Chapter 12 Risk Topics and Real Options in Capital Budgeting and Cash Flow Estimation

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# Chapter 12 Risk Topics and Real Options in Capital Budgeting and Cash Flow Estimation - PowerPoint PPT Presentation

Chapter 12 Risk Topics and Real Options in Capital Budgeting and Cash Flow Estimation. Cash Flows as Random Variables. “Risk” in every day usage: the probability that something bad will happen “Risk” in financial theory: Associated with random variables and their probability distributions.

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Presentation Transcript
Cash Flows as Random Variables
• “Risk” in every day usage: the probability that something bad will happen
• “Risk” in financial theory: Associated with random variables and their probability distributions
Cash Flows as Random Variables
• Risk – the chance that a random variable will take on a value significantly different from the expected value
• In capital budgeting the future period's cash flow estimate is a random variable
Cash Flows as Random Variables
• The NPV and IRR are random variables with their own probability distributions
• Actual value may be different than the mean
• The amount the actual value is different from expected is related to the variance or standard deviation
The Importance of Risk in Capital Budgeting
• Until now we have viewed cash flows as point estimates – a single number rather than a range of possibilities
• Actual cash flows are estimates, a wrong decision could be made using point estimates for NPV and IRR
• The riskiness of a project's cash flows must be considered
The Importance of Risk in Capital Budgeting
• Risk Aversion
• Changing the Nature of a Company
• A company is a portfolio of projects
• Ignoring risk when undertaking new projects can change the firm’s overall risk characteristics
Scenario/Sensitivity Analysis
• Select a worst, most likely, and best case for each cash flow
• Recalculate the project's NPV (or IRR) under several scenarios
• Gives an intuitive sense of the variability of NPV
• Also called sensitivity analysis
Decision Tree Analysis
• Decision Tree: A graphic representation of a project in which certain events have multiple outcomes
• Decision Tree Analysis – Develops a probability distribution of NPV given the probabilities of certain events within the project
Computer (Monte Carlo) Simulation
• Assume separate probability distribution for each cash flow
• Computer draws observation from each and calculates NPV
• Sort outcomes into histogram of probability distribution of NPV (next slide)
• Drawbacks
• Probability distributions are difficult to estimate
• Cash flows tend to be correlated
• Interpretation of results is subjective
Concept Connection Example 12-2 Decision Tree Analysis

The Wing Foot Shoe Company is considering a new running shoe. A market study indicates a 60% probability that demand will be good and a 40% chance that it will be poor.

C0 is \$5M. Cash inflows are estimated at \$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%.

Develop a rough probability distribution for NPV.

Concept Connection Example 12-2 Decision Tree Analysis

A decision tree diagram and NPVs along each path are:

NPV

0

1

2

3

\$2.461M

\$3M

\$3M

\$3M

P = .6

(\$5M)

\$-1.270M

P = .4

\$1.5M

\$1.5M

\$1.5M

The expected NPV is:

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

Concept Connection Example 12-3 More Complex Decision Trees

Wing Foot now feels there are two possibilities along the upper branch.

If first year demand is good, there’s a 30% chance it will be excellent in the second and third years, and a \$1 million factory expansion will generate cash inflows of \$5 million in years 2 and 3.

That means net cash inflows will be \$4 million in year 2 and \$5 million in year 3.

A decision tree for the project with this additional possibility is on the next slide

Concept Connection Example 12-3 More Complex Decision Trees

The project’s probability distribution expected return are as follows.

Real Options
• An option is the right or ability to take a certain course of action
• A real option is a course of action that usually
• Improves financial results under certain conditions
• Exists in a real, physical business sense
• Frequently occurs in capital budgeting
• Generally increases a project's expected NPV
The Abandonment Option
• A poorly performing project can sometimes be abandoned
• Usually by redeploying project resources to another use
• Avoids continuing losses along a decision tree path
• It usually takes planning early in a project’s life to preserve an abandonment option
Valuing Real Options
• Real Options usually
• have definite costs early in projects
• Create additional income along only one path
• The chance of more income increases NPV
• An option’s value is at least the increase in NPV less the option’s cost
• But the real option may be worth more if it also reduces project risk (e.g. abandonment )
Valuing Real Options
• The Risk Effect is Tricky –
• Not all real options have a risk effect
• To lower risk an option has to reduce a potential loss not make a success better
• A case by case analysis is necessary
• An Approach Through Rate of Return
• If lower risk is associated with a lower rate of return in NPV calculations, the result is higher NPV
Designing Real Options into Projects
• Abandonment option
• Usually increase NPV and lower risk
• Contract obligations can make abandonment tough
• Expansion options
• Often require little or no early commitment
• Should be planned in whenever possible
• Investment timing options
• Permit delaying investment until more certain about surrounding issues
• Flexibility options
• Preserve ability to respond to changing business conditions
Incorporating Risk Into Capital Budgeting
• For NPV
• k is used as the discount rate
• A higher k leads to lower NPV reducing the chance of project acceptance
• For IRR
• Compare IRR to k
• A higher k leads to a lower chance that IRR>k reducing probability of project acceptance

