Health & Medical Capital Budgeting at Cleveland Clinic Discussion

Respond to each of the following prompts or questions:

Using the information provided in the Los Reyes Hospital case study from Module Three, what capital expenditures may the selected departments need to budget?

Considering the organization you selected, what is a capital expenditure that may be needed that would result in a tangible asset?

Select a risk assessment tool in Chapter 12 of Understanding Healthcare Financial Management that may help with the capital budget plans for your proposed capital expenditure project

CHAPTER
PROJECT RISK ANALYSIS
12
Learning Objectives
Copyright 2020. AUPHA/HAP Book.
All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.
After studying this chapter, readers should be able to
• describe the three types of risk relevant to capital budgeting
decisions,
• discuss the techniques used in project risk assessment,
• conduct a project risk assessment,
• discuss several types of real options and their impact on a
project’s value, and
• explain how risk is incorporated into the capital budgeting
process.
Introduction
Chapter 11 covered the basics of capital budgeting, including cash flow estimation, breakeven analysis, and profitability measures. This chapter extends
the discussion of capital budgeting to include risk analysis, which is composed
of three elements: (1) defining the type of risk relevant to the project, (2)
measuring the project’s risk, and (3) incorporating that risk assessment into
the capital budgeting decision process. Although risk analysis is a key element
in all financial decisions, the importance of capital investment decisions to a
healthcare organization’s success makes risk analysis vital.
The higher the risk associated with an investment, the higher its
required rate of return. This principle is just as valid for healthcare businesses
that make capital expenditure decisions as it is for individuals who make
personal investment decisions. Thus, the ultimate goal in project risk analysis
is to ensure that the cost of capital used as the discount rate in a project’s
profitability analysis properly reflects the riskiness of that project. The corporate cost of capital, which is covered in detail in chapter 9, reflects the cost
of capital to the organization on the basis of its aggregate risk—that is, the
riskiness of the business’s average project.
In project risk analysis, a project’s risk is assessed relative to the firm’s
average project: Does the project have average risk, below-average risk, or
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above-average risk? The corporate cost of capital is then adjusted to reflect
any differential risk, resulting in a project cost of capital. In general, high-risk
projects are assigned a project cost of capital that is higher than the corporate
cost of capital, average risk projects are evaluated at the corporate cost of
capital, and low-risk projects are assigned a discount rate that is less than the
corporate cost of capital. (Note that when capital budgeting is conducted at
the divisional level, the adjustment process is handled in a similar manner but
the starting value is the divisional cost of capital.)
Types of Project Risk
Three types of project risk can be defined and, at least in theory, measured:
1. Stand-alone risk, which views the risk of a project as if it were held
in isolation and hence ignores portfolio effects in the firm and among
equity investors
2. Corporate risk, which views the risk of a project in the context of the
business’s portfolio of projects
3. Market risk, which views a project’s risk from the perspective of the
business’s owners, who are assumed to hold a well-diversified portfolio
of stocks1
The type of risk that is most relevant to a particular capital budgeting decision depends on the business’s ownership and the number of projects the
business operates.
Stand-Alone Risk
Stand-alone risk is present in a project whenever there is a chance of a return
that is less than the expected return. A project is risky whenever its cash flows
are not known with certainty because uncertain cash flows mean uncertain
profitability. Furthermore, the greater the probability of a return far below
the expected return, the greater the risk. Stand-alone risk can be measured
by the standard deviation of the project’s profitability (return on investment
[ROI]), as measured typically by net present value (NPV) or internal rate
of return (IRR). Because standard deviation measures the dispersion of a
distribution about its expected value, the larger the standard deviation, the
greater the probability that the project’s profitability (NPV or IRR) will be
far below that expected.
An alternative measure of stand-alone risk is the project’s coefficient of
variation, which is the standard deviation divided by the project’s expected
NPV. Conceptually, stand-alone risk is relevant in only one situation: when a
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not-for-profit firm is evaluating its first project. In this situation, the project
will be operated in isolation, so no portfolio diversification is present; that is,
the business does not have a collection of different projects, nor does it have
stockholders who hold diversified portfolios of stocks.
Corporate Risk
In reality, businesses usually offer many different products or services and
thus can be thought of as having a large number (perhaps even hundreds)
of individual projects. For example, MinuteMan Healthcare, a New England
HMO (health maintenance organization), offers healthcare services to a large
number of diverse employee groups in numerous service areas, and each
different group can be considered a separate project. In this situation, the
stand-alone risk of a project (service line) under consideration by MinuteMan
is not relevant because the project will not be held in isolation. The relevant
risk of a new project to MinuteMan is its contribution to the HMO’s overall
risk—the impact of the project on the variability of the overall profitability of
the business. This type of risk, which is relevant when the project is part of a
not-for-profit business’s portfolio of projects, is called corporate risk.
A project’s corporate risk depends on the context (i.e., the firm’s other
projects), so a project may have high corporate risk to one business but low
corporate risk to another, particularly when the two businesses operate in
widely different industries.
Market Risk
Market risk is generally viewed as the relevant risk for projects being evaluated by investor-owned businesses. The goal of shareholder (owner) wealth
maximization implies that a project’s returns as well as its risk should be
defined and measured from the owners’ perspective. The riskiness of an individual project to a well-diversified owner is not the risk the project would
have if it were owned and operated in isolation (i.e., stand-alone risk), nor
is it the contribution of the project to the riskiness of the business (i.e.,
corporate risk). Most business owners hold a large diversified portfolio of
stocks of many firms, which can be thought of as a large diversified portfolio of individual projects. Thus, the risk of any single project to a for-profit
business’s owners is its contribution to the riskiness of their well-diversified
stock portfolios.
1. What are the three types of project risk?
2. How is each type of project risk measured, both in absolute and
relative terms?
SELF-TEST
QUESTIONS
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Relationships Among Stand-Alone, Corporate, and
Market Risks
After discussing the three types of project risk and the situations in which
each is relevant, it is tempting to say that stand-alone risk is almost never
important because not-for-profit businesses should focus on a project’s corporate risk and investor-owned businesses should focus on a project’s market
risk. Unfortunately, the situation is not that simple. First, it is almost impossible in practice to quantify a project’s corporate or market risk because it is
extremely difficult—some practitioners would say impossible—to estimate
the prospective return distributions for given economic states for either the
project, the firm as a whole, or the market. If these return distributions cannot be estimated, the appropriate beta cannot be estimated, and hence a
project’s corporate or market risk cannot be quantified.
Fortunately, as demonstrated in the next section, it is possible to get
a rough idea of the relative stand-alone risk of a project. Thus, managers can
make statements such as “project A has above-average risk, project B has
below-average risk, and project C has average risk,” all in the stand-alone
sense. After a project’s stand-alone risk has been assessed, the primary factor
in converting stand-alone risk to corporate or market risk is correlation. If
a project’s returns are expected to be highly positively correlated with the
firm’s returns, high stand-alone risk translates to high corporate risk. Similarly, if the firm’s returns are expected to be highly correlated with the stock
market’s returns, high corporate risk translates to high market risk. The same
relationships hold when the project is judged to have average or low standalone risk.
Most projects will be in a firm’s primary line of business and hence
will be in the same line of business as the firm’s average project. Because all
projects in the same line of business are generally affected by the same economic factors, such projects’ returns are usually highly correlated. When this
situation exists, a project’s stand-alone risk is a good proxy for its corporate
risk. Furthermore, most projects’ returns are also positively correlated with
the returns on other assets in the economy; that is, most assets have high
returns when the economy is strong and low returns when the economy is
weak. When this situation holds, a project’s stand-alone risk is a good proxy
for its market risk.
Thus, for most projects, the stand-alone risk assessment also provides
good insights into a project’s corporate and market risk. The only exception
is a situation in which a project’s returns are expected to be independent
of, or negatively correlated to, the business as a whole. In these situations,
considerable judgment is required because the stand-alone risk assessment
will over-state the project’s corporate risk. Similarly, if a project’s returns
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are expected to be independent of or negatively correlated to the market’s
returns, the project’s stand-alone risk will overstate its market risk.
An additional problem arises with investor-owned healthcare businesses. Finance theory specifies that investor-owned businesses should focus
on market risk when making capital budgeting decisions. However, most
healthcare businesses (even proprietary ones) have corporate goals that focus
on the provision of quality healthcare services in addition to owner (shareholder) wealth maximization. Furthermore, a proprietary healthcare business’s stability and financial condition, which primarily depend on corporate
risk, are important to all the firm’s other stakeholders: its managers, physicians, patients, community, and so on. Some financial theorists even argue
that stockholders, including those that are well diversified, consider factors
other than market risk when setting required returns. This point is especially
meaningful for small businesses because their owners and managers are not
well diversified in their relationship to the business. Considering all the factors, it may be reasonable for managers of investor-owned healthcare businesses, particularly small ones, to be just as concerned about corporate risk
as are managers of not-for-profit businesses. Fortunately, in most real-world
situations, a project’s risk in the corporate sense will be the same as its risk
in the market sense.2
1. Name and define the three types of risk relevant to capital
budgeting.
2. How are these risks related?
3. Should managers of investor-owned providers focus exclusively on
a project’s market risk?
