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Year 0 Years 1“12
Cash-flow forecasts for
Finefodder™s new superstore Investment “$5,400,000
1. Sales $16,000,000
2. Variable costs 13,000,000
3. Fixed costs 2,000,000
4. Depreciation 450,000
5. Pretax profit (1 “ 2 “ 3 “ 4) 550,000
6. Taxes (at 40%) 220,000
7. Profit after tax 330,000
8. Cash flow from operations (4 + 7) 780,000
Net cash flow “$5,400,000 $ 780,000

and your staff members have prepared the figures shown in Table 5.1. The figures are
fairly typical for a new supermarket, except that to keep the example simple we have
assumed no inflation. We have also assumed that the entire investment can be depreci-
ated straight-line for tax purposes, we have neglected the working capital requirement,
and we have ignored the fact that at the end of the 12 years you could sell off the land
and buildings.
As an experienced financial manager, you recognize immediately that these cash
flows constitute an annuity and therefore you calculate present value by multiplying the
$780,000 cash flow by the 12-year annuity factor. If the cost of capital is 8 percent,
present value is
PV = $780,000 — 12-year annuity factor
= $780,000 — 7.536 = $5.878 million
Subtract the initial investment of $5.4 million and you obtain a net present value of
NPV = PV “ investment
= $5.878 million “ $5.4 million = $478,000
Before you agree to accept the project, however, you want to delve behind these fore-
casts and identify the key variables that will determine whether the project succeeds or
Some of the costs of running a supermarket are fixed. For example, regardless of the
level of output, you still have to heat and light the store and pay the store manager.
These fixed costs are forecast to be $2 million per year.
Other costs vary with the level of sales. In particular, the lower the sales, the less
that do not depend on the
food you need to buy. Also, if sales are lower than forecast, you can operate a lower
level of output.
number of checkouts and reduce the staff needed to restock the shelves. The new su-
perstore™s variable costs are estimated at 81.25 percent of sales. Thus variable costs =
.8125 — $16 million = $13 million.
Costs that change as the
The initial investment of $5.4 million will be depreciated on a straight-line basis over
level of output changes.
the 12-year period, resulting in annual depreciation of $450,000. Profits are taxed at a
rate of 40 percent.
These seem to be the important things you need to know, but look out for things that
may have been forgotten. Perhaps there will be delays in obtaining planning permission,
Project Analysis 471

Sensitivity analysis for superstore project

Range NPV
Variable Pessimistic Expected Optimistic Pessimistic Expected Optimistic
Investment 6,200,000 5,400,000 5,000,000 “121,000 +478,000 +778,000
Sales 14,000,000 16,000,000 18,000,000 “1,218,000 +478,000 +2,174,000
Variable cost as
percent of sales 83 81.25 80 “788,000 +478,000 +1,382,000
Fixed cost 2,100,000 2,000,000 1,900,000 +26,000 +478,000 +930,000

or perhaps you will need to undertake costly landscaping. The greatest dangers often lie
in these unknown unknowns, or “unk-unks,” as scientists call them.
Having found no unk-unks (no doubt you™ll find them later), you look at how NPV
may be affected if you have made a wrong forecast of sales, costs, and so on. To do this,
you first obtain optimistic and pessimistic estimates for the underlying variables. These
are set out in the left-hand columns of Table 5.2.
Next you see what happens to NPV under the optimistic or pessimistic forecasts for
each of these variables. You recalculate project NPV under these various forecasts to de-
termine which variables are most critical to NPV .

Sensitivity Analysis
The right-hand side of Table 5.2 shows the project™s net present value if the variables are
set one at a time to their optimistic and pessimistic values. For example, if fixed costs
are $1.9 million rather than the forecast $2.0 million, annual cash flows are increased
by (1 “ tax rate) — ($2.0 million “ $1.9 million) = .6 — $100,000 = $60,000. If the cash
flow increases by $60,000 a year for 12 years, then the project™s present value increases
by $60,000 times the 12-year annuity factor, or $60,000 — 7.536 = $452,000. Therefore,
NPV increases from the expected value of $478,000 to $478,000 + $452,000 =
$930,000, as shown in the bottom right corner of the table. The other entries in the three
columns on the right in Table 5.2 similarly show how the NPV of the project changes
when each input is changed.
Your project is by no means a sure thing. The principal uncertainties appear to be
sales and variable costs. For example, if sales are only $14 million rather than the fore-
cast $16 million (and all other forecasts are unchanged), then the project has an NPV
of “$1.218 million. If variable costs are 83 percent of sales (and all other forecasts are
unchanged), then the project has an NPV of “$788,000.

Recalculate cash flow as in Table 5.1 if variable costs are 83 percent of sales. Confirm
Self-Test 1
that NPV will be “$788,000.

Value of Information. Now that you know the project could be thrown badly off
course by a poor estimate of sales, you might like to see whether it is possible to resolve

some of this uncertainty. Perhaps your worry is that the store will fail to attract suffi-
cient shoppers from neighboring towns. In that case, additional survey data and more
careful analysis of travel times may be worthwhile.
On the other hand, there is less value to gathering additional information about
fixed costs. Because the project is marginally profitable even under pessimistic assump-
tions about fixed costs, you are unlikely to be in trouble if you have misestimated that

