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Session 7

Capital Budgeting - Risk Analysisand Real Options

Types of risk: stand-alone,corporate, and market

Project risk and capital structure

Risky outflows

Effects of abandonment possibilities

Real options

Optimal capital budget

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What does risk mean in

capital budgeting?

Uncertainty about a projects futureprofitability.

Measured by WNPV, WIRR, beta.

Will taking on the project increasethe firms and stockholders risk?

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Is risk analysis based on historical data

or subjective judgment?

Can sometimes use historical data,but generally cannot.

So risk analysis in capital

budgeting is usually based onsubjective judgments.

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How is each type of risk measured, and

how do they relate to one another?

1. Stand-Alone Risk:

The projects risk if it were the firmsonly asset and there were noshareholders.

Ignores both firm and shareholderdiversification.

Measured by the W or CV ofNPV,IRR, or MIRR.

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0 E(NPV)

Probability Density

Flatter distribution,

largerW, larger

stand-alone risk.

Such graphics are increasingly used

by corporations.

NPV

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2. Corporate Risk:

Reflects the projects effect oncorporate earnings stability.

Considers firms other assets

(diversification within firm).Depends on:

projects W, and

its correlation wit

hreturns onfirms other assets.

Measured by the projectscorporate beta.

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Profitability

0 Years

Project X

Total Firm

Rest of Firm

1. Project X is negatively correlated tofirms other assets.

2. If r < 1.0, some diversification benefits.3. If r = 1.0, no diversification effects.

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3. Market Risk:

Reflects the projects effect on awell-diversified stock portfolio.

Takes account of stockholdersother assets.

Depends on projects W andcorrelation with the stock market.

Measured by the projects marketbeta.

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How is each type of risk used?

Market risk is theoretically best in

most situations.However, creditors, customers,

suppliers, and employees are moreaffected by corporate risk.

Therefore, corporate risk is alsorelevant.

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Stand-alone risk is easiest tomeasure, more intuitive.

Core projects are

high

lycorrelated with other assets, sostand-alone risk generally reflectscorporate risk.

If the project is highly correlatedwith the economy, stand-alonerisk also reflects market risk.

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What is sensitivity analysis?

Shows how changes in a variablesuch as unit sales affect NPV orIRR.

Each variable is fixed except one.Change this one variable to see

the effect on NPV or IRR.

Answers what if questions, e.g.What if sales decline by 30%?

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Illustration

-30% $ 10 $78 $105-20 35 80 97

-10 58 81 89

0 82 82 82

+10 105 83 74

+20 129 84 67

+30 153 85 61

Change from Resulting NPV (000s)

Base Level Unit Sales Salvage k

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-30 -20 -10 Base 10 20 30

Value

82

NPV

(000s)

Unit Sales

Salvage

k

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Steeper sensitivity lines show

greater risk. Small changes resultin large declines in NPV.

Unit sales line is steeperthan

salvage value or k, so for th

isproject, should worry most aboutaccuracy of sales forecast.

Results of Sensitivity Analysis

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What are the weaknesses of

sensitivity analysis?

Does not reflect diversification.

Says nothing about the likelihoodof change in a variable, i.e. a steepsales line is not a problem if sales

wont fall.

Ignores relationships amongvariables.

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Why is sensitivity analysis useful?

Gives some idea of stand-alone

risk. Identifies dangerous variables.

Gives some breakeven

information.

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What is scenario analysis?

Examines several possible

situations, usually worst case,most likely case, and best case.

Provides a range of possible

outcomes.

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Scenario ProbabilityN

PV(000

)

Assume we know with certainty all

variables except unit sales, whichcould range from 900 to 1,600.

Worst 0.25 $ 15Base 0.50 82Best 0.25 148

E(NPV) = $ 82W(NPV) = 47

CV(NPV) = W(NPV)/E(NPV) = 0.57

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If the firms average project has a CV of

0.2 to 0.4, is this a high-risk project?What type of risk is being measured?

Since CV = 0.57 > 0.4, this projecthas high risk.

CV measures a projects stand-alone risk. It does not reflect firmor stockholder diversification.

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Would a project in a firms core

business likely be highly correlatedwith the firms other assets?

Yes. Economy and customer demandwould affect all core products.

But each product would be more or

less successful, so correlation < +1.0.

Core projects probably have corre-lations within a range of+0.5 to +0.9.

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How do correlation and W affect

a projects contribution tocorporate risk?

IfWP

is relatively high, then projectscorporate risk will be high unlessdiversification benefits are significant.

If project cash flows are highly cor-

related with the firms aggregate cashflows, then the projects corporate riskwill be high ifWP is high.

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Would a core project in the furniture

business be highly correlated with thegeneral economy and thus with the

market?