SELF-TEST
QUESTIONS
Risk Analysis Illustration
To illustrate project risk analysis, consider Ridgeland Community Hospital’s
evaluation of a new MRI (magnetic resonance imaging) system presented in
chapter 11. Exhibit 12.1 contains the project’s cash flow analysis. If all of
the project’s component cash flows were known with certainty, the project’s
projected profitability would be known with certainty and hence the project
would have no risk. However, in most project analyses, future cash flows—
and hence profitability—are uncertain and, in many cases, highly uncertain,
so risk is present.
The component cash flow distributions and their correlations with
one another determine the project’s profitability distribution and hence the
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Profitability measures:
Net present value (NPV) = $82,493.
Internal rate of return (IRR) = 11.1%.
1. System cost
($1,500,000)
2. Related expenses)
(1,000,000)
3. Gross revenues
4. Deductions
5. Net revenues
6. Labor costs
7. Maintenance costs
8. Supplies
9. Incremental overhead
10. Depreciation
11. Operating cash flow
12. Taxes
13. Net operating cash flow
14. Depreciation
15. Net salvage value
16. Net cash flow
($2,500,000)
0
$1,050,000
   262,500
$   787,500
52,500
157,500
31,500
10,500
350,000
$    185,500
0
$    185,500
350,000
$  535,500
$   510,000
2
$ 562,275
$1,102,500
  275,625
$  826,875
55,125
165,375
33,075
11,025
350,000
$   212,275
0
$   212,275
350,000
3
Annual Cash Flows
$1,000,000
   250,000
$   750,000
50,5000
150,000
30,000
10,000
350,000
$    160,000
0
$    160,000
350,000
1
EXHIBIT 12.1
Ridgeland Community Hospital: MRI Site Cash Flow Analysis
$ 590,389
$1,157,625
289,406
$  868,219
57,881
173,644
34,729
11,576
350,000
$ 240,389
0
$ 240,389
350,000
4
$1,215,506
  303,876
$    911,630
60,775
182,326
36,465
12,155
350,000
$  269,908
0
$  269,908
350,000
750,000
$1,369,908
5
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project’s risk. In the following sections, three quantitative techniques for
assessing a project’s risk are discussed: (1) sensitivity analysis, (2) scenario
analysis, and (3) Monte Carlo simulation. In a later section, we present a
qualitative approach to risk assessment.
1. What condition creates project risk?
2. What makes one project riskier than another?
3. What type of risk is initially assessed?
SELF-TEST
QUESTIONS
Sensitivity Analysis
Historically, sensitivity analysis has been classified as a risk assessment tool.
In reality, it is not very useful in assessing a project’s risk. However, it does
have significant value in project analysis, so we discuss it in some detail here.
Many of the variables that determine a project’s cash flows are subject
to some type of probability distribution, not known with certainty. If the realized value of such a variable is different from its expected value, the project’s
profitability will differ from its expected value. Sensitivity analysis indicates
exactly how much a project’s profitability—NPV, IRR, or modified internal
rate of return (MIRR)—will change in response to a given change in a single
input variable, with all other input variables held constant.
Sensitivity analysis begins with the base case developed using expected
values (in the statistical sense) for all uncertain variables. For example, assume
that Ridgeland’s managers believe that all of the MRI project’s component
cash flows—except for weekly volume and salvage value—are known with
relative certainty. The expected values for these variables (volume = 40, salvage value = $750,000) were used in exhibit 12.1 to obtain the base case
NPV of $82,493. Sensitivity analysis is designed to provide managers with
the answers to such questions as, What if volume turns out to be more or
less than the expected level? What if salvage value turns out to be more or
less than expected? (Typically, more than two variables would be examined
in a sensitivity analysis. We use only two to keep the illustration manageable.)
In a sensitivity analysis, each uncertain input variable typically is
changed by a fixed percentage amount above and below its expected value,
while all other variables are held constant at their expected values. Thus, all
input variables except one are held at their base case values. The resulting
NPVs (or IRRs or MIRRs) are recorded and plotted. Exhibit 12.2 contains
the NPV sensitivity analysis for the MRI project, assuming that there are two
uncertain variables: (1) volume and (2) salvage value.
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EXHIBIT 12.2
MRI Project
Sensitivity
Analysis
Net Present Value
Change from
Base Case Level (%)
Volume
Salvage
Value
–30
–20
–10
0
+10
+20
+30
($814,053)
(515,193)
(216,350)
82,493
381,335
680,178
979,020
($ 57,215)
(10,646)
35,923
82,493
129,062
175,631
222,200
Note that the NPV is a constant $82,493 when there is no change in
either of the uncertain variables because a 0 percent change recreates the base
case. The values in exhibit 12.2 give managers a feel for which input variable
will have the greatest impact on the MRI project’s profitability—the larger
the NPV change for a given percentage input change, the greater the impact.
Considering only these two variables, we see that the MRI project’s NPV is
affected by changes in volume to a much greater degree than it is by changes
in salvage value.
Often, the results of sensitivity analyses are shown in graphical form.
For example, the exhibit 12.2 sensitivity analysis is graphed in exhibit 12.3.
Here, the slopes of the lines show how sensitive the MRI project’s NPV is to
changes in each of the uncertain input variables—the steeper the slope, the
more sensitive the NPV is to a change in the variable. Note that the sensitivity lines intersect at the base case values—0 percent change from base case
level and $82,493. Also, spreadsheet models are ideally suited for performing
sensitivity analyses because such models automatically recalculate NPV when
an input value is changed and facilitate graphing.3
Exhibit 12.3 illustrates that the MRI project’s NPV is very sensitive
to volume and only mildly sensitive to changes in salvage value. A sensitivity plot that has a negative slope indicates that increases in the value of that
variable decrease the project’s NPV. If two projects were being compared,
the one with the steeper sensitivity lines would be regarded as riskier because
a relatively small error in estimating a variable—for example, volume—would
produce a large difference in the project’s realized NPV. Thus, a realized volume that turns out to be smaller than that expected means that the project’s
actual NPV will be far less than that expected. If information were available
on the sensitivity of NPV to input changes to Ridgeland’s average project,
similar judgments regarding the riskiness of the MRI project could be made,
but they would be relative to the firm’s average project.
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EXHIBIT 12.3
Sensitivity
Analysis Graph
Although sensitivity analysis historically has been thought of as a risk
assessment tool, it has severe limitations in this role. For example, suppose
that Ridgeland had a contract with an HMO that guaranteed a minimum
MRI volume at a fixed reimbursement rate. In that situation, volume would
not contribute to project risk at all, despite the sensitivity analysis showing
NPV to be highly sensitive to changes in volume. In general, a project’s
stand-alone risk depends on the sensitivity of its profitability to changes in
key input variables and the ranges of likely values of these variables. Because
sensitivity analysis considers only the first factor, its results can be misleading.
Furthermore, sensitivity analysis does not consider interactions among the
uncertain input variables; it considers each variable independently.
Despite its shortcomings in risk assessment, sensitivity analysis does
provide managers with valuable information. First, it provides some breakeven information about the project’s uncertain variables. For example,
exhibits 12.2 and 12.3 show that just a small decrease in expected volume
makes the project unprofitable, whereas the project remains profitable even
if salvage value falls by more than 10 percent. Although somewhat rough,
this breakeven information is clearly valuable to Ridgeland’s managers. (The
breakeven points can be easily refined by using Excel’s Goal Seek capability.)
Second, and perhaps more important, sensitivity analysis helps managers identify which input variables are most critical to the project’s profitability
and hence to the project’s financial success. In this MRI example, volume is
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clearly the key input variable of the two that were examined, so Ridgeland’s
managers should ensure that the volume estimate is the best possible. The
concept here is that Ridgeland’s managers have a limited amount of time to
spend on analyzing the MRI project, and sensitivity analysis enables them to
focus on what’s most important.
The ability to identify the critical input variables is also useful postaudit. If the project is performing poorly and changes must be made, such
changes will have the greatest positive impact if they are made to one of the
critical variables. In our illustration, if the MRI project is initiated but its
profitability is not meeting forecasts, it clearly is better to focus on increasing
volume than on increasing the salvage value.
SELF-TEST
QUESTIONS
1. Briefly describe sensitivity analysis.
2. What type of risk does it attempt to measure?
3. Is sensitivity analysis a good risk assessment tool? If not, what is its
value in the capital budgeting process?
Scenario Analysis
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Scenario analysis is a stand-alone risk-analysis technique that considers (1) the
sensitivity of NPV or another profitability measure to changes in key variables, (2) the likely range of variable values, and (3) the interactions among
the variables. To conduct a scenario analysis, managers pick a “bad” set of circumstances (e.g., low volume, low salvage value), an average or “most likely”
set, and a “good” set (e.g., high volume, high salvage value). The resulting
input values are then used to create a probability distribution of NPV.
For an illustration of scenario analysis, assume that Ridgeland’s managers regard a drop in weekly volume below 30 scans as very unlikely; they
also feel that a volume above 50 is also improbable. On the other hand,
salvage value can be as low as $500,000 or as high as $1 million. The most
likely values are 40 scans per week for volume and $750,000 for salvage
value. Thus, a volume of 30 and a $500,000 salvage value define the lower
bound (or worst-case scenario), while a volume of 50 and a salvage value of
$1 million define the upper bound (or best-case scenario).
Ridgeland can now use the worst-, most likely, and best-case values
for the input variables to obtain the NPV corresponding to each scenario.
