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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
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 variables1
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 variables2
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
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 budgeting1
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
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 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
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
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 analysis1
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
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 trees4
Concept Connection Example 12-3 More Complex Decision Trees

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

real options
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
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
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 options1
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
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
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 budgeting1
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 budgeting2
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 budgeting3
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
estimating risk adjusted rates using capm
Estimating Risk-Adjusted Rates Using CAPM
  • 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
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
estimating risk adjusted rates using capm1
Estimating Risk-Adjusted Rates Using CAPM
  • 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
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 sml1
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
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
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
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