b) assuming the appropriate interest rate is 10 percent and all cash flows
occur at the end of the year.
4. What assumption did the analysis in the previous parts make about the resale value of each car?
27. Break-Even Analysis (LO3) In an effort to capture the large jet market, Airbus invested $13 billion
developing its A380, which is capable of carrying 800 passengers. The plane has a list price of $280
million. In discussing the plane, Airbus stated that the company would break even when 249 A380s
were sold.
1. Assuming the break-even sales figure given is the cash flow break-even, what is the cash flow
per plane?
2. Airbus promised its shareholders a 20 percent rate of return on the investment. If sales of the
plane continue in perpetuity, how many planes must the company sell per year to deliver on this
promise?
3. Suppose instead that the sales of the A380 last for only ten years. How many planes must Airbus
sell per year to deliver the same rate of return?
Challenge (Questions 28–33)
28. Break-Even and Taxes (LO3) Victoria Sailboats Limited is considering whether to launch its new
Mona-class sailboat. The selling price would be $40,000 per boat. The variable costs would be about
half that, or $20,000 per boat, and fixed costs will be $500,000 per year.
The Base Case: The total investment needed to undertake the project is $3.5 million for leasehold
improvements to the company’s factory. This amount will be depreciated straight-line to zero over the
five-year life of the equipment. The salvage value is zero, and there are no working capital
consequences. Victoria has a 20 percent required return on new projects.
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1. Show that, when we consider taxes, the general relationship between operating cash flow, OCF,
and sales volume, Q, can be written as:
Click here for a description of Equation: Questions and Problems 28a.
2. Use the expression in part (a) to find the cash, accounting, and financial break-even points for the
Victoria Sailboats example in the chapter. Assume a 38 percent tax rate.
3. In part (b), the accounting break-even should be the same as before. Why? Verify this
algebraically.
29. Operating Leverage and Taxes (LO4) Show that if we consider the effect of taxes, the degree of
operating leverage can be written as:
Click here for a description of Equation: Questions and Problems 29.
Notice that this reduces to our previous result if T = 0. Can you interpret this in words?
30.
Scenario Analysis (LO2) Consider a project to supply Thunder Bay with 35,000 tons of machine
screws annually for automobile production. You will need an initial $5,200,000 investment in threading
equipment to get the project started; the project will last for five years. The accounting department
estimates that annual fixed costs will be $985,000 and that variable costs should be $185 per ton; the
CCA rate for threading equipment is 20 percent. It also estimates a salvage value of $500,000 after
dismantling costs. The marketing department estimates that the automakers will let the contract at a
selling price of $280 per ton. The engineering department estimates you will need an initial net
working capital investment of $410,000. You require a 13 percent return and face a marginal tax rate of
38 percent on this project.
1. What is the estimated OCF for this project? The NPV? Should you pursue this project?
2. Suppose you believe that the accounting department’s initial cost and salvage value projections
are accurate only to within ±15 percent; the marketing department’s price estimate is accurate
only within ±10 percent; and the engineering department’s net working capital estimate is
accurate only to within ±5 percent. What is your worst-case scenario for this project? Your bestcase scenario? Do you still want to pursue the project?
31. Sensitivity Analysis (LO1) In Problem 30, suppose you’re confident about your own projections, but
you’re a little unsure about Thunder Bay’s actual machine screw requirement. What is the sensitivity of
the project OCF to changes in the quantity supplied? What about the sensitivity of NPV to changes in
quantity supplied? Given the sensitivity number you calculated, is there some minimum level of output
below which you wouldn’t want to operate? Why?
32. Break-Even Analysis (LO3) Use the results of Problem 28 to find the accounting, cash, and financial
break-even quantities for the company in Problem 30.
33. Operating Leverage (LO4) Use the results of Problem 29 to find the degree of operating leverage for
the company in Problem 30 at the base-case output level of 35,000 units. How does this number
compare to the sensitivity figure you found in Problem 31? Verify that either approach will give you
the same OCF figure at any new quantity level.