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

Incorporating Risk Into Capital Budgeting
• Riskier Projects Should Be Less Acceptable
• Using a higher, risk-adjusted rates for risky projects lowers their chance of acceptance
• The Starting Point for Risk-Adjusted Rates is the firm’s current risk level reflected in its cost of capital
Incorporating Risk Into Capital Budgeting
• Relating Interest Rates to Risk
• Interest rates are comprised of a base rate plus a risk premium
• Investors demand a higher risk premiums  higher interest rates if they are to bear more risk
• In capital budgeting the company is the investor
Incorporating Risk Into Capital Budgeting
• Choosing the Risk-Adjusted Rate for Various Projects
• An arbitrary, subjective process
• Three categories of increasing risk
• Replacements – low risk, use cost of capital
• Expansion projects - slightly more risky than the current level
• New ventures – generally involve a lot more risk
• The project as a diversification
• If viewed as a collection of projects, a new venture diversifies the firm
• A new venture also diversifies the stockholders’ investment portfolios
Estimating the Risk-Adjusted Rate Through Beta
• The Security Market Line (SML) can be used to determine a risk-adjusted rate for a new venture
• SML: kx = kRF + (kM - kRF) bX
• bX = beta = the measure of a company's systematic risk
• If a project is viewed as a business in a particular field, use a beta common to that field to estimate a risk-adjusted rate for project analysis
• The project as a diversification
• Diversifiable and non-diversifiable risk for projects
• Projects have two levels of diversifiable risk
• Some risk diversified away within the firm's portfolio of projects
• Some risk diversified away by the shareholders' investment portfolios
• The remaining risk is systematic risk
Concept Connection Example 12-6 Risk-Adjusted Rates - SML
• Orion Inc. makes radio communications equipment.
• beta = 1.1 cost of capital = 8%
• Considering a venture into risky military radios.
• Military radio market is dominated by
• MilradInc. - 60% market share, beta = 1.4
• AntexRadio Corp. - 20% market share, beta = 2.0
• Both make only military radios.
• kM = 10% , kRF = 5%.
• C0 = \$10M, Ci= \$3M n = 5 years
• Should Orion undertake the project?
Concept Connection Example 12-6 Risk-Adjusted Rates - SML

Calculate the risk-adjusted rate for the project:

k = 5% + (10% - 5%)2.0 = 15.0%

Then calculate the project's NPV using the 15% risk-adjusted rate:

NPV = -\$10.0M + \$3M[PVFA15,5]

= -\$10M + \$3M[3.3522]

= \$0.1M

NPV at Orion’s own 8% cost of capital is \$2.0M clearly indicating acceptance. Adjusted for risk, however, the project is marginal . This is a crucial insight!

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

Problems with the Theoretical Approach
• It is often difficult to find a pure play firm from which to obtain an appropriate beta
• If a pure play division is found within a corporation, estimate the beta of that division using the accounting beta method
• Systematic risk may not be only important risk
• If total risk is important, an even higher risk-adjusted rate would be appropriate
Certainty Equivalents (CE)
• For every cash flow management develops a lower risk free (certain) figure that is as attractive as the forecast risky figure.
• Then calculate a risk adjusted NPV or IRR with those cash flows
• Alternatively choose a CE factor (0< 1) for each cash flow and multiply.
• CE factors generally decline as they proceed further into the future
A Final Comment on Risk in Capital Budgeting
• Virtually every firm of any size uses capital budgeting techniques
• But few explicitly include risk
• Business managers do recognize risk but they do it through subjective judgments