Chapter 11 – Project Analysis and Evaluation
Chapter 11
PROJECT ANALYSIS AND EVALUATION
CHAPTER ORGANIZATION
11.1 Evaluating NPV Estimates
The Basic Problem
Projected versus Actual Cash Flows
Forecasting Risk
Sources of Value
11.2 Scenario and Other What-If Analyses
Getting Started
Scenario Analysis
Sensitivity Analysis
Simulation Analysis
11.3 Break-Even Analysis
Fixed and Variable Costs
Accounting Break-Even
Accounting Break-Even: A Closer Look
Uses for the Accounting Break-Even
11.4 Operating Cash Flow, Sales Volume, and Break-Even
Accounting Break-Even and Cash Flow
Sales Volume and Operating Cash Flow
Cash Flow, Accounting, and Financial Break-Even Points
11.5 Operating Leverage
The Basic Idea
Implications of Operating Leverage
Measuring Operating Leverage
Operating Leverage and Break-Even
11.6 Capital Rationing
Soft Rationing
Hard Rationing
11.7 Summary and Conclusions
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ANNOTATED CHAPTER OUTLINE
1. Evaluating NPV Estimates
A. The Basic Problem
Computing an NPV is putting a market value on uncertain future
cash flows. Projecting the future involves the potential for error.
Major error sources are biases and omissions.
There are two main reasons for positive NPVs: (1) we have
constructed a good project or (2) we have done a bad job of
estimating NPV.
Similarly, a negative computed NPV might be reflective of a bad
project or of a bad job of estimating NPV.
B. Projected versus Actual Cash Flows
Estimated cash flows are expectations of averages of possible cash
flows, not exact figures (although if an exact figure were available,
you would use it).
C. Forecasting Risk
Forecasting risk – the danger of making a bad (value destroying)
decision because of errors in projected cash flows. This risk is
reduced if we systematically investigate common problem areas.
D. Sources of Value
The first and best guard against forecasting risk is to keep in mind
that positive NPVs are economic rarities in competitive markets. In
other words, for a project to have a positive NPV, it must have
some competitive edge – e.g., be first, be best, be the only. Keep in
mind the economic axiom that in a competitive market, excess
profits (the source of positive NPVs) are zero.
Lecture Tip: Perhaps the single largest source of positive NPVs is
the economic concept of monopoly rents – positive profits that
occur from being the only one able or allowed to do something.
Monopoly rents are often associated with patent rights and
technological edges and they quickly disappear in a competitive
market. Introducing this notion in class provides a springboard for
discussions of both business and financial strategy, as well as for
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discussion of the application of economic theory to the real world.
Real-World Tip: In “Corporate Strategy and the Capital
Budgeting Decision” (Midland Corporate Finance Journal,
Spring, 1985, pp. 22-36), Alan Shapiro states that a firm’s capital
budgeting program should “establish strategic options in order to
gain competitive advantage.” Further, successful investments,
according to Shapiro, are those investments “that involve creating,
preserving, and even enhancing competitive advantages that serve
as barriers to entry.” The following are project characteristics
associated with positive NPVs.
1) Economies of scale
2) Product differentiation
3) Cost advantages
4) Access to distribution channels
5) Favorable government policy
Shapiro’s article takes students past standard number-crunching
and encourages them to think of capital budgeting from the
strategic, or “big-picture,” standpoint: how will this project (or
group of projects) benefit the firm as a whole?
2. Scenario and Other What-If Analyses
A. Getting Started
“And time yet for a hundred indecisions,
And for a hundred visions and revisions,
Before the taking of a toast and tea.”
-T.S. Eliot
What things are likely to be wrong, and what will be the effect if
they are?
Start with a base case – the expected cash flows – then ask “what if
…?”
B. Scenario Analysis
Worst-case/Best-case scenarios: putting lower and upper bounds on
cash flows. Common exercises include poor revenues/high costs
and high revenues/low costs. Note that a thorough scenario
analysis starts with Base-case/Worst-case/Best-case and then
expands from there.