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MINI CASE
As a financial analyst at Glencolin International (GI) you have been asked to revisit your analysis of the two
capital investment alternatives submitted by the production department of the firm. (Detailed discussion of
these alternatives is in the Mini Case at the end of Chapter 10.) The CFO is concerned that the analysis to
date has not really addressed the risk in this project. Your task is to employ scenario and sensitivity analysis
to explore how your original recommendation might change when subjected to a number of “what-ifs.”
In your discussions with the CFO, the CIO and the head of the production department, you have pinpointed
two key inputs to the capital budgeting decision: initial software development costs and expected savings in
production costs (before tax). By properly designing the contract for software development, you are confident
that initial software costs for each alternative can be kept in a range of plus or minus 15 percent of the
original estimates. Savings in production costs are less certain because the software will involve new
technology that has not been implemented before. An appropriate range for these costs is plus or minus 40
percent of the original estimates.
As the capital budgeting analyst, you are required to answer the following in your memo to the CFO:
1. a) Conduct sensitivity analysis to determine which of the two inputs has a greater input on the choice
between the two projects.
2. b) Conduct scenario analysis to assess the risks of each alternative in turn. What are your conclusions?
3. c) Explain what your sensitivity and scenario analyses tell you about your original recommendations.
* We recommend using a spreadsheet in analyzing this Mini Case.
INTERNET APPLICATION QUESTIONS
1. The following website allows you to download a cash flow sensitivity analysis spreadsheet:
bizfilings.com/toolkit/tools-forms/finance/business-finances/cash-flow-budget-worksheet.aspx. You are
faced with two technologies, one with a higher cash flow but greater risk, and the second with a lower
cash flow and less risk. How would you use the cash flow sensitivity spreadsheet to pick the right
technology? What factors would you consider in the analysis?
2. Imperial Oil Ltd. is an integrated energy company based in Calgary. The company’s website,
imperialoil.ca, describes its businesses many of which involve real options. Go to the website and make
a list of the real options of Imperial Oil. Identify those which you think are most valuable today and
explain why.
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Best Buy
In March 2015, Best Buy Canada closed 131 Future Shop stores in Canada—66 of them permanently while
the remaining 65 reopened one week later under the Best Buy brand. The move was meant to stop the two
brands from cannibalizing each other’s sales, as they often were located too close to each other. At the same
time, the company announced that it would invest up to $200 million over the following two years in
improving website integration and customer experience.
Both the closing of Future Shop stores and the future investment represent capital budgeting decisions. In this
chapter, we will investigate, in detail, capital budgeting decisions—how they are made and how to look at
them objectively.
This chapter follows up on the previous one by delving more deeply into capital budgeting. In the last
chapter, we saw that cash flow estimates are a critical input into a net present value analysis but didn’t say
much about where these cash flows come from. We will now examine that question in some detail.
LEARNING OBJECTIVES
After studying this chapter, you should understand:
1.
2.
3.
4.
5.
6.
7.
8.
LO1 How to determine relevant cash flows for a proposed project.
LO2 How to project cash flows and determine if a project is acceptable.
LO3 How to calculate operating cash flow using alternative methods.
LO4 How to calculate the present value of a tax shield on CCA.
LO5 How to evaluate cost-cutting proposals.
LO6 How to analyze replacement decisions.
LO7 How to evaluate the equivalent annual cost of a project.
LO8 How to set a bid price for a project.
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So far, we’ve covered various parts of the capital budgeting decision. Our task in this chapter is to start
bringing these pieces together. In particular, we show you how to “spread the numbers” for a proposed
investment or project and, based on those numbers, make an initial assessment about whether or not the
project should be undertaken.
bestbuy.ca
In the discussion that follows, we focus on setting up a discounted cash flow analysis. From the last chapter,
we know that the projected future cash flows are the key element in such an evaluation. Accordingly, we
emphasize working with financial and accounting information to come up with these figures.
In evaluating a proposed investment, we pay special attention to deciding what information is relevant to the
decision at hand and what information is not. As we shall see, it is easy to overlook important pieces of the
capital budgeting puzzle.