Ridgeland’s managers used a spreadsheet model to conduct the analysis, and
exhibit 12.4 summarizes the results. The most likely case results in a positive
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NPV, the worst case produces a large negative NPV, and the best case results
in an even larger positive NPV. These results, along with each scenario’s
probability of occurrence, can now be used to determine the expected NPV
and standard deviation of NPV. Suppose that Ridgeland’s managers estimate
that there is a 20 percent chance that the worst case will occur, a 60 percent
chance that the most likely case will occur, and a 20 percent change that the
best case will occur. Of course, it is difficult to estimate scenario probabilities
with any confidence, and, in most situations, the probabilities used will not
be symmetric. For example, in an environment of increasing managed care
penetration and increasing competition among providers, the probability
may be higher for the worst-case scenario than for the best-case scenario.
Exhibit 12.4 contains a discrete distribution of returns, so the expected
NPV can be found as follows:
Expected NPV = (0.20 × [−$819,844]) + (0.60 × $82,493)
+ (0.20 × $984,829)
= $82,493.
The expected NPV in the scenario analysis is the same as the base case NPV—
$82,493. The results are consistent because, when coupled with the scenario
probabilities, the values of the uncertain variables used in the scenario analysis—30, 40, and 50 scans for volume and $500,000, $750,000, and $1 million for salvage value—produce the same expected values that were used in
the exhibit 12.1 base case analysis. If inconsistencies exist between the base
case NPV and the expected NPV in the scenario analysis, the two analyses
have inconsistent input assumptions. In general, such inconsistencies should
be identified and removed to ensure that common assumptions are used
throughout the project risk analysis. However, remember that our purpose
here is to conduct a risk assessment, not to measure profitability. Ultimately,
Scenario
Worst case
Most likely case
Best case
Expected value
Standard deviation
Probability
of Outcome
Volume
Salvage Value
NPV
0.20
0.60
0.20
30
40
50
$ 500,000
750,000
1,000,000
($ 819,844)
82,493
984,829
40
$ 750,000
$ 82,493
$ 570,688
EXHIBIT 12.4
MRI Project
Scenario
Analysis
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we will use the base case (expected value) cash flows to reassess the project’s
profitability when we have completed the risk assessment.
The standard deviation of NPV, as shown here, is $570,688:
σNPV = [0.20 × (−$819,844 − $82,493)2 + 0.60 × ($82,493 − $82,493)2
+ 0.20 × ($984,829 − $82,493)2]1/2
= $570,688,
while the coefficient of variation (CV) of NPV is 6.9:
CV =
σ NPV
$570, 688
=
= 6.9.
Expected NPV $82, 493
The MRI project’s standard deviation and coefficient of variation
measure its stand-alone risk. Suppose that when a similar scenario analysis
is applied to Ridgeland’s aggregate cash flows (average project), the result
is a coefficient of variation of NPV in the range of 2.5 to 5.0. Then, on the
basis of its stand-alone risk measured by coefficient of variation, along with
subjective judgments, Ridgeland’s managers might conclude that the MRI
project is riskier than the firm’s average project, so it would be classified as a
high-risk project.
Scenario analysis can also be interpreted in a less mathematical way.
The worst-case NPV—a loss of about $800,000—is an estimate of the worst
possible financial consequences of the MRI project. If Ridgeland can absorb
such a loss in value without much impact on its financial condition, the project does not pose significant financial danger to the hospital. Conversely, if
such a loss would mean financial ruin for the hospital, its managers might be
unwilling to undertake the project, regardless of its profitability under the
most likely and best-case scenarios. Note that the risk of the project is not
changing in these two situations. The difference is in the organization’s ability to bear the risk inherent in the project.
While scenario analysis provides useful information about a project’s
stand-alone risk, it is limited in two ways. First, it considers only a few discrete
states of the economy and hence provides information on only a few potential
profitability outcomes for the project. In reality, an almost infinite number of
possibilities exist. Although the illustrative scenario analysis contained only
three scenarios, it can be expanded to include more states of the economy—
say, five or seven. However, there is a practical limit on how many scenarios
can be included in a scenario analysis.
Second, scenario analysis—at least as normally conducted—implies a
definite relationship among the uncertain variables involved. For example,
our analysis assumed that the worst value for volume (30 scans per week)
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would occur at the same time as the worst value for salvage value ($500,000)
because the worst-case scenario is defined by combining the worst possible
value of each uncertain variable. Although this relationship (all worst values
occurring together) may hold in some situations, it may not hold in others.
If volume is low, for example, maybe the MRI will withstand less wear and
tear and hence be worth more after five years of use. The worst value for
volume, then, should be coupled with the best salvage value. Conversely,
poor volume may be symptomatic of poor medical effectiveness of the MRI
and hence lead to limited demand for used equipment and a low salvage
value. Scenario analysis tends to create extreme profitability values for the
worst and best cases because it automatically combines all worst and best
input values, even if these values have only a remote chance of occurring
together. This problem can be mitigated, but not eliminated, by assigning
relatively low probabilities to the best and worst cases. The next section
describes a method of assessing a project’s stand-alone risk that deals with
these two problems.
1. Briefly describe scenario analysis.
2. What type of risk does it attempt to measure?
3. What are its strengths and weaknesses?
SELF-TEST
QUESTIONS
Monte Carlo Simulation
Monte Carlo simulation, so named because it developed out of work on the
mathematics of casino gambling, describes uncertainty in terms of continuous probability distributions, which have an infinite number of outcomes
rather than just a few discrete values. Thus, Monte Carlo simulation provides
a more realistic view of a project’s risk than does scenario analysis and can
be installed on personal computers as an add-on to a spreadsheet program.
Because most financial analysis today is done with spreadsheets, Monte Carlo
simulation is now accessible to virtually all health services organizations, both
large and small.
The first step in a Monte Carlo simulation is to create a model that
calculates the project’s net cash flows and profitability measures, just as was
done for Ridgeland’s MRI project. The relatively certain variables are estimated as single, or point, values in the model, while continuous probability
distributions are used to specify the uncertain cash flow variables. After the
model has been created, the simulation software automatically executes the
following steps:
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1. The Monte Carlo program chooses a single random value for each
uncertain variable on the basis of its specified probability distribution.
2. The values selected for each uncertain variable, along with the point
values for the relatively certain variables, are combined in the model to
estimate the net cash flow for each year.
3. Using the net cash flow data, the model calculates the project’s
profitability—for example, as measured by NPV. A single completion of
these three steps constitutes one iteration, or run, in the Monte Carlo
simulation.
4. The Monte Carlo software repeats these steps many times (e.g.,
5,000). Because each run is based on different input values, each run
produces a different NPV.
The ultimate result of the simulation is an NPV probability distribution
based on a large number of individual scenarios, which encompasses almost
all of the likely financial outcomes. Monte Carlo software usually displays
the results of the simulation in both tabular and graphical forms and automatically calculates summary statistical data such as expected value, standard
deviation, and skewness.4
For an illustration of Monte Carlo simulation, again consider Ridgeland’s MRI project. As in the scenario analysis, the illustration has been simplified by specifying the distributions for only two key variables: (1) weekly
volume and (2) salvage value. Weekly volume is not expected to vary by more
than ±10 scans from its expected value of 40 scans. Because this situation is
symmetrical, the normal (bell-shaped) distribution can be used to represent
the uncertainty inherent in volume. In a normal distribution, the expected
value ±3 standard deviations will encompass almost the entire distribution.
Thus, a normal distribution with an expected value of 40 scans and a standard
deviation of 10 ÷ 3 = 3.33 scans is a reasonable description of the uncertainty
inherent in weekly volume.
A triangular distribution was chosen for salvage value because it
specifically fixes the upper and lower bounds, whereas the tails of a normal
distribution are, in theory, limitless. The triangular distribution is also used
extensively when the input distribution is nonsymmetrical because it can
easily accommodate skewness. Salvage value uncertainty was specified by a
triangular distribution with a lower limit of $500,000, a most likely value of
$750,000, and an upper limit of $1 million.
The basic MRI model containing these two continuous distributions
was used, plus a Monte Carlo add-on to the spreadsheet program, to conduct a simulation with 5,000 iterations. The output is summarized in exhibit
12.5, and the resulting probability distribution of NPV is plotted in exhibit
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C hap ter 12: Proj ec t Risk A naly sis
473
12.6. The mean, or expected, NPV ($82,498) is about the same as the base
case NPV and expected NPV indicated in the scenario analysis ($82,493).
In theory, all three results should be the same because the expected values
for all input variables are the same in the three analyses. However, some randomness exists in the Monte Carlo simulation that leads to an expected NPV
that is slightly different from the others. The more iterations that are run,
the more likely the Monte Carlo NPV will be the same as the base case NPV,
assuming that the assumptions are consistent.
The standard deviation of NPV is lower in the simulation analysis
because the NPV distribution in the simulation contains values within the
Expected NPV
$ 82,498
Minimum NPV
($ 951,760)
Maximum NPV
$ 970,191
Probability of a positive NPV
Standard deviation
Skewness
EXHIBIT 12.5
Simulation
Results
Summary
62.8%
$256,212
0.002
EXHIBIT 12.6
NPV Probability
Distribution
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entire range of possible outcomes, while the NPV distribution in the scenario
analysis contains only the most likely value and the best-case and worst-case
extremes. In this illustration, one value for volume uncertainty was specified
for all five years; that is, the value chosen by the Monte Carlo software for
volume in year 1—for example, 40 scans—was used as the volume input for
the remaining four years in that iteration of the simulation analysis. As an
alternative, the normal distribution for year 1 can be applied to each year
separately, which would allow the volume forecasts to vary from year to year.