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If, under most circumstances, the discounted projected cash flows
are sufficient to cover the outlay, we can have a high level of
confidence that the NPV is positive. Beyond that, it is difficult to
interpret the meaning of the scenarios.
Lecture Tip: A major misconception about a project’s estimated
NPV at this point is that it depends upon how the cash flows
actually turn out. This thinking misses the point that NPV is
an ex ante valuation of an uncertain future. The distinction
between the valuation of what is expected versus the ex post value
of what transpired is often difficult for students to appreciate.
A useful analogy for getting this point across is the market value of
a new car. The potential to be a “lemon” is in every car, as is the
possibility of being a “cream puff.” The greater the likelihood that
a car will have problems, the lower the price will be. The point,
however, is that a new car doesn’t have many different prices right
now – one for each conceivable repair record. Rather, there is one
price embodying the different potential outcomes and their
expected value. So it is with NPV – the potential for good and bad
cash flows is reflected in a single market value.
Lecture Tip: You may wish to integrate this discussion of risk with
some of the topics to be discussed in forthcoming chapters. The
variability between best- and worst-case scenarios is the essence
of forecasting risk. Similarly, we link the risk of a security with the
variability of its expected return. This point provides another
opportunity to link economic theory (investor/manager rationality
versus required returns) with real-world decision-making.
You might also want to point out that the cases examined in this
type of analysis typically aren’t literally the best and worst cases
possible. The true worst-case scenario is something absurdly
unlikely, such as an earthquake that swallows our production
plant. Instead, the worst-case used in scenario analysis is simply a
pessimistic (but possible) forecast used to develop expected cash
flows.
C. Sensitivity Analysis
To conduct a sensitivity analysis, hold all projections constant
except one; alter that one, and see how sensitive cash flow is to the
change – the point is to get a fix on where forecasting risk may be
especially severe. You may want to use the worst-case/best-case
idea for the item being varied. Common exercises include varying
sales, variable costs, and fixed costs.
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Lecture Tip: If desired, it may be a good point at which to
demonstrate the Solver function in Excel, as you can identify how
high/low an input could go before NPV becomes negative.
D. Simulation Analysis
Computers are used to estimate thousands of possible scenarios.
The interactions between variables are estimated and incorporated
into the model. We can then get an estimate of the probability
distribution for the NPV.
Care must be exercised to accurately assess the interaction between
variables. The old computer acronym, GIGO (garbage in, garbage
out), still holds. The probability distribution is worse than useless
if we are careless in defining the model.
Lecture Tip: A very useful software is Crystal Ball, which is a
simulation package that integrates with Excel. It is relatively
inexpensive, yet it is very useful for basic-to-moderate simulation
analysis. For example, the software allows you to build models
(such as NPV) in Excel, then define the assumptions behind the
inputs (such as distribution, possible extreme values, etc.), as well
as the interaction (i.e., correlation) between the inputs. Output is
then generated based on a simulation of 1,000 runs, providing
distribution analysis and numerical summary statistics.
3. Break-Even Analysis
Break-even analysis is a widely used technique for analyzing sales
volume and profitability. More to the point, it determines the sales
volume necessary to cover costs and implicitly asks, “Are things
likely to go that well?”
Ethics Note: The following case might be used to discuss the
nature of break-even analysis and a possible ethical quandary
involved with this form of analysis.
Researchers associated with South Miami Hospital (SMH)
developed a new experimental laser treatment for heart patients.
Its development team and the physicians who use the laser
consider it to be a lifesaving advance. It should be noted that the
physicians who are touting the laser hold a significant stake in the
company that produces the laser.
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To offer a substitute for a balloon angioplasty to treat heart
blockages, the experimental laser was developed at a cost of
$250,000. SMH estimates that it will cost $20,000 to install the
laser. The procedure requires a nurse at $50 per hour, a technician
at $30 per hour, and a physician who is paid $750 per hour.
Patients are billed $3,000 for the procedure compared to $1,500
for the traditional balloon treatment.