We wait until the next chapter to describe in detail how to evaluate the results of our discounted cash flow
analysis. Also, where needed, we assume that we know the relevant required return or discount rate reflecting
the risk of the project. We continue to defer discussion of this subject to Part 5.
10.1 | Project Cash Flows: A First Look
The effect of undertaking a project is to change the firm’s overall cash flows today and in the future. To
evaluate a proposed investment, we must consider these changes in the firm’s cash flows and then decide
whether they add value to the firm. The most important step, therefore, is to decide which cash flows are
relevant and which are not.
Relevant Cash Flows
What is a relevant cash flow for a project? The general principle is simple enough; a relevant cash flow for a
project is a change in the firm’s overall future cash flow that comes about as a direct consequence of the
decision to take that project. Because the relevant cash flows are defined in terms of changes in or increments
to the firm’s existing cash flow, they are called the incremental cash flows associated with the project.
The concept of incremental cash flow is central to our analysis, so we state a general definition and refer back
to it as needed:
The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash
flows that are a direct consequence of taking the project.
This definition of incremental cash flows has an obvious and important corollary—any cash flow that exists
regardless of whether or not a project is undertaken is not relevant.
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The Stand-Alone Principle
In practice, it would be very cumbersome to actually calculate the future total cash flows to the firm with and
without a project, especially for a large firm. Fortunately, it is not really necessary to do so. Once we identify
the effect of undertaking the proposed project on the firm’s cash flows, we need focus only on the resulting
project’s incremental cash flows. This is called the stand-alone principle.
What the stand-alone principle says is that, once we have determined the incremental cash flows from
undertaking a project, we can view that project as a kind of minifirm with its own future revenues and costs,
its own assets, and, of course, its own cash flows. We are then primarily interested in comparing the cash
flows from this minifirm to the cost of acquiring it. An important consequence of this approach is that we
evaluate the proposed project purely on its own merits, in isolation from any other activities or projects.
Concept Questions
1. What are the relevant incremental cash flows for project evaluation?
2. What is the stand-alone principle?
10.2 | Incremental Cash Flows
We are concerned here only with those cash flows that are incremental to a project. Looking back at our
general definition, it seems easy enough to decide whether a cash flow is incremental or not. Even so, there
are a few situations when mistakes are easy to make. In this section, we describe some of these common
pitfalls and how to avoid them.
Sunk Costs
A sunk cost, by definition, is a cost we have already paid or have already incurred the liability to pay. Such a
cost cannot be changed by the decision today to accept or reject a project. Put another way, the firm has to
pay this cost no matter what. Based on our general definition of incremental cash flow, such a cost is clearly
not relevant to the decision at hand. So, we are always careful to exclude sunk costs from our analysis.
That a sunk cost is not relevant seems obvious given our discussion. Nonetheless, it’s easy to fall prey to the
sunk cost fallacy. For example, suppose True North Distillery Ltd. hires a financial consultant to help
evaluate whether or not a line of maple sugar liqueur should be launched. When the consultant turns in the
report, True North objects to the analysis because the consultant did not include the hefty consulting fee as a
cost to the liqueur project.
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Who is correct? By now, we know that the consulting fee is a sunk cost, because the consulting fee must be
paid whether or not the liqueur line is launched (this is an attractive feature of the consulting business).
A more subtle example of a cost that can sometimes be sunk is overhead. To illustrate, suppose True North
Distillery is now considering building a new warehouse to age the maple sugar liqueur. Should a portion of
overhead costs be allocated to the proposed warehouse project? If the overhead costs are truly sunk and
independent of the project, the answer is no. An example of such an overhead cost is the cost of maintaining a
corporate jet for senior executives. But if the new warehouse requires additional reporting, supervision, or
legal input, these overheads should be part of the project analysis.
Opportunity Costs
When we think of costs, we normally think of out-of-pocket costs; namely, those that require us to actually
spend some amount of cash. An opportunity cost is slightly different; it requires us to give up a benefit. A
common situation arises where another division of a firm already owns some of the assets that a proposed
project will be using. For example, we might be thinking of converting an old rustic water-powered mill that
we bought years ago for $100,000 into upscale condominiums.