Probably. Furniture is a deferrableluxury good, so sales are probably

correlated withbut more volatilethan the general economy.

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Would correlation with the

economy affect market risk?

Yes.

High correlation increasesmarket risk (beta).

Low correlation lowers it.

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With a 3% risk adjustment, should

our project be accepted?

Project k = 10%+ 3%= 13%.Thats 30% above base k.

NPV = $60,541.

Project remains acceptable afteraccounting for differential (higher)risk.

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Should subjective risk factors be

considered?

Yes. A numerical analysis may notcapture all of the risk factors inherentin the project.

For example, if the project has thepotential for bringing on harmfullawsuits, then it might be riskierthana standard analysis would indicate.

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Are there any problems with scenario

analysis?

Only considers a few possible out-

comes.Assumes that inputs are perfectly

correlated--all bad values occurtogether and all good values occurtogether.

Focuses on stand-alone risk, althoughsubjective adjustments can be made.

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What is a simulation analysis?

A computerized version of scenario

analysis which uses continuousprobability distributions.

Computer selects values for each

variable based on given probabilitydistributions.

(More...)

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NPV and IRR are calculated.

Process is repeated many times

(1,000 or more).End result: Probability

distribution ofNPV and IRR basedon sample of simulated values.

Generally shown graphically.

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0 E(NPV) NPV

Probability Density

Also gives WNPV, CVNPV, probability

ofNPV > 0.

x x x x

x x x x x x

x x x x x x

x x x x x x

x x x x x x

x

x x

x x x x

x

x x

x x x

x x x x xx x x x x x x x x x x x x x x x x x x x x x x x x

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What are the advantages of simulation

analysis?

Reflects the probabilitydistributions of each input.

Shows range ofNPVs, the

expected NPV,W

NPV, and CVNPV.Gives an intuitive graphof the risk

situation.

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What are the disadvantages of

simulation?

Difficult to specify probability

distributions and correlations.

If inputs are bad, output will be bad:Garbage in, garbage out.

May look more accurate than it reallyis. It is really a SWAG (ScientificWild A__ Guess). (More...)

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Sensitivity, scenario, and simulationanalyses do not provide a decisionrule. They do not indicate whether a

projects expected return is sufficientto compensate for its risk.

Sensitivity, scenario, and simulation

analyses all ignore diversification.Thus they measure only stand-alonerisk, which may not be the mostrelevant risk in capital budgeting.

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Find the projects market risk and cost

of capital based on the CAPM.

Target debt ratio = 50%.

kd = 12%.

Tax rate = 40%.

kRF = 10%.

beta Project = 1.2.

Market risk premium = 6%.

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Beta = 1.2, so project has more marketrisk than average.

Projects required return on equity:

ksP

= kRF

+ (kM

- kRF

)bP

= 10%+ (6%)1.2 = 17.2%.

WACCP = wdkd(1 - T) + weksP

= 0.5(12%)(0.6) +0.5(17.2%)

= 12.2%.

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How does the projects market

risk compare with the firmsoverall market risk?

Project k = 12.2% versuscompanys k = 10%.

Indicates that projects marketrisk is greaterthan firms averageproject.

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Is the projects relative market risk

consistent with its stand-alone risk?

Yes. Project CV = 0.57 versus 0.3for an average project, which isconsistent with projects higher

market risk.

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Methods for estimating a projects beta

Pure play. Find several publicly

traded companies exclusively inprojects business. Use average oftheir betas as proxy for projectsbeta.

Hard to find such companies.

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Accounting beta. Run regressionbetween projects ROA and S&Pindex ROA.

Accounting betas are correlated(0.5-0.6) with market betas.

But normally cant get data on newprojects ROAs before the capitalbudgeting decision has been made.

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Advantages and disadvantages of

applying the CAPM in capital budgeting

Advantages:

A projects market risk is the mostrelevant risk to stockholders,hence to determine the effect of

the project on stock price.

It results in a definite hurdle ratefor use in evaluating the project.

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Disadvantages:

It is virtually impossible to

estimate betas for many projects.

People sometimes focus onmarket risk to the exclusion of

corporate risk, and th

is may be amistake.

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Divisional Costs of Capital

Debt Cost of

Division Beta Capacity Capital

Heirloom High Low 14%

Maple Avg. Avg. 10%

School Low High 8%

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Project Risk Adjustments

Crockett Furniture classifies eachproject within a division as high risk,

average risk, and low risk. Crockettadjusts divisional costs of capital by:

Adding 2% forhigh risk project

No adjustment for average riskproject

Subtracting 1% for low risk project

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What are the project costs of capital?