Now ask the students to determine the break-even quantity for the
new procedure:
Fixed cost = 250,000 + 20,000 = 270,000
Variable cost = 50 + 30 + 750 = 830 per hour
Cash Break-Even = 250,000 / (3,000 – 830) = 115.2 hours
or approximately 116 patients (assuming a one-hour procedure per
patient).
This procedure is considered experimental; therefore, it would not
be covered under most insurance plans. The experimental nature
of the procedure means that part of the development costs are
being paid by the patient. Is it ethical for the patient to pay for
R&D costs prior to the introduction of the final product? Is it
proper for physicians to recommend this procedure when they have
a vested interest in its usage?
A. Fixed and Variable Costs
Variable costs (VC) are the costs that change as the volume of sales
changes (direct labor and materials, for example)
A simplifying assumption is to make variable costs constant per
unit of output, i.e.,
variable costs = quantity*cost per unit
VC = Q*v
When this is assumed, v is the marginal cost.
Lecture Tip: You may wish to emphasize that, in computing total
variable costs, the only relevant costs are those that are directly
related to the manufacture and sale of the product. Allocated (or
indirect) costs should not enter the analysis. Suggest to the
students that when they are uncertain, they should use the
“with/without” criterion: will the costs be different if the
investment is made? If not, the cost is, by definition, not directly
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related to the decision and should not be included.
Fixed costs (FC) are those that are constant over a period
regardless of the level of sales.
Total costs (TC) are the sum of fixed costs and variable costs.
TC = FC + VC
TC = FC + (Q*v)
Lecture Tip: Students should recognize that as quantity increases,
total fixed costs remain constant, but, on a per unit basis, they
decrease with increasing volume. And, as quantity increases, total
cost per unit approaches variable cost per unit. If a company
expects a high unit sales volume, the company may desire to
exploit the possible economies of scale by investing more in fixed
costs in an effort to lower variable cost per unit. However, this
could create future financial problems if sales expectations fail to
materialize. You might mention that this sensitivity to earnings
declines will be examined later in this chapter through the
discussion of the degree of operating leverage.
If you wish to expand on this issue, introduce two alternative cost
structures and have the students consider what minimum quantity
of sales would be required to favor one project over another.
FCA + VCA(Q) = FCB + VCB(Q)
10,000 + 6Q = 25,000 + 3Q
Q* = 5,000 units
Now point out that a company would have to expect more than
5,000 units in sales to justify accepting the increased fixed costs
and operating risk associated with project B. Additionally, the
forecasting risk is much greater with project B.
Average cost versus marginal cost – total cost divided by output
gives the average cost. Average cost will exceed marginal cost in
all cases except where fixed costs are $0. But, since fixed costs are
a type of sunk cost (in the current period at least), the relevant cost
in considering additional production is variable or marginal cost
B. Accounting Break-Even
The sales volume at which the project net income = $0.
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C. Accounting Break-Even: A Closer Look
What sales level gives $0 net income (assuming things are the
same each year)? This happens when sales equal total costs.
P = price per unit
v = variable cost per unit
Q = # of units or quantity
FC = fixed costs
D = depreciation
T = tax rate
Net income = sales – costs – taxes
NI = [Q*P – FC – Q*v – D](1 – T) = 0
Q*P – Q*v = FC + D
Q(P – v) = FC + D
Q = (FC + D) / (P – v)
D. Uses for the Accounting Break-Even
Knowledge of the accounting break-even point allows us to better
evaluate the level of forecast risk inherent in our cash flow
estimates, as well as provides clues as to the likelihood that the
firm will break-even in terms of accounting earnings.
4. Operating Cash Flow, Sales, Volume, and Break-Even
A. Accounting Break-Even and Cash Flow
Ignore taxes for simplification:
1. Calculate the quantity (Q) necessary for accounting break-even.
Using the following information:
Fixed costs = 40,000
Depreciation = 4,000
Price per unit = 3
Variable cost per unit = 0.30
Q = (FC + D) / (P – v)
Q = (40,000 + 4,000) / (3 – .3) = 16,296 units
Since operating cash flow = net income + depreciation, when Q =
16,296 units, operating cash flow = 0 + 4,000 = 4,000
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2. At accounting break-even, the sum of the undiscounted cash
flows is just equal to the depreciable investment.