If we undertake this project, there will be no direct cash outflow associated with buying the old mill since we
already own it. For purposes of evaluating the condo project, should we then treat the mill as free? The
answer is no. The mill is a valuable resource used by the project. If we didn’t use it here, we could do
something else with it. Like what? The obvious answer is that, at a minimum, we could sell it. Using the mill
for the condo complex thus has an opportunity cost—we give up the valuable opportunity to do something
else with it.
There is another issue here. Once we agree that the use of the mill has an opportunity cost, how much should
the condo project be charged? Given that we paid $100,000, it might seem we should charge this amount to
the condo project. Is this correct? The answer is no, and the reason is based on our discussion concerning
sunk costs.
The fact that we paid $100,000 some years ago is irrelevant. It’s sunk. At a minimum, the opportunity cost
that we charge the project is what it would sell for today (net of any selling costs) because this is the amount
that we give up by using it instead of selling it.1
Side Effects
Remember that the incremental cash flows for a project include all the resulting changes in the firm’s future
cash flows. It would not be unusual for a project to have side, or spillover, effects, both good and bad. For
example, when Shoppers Drug Mart introduced fresh foods to its shelf in early 2015, Loblaw had to
recognize the possibility that incremental sales from Shoppers would come at the expense of sales from its
own stores. The negative impact on cash flows is called erosion, and the same general problem anticipated
by Air Canada could occur for any multiline consumer product producer or seller.2 In this case, the cash
flows from the new line should be adjusted downwards to reflect lost profits on other lines.
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In accounting for erosion, it is important to recognize that any sales lost as a result of launching a new
product might be lost anyway because of future competition. Erosion is only relevant when the sales would
not otherwise be lost.
Side effects show up in a lot of different ways. For example, one of Walt Disney’s concerns when it built Euro
Disney was that the new park would drain visitors from the Florida park, a popular vacation destination for
Europeans.
disneyworld.disney.go.com
hp.com
There are beneficial side effects, of course. For example, you might think that Hewlett-Packard would have
been concerned when the price of a printer that sold for $500 to $600 in 2003 declined to below $100 by
2014, but they weren’t. What HP realized was that the big money is in the consumables that printer owners
buy to keep their printers going, such as ink-jet cartridges, laser toner cartridges, and special paper. The profit
margins for these products are substantial.
Net Working Capital
Normally, a project requires that the firm invest in net working capital in addition to long-term assets. For
example, a project generally needs some amount of cash on hand to pay any expenses that arise. In addition, a
project needs an initial investment in inventories and accounts receivable (to cover credit sales). Some of this
financing would be in the form of amounts owed to suppliers (accounts payable), but the firm has to supply
the balance. This balance represents the investment in net working capital.
It’s easy to overlook an important feature of net working capital in capital budgeting. As a project winds
down, inventories are sold, receivables are collected, bills are paid, and cash balances can be drawn down.
These activities free up the net working capital originally invested. So, the firm’s investment in project net
working capital closely resembles a loan. The firm supplies working capital at the beginning and recovers it
toward the end.
Financing Costs
In analyzing a proposed investment, we do not include interest paid or any other financing costs such as
dividends or principal repaid, because we are interested in the cash flow generated by the assets from the
project. As we mentioned in Chapter 2, interest paid, for example, is a component of cash flow to creditors,
not cash flow from assets.
More generally, our goal in project evaluation is to compare the cash flow from a project to the cost of
acquiring that project to estimate NPV. The particular mixture of debt and equity that a firm actually chooses
to use in financing a project is a managerial variable and primarily determines how project cash flow is
divided between owners and creditors. This is not to say that financing costs are unimportant. They are just
something to be analyzed separately, and are included as a component of the discount rate. We cover this in
later chapters.
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Inflation
Because capital investment projects generally have long lives, price inflation or deflation is likely to occur
during the project’s life. It is possible that the impact of inflation will cancel out—changes in the price level
will impact all cash flows equally—and that the required rate of return will also shift exactly with inflation.