Then, the Monte Carlo software might choose 35 as the value for year 1, 43
as the year 2 input, 32 for year 3, and so on. This approach, however, probably does not do a good job of describing real-world behavior; high usage
in the first year presumably means strong acceptance of the MRI system and
hence high usage in the remaining years. Similarly, low usage in the first year
probably portends low usage in future years.
The volume and salvage value variables were treated as independent
in the simulation; that is, the value chosen by the Monte Carlo software
from the salvage value distribution was not related to the value chosen
from the volume distribution. Thus, in any run, a low volume can be
coupled with a high salvage value and vice versa. If Ridgeland’s managers believe that high utilization at the hospital indicates a strong national
demand for MRI systems, they can specify a positive correlation between
these variables. A positive correlation would tend to increase the riskiness
of the project because a low-volume pick in one iteration cannot be offset
by a high–salvage value pick. Conversely, if the salvage value is more a
function of the technological advances that occur over the next five years
than local utilization, it may be best to specify the variables as independent, as was done.
As in scenario analysis, the project’s simulation results must be compared with a similar analysis of the firm’s average project. If Ridgeland’s
average project were considered to have less stand-alone risk when a Monte
Carlo simulation was conducted, the MRI project would be judged to have
above-average (high) stand-alone risk.
Monte Carlo simulation has two primary advantages over scenario
analysis: (1) All possible input variable values are considered, and (2) correlations among the uncertain inputs can be incorporated into the analysis. However, there is a downside to these two advantages: Although it is mechanically
easy to input the probability distributions for the uncertain variables as well
as their correlations into a Monte Carlo simulation, it is much more difficult
to determine what those distributions and correlations are. The problem is
that the more information a risk-analysis technique requires, the harder it is
to develop the data with any confidence; hence, managers are left with an
elegant result of questionable value.
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1. Briefly, what is Monte Carlo simulation?
2. What type of risk does it attempt to measure?
3. What are its strengths and weaknesses?
SELF-TEST
QUESTIONS
Qualitative Risk Assessment
In some situations, it may be difficult to conduct a quantitative risk assessment because the input variable estimates are nebulous. In other situations, a
quantitative assessment may be possible, but a verification of results provides
managers with additional confidence. More and more healthcare organizations are using qualitative risk assessment techniques to confirm quantitative
assessment results or as the sole basis for the risk assessment.
Qualitative risk assessment is based on the answers to a set of questions. For example, one large healthcare clinic uses these questions:
• Does the project require additional market share or represent a new
service initiative?
• Is the project outside the scope of current management expertise?
• Does the project require difficult-to-recruit physicians, nurses, or
technical specialists?
• Will the project pit the organization against a strong competitor?
• Does the project involve new, unproven technology?
Each “yes” answer is assigned one point (while each “no” answer
receives zero points). If the total point count for the project is zero, it is
judged to have low risk; one or two points indicate moderate risk, and three
or more points indicate high risk. Although such a subjective approach
appears to have little theoretical basis, a closer examination reveals that each
question in the list seen earlier is tied to cash flow uncertainty. The greater
the number of “yes” answers, the greater the cash flow uncertainty and hence
the greater the stand-alone risk of the project.
The value of using the qualitative risk assessment approach in conjunction with a quantitative risk assessment is that it forces managers to think
about project risk in alternative frameworks. If the quantitative and qualitative assessments do not agree, the project’s risk assessment requires more
consideration.
After some discussion, Ridgeland’s managers concluded that the
MRI project’s qualitative risk assessment score was 3. Thus, the quantitative
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and qualitative assessments reached the same conclusion: The project has
high risk.
SELF-TEST
QUESTIONS
1. Describe qualitative risk assessment.
2. Why does a qualitative risk assessment work?
3. Assume a quantitative risk assessment has been conducted on a
project. Is a qualitative risk assessment necessary?
Incorporating Risk into the Decision Process
Thus far, the MRI illustration has demonstrated that a project’s riskiness is
difficult to quantify. It may be possible to reach a general conclusion that
one project is more or less risky than another or to compare the riskiness of
a project with the business as a whole, but
it is difficult to develop a good measure of
project risk. This lack of precision in meaHow Many Scenarios in a
suring project risk adds to the difficulties
Scenario Analysis?
involved in incorporating differential risk
into the capital budgeting decision.
In the scenario analysis of Ridgeland’s MRI project, we used three scenarios. However, three is
There are two methods for incorno magic number, given that the more scenarios
porating project risk into the capital budused, the more information is obtained from the
geting decision process: (1) the certainty
analysis. Furthermore, more scenarios lessen
equivalent method, which adjusts a projthe problem associated with extreme values
ect’s expected cash flows to reflect project
because the best- and worst-case scenarios can
risk, and (2) the risk-adjusted discount rate
be assigned low probabilities (which are probably
realistic) without causing the risk inherent in the
method, which deals with differential risk
project to be understated.
by changing the cost of capital. Although
Although more scenarios add additional realmost businesses use the risk-adjusted disism and provide more information for decision
count rate method, there are some theomakers, a greater number of scenarios increases
retical advantages to using the certainty
forecasting difficulty and makes the analysis more
equivalent method. Furthermore, it raises
time-consuming. Furthermore, the greater the number of scenarios, the more difficult it is to interpret
some interesting issues related to the riskthe results. Thus, the entire process is easier if
adjustment process.
three scenarios are used rather than, say, nine.
What do you think? Are three scenarios
sufficient or should more be used? How many
scenarios are too many? Is it better to have an
odd number than an even number of scenarios? Is
there an optimal number of scenarios?
Certainty Equivalent Method
The certainty equivalent (CE) method
directly follows the economic concept of
utility.5 Under the CE approach, managers must first evaluate a cash flow’s risk
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C hap ter 12: Proj ec t Risk A naly sis
and then specify how much money, with certainty, would be required for an
individual to be indifferent between the riskless (certain) sum and the risky
cash flow’s expected value. For example, suppose that a rich eccentric offered
someone the following choices:
• Flip a coin. If it is a head, the individual receives $1 million; if it
is a tail, the individual receives nothing. The expected value of the
gamble is (0.5 × $1,000,000) + (0.5 × $0) = $500,000, but the actual
outcome will be either zero or $1 million, so the gamble is highly risky.
• Do not flip the coin. Simply pocket $400,000 in cash.
If the individual is indifferent to the two alternatives, $400,000 is defined to
be her CE amount for this particular risky expected $500,000 cash flow. The
riskless $400,000 provides that individual with the same satisfaction (utility)
as the risky $500,000 expected return.
In general, investors are risk averse, so the CE amount for this gamble
will be something less than the $500,000 expected value. Each individual
would have his own CE value—the greater the individual’s degree of risk
aversion, the lower the CE amount.
The CE concept can be applied to capital budgeting decisions, at least
in theory, in this way:
• Convert each net cash flow of a project to its CE value. Here, the
riskiness of each cash flow is assessed, and a CE cash flow is chosen on
the basis of that risk. The greater the risk, the greater the difference
between the expected value and its lower CE value. (If a cash outflow
is being adjusted, the CE value is higher than the expected value. The
unique risk adjustments required on cash outflows will be discussed in
a later section.)
• Once each cash flow is expressed as a CE, discount the project’s CE
cash flow stream by the risk-free rate to obtain the project’s differential
risk adjusted NPV.6 Here, the term “differential risk-adjusted” implies
that the unique riskiness of the project, as compared to the overall
riskiness of the business, has been incorporated into the decision
process. The risk-free rate is used as the discount rate because CE cash
flows are analogous to risk-free cash flows.
• A positive differential risk-adjusted NPV indicates that the project is
profitable even after adjusting for differential (project-specific) risk.
The CE method is simple and neat. Furthermore, it can easily handle
differential risk among the individual cash flows. For example, the final year’s
CE cash flow might be adjusted downward an additional amount to account
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for salvage value risk if that risk is considered to be greater than the risk inherent in the operating cash flows.
Unfortunately, there is no practical way to estimate a risky cash flow’s
CE value. No benchmarks are available to inform the estimate, so each individual would have her own estimate, and they can vary significantly. Also, the
risk assessment techniques—for example, scenario analysis—focus on profitability and hence measure the stand-alone risk of a project in its entirety. This
process provides no information about the riskiness of individual cash flows,
so there is no basis for adjusting each cash flow to reflect its own unique risk.
Risk-Adjusted Discount Rate Method
In the risk-adjusted discount rate (RADR) method, expected cash flows
are used in the valuation process, and the risk adjustment is made to the
discount rate (the opportunity cost of capital). All average-risk projects are
discounted at the business’s corporate cost of capital, which represents the
opportunity cost of capital for average-risk projects; high-risk projects are
assigned a higher cost of capital; and low-risk projects are discounted at a
lower cost of capital.