3. A project that just breaks even on an accounting basis will have
a negative NPV at any positive discount rate.
B. Sales Volume and Operating Cash Flow
Again, ignore taxes for simplification:
OCF = net income + depreciation
OCF = [(P – v)Q – FC – D] + D = (P – v)Q – FC
This is a linear relation (y = mx + b) with a y intercept = -FC and
the slope = P – v
C. Cash Flow, Accounting and Financial Break-Even Points
Use the following information. The price is $3 per unit and the
variable costs are $0.30 per unit. The fixed costs are $40,000.
Assume no taxes. Rearrange the OCF equation and solve for Q.
OCF = (P – v)Q – FC
Q = (FC + OCF) / (P – v)
1. To find the accounting break-even point: Q = (FC + D) / (P – v)
2. To find the cash break-even point (where OCF = 0):
Q = FC / (P – v)
Q = 40,000 / (3 – .3) = 14,815 units
3. To find the financial break-even, find the OCF of the 5-year
project that has a present value equal to the initial investment
($20,000), using a cost of capital of 15%.
PV = 20,000; N = 5; I/Y = 15; CPT PMT = OCF = 5,967
Q = (40,000 + 5,967) / (3 – .3) = 17,025 units
Lecture Tip: Inquisitive students may ask how the computations
change when you include taxes. The equations change as follows:
OCF = [(P – v)Q – FC – D](1 – T) + D
Use a tax rate = 40% and rework the Wettways example from the
book:
Need 1170 in OCF to break-even on a financial basis
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OCF = [(40 – 20)(Q) – 500 – 700](1 – .4) + 700 = 1170
Q = 99.2
You end up with a new quantity of 100 units. The firm must sell an
additional 16 units to offset the effects of taxes.
5. Operating Leverage
There is almost always some flexibility in production to decide between
fixed and variable costs. Fixed costs generally magnify forecasting errors,
as well as reduce the firm’s flexibility in the production process.
A. The Basic Idea
Operating leverage is the degree to which a project or firm uses
fixed costs in production. Plant and equipment and non-cancelable
rentals are typical fixed cost items.
B. Implications of Operating Leverage
Since fixed costs do not change with sales, they make good
situations better and bad situations worse, i.e., they “lever” results.
C. Measuring Operating Leverage
Degree of Operating Leverage (DOL) is the percentage change in
OCF relative to a percentage change in quantity.
Percentage change in OCF = DOL*(percentage change in Q)
DOL = 1 + FC / OCF
DOL depends on your starting point – what quantity you use to
determine the OCF.
Example:
FC = 40,000
D = 4,000
P = 3
v = 0.30
T = 0
At Q = 20,000, OCF = 14,000
DOL = 1 + (40,000 / 14,000) = 3.857
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If the number of units increases by 5%, the OCF should increase
by 3.857(5%) = 19.29%. At 21,000 units, OCF = $16,700
D. Operating Leverage and Break-Even
In general, the lower the fixed costs and the degree of operating
leverage, the lower is the break-even point. If a project can be
started with low fixed costs and later switched to high fixed costs
(with lower variable costs per unit) if it turns out well, this is a
valuable option.
6. Capital Rationing
A. Soft Rationing – management decides to limit capital that will be
raised
May have little to do with increasing value. The profitability index
may be helpful in this situation.
B. Hard Rationing – cannot raise capital under any circumstances
This is often associated with financial distress.
Lecture Tip: In 2008, the economy was suffering from a real estate
and credit crisis. As a result, lenders essentially withdrew from the
market and credit dried up. This is a perfect example of an issue
that would create a situation very close to hard rationing for many
businesses.
7. Summary and Conclusions
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