But this is unlikely, so we need to add a brief discussion of how to handle inflation.
As we explained in more detail in Chapter 7, investors form expectations of future inflation. These are
included in the discount rate as investors wish to protect themselves against inflation. Rates including
inflation premiums are called nominal rates. In Brazil, for example, where the inflation rate is very high,
discount rates are much higher than in Canada.
Given that nominal rates include an adjustment for expected inflation, cash flow estimates must also be
adjusted for inflation.3 Ignoring inflation in estimating the cash inflows would lead to a bias against accepting
capital budgeting projects. As we go through detailed examples of capital budgeting, we comment on making
these inflation adjustments. Appendix 10A discusses inflation effects further.
Capital Budgeting and Business Taxes in Canada
In Canada, various levels of government commonly offer incentives to promote certain types of capital
investment. These include grants, investment tax credits, more favourable rates for capital cost allowance
(CCA), and subsidized loans. Since these change a project’s cash flows, they must be factored into capital
budgeting analysis.
Other Issues
There are other things to watch for. First, we are interested only in measuring cash flow. Moreover, we are
interested in measuring it when it actually occurs, not when it arises in an accounting sense. Second, we are
always interested in after-tax cash flow since tax payments are definitely a cash outflow. In fact, whenever we
write incremental cash flows, we mean after-tax incremental cash flows. Remember, however, that after-tax
cash flow and accounting profit or net income are different things.
Concept Questions
1. What is a sunk cost? An opportunity cost? Provide examples of each.
2. Explain what erosion is and why it is relevant.
3. Explain why interest paid is not a relevant cash flow for project valuation.
4. Explain how consideration of inflation comes into capital budgeting.
1 Economists sometimes use the acronym TANSTAAFL, which is short for “there ain’t no such thing as a
free lunch,” to describe the fact that only very rarely is something truly free. Further, if the asset in question is
unique, the opportunity cost might be higher because there might be other valuable projects we could
undertake that would use it. However, if the asset in question is of a type that is routinely bought and sold (a
used car, perhaps), the opportunity cost is always the going price in the market because that is the cost of
buying another one.
2 More colourfully, erosion is sometimes called piracy or cannibalism.
3 In Chapter 7, we explained how to calculate real discount rates. The term real, in finance and economics,
means adjusted for inflation; that is, net of the inflation premium. A less common alternative approach uses
real discount rates to discount real cash flows.
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10.3 | Pro Forma Financial Statements and Project Cash Flows
When we begin evaluating a proposed investment, we need a set of pro forma, or projected, financial
statements. Given these, we can develop the projected cash flows from the project. Once we have the cash
flows, we can estimate the value of the project using the techniques we described in the previous chapter.
In calculating the cash flows, we make several simplifying assumptions to avoid bogging down in technical
details at the outset. We use straight-line depreciation as opposed to capital cost allowance. We also assume
that a full year’s depreciation can be taken in the first year. In addition, we construct the example so the
project’s market value equals its book cost when it is scrapped. Later, we address the real-life complexities of
capital cost allowance and salvage values introduced in Chapter 2.
Getting Started: Pro Forma Financial Statements
Pro forma financial statements introduced in Chapter 4 are a convenient and easily understood means of
summarizing much of the relevant information for a project. To prepare these statements, we need estimates
of quantities such as unit sales, the selling price per unit, the variable cost per unit, and total fixed costs. We
also need to know the total investment required, including any investment in net working capital.
To illustrate, suppose we think we can sell 50,000 cans of shark attractant per year at a price of $4.30 per can.
It costs us about $2.50 per can to make the attractant, and a new product such as this one typically has only a
three-year life (perhaps because the customer base dwindles rapidly). We require a 20 percent return on new
products.
Fixed operating costs for the project, including such things as rent on the production facility, would run
$12,000 per year.4 Further, we need to invest $90,000 in manufacturing equipment. For simplicity, we assume
this $90,000 will be 100 percent depreciated over the three-year life of the project in equal annual amounts.5…