One advantage to using the RADR method is that it has a starting
benchmark: the business’s corporate cost of capital. This discount rate reflects
the riskiness of the business in the aggregate, or the riskiness of the firm’s
average project. Another advantage is that project risk-assessment techniques
identify a project’s aggregate risk—the combined risk of all of the cash
flows—and the RADR applies a single adjustment to the cost of capital rather
than attempts to adjust individual cash flows. However, the disadvantage is
that, typically, there is no theoretical basis for setting the size of the RADR
adjustment, so the amount of adjustment remains a matter of judgment.
There is one additional disadvantage to using the RADR method.
RADR combines the factors that account for time value (the risk-free rate)
and the adjustment for risk (the risk premium): Project cost of capital = Differential risk-adjusted discount rate = Risk-free rate + Risk premium. The
CE approach, on the other hand, keeps risk adjustment and time value separate—time value in the discount rate and risk adjustment in the cash flows. By
lumping together risk and time value, the RADR method compounds the risk
premium over time, just as interest compounds over time. This compounding of the risk premium means that the RADR method automatically assigns
more risk to cash flows that occur in the distant future, and the farther into
the future, the greater the implied risk. Because the CE method assigns risk
to each cash flow individually, it does not impose assumptions regarding the
relationship between risk and time.
The RADR model is one method used to incorporate risk in the capital budgeting decision process. It is based on the following concept:
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C hap ter 12: Proj ec t Risk A naly sis
Key Equation 12.1: Risk-Adjusted Discount Rate (RADR) Theoretical Model
Project cost of capital = Risk-free rate + Risk premium.
The idea here is that the risk-free rate accounts for the time value
of money, while the risk premium accounts for the unique (below average,
average, or above average) risk of the project. The RADR method as it is
normally used—with a constant discount rate applied to all cash flows of
a project—implies that risk increases with time. This implication imposes a
greater burden on long-term projects, so short-term projects tend to look
better financially than do long-term projects. For most projects, the assumption that risk increases over time is probably reasonable because cash flows
are more difficult to forecast the farther one moves into the future. However,
managers should be aware that the RADR approach automatically penalizes
distant cash flows, and an additional explicit penalty based solely on cash flow
timing is not warranted unless some specific additional risk can be identified.
1. What are the differences between the CE and RADR methods for
risk incorporation?
2. What assumptions about time and risk are inherent in the RADR
method?
3. How do most businesses incorporate differential risk into the
capital-budgeting decision process?
SELF-TEST
QUESTIONS
Final Risk Assessment and Incorporation for the MRI
Project
In most project risk analyses, it is impossible to assess the project’s corporate
or market risk quantitatively, and managers are left with only an assessment of
the project’s stand-alone risk. However, like the MRI project, most projects
being evaluated are in the same line of business as the firm’s other projects,
and the profitability of most firms is highly correlated with the overall economy. Thus, stand-alone, corporate, and market risk are usually highly correlated, which suggests that managers can get a feel for the relative risk of most
projects on the basis of the quantitative and qualitative analyses conducted
to assess the project’s stand-alone risk. In Ridgeland’s case, its managers
concluded that the MRI project, with its above-average stand-alone risk, also
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had above-average corporate risk, which is the risk most relevant to not-forprofit organizations; hence, the project was categorized as a high-risk project.
The business’s corporate cost of capital provides a basis for estimating
a project’s differential RADR—average-risk projects are discounted at the
corporate cost of capital, high-risk projects are discounted at a higher cost of
capital, and low-risk projects are discounted at a rate below the corporate cost
of capital. Unfortunately, there is no good
Uncertainty in Initial Cash Outflows
way of specifying exactly how much higher
In many capital budgeting situations, the initial
or lower these discounts rates should be;
cost of the project—especially when occurring
given the present state of the art, risk
only at time 0—is assumed to be known with
adjustments are necessarily judgmental
certainty. The idea here is that, in most cases,
and somewhat arbitrary.
bids have already been received from vendors,
Ridgeland’s standard procedure is
so the initial cost can be predicted with relative
precision. However, in some circumstances, there
to add 4 percentage points to its 10
can be substantial uncertainty in initial costs. For
percent corporate cost of capital when
example, there can be a great deal of uncertainty
evaluating high-risk projects and to subin the cost of a building that will not be contract 2 percentage points when evaluating
structed for several years. Or there can be uncerlow-risk projects. Thus, to estimate the
tainty in the cost of a major construction project
high-risk MRI project’s differential riskthat will take several years to complete.
When there is uncertainty in initial cost, how
adjusted NPV, the project’s expected (base
should that risk be incorporated into the analycase) cash flows shown in exhibit 12.1
sis? If the entire cost (or even the major portion)
are discounted at 10% + 4% = 14%. This
occurs at time 0, the discount rate is not applied
rate is called the project cost of capital, as
to the cash flow, so the RADR method will not get
opposed to the corporate cost of capital,
the job done.
because it reflects the risk characteristics
What do you think? Can the CE method be
used? Assume that time 0 costs on a project could
of a specific project rather than the aggrebe $100,000 or $150,000 with equal profitability,
gate risk characteristics of the business.
so the expected initial cost is $125,000. What is
The resultant NPV is −$200,017, so the
your estimate of the CE cash flow? (Hint: Rememproject becomes unprofitable when the
ber that risk adjustments to cash outflows are the
analysis is adjusted to reflect its high risk.
opposite of those applied to inflows.)
Ridgeland’s managers may still decide to
go ahead with the MRI project, but at
least they know that its expected profitability is not sufficient to make up for its riskiness.
The RADR method is implemented as follows:
Key Equation 12.2: Risk-Adjusted Discount Rate (RADR)
Implementation Model
Project cost of capital = Corporate cost of capital + Risk adjustment.
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C hap ter 12: Proj ec t Risk A naly sis
Here, the corporate cost of capital is used as the base rate (starting point),
and a risk adjustment is applied if the project has non-average risk. For aboveaverage risk projects, the risk premium is added to the base rate, while the
risk premium is subtracted for those projects judged to have below-average
risk. To illustrate, assume a project having above-average risk is being evaluated. The corporate cost of capital is 10 percent, and the standard adjustment
amount is 3 percentage points. With these assumptions, the project cost of
capital is 13 percent:
Project cost of capital = Corporate cost of capital + Risk adjustment
= 10% + 3% = 13%.
1. How did Ridgeland’s managers translate the MRI project’s standalone risk assessment into a corporate risk assessment?
2. How was risk incorporated into the MRI project decision process?
3. Is the risk adjustment objective or subjective?
4. What is a project cost of capital?
SELF-TEST
QUESTIONS
Incorporating Debt Capacity into the Decision Process
Just as different businesses have different optimal capital structures, so do
individual projects. In any business, the overall optimal capital structure,
which is reflected by the weights used in the corporate cost of capital estimate, is an aggregation of the optimal capital structures of the business’s
individual projects. However, some projects support only a little debt, while
other projects support a high level of debt. The proportion of debt in a
project’s, or a business’s, optimal capital structure is called the project’s, or
business’s, debt capacity.
One mistake often made when considering a project’s debt capacity
is to look at how the project is actually financed. For example, even though
Ridgeland may be able to obtain a secured loan for the entire cost of the MRI
equipment, the MRI project does not have a debt capacity of 100 percent.
The willingness of lenders to furnish 100 percent debt capital for the MRI
project is based more on Ridgeland’s overall creditworthiness than on the
financial merits of the MRI project because all of the hospital’s operating
cash flow, less interest payments on embedded debt, is available to pay the
lender. Think of it this way: Would lenders provide 100 percent financing if
Ridgeland were a start-up business and the MRI project was its sole source
of income?
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The logical question here is whether debt capacity differences should
be taken into consideration in the capital budgeting process. In theory, if
there are meaningful debt capacity differences between a project and the
business, capital structure differentials—as well as risk differentials—should
be taken into account in the capital budgeting process. For example, an academic health center might be evaluating two projects: one involves research
and development (R&D) of a new surgical procedure, and the other involves
building a primary care clinic in a local upscale residential area. The R&D
project would have relatively low debt capacity because it has high business
risk and no assets suitable as loan collateral. Conversely, the clinic project
would have relatively high debt capacity because it has low business risk and
involves real estate suitable as collateral.
Incorporating capital structure differentials is mechanically easy. We
merely change the weights used to compute the corporate cost of capital to
reflect project debt capacity rather than use the standard weights that reflect
the business’s target capital structure. Projects with higher-than-average debt
capacity would use a relatively high value for the weight of debt and a relatively low value for the weight of equity and vice versa. However, a problem
arises when attempting to make debt capacity adjustments. We know from
chapter 10 that increased debt usage raises capital costs, so both the cost of
debt and the cost of equity must increase as more debt financing is used. This
dependency of capital costs on capital structure means that as the weights are
changed in the cost-of-capital calculation, so should the component costs.
However, it is very difficult, if not impossible, to estimate individual project
costs of debt and equity that correspond to the project’s optimal capital
structure. Thus, capital structure adjustments quickly become a somewhat
futile guessing game, so most businesses do not make such adjustments
unless there are specific benchmark values that can be used for both a project’s unique debt capacity and the corresponding capital costs.7
SELF-TEST
QUESTION
1. Discuss the advantages and disadvantages of incorporating debt
capacity differences into the capital budgeting decision process.
Adjusting Cash Outflows for Risk
Although most projects are evaluated on the basis of profitability, some are
evaluated solely on the basis of costs. Such evaluations are done when it is
impossible to allocate revenues to a particular project or when two competing projects will produce the same revenue stream. For example, suppose that
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C hap ter 12: Proj ec t Risk A naly sis
483
Ridgeland must choose one of two ways of disposing of its medical waste.
