Transcript Chapter 1: Risk Topics and Real Options in Capital Budgeting

Chapte
14
Slides Developed by:
Terry Fegarty
Seneca College
Risk Topics and Real
Options in Capital
Budgeting
Chapter 14 – Outline (1)
• Risk in Capital Budgeting—General
Considerations
 Cash Flows as Random Variables
 The Importance of Risk in Capital Budgeting
• Incorporating Risk in Capital Budgeting—
Scenario / Sensitivity Analysis and Simulation
 Scenario/Sensitivity Analysis
 Computer (Monte Carlo) Simulation
 Decision Tree Analysis
• Real Options
 Valuing Real Options
 Designing for Real Options
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Chapter 14 – Outline (2)
• Incorporating Risk Into Capital Budgeting—The
Theoretical Approach and Risk-Adjusted Rates
of Return
 Estimating Risk-Adjusted Rates Using the Capital
Asset Pricing Model (CAPM)
 Estimating the Risk-Adjusted Rate Through Beta
 Problems with the Theoretical Approach
 Projects in Divisions—The Accounting Beta Method
 A Final Comment on Risk in Capital Budgeting
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Cash Flows as Random Variables
• Risk is chance that a random variable will take
on a value significantly different from the
expected value (mean)
 In capital budgeting estimate of each future period's
cash flow is random variable
 NPV and IRR of project are random variables with
expected values and variances that reflect risk
• Thus, actual value is likely to be different than mean
• Amount that actual value is likely to differ from expected
value related to variance or standard deviation
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Figure 14.1: The Probability Distribution of a
Future Cash Flow as a Random Variable
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Figure 14.2:
Flows
Risk in Estimated Cash
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The Importance of Risk in Capital
Budgeting
• Thus far we've viewed cash flows as point
estimates
• We could be making wrong decision by using
point estimates for NPV and IRR
• The riskiness of project's cash flows must be
considered when deciding upon a project
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Figure 14.3: Project NPVs Reflecting
Risky Cash Flows
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The Importance of Risk in Capital
Budgeting
• Risk Aversion
 All other things being equal, we prefer less risky
capital projects to those with more risk
• Changing the Nature of the Company
 A company is a portfolio of projects
 Thus, if a firm undertakes new projects while
ignoring risk, it could change its fundamental risk
characteristics
• A company adopting riskier projects than it used to will
become a riskier company
• Will lead to a higher beta
• Can generally lead to a share price reduction
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Scenario/Sensitivity Analysis
• Involves selecting a worse, most likely and
best case for each cash flow
 Most likely is cash flow estimate we've worked with
before
• Recalculate the project's NPV (or IRR) under
each scenario
 Gives subjective feel for variability of NPV to changes
in assumptions
• Referred to as sensitivity analysis
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Example
Example 14.1:
Scenario/Sensitivity
Analysis
Q: Project A has an initial outflow of $1,400 and three variable
cash inflows:
C1
C2
C3
Worst case
$450 $400 $700
Most likely
550
450
800
Best case
650
500
900
Analyze project A’s NPV. Assume the cost of capital is 9%.
A:
Worst case: NPV = –$1,400 + $450[PVF9,1] + $400[PVF9,2]
+$700[PVF9,3]
= –$1,400 + $450[0.9174] + $400[0.8417] + $700[0.7722]
= –$109.95
Most likely: NPV = $101.10 (the project’s traditional NPV)
Best case: NPV = $312.14
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Computer (Monte Carlo)
Simulation
• Involves making assumptions about shape of
probability distribution for each future cash
flow in project
• Computer model draws a set of random
observations for each cash flow and calculates
NPV of project
• Repeats process to generate many (1000s?)
possible values for NPV (IRR)
• Computer then simulates project by
constructing probability distribution of the
project's NPV (IRR)
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Computer (Monte Carlo)
Simulation
• Benefits
 Provides most likely values for NPV (IRR)
• Expected profitability
 Provides approximate shapes of probability
distribution for NPV (IRR)
• Risk assessment
• Drawbacks
 Probability distributions have to be estimated
subjectively
 Project cash flows tend to be positively correlated—
hard to estimate the extent of that correlation
 Interpretation of results is subjective
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Figure 14.4:
Results of Monte Carlo
Simulation for NPV
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Computer (Monte Carlo)
Simulation
Forecast: NPV
3,000 Trials
Frequency Chart
13 O utlie rs
.026
78
.020
58.5
.013
39
.007
19.5
.000
0
-20,000,000.00
0.00
20,000,000.00
40,000,000.00
60,000,000.00
Certainty i s 81.83% from 0.00 to +Infinity Dol lars
Sample output from Crystal Ball simulation.
