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Risk Topics and Real Options in Capital Budgeting. Chapter 11. © 2003 South-Western/Thomson Learning. Cash Flows as Random Variables. Risk is chance that a random variable will take on a value significantly different from the expected value

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Risk topics and real options in capital budgeting

Risk Topics and Real Options in Capital Budgeting

Chapter 11

© 2003 South-Western/Thomson Learning

Cash flows as random variables
Cash Flows as Random Variables

  • Risk is chance that a random variable will take on a value significantly different from the expected value

    • In capital budgeting the estimate of each future period's cash flow is a random variable

    • The NPV and IRR of any project are random variables with expected values and variances that reflect risk

      • Thus, the actual value is likely to be different than the mean

      • The amount the actual value is likely to differ from the expected is related to the variance or standard deviation

The importance of risk in capital budgeting
The Importance of Risk in Capital Budgeting Flow as a Random Variable

  • Thus far we've viewed cash flows as point estimates

  • However, since a project's actual cash flows are estimates we could be making a wrong decision by using point estimates for NPV and IRR

  • The riskiness of a project's cash flows must be considered when deciding upon a project

The importance of risk in capital budgeting1
The Importance of Risk in Capital Budgeting Flow as a Random Variable

  • Risk Aversion

    • All other things 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 stock price reduction

Scenario sensitivity analysis
Scenario/Sensitivity Analysis Flow as a Random Variable

  • Involves selecting a worse, most likely and best case for each cash flow

    • Most likely is the cash flow estimate we've worked with before

  • Recalculate the project's NPV (or IRR) under each scenario

    • Evaluating a number of scenarios gives a subjective feel for the variability of the NPV to changes in our assumptions

      • Referred to as sensitivity analysis

Computer monte carlo simulation
Computer (Monte Carlo) Simulation Flow as a Random Variable

  • Involves making assumptions about the shape of each future cash flow

  • A computer is used to quickly determine random observations for each uncertain cash flows and determine numerous possible outcomes (1000s)

  • Computer then simulates project by constructing a probability distribution of the project's NPV (IRR)

  • 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

Decision tree analysis
Decision Tree Analysis Flow as a Random Variable

  • Decision Tree analysis lets us approximate the NPV distribution if we can estimate the probability of certain events within the project

  • A decision tree is an expanded time line which branches into alternate paths whenever an event can turn out more than one way

    • The 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%)

    • A path represents following the tree along a branch

      • Evaluating a project involves calculating NPVs along all possible paths and developing a probability distribution

Decision tree analysis example

Q: The Wing Foot Shoe Company is considering a three-year project to market a running shoe based on new technology. Success depends on how well consumers accept the new idea and demand the product. Demand can vary from great to terrible, but for planning purposes management has collapsed that variation into just two possibilities, good and poor. 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.


Decision Tree Analysis—Example

Decision tree analysis example1

A: First, draw a decision tree diagram for the project. Then calculate the NPV along each path.









P = .6



P = .4






Then calculate the weighted NPV for the tree.

The decision tree explicitly calls out the fact that a big loss is quite possible, although the expected NPV is positive.













Expected NPV =


Decision Tree Analysis—Example

Real options
Real Options calculate the NPV along each path.

  • An option is the ability or right to take a certain course of action

  • Real options represent those that exist in a real physical, business sense

  • Real options frequently occur in capital budgeting

    • Generally increase a project's expected NPV

      • This increase is often a good estimate of the option's value

Real options1
Real Options calculate the NPV along each path.

  • For example, suppose a sports apparel company sells jackets/sweatshirts with professional football team insignias and it depends on bank credit to support routine operations

    • Firm usually has a bank loan of $1 million, but if local professional team makes it to the Super Bowl demand is expected to double and the firm expects to need $2 million in bank credit

      • Manager doesn't want to borrow the extra $1M--what if football team doesn't make it to Super Bowl?

      • Company can pay a consultant fee to bank in which the bank agrees to lend firm the money if the company wants it

        • Commitment fees usually about 1/4% annually of he unborrowed, but committed, amount (or 1/4% x $1M = $2,500)

        • Bank charges normal interest rate on money once it is borrowed

      • This arrangement gives the business the ability to take advantage of the potential increase, because it has the right (but not the obligation) to borrow the extra $1M

The abandonment option
The Abandonment Option calculate the NPV along each path.

  • If a project is undertaken and eventually experiences poor demand, it is likely that the project will be abandoned

    • The facilities and equipment (or the cash flows generated from their sale) must be expected to have better use elsewhere

Valuing real options
Valuing Real Options calculate the NPV along each path.