There is no question about the necessity of the project, and neither method
will affect the hospital’s revenue stream. In this situation, the decision will
be based on the present value of expected future costs; the method with the
lower present value of costs will be chosen.
Exhibit 12.7 lists the projected annual costs associated with each
method. A large expenditure would be required at year 0 to upgrade the
hospital’s current disposal system, but the yearly operating costs would be
relatively low. Conversely, if Ridgeland contracts for disposal services with an
outside contractor, it will have to pay only $25,000 up front to initiate the
contract. However, the annual contract fee would be $200,000 a year. Note
that inflation effects are ignored in this illustration to simplify the discussion.
If both methods were judged to have average risk, Ridgeland’s corporate cost of capital—10 percent—would be applied to the cash flows to
obtain the present value (PV) of costs for each method. Because the PVs of
costs for the two waste disposal systems—$784,309 for the in-house system
and $783,157 for the contract method—are roughly equal at a 10 percent discount rate, Ridgeland’s managers would be indifferent as to which
method should be chosen if they were basing the decision on financial considerations only.
However, Ridgeland’s managers actually believe that the contract
method is much riskier than the in-house method. They know the cost of
modifying the current system to the dollar, and they can predict operating
costs fairly well. Furthermore, the in-house system’s operating costs are under
the control of Ridgeland’s management. Conversely, if the hospital relies on
Cash Flows
Year
In-House System
Outside Contract
0
1
2
3
4
5
($500,000)
(75,000)
(75,000)
(75,000)
(75,000)
(75,000)
($ 25,000)
(200,000)
(200,000)
(200,000)
(200,000)
(200,000)
Present value of costs at a discount rate of:
10%
($784,309)
14%
–  
6%
–  
($ 783,157)
($ 711,616)
($ 867,473)
EXHIBIT 12.7
Ridgeland
Community
Hospital:
Waste Disposal
Analysis
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the contractor for waste disposal, it more or less will have to continue the
contract because it will lose in-house capability. Because the contractor was
willing to guarantee the price only for the first year, perhaps the bid was lowballed and large price increases will occur in future years. The two methods
have about the same PV of costs when both are considered to have average
risk—so which method should be chosen if the contract method is judged to
have high risk? Clearly, if the costs are the same under a common discount
rate, the lower-risk in-house project should be chosen.
Now, try to incorporate this intuitive differential risk conclusion into
the quantitative analysis. Conventional wisdom is to increase the corporate
cost of capital for high-risk projects, so the contract cash flows would be
discounted using a project cost of capital of 14 percent, which is the rate
that Ridgeland applies to high-risk projects. However, at a 14 percent discount rate, the contract method has a PV of costs of only $711,616, which
is about $70,000 lower than that for the in-house method. If the discount
rate on the contract method’s cash flows were increased to 20 percent, an
even greater amount, it would appear to be $161,000 cheaper than the inhouse method. Thus, the riskier the contract method is judged to be, the
better it looks.
Something is obviously wrong here! For a cash outflow to be penalized for higher-than-average risk, it must have a higher present value, not a
lower one. Therefore, a cash outflow that has higher-than-average risk must
be evaluated with a lower-than-average cost of capital. Recognizing this,
Ridgeland’s managers applied a 10% − 4% = 6% discount rate to the highrisk contract method’s cash flows. The result is a PV of costs for the contract
method of $867,473, which is about $83,000 more than the PV of costs for
the average-risk in-house method.
The appropriate risk adjustment for cash outflows is also applicable in other situations. For example, the city of Detroit offered Ann
Arbor Health Care Inc. the opportunity to use a city-owned building in a
blighted area for a walk-in clinic. The city offered to pay to refurbish the
building, and all profits made by the clinic would accrue to Ann Arbor.
However, after ten years, Ann Arbor would have to buy the building from
the city at the then-current market value. The market value estimate that
Ann Arbor used in its analysis was $2 million, but the realized cost could
be much greater, or much less, depending on the economic condition of
the neighborhood at that time. The project’s other cash flows were of
average risk, but this single outflow was high risk, so Ann Arbor lowered
the discount rate that it applied to this one cash flow. This action created a
higher present value for the $2 million cost (outflow) and hence lowered
the project’s NPV.
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C hap ter 12: Proj ec t Risk A naly sis
The bottom line here is that risk adjustment for cash outflows is the
opposite of adjustment for cash inflows. When cash outflows are being evaluated, higher risk calls for a lower discount rate.8
1. Why are some projects evaluated on the basis of present value of
costs?
2. Is there any difference between the risk adjustments applied to
cash inflows and cash outflows? Explain your answer.
3. Can differential risk adjustments be made to single cash flows, or
must the same adjustment be made to all of a project’s cash flows?
SELF-TEST
QUESTIONS
Real (Managerial) Options
According to traditional capital budgeting analysis techniques, a project’s
NPV is the present value of its expected future cash flows when discounted
at an opportunity cost rate that reflects the riskiness of those flows. However, as discussed in chapter 11 in the section on strategic value, such valuations generally do not incorporate the value inherent in additional actions
that the business can take only if the project is accepted. In other words,
traditional capital budgeting can be likened to playing roulette: A bet is
made (the project is accepted) and the wheel is spun, but nothing can be
done to influence the outcome of the game. In reality, capital projects are
more like draw poker: Chance does play a role, but the players can influence the final result by discarding the right cards and assessing the other
players’ actions.
The opportunities that managers have to change a project in response
to changing conditions or to build on a project are called real, or managerial,
options. These terms denote that such options arise from investments in real,
rather than financial, assets and that the options are available to managers of
businesses as opposed to individual investors. To illustrate the concept of real
options, we introduce decision tree analysis.
Although risk analysis is an integral part of capital budgeting, managers are at least as concerned (or maybe more concerned) about managing risk
than they are about measuring it. One way of managing risk is to structure
large projects as a series of decision points that provide the opportunity to
reevaluate decisions as additional information becomes available, and possibly
to cancel—or once it begins, to abandon—the project if events take a turn
for the worse.
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Projects that are structured as a series of decision points over time
are evaluated using decision trees. For example, suppose Medical Equipment
International (MEI) is considering the production of a new and innovative
intensive care monitoring system. The net investment for this project is broken down into three stages, as set forth in exhibit 12.8. If the go-ahead is
given for stage 1 (year 0), the firm will conduct a $500,000 study of the market potential for the new monitoring system, which will take about one year.
If the results of the study are unfavorable, the project will be canceled, but if
the results are favorable, MEI will (at year 1) spend $1 million to design and
fabricate several prototype systems. These systems will then be tested at two
hospitals, and MEI will base its decision to proceed with full-scale production
on their medical staffs’ reactions to them.
If their reactions are positive, MEI will establish a production line for
the monitoring systems at one of its plants at a net cost of $10 million. If
this stage is reached, MEI’s managers estimate that the project will generate
net cash flows over the following four years that will depend on the vitality
of the hospital sector at that time and the overall performance of the system.
A decision tree such as the one in exhibit 12.8 often is used to analyze
such multistage, or sequential, decisions. Here, for simplicity, let’s assume that
one year goes by between decisions. Each circle represents a decision point
or stage. The dollar value to the left of each decision point represents the net
investment required to go forward at that decision point, and the cash flows
under the t = 3 to t = 6 headings represent the cash inflows that would occur
if the project is carried to completion. Each diagonal line represents the beginning of a branch of the decision tree, and each carries a probability that MEI’s
managers estimate on the basis of the information available to them today. For
example, management estimates that there is a probability of 0.8 that the initial study will produce favorable results, which would lead to the expenditure
of $1 million at stage 2, and a 0.2 probability that the initial study will produce
unfavorable results, which would lead to cancellation after stage 1.
The joint probabilities shown in exhibit 12.8 give the probability of
occurrence of each final outcome—that is, the probability of moving completely along each branch. Each joint probability is obtained by multiplying
together all the probabilities along a particular branch. For example, if stage
1 is undertaken, the probability that MEI will move through stages 2 and 3
and that a strong demand will produce $10 million in net cash flows in each
of the next four years is 0.8 × 0.6 × 0.3 = 0.144 = 14.4%.
The NPV of each final outcome is also given in exhibit 12.8. MEI
has a corporate cost of capital of 11.5 percent, and its management assumes
initially that all projects have average risk. For example, the NPV of the
top branch (the most favorable outcome) is about $15,250 (in thousands
of dollars):
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($500)
t=0
0.8
1
Stop
($1,000)
t=1
2
0.6
Stop
3
0.3
($10,000)
t=2
0.144
$ 2,000 $ 2,000 ($ 2,000) ($ 2,000)
0.200
1.000
0.320
0.192
$ 4,000
0.144
(1,397)
(14,379)
436
$15,250
NPV
(447)
(2,701)
84
$ 2,196
Product:
Prob. × NPV
(500)
(100)
Expected NPV = ($ 338)
σNPV= $7,991
Joint
Probability
0.4$ 4,000 $ 4,000 $ 4,000
t=6
$10,000
$10,000
$10,000
t=5
$10,000
t=4
t=3
Time
EXHIBIT 12.8
Decision Tree Analysis (in thousands of dollars)
C hap ter 12: Proj ec t Risk A naly sis
0.3
0.4
0.2
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$1, 000 $10, 000 $10, 000 $10, 000
−
+
+
(1.115)1 (1.115)2 (1.115)3 (1.115)4
$10, 000 $10, 000
+
+
(1.115)5 (1.115)6
= $15, 250.
