13-1
Risk and Capital Budgeting
Author’s Overview
Though risk is discussed throughout the text, Chapter 13 provides the most explicit portrayal of its
impact on the decision-making process of the firm. The actual measurement of risk through the
computation of the mean, standard deviation, and coefficient of variation is presented in detail. The
introduction of the risk-adjusted discount rate brings together the key material in Chapter 12 and this
chapter. Simulation analysis also is introduced to emphasize how complicated decision variables can
be reduced to a more manageable scale through examining, in advance, outcomes and probabilities of
outcomes. Decision trees are introduced after simulation models to path dependent outcomes
combined with probability estimates. Finally, the portfolio effect of an investment is introduced. The
coefficient of correlation is defined in a general sense that should prove quite workable to the student.
An example of the efficient frontier is demonstrated in Figure 13-2 titled “Risk-return trade-off.”
Chapter Concepts
LO2. Most investors are risk-averse, which means they dislike uncertainty.
LO4. Simulation models and decision trees can be used to help assess the risk of an investment.
13
13-2
Annotated Outline and Strategy
I. Definition of Risk in Capital Budgeting
A. Management’s ability to achieve the goal of owner’s wealth maximization will largely
depend on success in dealing with risk.
B. Definition: Variability of possible outcomes. The wider the distribution of possible
II. The Concept of Risk-Averse
A. Risk aversion is a basic assumption of financial theory. Investors require a higher
expected return the riskier an investment is perceived to be.
Perspective 13-1: We provide statistics briefly, but most students should not have to spend too
much time on the statistics. Instead, focus on applying these measures to financial decision-making.
PPT Variability and Risk Continued (Figure 13-1)
PPT Risk-Return Trade-Off (Figure 13-2)
III. Actual Measurement of Risk
A. The basic risk measurement is the standard deviation, which is a measure of dispersion
around an expected value.
1. The expected value is a weighted average of the possible outcomes of an event
2. The formula for computing the standard deviation is:
D (expected value) = DP
å
s
(standard deviation) = å(D – D2
)P
1. The standard deviation is limited as a risk measure for comparison purposes.
2. The size problem is eliminated by employing the coefficient of variation, V,
which is the ratio of the standard deviation of an investment to its expected
value. The higher the coefficient of variation, the higher the risk.
A
V = $600
$6,000 = .10 B
V = $190
$600 = .317
PPT Probability Distribution of Outcomes (Table 13-1)
PPT Probability Distribution with Differing Degrees of Risk (Figure 13-3)
PPT Probability Distribution with Differing Degrees of Risk (Figure 13-4)
C. Beta () is another measure of risk that is widely used in portfolio management. Beta
measures the volatility of returns on an individual stock relative to a stock market
index of returns. (See Appendix 11A for a thorough discussion.)
PPT Average Betas for a Five-Year Period (Ending January 2018)
(Table 13-2)
Perspective 13-2: Table 13-2 allows for a good discussion of industry/company factors that may
cause risk.
IV. Risk and the Capital Budgeting Process
A. The expected inflows from capital projects are usually risky and uncertain.
B. Cash flows of projects bearing a normal amount of risk undertaken by the firm should
Coefficient of variation ( ) VD
=
13-4
adjusted real rate of return) plus a risk premium (risk associated with usual projects of
a business).
E. Adjustments must be made in the evaluation process for projects bearing other than
(more or less) normal risk levels.
1. Risk-adjusted discount rate approach: The discount rate is adjusted upward for
2. Risk-adjusted discount rates may be based on several measures of risk such as
the standard deviation, coefficient of variation, or beta.
PPT Relationship of Risk to Discount Rate (Figure 13-5)
Perspective 13-3: Discuss foreign projects and how they are evaluated based on risk. International
capital budgeting often has higher risks associated with emerging market systems or political
instability.
F. Increasing risk over time: Our ability to forecast diminishes as we forecast farther out
in time. See Figure 13-6 on page 425.
PPT Risk over Time (Figure 13-6)
G. Qualitative measures may mean that management makes up various risk classes for
projects having similar characteristics.
Finance in Action: Energy: A High-Risk Industry
The focus of the discussion should be on the risk assigned by energy companies to the many
Perspective 13-4: Tables 13-4 and 13-5 bring back investments A and B from Chapter 12 and
demonstrate how a different decision would be made if Investment B had been adjusted for risk.
PPT Risk Categories and Associated Discount Rates (Table 13-3)
PPT Capital Budgeting Analysis (Table 13-4)
13-5
PPT Capital Budgeting Decision Adjusted for Risk (Table 13-5)
V. Simulation Models
A. The uncertainty associated with a capital budgeting decision may be reduced by
projecting and preparing for the various possible outcomes resulting from the decision.
B. Simulation models—various values for economic and financial variables affecting the
capital budgeting decision are randomly selected and used as inputs in the simulation
model. Although the process does not ensure that a manager’s decision will be correct
(in terms of actual events), decisions can be made with a greater understanding of
possible outcomes.
PPT Simulation Flow Chart (Figure 13-7)
C. Decision trees—the sequential pattern of decisions and resulting outcomes and
associated probabilities (managerial estimates based on experience and statistical
processes) are tracked along the branches of the decision tree. Tracing the sequence of
possible events in this fashion is a valuable analytical tool in the decision-making
process.
PPT Decision Trees (Table 13-6)
VI. The Portfolio Effect
A. A risky project may actually reduce the total risk of the firm through the portfolio
effect.
B. Projects that move in opposite directions in response to the same economic stimulus
correlation that varies from the extremes of –1 (perfectly negative) to +1 (perfectly
positive) correlation. Noncorrelated projects have a correlation coefficient of zero.
PPT Portfolio Considerations in Evaluating Risk (Figure 13-8)
13-6
D. Although projects with correlation coefficients of –1 are seldom found, some risk
reduction will occur, however minor, when projects are negatively correlated or have
low positive correlation.
PPT Measures of Correlation (Table 13-7)
PPT Levels of Risk Reduction as Measured by the Coefficient of
Correlation (Figure 13-9)
PPT Rates of Return for Conglomerate Inc. and Two Merger Candidates
(Table 13-8)
Perspective 13-5: Table 13-8 is a good example of how negatively correlated projects can reduce
risk when combined.
E. The firm should strive to achieve two objectives in combining projects according to
their risk-return characteristics.
1. Achieve the highest possible return at a given risk level.
2. Provide the lowest possible risk at a given return level.
F. The various optimal combinations of projects are located along a risk-return line
referred to as the “efficient frontier.”
PPT Risk-Return Trade-Offs (Figure 13-10)
Finance in Action: Real Options Add a New Dimension to Capital Budgeting
This article discusses real options not considered under traditional capital budgeting decisions.
VII. The Share Price Effect
A. Higher earnings do not necessarily contribute to the firm’s goal of owner’s wealth
maximization. The firm’s earnings may be discounted at a higher rate because
investors perceive that the firm is pursuing riskier projects to generate the earnings.
13-7
Other Chapter Supplements
Cases for Use with Foundations of Financial Management
Case 20, Global Resources. (Risk-Adjusted Discount Rates)