Limits to Sensitivity Analysis. Your analysis of the forecasts for Finefodder™s new
superstore is known as a sensitivity analysis. Sensitivity analysis expresses cash flows
in terms of unknown variables and then calculates the consequences of misestimating
those variables. It forces the manager to identify the underlying factors, indicates where
additional information would be most useful, and helps to expose confused or inappro-
priate forecasts.
Of course, there is no law stating which variables you should consider in your sen-
sitivity analysis. For example, you may wish to look separately at labor costs and the
costs of the goods sold. Or, if you are concerned about a possible change in the corpo-
rate tax rate, you may wish to look at the effect of such a change on the project™s NPV.
One drawback to sensitivity analysis is that it gives somewhat ambiguous results. For
example, what exactly does optimistic or pessimistic mean? One department may be in-
terpreting the terms in a different way from another. Ten years from now, after hundreds
of projects, hindsight may show that one department™s pessimistic limit was exceeded
twice as often as the other™s; but hindsight won™t help you now while you™re making the
investment decision.
Another problem with sensitivity analysis is that the underlying variables are likely
to be interrelated. For example, if sales exceed expectations, demand will likely be
stronger than you anticipated and your profit margins will be wider. Or, if wages are
higher than your forecast, both variable costs and fixed costs are likely to be at the upper
end of your range.
Because of these connections, you cannot push one-at-a-time sensitivity analysis too
far. It is impossible to obtain expected, optimistic, and pessimistic values for total proj-
ect cash flows from the information in Table 5.2. Still, it does give a sense of which vari-
ables should be most closely monitored.

When variables are interrelated, managers often find it helpful to look at how their proj-
ect would fare under different scenarios. Scenario analysis allows them to look at dif-
ferent but consistent combinations of variables. Forecasters generally prefer to give an
Project analysis given a
estimate of revenues or costs under a particular scenario rather than giving some ab-
particular combination of
solute optimistic or pessimistic value.

Scenario Analysis
You are worried that Stop and Scoff may decide to build a new store in nearby Salome.
That would reduce sales in your Gravenstein store by 15 percent and you might be
forced into a price war to keep the remaining business. Prices might be reduced to the
point that variable costs equal 82 percent of revenue. Table 5.3 shows that under this
Project Analysis 473

Cash Flows Years 1“12
Scenario analysis, NPV of
Finefodder™s Gravenstein Competing Store Scenarioa
Base Case
superstore with scenario of
1. Sales $16,000,000 $13,600,000
new competing store in
2. Variable costs 13,000,000 11,152,000
nearby Salome
3. Fixed costs 2,000,000 2,000,000
4. Depreciation 450,000 450,000
5. Pretax profit (1 “ 2 “ 3 “ 4) 550,000 “2,000
6. Taxes (40%) 220,000 “800
7. Profit after tax 330,000 “1,200
8. Cash flow from operations (4 + 7) 780,000 448,800
Present value of cash flows 5,878,000 3,382,000
NPV 478,000 “2,018,000

a Assumptions: Competing store causes (1) a 15 percent reduction in sales, and (2) variable costs to
increase to 82 percent of sales.

scenario of lower sales and smaller margins your new venture would no longer be

An extension of scenario analysis is called simulation analysis. Here, instead of
specifying a relatively small number of scenarios, a computer generates several hundred
ANALYSIS Estimation of
or thousand possible combinations of variables according to probability distributions
the probabilities of different
specified by the analyst. Each combination of variables corresponds to one scenario.
possible outcomes, e.g.,
Project NPV and other outcomes of interest can be calculated for each combination of
from an investment project.
variables, and the entire probability distribution of outcomes can be constructed from
the simulation results.

What is the basic difference between sensitivity analysis and scenario analysis?
Self-Test 2

Break-Even Analysis
When we undertake a sensitivity analysis of a project or when we look at alternative
scenarios, we are asking how serious it would be if we have misestimated sales or costs.
Managers sometimes prefer to rephrase this question and ask how far off the estimates
could be before the project begins to lose money. This exercise is known as break-even
ANALYSIS Analysis of
For many projects, the make-or-break variable is sales volume. Therefore, managers
the level of sales at which the
most often focus on the break-even level of sales. However, you might also look at other
company breaks even.
variables, for example, at how high costs could be before the project goes into the red.
As it turns out, “losing money” can be defined in more than one way. Most often,
the break-even condition is defined in terms of accounting profits. More properly, how-
ever, it should be defined in terms of net present value. We will start with accounting

break-even, show that it can lead you astray, and then show how NPV break-even can
be used as an alternative.

The accounting break-even point is the level of sales at which profits are zero or, equiv-
alently, at which total revenues equal total costs. As we have seen, some costs are fixed
regardless of the level of output. Other costs vary with the level of output.
When you first analyzed the superstore project, you came up with the following es-

Sales $16 million
Variable cost 13 million
Fixed costs 2 million
Depreciation 0.45 million

Notice that variable costs are 81.25 percent of sales. So, for each additional dollar of
sales, costs increase by only $.8125. We can easily determine how much business
the superstore needs to attract to avoid losses. If the store sells nothing, the income
statement will show fixed costs of $2 million and depreciation of $450,000. Thus
there will be a loss of $2.45 million. Each dollar of sales reduces this loss by $1.00 “
$.8125 = $.1875. Therefore, to cover fixed costs plus depreciation, you need sales of
2.45 million/.1875 = $13.067 million. At this sales level, the firm will break even. More
fixed costs
including depreciation
Break-even level of revenues =
additional profit
from each additional dollar of sales
Table 5.4 shows how the income statement looks with only $13.067 million of sales.
Figure 5.1 shows how the break-even point is determined. The 45-degree line shows
accounting revenues. The cost line shows how costs vary with sales. If the store
doesn™t sell a cent, it still incurs fixed costs and depreciation amounting to $2.45 mil-
lion. Each extra dollar of sales adds $.8125 to these costs. When sales are $13.067 mil-
lion, the two lines cross, indicating that costs equal revenues. For lower sales, revenues
are less than costs and the project is in the red; for higher sales, revenues exceed costs
and the project moves into the black.
Is a project that breaks even in accounting terms an acceptable investment? If you


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