NPV = −$500 −
Other NPVs are calculated similarly.
The last column in exhibit 12.8 indicates the product of the NPV for
each branch and the joint probability that that branch will occur; the sum
of the NPV products is the expected NPV of the project. Considering the
expectations set forth in exhibit 12.8, and assuming a cost of capital of 11.5
percent, we determine that the monitoring equipment project’s expected
NPV is −$338,000.
Because the expected NPV is negative, it appears that this project
would be unprofitable and hence should be rejected by MEI unless other
considerations prevail. However, this initial judgment may not be correct.
MEI must now consider whether this project is more, less, or about as risky
as the firm’s average project. The expected NPV is a negative $338,000, and
the standard deviation of NPV is $7,991,000, so the coefficient of variation
of NPV is $7,991,000 ÷ $338,000 = 23.6, which is quite large. (Note that
the negative sign for NPV does not enter into the calculation.) The value for
the coefficient of variation suggests that the project is highly risky in terms
of stand-alone risk. Note also that there is a 0.144 + 0.320 + 0.200 = 0.664
= 66.4% probability of incurring a loss. On the basis of these findings, the
project appears to be unacceptable financially unless it has some embedded
real options that will increase its value or reduce its risk.
The Real Option of Abandonment
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Abandonment, which is discussed in chapter 11 in connection with estimating a project’s economic life, is one type of real option that many projects
possess. For an illustration of this real option’s impact, suppose that MEI is
not contractually bound to continue the project once production has begun.
Thus, if sales are poor during year 3 (t = 3), if MEI experiences a cash flow
loss of $2 million, and if similar results are expected for the remaining three
years, MEI can abandon the project at the end of year 3 rather than continue
to suffer losses. In this situation, low first-year sales signify that the monitoring equipment is not selling well, so future sales will also be poor, and MEI
can act on this new information when it becomes available.
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C hap ter 12: Proj ec t Risk A naly sis
MEI’s ability to abandon the project changes the branch of the decision tree that contains the series of $2 million losses in exhibit 12.8. It now
appears as follows (in thousands of dollars):
3
0.3
($2,000)
4
Stop
Joint
Probability
NPV
Product:
Prob. × NPV
0.144
($10,883)
($1,567)
Changing this branch to reflect abandonment eliminates the $2 million cash losses in years 4, 5, and 6 and thus causes the NPV for the branch
to be higher, although still negative. This change increases the project’s
expected NPV from −$338,000 to about $166,000 and lowers the project’s
standard deviation from $7,991,000 to $7,157,000. Thus, the abandonment
real option changes the project’s expected NPV from negative to positive and
also lowers its stand-alone risk as measured either by standard deviation or by
coefficient of variation of NPV.
We can use the data just developed to estimate the value of the abandonment option. The NPV with the abandonment option is $166,000, while
the NPV without this option is −$338,000, so the value of the real option is
$166,000 − (−$338,000) = $504,000. However, this value understates the
true value of the option because the ability to abandon the project also lowers
the riskiness of the project. With lower risk, the difference between the two
NPVs is greater than that calculated, although the added value of risk reduction would be relatively small in this illustration as well as difficult to quantify
with confidence. Because of this and similar complications, discounted cash
flow techniques (when they can be used to value real options) generally will
not produce an accurate estimate of the option’s value.
Here are some additional points to note concerning decision tree
analysis and abandonment:
• Managers can reduce project risk if they can structure the decision
process to include several decision points rather than just one. If
MEI were to make a total commitment to the monitoring equipment
project at t = 0 and sign contracts that would require completion of
the project, it might save some money and accelerate the project, but
doing so would substantially increase the project’s riskiness.
• Once production or service begins, a business’s ability to abandon a
project can dramatically reduce the project’s risk.
• The cost of abandonment generally is reduced if the firm has
alternative uses for the project’s assets. If MEI can convert the
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abandoned monitoring equipment production line to a different, more
productive use, the cost of abandonment would be reduced and the
monitoring equipment project would become more attractive.
Finally, note that capital budgeting is a dynamic process. Virtually all
inputs to a capital budgeting decision change over time, and firms must periodically review both their expenditure plans and their ongoing projects. In
the MEI example, conditions might change between decision points 1 and 2;
if they do, this new information should be used to revise the probability and
cash flow estimates. If a capital budgeting decision can be structured with
multiple decision points, including abandonment, and if the firm’s managers have the fortitude to admit when a project is not working out as initially
planned, risks can be reduced and expected profitability can be increased.
Other Real Options
The MEI monitoring system project demonstrates that the real option of
abandonment can add value to a project. In addition to abandonment, there
are many other types of real options.
Flexibility Options
The flexibility option allows managers to switch inputs between alternative
production or service processes. For example, by training clinical personnel
to perform multiple tasks, individuals hired for a new service can potentially
be used productively in other parts of the business. Thus, labor costs associated with the new service can be easily reduced if demand estimates are not
met. This flexibility option reduces costs in poor utilization scenarios and
hence increases the value of the project.
Capacity Options
The capacity option allows businesses to manage their productive capacity in
response to changing market conditions. If a project can be structured so that
its operations can be reduced or suspended if warranted rather than completely shut down, the value of the project increases. The option to expand
new services from a relatively small scale to a large scale also adds value.
New Service Options
It is easy to envision a situation in which a negative NPV project is accepted
because embedded in it is an option to add complementary services or successive “generations of services.” A managed care organization’s first move
into a new geographic area and the introduction of transplant services at a
hospital are two examples. In such situations, the first project may not be
profitable, but it can lead to additional opportunities that are.
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C hap ter 12: Proj ec t Risk A naly sis
Timing Options
In our examples thus far, new projects brought with them embedded real
options that could be exercised in the future and hence added value to the
project. Timing options can be somewhat different, in that in some circumstances they involve extinguishing existing real options. Timing options
were first analyzed in situations involving natural resources, such as when to
harvest a forested area or how much oil to pump out of a well. By harvesting or pumping now, the project can produce immediate cash flows, but
doing so eliminates the opportunity to obtain future cash flows from the
same resource.
Of most interest to healthcare businesses is the option to delay, which
is another type of timing option. If a project can be postponed, it might be
more valuable in the future because, for example, managed care power is
diminishing, technology is advancing, or information that will decrease the
project’s risk is expected to become available. Of course, the option to delay
is valuable only if it is worth more than the costs of delaying, which include
time value of money costs, costs associated with competitor actions, and
patient satisfaction costs. Thus, in general, the option to delay is most valuable to businesses that have proprietary technology or some other barrier to
entry that lessens the costs associated with postponement.
491
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Valuation of Projects That Have Real Options
In general, the true value of a project with real options can be thought of
as the discounted cash flow (DCF) NPV plus the value of the real options:
True NPV = DCF NPV + Value of real options.
In most healthcare situations, a dollar value cannot be placed on any real
options associated with a project. However, managers should still think about
the value of many projects in terms of this equation. Here are some points
to consider:
• Real options can add considerable value to many projects, so failure
to consider such options leads to downward-biased NPVs and thus to
systematic underinvestment.
• In general, the longer a real option lasts before it must be “exercised,”
the more valuable it is. For example, suppose the real option is to
expand into related services, such as expanding rehabilitative services
into sports medicine services. The longer the expansion can be delayed
and still retain its value, the more valuable the option.
• The more volatile the value of the underlying source of the real option,
the more valuable the option. Thus, the more return volatility there is
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in the return on sports medicine services, the greater the value of a real
option to expand into such services.
• The higher the cost of capital (the higher the general level of interest
rates), the more valuable the real option. This point is not intuitive,
but we explain the rationale in chapter 18 (available online) in our
discussion of stock options.
SELF-TEST
QUESTIONS
1. How can the possibility of abandonment affect a project’s
profitability and stand-alone risk?
2. What are the costs and benefits of structuring large capital
budgeting decisions in stages rather than in a single decision?
3. Why might DCF valuation underestimate the true value of a
project?
4. What are some different types of real options?
5. How does the presence of real options influence capital budgeting
decisions?
An Overview of the Capital Budgeting Decision Process
The discussion of capital budgeting thus far has focused on how managers
evaluate individual projects. For capital planning purposes, healthcare managers also need to forecast the total number of projects that will be undertaken
and the dollar amount of capital needed to fund these projects. The list of
projects to be undertaken is called the capital budget, and the optimal selection of new projects is called the optimal capital budget.
While every healthcare provider estimates its optimal capital budget
in its own way, some procedures are common to all businesses. We use the
procedures followed by CALFIRST Health System to illustrate the process:
• The chief financial officer (CFO) estimates the system’s corporate cost
of capital. As discussed in chapter 9, this estimate depends on market
conditions, the business risk of CALFIRST’s assets in the aggregate,
and the systemwide optimal capital structure.
• The CFO then scales the corporate cost of capital up or down to
reflect the unique risk and capital structure features of each division.
Assume that CALFIRST has three divisions: LRD (low-risk division),
ARD (average-risk division), and HRD (high-risk division).