High------- 16%

Heirloom Avg.------- 14%

Low-------- 13%

High------- 12%

Maple Avg.------- 10%

Low-------- 9%

High------- 10%

School Avg.------- 8%

Low-------- 7%

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Evaluating Our Project

Our project is ah

igh

risk project inthe Heirloom division.

Project cost of capital = 16%

NPV = $42 thousand

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Evaluating Risky Outflows

Company is evaluating twoalternative production processes.Plan Wrequires more workers butless capital. Plan C requires morecapital but fewer workers.

Both systems have 3-year lives.

The choice will have no impact onrevenues, so the decision will bebased on relative costs.

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Year Plan W Plan C

0 ($500) ($1,000)

1 (500) (300)

2 (500) (300)

3 (500) (300)

The two systems are of average risk, sok = 10%. Which to accept?

PVCOSTS-W = -$1,743. PVCOSTS-C = -$1,746.

Ws costs are slightly lower so pick W.

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Now suppose Plan W is riskier than

Plan C because future wage rates aredifficult to forecast. Would this affect

the choice?

If we add a 3% risk adjustment to the10% to get k

W= 13%, new PV would

be:

W now looks even better.

PVCOSTS-W= -$1,681

which is < old PVCOSTS-W= -$1,743.

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Plan W now looks better, but since itis riskier, it should look worse!

When costs are being discounted, we

must use a lower discount rate toreflect higher risk. Thus, theappropriate discount rate would be10% - 3% = 7%, making

PVCOSTS-W = -$1,812 > old -$1,743.With risk adjustment, PVCOSTS-W >

PVCOSTS-C, so now choose Plan C.

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Note that neither plan has an IRR.

IRR is the discount rate that equatesthe PV (inflows) to the PV (outflows).

Since there are only outflows, therecan be no IRR (or MIRR).

Similarly, a meaningful NPV can onlybe calculated if a project has both

inflows and outflows.

If CFs all have the same sign, theresult is a PV, not an NPV.

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Real Options

Real options occur when managersh

ave th

e opportunity to influence th

ecash flows of a project after theproject has been implemented.

Real options also are called:

Managerial options.

Strategic options.

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How do real options increase the

value of a project?

Real options allow managers to

avoid negative project cash flows ormagnify positive project cash flows.

Increases size of expected cash

flows.

Decreases risk of expected cashflows.

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How is the DCF method affected?

(1) Its easy to quantify the increase inthe size of the expected cash flows.

(2) Its very hard to quantify thedecrease in the risk of the expectedcash flows.

(3) The correct cost of capital cannotbe identified, so the DCF methoddoesnt work very well.

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Types of Real Options

Flexibility options

Abandonment optionsOptions to contract or temporarily

suspend operations

Options to expand volume of productOptions to expand into new

geographic areas (More...)

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Options to add complementaryproducts

Options to add successivegenerations of the same product

Options to delay

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What attributes increase the value of

real options?

All real options have a positive value.

Even if its not possible to determinea quantitative estimate of a realoptions value, its better to have a

qualitative estimate than to ignorethe real option.

(More...)

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Real options are more valuable if:

They have a long time until youmust exercise them.

The underlying source of risk isvery volatile.

Interest rates areh

igh

.

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Choosing the Optimal Capital Budget

Finance theory says to accept allpositive NPV projects.

Two problems can occur when thereis not enough internally generatedcash to fund all positive NPV projects:

An increasing marginal cost ofcapital.

Capital rationing

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Increasing Marginal Cost of Capital

Externally raised capital can have

large flotation costs, which increasethe cost of capital.

Investors often perceive large capital

budgets as being risky, which drivesup the cost of capital.

(More...)

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If external funds will be raised, thenthe NPV of all projects should beestimated using this higher marginal

cost of capital.

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Capital Rationing

Capital rationing occurs when acompany chooses not to fund all

positive NPV projects.

The company typically sets anupper limit on the total amount

of capital expenditures that it willmake in the upcoming year.

(More...)

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Reason: Companies want to avoid thedirect costs (i.e., flotation costs) andthe indirect costs of issuing new

capital.Solution: Increase the cost of capitalby enough to reflect all of these costs,and then accept all projects that still

have a positive NPV with the highercost of capital.

(More...)

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Reason: Companies dont haveenoughmanagerial, marketing, orengineering staff to implement all

positive NPV projects.

Solution: Use linear programming to

maximize NPV subject to notexceeding the constraints on staffing.

(More...)

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Reason: Companies believe that theprojects managers forecastunreasonably high cash flow estimates,so companies filter out the worstprojects by limiting the total amount ofprojects that can be accepted.

Solution: Implement a post-audit

process and tie the managerscompensation to the subsequentperformance of the project.