14 Chapter Risk Topics and Real Options in Capital Budgeting Slides Developed by: Terry Fegarty...

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Risk Topics and Real Options in Capital

Budgeting

Risk Topics and Real Options in Capital

Budgeting

Slides Developed by:

Terry FegartySeneca College

© 2006 by Nelson, a division of Thomson Canada Limited 2

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


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


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


Figure 14.1: The Probability Distribution of a Future Cash Flow as a

Random Variable


Figure 14.2: Risk in Estimated Cash Flows


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


Figure 14.3: Project NPVs Reflecting Risky Cash Flows


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


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


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 $700Most likely 550 450 800Best 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)


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


Figure 14.4: Results of Monte Carlo Simulation for NPV


Computer (Monte Carlo) Simulation

Frequency Chart

Certainty is 81.83% from 0.00 to +Infinity Dollars

.000

.007

.013

.020

.026

0

19.5

39

58.5

78

-20,000,000.00 0.00 20,000,000.00 40,000,000.00 60,000,000.00

3,000 Trials 13 Outliers

Forecast: NPV

Sample output from Crystal Ball simulation.


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


Figure 14.5: A Simple Decision Tree


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.

Example 14.2: Decision Tree Analysis

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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.

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$1.5M$1.5M$1.5M

($5M)

$3M$3M$3M

3 2 10

P = .6

P = .4

NPV

$2.461M

$-1.270M

Then calculate the weighted NPV for the tree.

$1.077MExpected NPV =

$-.508M40%$-1.270MPoor

$1.585M60%$2.641MGood

ProductProbabilityNPVDemandThe decision

tree points out that a big loss is quite possible, although the

expected NPV is positive.


Figure 14.6: A More Complex Decision Tree


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


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


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


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


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


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


Estimating Risk-Adjusted Rates Using the Capital Asset Pricing Model (CAPM)

• Portfolio theory and the CAPM can sometimes be used to generate risk-adjusted 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


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


Figure 14.7: Components of Project Risk


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)


Example 14.6: Estimating the Risk- Adjusted Rate Through Beta

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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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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Estimating the Risk-Adjusted Rate Through Beta—Example

A: Next calculate the proposed project's NPV using the 15% risk-adjusted rate:

NPV = -$10.0M + $3M[PVFA15,5]= -$10M + $3M[3.3522]= $0.1M

NOTE: If the project had been evaluated at Orion's 8% cost of capital, it would have lead to an NPV of $2.0MHowever, adjusting for risk has shown the project to be only marginal.

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marginal at best.


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


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


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


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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