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C hap ter 12: Proj ec t Risk A naly sis
• Managers in each of the divisions evaluate the riskiness of the proposed
projects to their divisions by categorizing each project as LRP (low-risk
project), ARP (average-risk project), or HRP (high-risk project). These
project risk classifications are based on the riskiness of each project
relative to the other projects in the division, not to the system in the
aggregate.
• Each project is then assigned a project cost of capital that is based
on the divisional cost of capital and the project’s relative riskiness. As
discussed previously, this project cost of capital is then used to discount
the project’s expected net cash flows. From a financial standpoint, all
projects with positive NPVs are acceptable, while those with negative
NPVs should be rejected. Subjective factors are also considered,
and these factors may prompt a decision that differs from the one
established solely on the basis of financial considerations.
Exhibit 12.9 summarizes CALFIRST’s overall capital budgeting process. Here, the corporate cost of capital, 10 percent, is adjusted upward to
14 percent in the HRD and downward to 8 percent in the LRD. The same
adjustment—4 percentage points upward for HRPs and 2 percentage points
downward for LRPs—is applied to differential risk projects in each division.
The end result is a range of project costs of capital in CALFIRST that runs
from 18 percent for HRPs in the HRD to 6 percent for LRPs in the LRD.
The result is a financial analysis process that incorporates each project’s
debt capacity, at least at the divisional level, and riskiness. However, managers
also must consider other possible risk factors that may not have been included
in the quantitative analysis. For example, could the project being evaluated
significantly increase the business’s liability exposure? Conversely, does the
project have any real option value, social value, or other attributes that could
affect its profitability or riskiness? Such additional factors must be considered,
at least subjectively, before a final decision can be made. (A framework for
considering multiple decision factors—the project scoring approach—is discussed in chapter 11.) Typically, if the project involves new products or services and is large (in capital requirements) relative to the size of the business’s
average project, the additional subjective factors will be important to the final
decision; one large mistake can bankrupt a firm, so “bet-the-firm” decisions
are not made lightly. On the other hand, a decision on a small replacement
project would be made mostly on the basis of numerical analysis.
Ultimately, capital budgeting decisions require an analysis of a mix of
objective and subjective factors such as risk, debt capacity, profitability, medical staff (patient) needs, real option value, and social value. The process is
not precise, and often there is a temptation to ignore one or more important
factors because they are so nebulous and difficult to measure. Despite this
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EXHIBIT 12.9
CALFIRST:
Divisional and
Project Costs of
Capital
High-risk project
HRD cost
of capital = 14%
Average-risk project
Low-risk project
High-risk project
Corporate cost
of capital = 10%
ARD cost
of capital = 10%
Average-risk project
Low-risk project
High-risk project
LRD cost
of capital = 8%
Average-risk project
Low-risk project
18%
14%
12%
14%
10%
8%
12%
8%
6%
imprecision and subjectivity, a project’s risk, as well as its other attributes,
should be assessed and incorporated into the capital budgeting decision
process.
SELF-TEST
QUESTIONS
1. Describe a typical capital budgeting decision process.
2. Are decisions made solely on the basis of quantitative factors?
Explain your answer.
Capital Rationing
Standard capital budgeting procedures assume that businesses can raise virtually unlimited amounts of capital to meet capital budgeting needs. Presumably, as long as a business is investing the funds in profitable (i.e., positive
NPV) projects, it should be able to raise the debt and equity needed to fund
all such projects. In addition, standard capital budgeting procedures assume
that a business raises the capital needed to finance its optimal capital budget
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C hap ter 12: Proj ec t Risk A naly sis
roughly in accordance with its target capital structure and at an average cost
equal to the estimated corporate cost of capital.
This picture of a business’s capital financing and capital investment process is probably appropriate for large investor-owned firms in most situations.
However, not-for-profit firms and small investor-owned businesses typically do
not have unlimited access to capital. Their ability to raise equity capital often
is limited, and their debt capital is constrained to the amount supported by
the equity capital base. Thus, such businesses will likely face periods in which
the capital needed for investment in worthwhile new projects will exceed the
amount of capital available. This situation is called capital rationing.
If capital rationing exists (i.e., a business has more acceptable projects
than capital), from a financial perspective the business should accept the set
of capital projects that maximizes aggregate NPV and still meets the capital
constraint. This approach can be called “getting the most bang for the buck”
because it picks projects that have the most positive impact on the business’s
financial condition.
Another ROI measure—the profitability index (PI)—is useful in a
capital rationing situation. The PI is defined as the PV of cash inflows divided
by the PV of cash outflows. Thus, for Ridgeland’s MRI project discussed earlier in the chapter, PI = $2,582,493 ÷ $2,500,000 = 1.03. The PI measures
a project’s dollars of profitability per dollar of investment, all on a PV basis.
The MRI project promises three cents of profit for every dollar invested,
which indicates it is not very profitable. (The PI of 1.03 is before adjusting
for risk. After adjusting for risk, the project’s PI is less than 1.00, indicating
that the project is unprofitable.) In a capital rationing situation, the optimal
capital budget is determined by first listing all profitable projects in descending order of PI. Then, projects are selected from the top of the list downward
until the capital available is used up.
Of course, in healthcare businesses, priority may be assigned to some
low or even negative NPV projects, which is fine as long as these projects are
offset by the selection of profitable projects, which would prevent the lowprofitability priority projects from eroding the business’s financial condition.
1. What is capital rationing?
2. From a financial perspective, how are projects chosen when capital
rationing exists?
3. What is the profitability index, and why is it useful in a capital
rationing situation?
SELF-TEST
QUESTIONS
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Chapter Key Concepts
This chapter discussed project risk definition, assessment, and incorporation. Here are its key concepts:
• There are three types of project risk: (1) stand-alone risk, (2)
corporate risk, and (3) market risk.
• A project’s stand-alone risk is the risk the project would have if it
were the sole project of a not-for-profit firm. It is measured by
the variability of profitability, generally by the standard deviation
or coefficient of variation of NPV. Stand-alone risk often is used
as a proxy for corporate and market risk because (1) corporate
and market risk are often impossible to measure and (2) the three
types of risk are usually highly correlated.
• Corporate risk reflects a project’s contribution to the overall
riskiness of the business. Corporate risk ignores stockholder
diversification and is relevant to not-for-profit firms.
• Market risk reflects the contribution of a project to the overall
riskiness of the owners’ well-diversified investment portfolios.
In theory, market risk is relevant to investor-owned firms, but
many people argue that corporate risk is also relevant to owners,
especially the owners and managers of small businesses, and it is
certainly relevant to a business’s other stakeholders.
• Three quantitative techniques are commonly used to assess a
project’s stand-alone risk: (1) sensitivity analysis, (2) scenario
analysis, and (3) Monte Carlo simulation.
• Sensitivity analysis shows how much a project’s profitability—for
example, as measured by NPV—changes in response to a given
change in an input variable such as volume, other things held
constant.
• Scenario analysis defines a project’s best, most likely, and worst
possible outcomes and then uses these data to measure its standalone risk.
• Whereas scenario analysis focuses on only a few possible
outcomes, Monte Carlo simulation uses continuous distributions
to reflect the uncertainty inherent in a project’s component cash
flows. The result is a probability distribution of NPV, or IRR,
that provides a great deal of information about the project’s
riskiness.
(continued)
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C hap ter 12: Proj ec t Risk A naly sis
(continued from previous page)
• In addition to quantitative risk assessment techniques, the
qualitative approach uses the answers to yes-or-no questions to
assess project risk.
• Projects that require capital outlays in stages over time often
are evaluated using decision trees. The branches of the tree
represent different outcomes, and, when subjective probabilities
are assigned to the outcomes, the tree provides the profitability
distribution for the project.
• In addition to the DCF-calculated NPV, some projects have
additional value in the form of embedded real (managerial)
options.
• One type of real option is the ability to abandon a project once
operations have begun. This option can both increase a project’s
dollar return and decrease its riskiness and thus has a twofold
positive effect on value.
• There are two methods for incorporating project risk into the
capital budgeting decision process: (1) the certainty equivalent
(CE) method, which adjusts a project’s expected cash flows
to reflect project risk, and (2) the risk-adjusted discount rate
(RADR) method, which deals with differential risk by changing
the cost of capital.
• Projects are generally classified as high risk, average risk, or low
risk on the basis of their stand-alone risk assessment. High-risk
projects are evaluated at a discount rate greater than the firm’s
corporate cost of capital, average-risk projects are evaluated at
the corporate cost of capital, and low-risk projects are evaluated
at a rate less than the corporate cost of capital. In a business with
divisions, the risk-adjustment process often takes place at the
divisional level.
• In the evaluation of risky cash outflows, the risk adjustment
process is reversed—that is, lower rates are used to discount
more risky cash flows.
• Ultimately, capital budgeting decisions require an analysis of a
mix of objective and subjective factors such as risk, debt capacity,
profitability, medical staff needs, real option value, and social
value. The process is not precise, but good managers do their
best to ensure that none of the relevant factors are ignored.
(continued)
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• In a capital rationing situation, the business has more profitable
projects than investment capital. In such cases, the profitability
index (PI) is a useful measure of profitability (ROI).
This concludes our discussion of capital budgeting. In chapters
13 and 14, we discuss financial and operating analyses and financial
forecasting.
Chapter Models, Problems, and Minicases
The following ancillary resources in spreadsheet format ar…

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