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Chapter 7
RISK ANALYSIS, REAL OPTIONS, AND CAPITAL
BUDGETING
SLIDES
CHAPTER ORGANIZATION
7.1 Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis
Sensitivity Analysis and Scenario Analysis
Break-Even Analysis
7.2 Monte Carlo Simulation
Step 1: Specify the Basic Model
7.1 Key Concepts and Skills
7.2 Chapter Outline
7.3 Sensitivity, Scenario, and Break-Even
7.4 Example: Stewart Pharmaceuticals
7.5 NPV Following Successful Test
7.6 NPV Following Unsuccessful Test
7.7 Decision to Test
7.8 Sensitivity Analysis: Stewart
7.9 Scenario Analysis: Stewart
7.10 Break-Even Analysis
7.11 Break-Even Analysis: Stewart
7.12 Break-Even Analysis: Stewart
7.13 Break-Even Revenue: Stewart
7.14 Break-Even Analysis: PBE
7.15 Monte Carlo Simulation
7.16 Monte Carlo Simulation
7.17 Monte Carlo Simulation
7.18 Monte Carlo Simulation
7.19 Real Options
7.20 Real Options
7.21 Discounted CF and Options
7.22 The Option to Abandon: Example
7.23 The Option to Abandon: Example
7.24 The Option to Abandon: Example
7.25 The Option to Abandon: Example
7.26 Valuing the Option to Abandon
7.27 The Option to Delay: Example
7.28 Decision Trees
7.29 Example of a Decision Tree
7.30 Decision Tree for Stewart
7.31 Quick Quiz
Step 2: Specify a Distribution for Each Variable in the Model
Step 3: The Computer Draws One Outcome
Step 4: Repeat the Procedure
Step 5: Calculate NPV
7.3 Real Options
The Option to Expand
The Option to Abandon
Timing Options
7.4 Decision Trees
ANNOTATED CHAPTER OUTLINE
Slide 7.0 Chapter 7 Title Slide
Slide 7.1 Key Concepts and Skills
Slide 7.2 Chapter Outline
7.1. Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis
Slide 7.3 Sensitivity, Scenario, and Break-Even
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 poor job of estimating NPV.
Similarly, a negative computed NPV might be reflective of a bad project or of
a poor job of estimating NPV.
Estimated cash flows are expectations of averages of possible cash flows, not
exact figures (although if an exact figure were available, we would
use it).
Forecasting risk – the danger of making a bad (value destroying)
decision as a result of errors in projected cash flows. This risk is
reduced if we systematically investigate common problem areas.
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 – 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
discussion of the application of economic theory to the real world.
Lecture 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?
.A Sensitivity Analysis and Scenario Analysis
“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
…?”
Slide 7.4 Example: Stewart Pharmaceuticals
Slide 7.5 NPV Following Successful Test
Slide 7.6 NPV Following Unsuccessful Test
Slide 7.7 Decision to Test
Slide 7.8 Sensitivity Analysis: Stewart
Sensitivity Analysis
To conduct a sensitivity analysis, hold all projections constant
except one. Alter that one, and see how sensitive cash flows (and
NPV) are 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.
Slide 7.9 Scenario Analysis: Stewart
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.
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 does not 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 are not 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.
.B 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?”
Slide 7.10 Break-Even Analysis
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.
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 = 270,000 / (3,000 – 830) = 124.4 hours,
or approximately 125 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?
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. This
relation is a reflection 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.
Accounting Break-Even
The sales volume at which the project net income = $0.
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)
Example:
(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
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.
Calculating OCF and Financial Break-even:
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
Another Example:
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. The initial
investment is $20,000. The project lasts five years and has a
discount rate of 15%. 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 cash break-even point (where OCF = 0):
Q = FC / (P – v)
Q = $40,000 / ($3 - $.3) = 14,815 units
2. To find the financial break-even, find the OCF that has a present value
equal to the initial investment.
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 equation changes as follows:
OCF = [(P – v)Q – FC – D](1 – T) + D
Slide 7.11 –
Slide 7.12 Break-Even Analysis: Stewart
Slide 7.13 Break-Even Revenue: Stewart
Slide 7.14 Break-Even Analysis: PBE
8.2. Monte Carlo Simulation
Slide 7.15 –
Slide 7.18 Monte Carlo Simulation
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.
The basic process can be summarized by the following five steps:
.A Step 1: Specify the Basic Model
.B Step 2: Specify a Distribution for Each Variable in the Model
.C Step 3: The Computer Draws One Outcome
.D Step 4: Repeat the Procedure
.E Step 5: Calculate the NPV
8.3. Real Options
Slide 7.19 –
Slide 7.20 Real Options
Real options provide the right to buy or sell real assets. These
options often apply in capital budgeting situations and can be very
valuable.
Explicit options – contracts giving the holder the right to buy or
sell the asset
Implicit options – options that exist in many capital budgeting
situations, but are often “hidden”
Managerial options are options to modify a project once it has been
implemented.
Strategic options – using a project to explore possible new ventures
or strategies. These projects open up a wide number of future
opportunities, but they are more difficult to analyze with traditional
DCF analysis.
The presence of valuable options increases the value of potential
projects.
Slide 7.21 Discounted CF and Options
.A The Option to Expand
Option to expand – ability to make the project bigger if it is
successful. We underestimate the NPV if we ignore this option.
.B The Option to Abandon
Option to abandon - ability to shut down the project if things don’t
go as planned. We underestimate the NPV if we ignore this option.
Slide 7.22 –
Slide 7.25 The Option to Abandon: Example
Slide 7.26 Valuing the Option to Abandon
.C Timing Options
Virtually all projects can be viewed as real options if you think of
the initial investment as the strike price and the project as the asset.
Timing – if we take a project today, we cannot take it later.
Consequently, even though a project has a positive NPV, it does
not mean we should take it now. It may be worth more if we wait.
Investment Timing Decision – deciding when to take a project
Slide 7.27 The Option to Delay: Example
The option to wait is particularly valuable when the economy or
market is expected to be bigger in the future. It is not valuable
when trying to capitalize on current fads.
The option to wait may actually turn a bad project into a good
project – waiting a year or two may allow the firm to capture
higher cash flows.
8.4. Decision Trees
Slide 7.28 Decision Trees
Decision trees are a convenient way to represent sequential
decisions over time. Such decisions often arise when the
uncertainty surrounding an investment can be reduced by some
initial information-gathering such as test marketing a new product
or preparing a feasibility study.
Slide 7.29 Example of a Decision Tree
Slide 7.30 Decision Tree for Stewart
Slide 7.31 Quick Quiz