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Decision Tree Analysis
• Decision tree—time line which branches into
alternate paths whenever an event can turn out
more than one way
 Place at which branches separate is called a node
 Any number of branches can emanate from a node
but the probabilities must sum to 1.0 (or 100%)
 Path—following the tree along a branch
• Evaluating project involves calculating NPVs
along all possible paths and assigning
probability to each NPV
 From that, probability distribution for NPV is
developed
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Figure 14.5:
A Simple Decision
Tree
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Example
Example 14.2:
Decision Tree
Analysis
Q: The Wing Foot Shoe Company is considering a three-year project to
market a running shoe based on new technology. A market study
indicates a 60% probability that demand will be good and a 40%
chance that it will be poor.
It will cost $5M to bring the new shoe to market. Cash flow estimates
indicate inflows of $3M per year for three years at full manufacturing
capacity if demand is good, but just $1.5M per year if it’s poor. Wing
Foot’s cost of capital is 10%.
Analyze the project and develop a rough probability distribution for
NPV.
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Example 14.2:
Decision Tree
Analysis
A: First, draw a decision tree diagram for the project. Then
calculate the NPV along each path.
0
1
3
NPV
$3M
$3M
$3M
$2.461M
P = .4 $1.5M
$1.5M
$1.5M
$-1.270M
P = .6
Example
2
($5M)
Then calculate the weighted NPV for the tree.
Demand
NPV
Probability
Product
Good
$2.641M
60%
$1.585M
Poor
$-1.270M
40%
$-.508M
Expected
NPV =
$1.077M
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The decision
tree points out
that a big loss is
quite possible,
although the
expected NPV
is positive.
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Figure 14.6:
A More Complex
Decision Tree
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Real Options
• Option—ability or right to take certain
course of action
• Real options—options that exist in a real
physical, business sense
 Ex; a revolving credit agreement for a
commitment fee
• Firm has right but not obligation to borrow
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Valuing Real Options
• Real options frequently occur in capital
budgeting
 Generally increase project's expected
NPV
• Increase is estimate of option's value
• Real options are generally worth more
than their impact on expected NPV
because they generally reduce risk
 However, difficult to quantify reduction in risk
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Designing for Real Options
• Abandonment options
 can increase expected NPV and lower risk
 But contractual obligations can make abandonment tough
• Expansion options
 Frequently require little or no early commitment and should be
planned in whenever possible
• Investment timing options
 Allow a firm to delay an investment until it's sure about other
relevant issues
 Ex; a land option contract
• Flexibility options
 Allow company ability to respond more easily to changes in
business conditions
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Incorporating Risk Into Capital
Budgeting
• Cost of capital (k) plays key role in both
NPV and IRR
 For NPV, k used as discount rate
• A higher k leads to a lower NPV, reducing the
chance of project acceptance
 For IRR, IRR is compared to k
• A higher k leads to a lower chance of project
acceptance
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Incorporating Risk Into Capital
Budgeting
• Riskier Projects Should Be Less Acceptable
 Idea is to make risky projects less acceptable than
others with similar expected cash flows
 Using a higher, risk-adjusted rate for risky
projects lowers their chance of acceptance
• The Starting Point for Risk-Adjusted Rates
 The cost of capital is used to analyze projects if their
risk is comparable to the firm’s overall risk
 Higher rates are used for riskier projects
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Incorporating Risk Into Capital
Budgeting
• Choosing the Risk-Adjusted Rate for Various
Projects
 Arbitrary process, subjective
 Replacement projects—replacing something the
firm has already been doing
• Firm's cost of capital is nearly always appropriate for this
type of project
 Expansion projects—more risky than the current
level, but not much more
• Rule of thumb is to add 1-3% points to the cost of capital
 New venture projects—usually involve much more
risk than current projects
• Portfolio theory and the CAPM may be useful
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Estimating Risk-Adjusted Rates Using
the Capital Asset Pricing Model (CAPM)
• Portfolio theory and the CAPM can
sometimes be used to generate riskadjusted rates
• The Project as a Diversification
 If firm is viewed as a collection of projects,
