Practical financial managment 7e LASHER chapter 12

Concept Connection Example 12-2 Decision Tree Analysis17 The Wing Foot Shoe Company is considering a new running shoe.. Concept Connection Example 12-3 More Complex Decision TreesWing Fo

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

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

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Figure 12-1 The Probability Distribution of a Future Cash Flow as 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

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Figure 12-2 Risk in Estimated

Cash Flows

The Importance of Risk in

Figure 12-3 Project NPVs Reflecting Risky Cash Flows

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

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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

Concept Connection Example 12-1 Scenario Analysis

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Concept Connection Example 12-1 Scenario 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

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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

Figure 12-4 Results of Monte Carlo Simulation for NPV

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Figure 12-5 A Simple Decision Tree

Concept Connection Example 12-2 Decision Tree Analysis

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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:

$1.5M

$1.5M

$1.5M ($5M)

$3M

$3M

$3M

3 2

1 0

Figure 12-6 A More Complex

Decision Tree

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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

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The NPV for the new upper path is

Concept Connection Example 12-3 More Complex Decision Trees

Concept Connection Example 12-3 More Complex Decision Trees

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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

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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 –

An Approach Through Rate of Return

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 issuesFlexibility options

– Preserve ability to respond to changing business conditions

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Incorporating Risk Into Capital Budgeting

A higher k leads to lower NPV reducing the chance of project acceptance

A higher k leads to a lower chance that IRR>k reducing probability of project acceptance

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

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Incorporating Risk Into Capital Budgeting

Relating Interest Rates to Risk

– Investors demand a higher risk premiums  higher interest rates if they are to bear more risk

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

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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

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

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Estimating Risk-Adjusted Rates

Using CAPM

The project as a diversification

Diversifiable and non-diversifiable risk for projects

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

Figure 12-7 Components of Project Risk

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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

Milrad Inc - 60% market share, beta = 1.4

Antex Radio Corp - 20% market share, beta = 2.0

Both make only military radios

kM = 10% , kRF = 5%

C0 = $10M, Ci= $3M n = 5 years

Concept Connection Example 12-6 Risk-Adjusted Rates - SML

Problems with the Theoretical Approach

It is often difficult to find a pure play firm from which to obtain an appropriate beta

using the accounting beta method

Systematic risk may not be only important risk

Certainty Equivalents (CE)

For every cash flow management develops a lower risk free (certain) figure that is as attractive

as the forecast risky figure.

Alternatively choose a CE factor (0< 1) for each cash flow and multiply.

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