  • Real options are generally worth more than their impact on expected NPV because they generally reduce risk

    • However, difficult to place a quantitative value to the risk reduction

  • An Approach Through Rate of Return

    • Lower risk should be associated with a lower rate of return in NPV calculations—leads to a higher NPV calculation

      • Difficulty lies with choosing the right risk-adjusted rate

  • The Risk Effect is Tricky

    • The value of real options has to be considered on a case-by-case basis

Designing for real options
Designing for Real Options calculate the NPV along each path.

  • Abandonment option—can increase expected NPV and lower risk

    • Contractual obligations can make abandonment tough

  • Expansion options

    • Frequently require little or no early commitment and should be planned whenever possible

  • Investment timing options

    • Allow a firm to delay an investment until it's sure about other relevant issues

  • Flexibility options

    • Allow company ability to respond more easily to changes in business conditions

Incorporating risk into capital budgeting
Incorporating Risk Into Capital Budgeting calculate the NPV along each path.

  • The cost of capital (k) plays a key role in both NPV and IRR

    • For NPV, k is used as the 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 budgeting1
Incorporating Risk Into Capital Budgeting calculate the NPV along each path.

  • 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 current situation of the firm (in terms of risk) is the starting point

Incorporating risk into capital budgeting2
Incorporating Risk Into Capital Budgeting calculate the NPV along each path.

  • Relating Interest Rates to Risk

    • Interest rates are made up of a base rate plus a risk premium

    • Investors demand a higher risk premium and interest rate if they are to bear more risk

    • In capital budgeting the company is the investor, thus the firm's cost of capital is used as the discount rate for an average risk project

  • Choosing the Risk-Adjusted Rate for Various Projects

    • Somewhat of an arbitrary process, subjective

Incorporating risk into capital budgeting3
Incorporating Risk Into Capital Budgeting calculate the NPV along each path.

  • Some logic can aid in the process

    • Replacement projects involved replacing something the firm has already been doing

      • Thus, the firm's cost of capital is nearly always appropriate for this type of project

    • Expansion projects are more risky than the current level, but not much more

      • A 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

      • Choosing risk-adjusted rate is difficult and arbitrary

Estimating risk adjusted rates using capm
Estimating Risk-Adjusted Rates Using CAPM calculate the NPV along each path.

  • The Project as a Diversification

    • If the firm is viewed as a collection of projects, a new venture diversifies the company

    • A new venture also diversifies the investment portfolios of the firm's shareholders

  • Diversifiable and Non-Diversifiable Risk for Projects

    • Projects have two levels of diversifiable risk because they are effectively in two portfolios at once

      • Some risk is diversified away within the firm's portfolio of projects

      • Some risk is diversified away by the shareholders' investment portfolios

    • The remaining risk is known as systematic risk

Estimating the risk adjusted rate through beta
Estimating the Risk-Adjusted Rate Through Beta calculate the NPV along each path.

  • The Security Market Line (SML) can be used to determine a risk-adjusted rate for a new venture project

    • SML: kx = kRF + (KM - kRF)bX

    • Where bX is beta, or the measure of a company's systematic risk

  • If a capital budgeting project is viewed as a business in a particular field, it may make sense to use a beta common to that field in the SML to estimate a risk-adjusted rate for analysis of the project

    • This method is most appropriate when an independent, publicly traded firm can be found that is in the same business as the new venture (pure play firm)

      • Pure play firm must be solely in the business of the new venture

Estimating the risk adjusted rate through beta example

Q: calculate the NPV along each path.Orion Inc. Is a successful manufacturer of citizens band (CB) radios. Management is considering producing a sophisticated tactical radio for sale to the 'Army, 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 .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.

  On the basis of a five-year evaluation, should Orion undertake the project?


Estimating the Risk-Adjusted Rate Through Beta—Example

Estimating the risk adjusted rate through beta example1

S: 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, we 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.


Estimating the Risk-Adjusted Rate Through Beta—Example

Estimating the risk adjusted rate through beta example2

S: 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 $2.0M; however, adjusting for risk has shown the project to be only marginal.

Since the NPV is barely positive, the project is marginal at best.


Estimating the Risk-Adjusted Rate Through Beta—Example

Problems with the theoretical approach
Problems with the Theoretical Approach risk-adjusted rate:

  • The biggest problem is finding a pure play firm from which to obtain an appropriate beta

    • 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 the credibility of the technique

  • Another problem is that systematic risk may not be the only risk that is important

    • If total risk is what's really important, it would lead to an even higher risk-adjusted rate

Projects in divisions the accounting beta method
Projects in Divisions—The Accounting Beta Method risk-adjusted rate:

  • If a pure play division is found within a corporation, may be able to estimate the beta of that division using the accounting beta method

    • Develop a beta for the division from its accounting records (rather than stock price data)

      • Regress historical divisional return on equity against the return on a major stock market index

        • Slope of the regression line represents the division's beta

A final comment on risk in capital budgeting
A Final Comment on Risk in Capital Budgeting risk-adjusted rate:

  • 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