new venture diversifies the company
 New venture also diversifies investment
portfolios of the firm's shareholders
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Estimating Risk-Adjusted Rates Using
the Capital Asset Pricing Model (CAPM)
• Diversifiable and Non-Diversifiable Risk
for Projects
 Projects have two levels of diversifiable risk
•Some risk is diversified away within the
firm's portfolio of projects
•Some risk is diversified away by the
shareholders' investment portfolios
 Remaining risk is the market (systematic)
risk of the project
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Figure 14.7:
Components of
Project Risk
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Estimating the Risk-Adjusted Rate
Through Beta
• Security Market Line (SML) can be used to
determine a risk-adjusted rate for new venture
project
 SML: kx = kRF + (kM - kRF)X
 Where X is beta, used as a measure of new venture
project’s market risk
• If project is viewed as a business in a particular
field, use a beta common to that field
 Method most appropriate when independent, publicly
traded firm can be found that is in the same
business as the new venture (pure play firm)
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Estimating the RiskAdjusted Rate Through Beta
Example
Example 14.6:
Q: Orion Inc. is considering producing a sophisticated tactical radio
for sale to the Canadian Forces, but is concerned because the
military market is known to be quite risky.
The military radio market is dominated by Milrad Inc., which
holds a 60% market share. Antex Radio Corp. Is another
established competitor with a 20% share. Both Milrad and
Antex make only military radios. Milrad's beta is 1.4 and Antex's
is 2.0 Orion's beta is 1.1. The return on an average publicly
traded stock (kM) is about 10%. The yield on short-term Treasury
bills (kRF) is currently 5%. Orion's cost of capital is 8%.
The military ratio project is expected to require an initial
outlay of $10 million. Subsequent cash inflows are expected to
be $3 million per year over a five-year contract.
Should Orion undertake the project?
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Example
Estimating the Risk-Adjusted Rate
Through Beta—Example
A: The military radio business division would clearly be more risky
than Orion's current business projects given the high betas of
Milrad and Antex vs. Orion. Milrad and Antex are both pure play
firms, but since Milrad is the market leader it probably has less
risk than Antex. We need to use a beta from a company that will
be in a similar position as our own firm; thus, we will use Antex's
beta of 2.0 to evaluate the military radio project.
First, calculate the risk-adjusted beta for the project:
K = 5% + (10% - 5%)2.0 = 15.0%
Note that this rate is considerably higher than Orion's current
8% cost of capital.
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Example
Estimating the Risk-Adjusted Rate
Through Beta—Example
A: Next calculate the proposed project's NPV using the 15% riskadjusted rate:
NPV = -$10.0M + $3M[PVFA15,5]
= -$10M + $3M[3.3522]
= $0.1M
Since the NPV is
barely positive,
the project is
marginal at best.
NOTE: If the project had been evaluated at Orion's 8% cost of
capital, it would have lead to an NPV of $2.0M
However, adjusting for risk has shown the project to be only
marginal.
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Problems with the Theoretical
Approach
• Pure play firm must be solely in the
business of the new venture
• Finding pure play firm is difficult
 Betas of conglomerates are influenced by
other divisions (in other industries)
 Thus, we have to estimate betas by using
firms in similar (but not exactly) the same
businesses
• Reduces credibility of technique
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Problems with the Theoretical
Approach
• Another problem—market risk may not
be only risk that is important
 Major business-specific risks may be present
(not diversified away)
 If total risk is much higher than market risk,
it would lead to an even higher risk-adjusted
rate
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Projects in Divisions—The
Accounting Beta Method
• If pure play division is found within a
corporation, may be able to estimate the beta
of that division using the accounting beta
method
 Develop beta for division from its accounting records
(rather than share price data)
• Regress historical divisional return on equity against return
on a major market index (TSX/S&P Composite Index)
• Slope of the regression line represents the division's beta
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A Final Comment on Risk in
Capital Budgeting
• Virtually every firm uses capital
budgeting techniques but only a few
overtly try to incorporate risk
• Business managers do recognize risk but
they do it judgmentally
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