1 Cost of Capital & Risk Analysis MBA Fellows Corporate Finance Learning Module Part II.

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Cost of Capital & Risk Analysis

MBA FellowsCorporate Finance Learning ModulePart II

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Class Topics Incorporating risk in Capital Budgeting Cost of Capital Components: cost of

debt, preferred stock, common equity. Calculating the Weighted Average Cost

of Capital (WACC) Capital Structure Decisions EVA

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Capital Budgeting and Risk

Prior discussion of alternative projects assumed that the level of risk associated with each project was the same.

How do you evaluate projects when they have different levels of risk?

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Project Risk

Reflects the the potential variability of returns.

Portfolio effect - if a project’s proposed returns are not perfectly correlated with the returns from the firm’s other projects.

Diversification - influences risk. The total risk of the firm may be reduced by accepting the proposed project, if its returns are not perfectly correlated with the returns from the firm’s other investments.

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Types of Project Risk

Stand-alone Risk Corporate/Within Firm Risk Market/Beta Risk All Risk is not equal - some risk can be

diversified away, and some cannot.

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Stand-Alone Risk

The risk associated with a particular project, ignoring the firm’s other projects/assets and firm/shareholder diversification.

Measured by the (standard deviation) or CV (coefficient of variation) of NPV, IRR, or MIRR.

Methods for estimating stand-alone risk: Sensitivity Analysis, Scenario Analysis, Monte Carlo Simulation

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Stand-alone risk

Stand-alone risk is easiest to measure, more intuitive.

Core projects are highly correlated with other assets, so stand-alone risk generally reflects corporate risk.

If the project is highly correlated with the economy, stand-alone risk also reflects market risk.

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Coefficient of Variation (COV) COV is a relative measure of stand-alone

risk used. It used to compare the risk of 2 or more assets because it enables us to choose between 2 investments when one has a higher expected rate of return, but the other has a lower standard deviation.

It measures the the risk per unit of return.COV = Standard Deviation

Expected Return

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Measuring Stand-Alone Risk

Entails determining:1. the uncertainty inherent in the

project’s cash flows. 2. the nature of the individual cash flow

distributions and their correlations with each other to determine the nature of the NPV probability distribution.

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0 E(NPV)

Probability Density

Flatter distribution,larger , largerstand-alone risk.

NPV

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Corporate Risk

The risk that the project contributes to the firm as a whole (the effect of the project on the earnings and cash flow variability of the firm).

Corporate risk considers the fact that some of the project's risk will be “diversified away” when the project is combined with the firm’s other projects.

However, corporate risk ignores shareholder diversification.

Depends on the project’s , and its correlation with returns on the firm’s other projects.

Measured by the project’s beta.

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Profitability

0 Years

Project X

Total Firm

Rest of Firm

1. Project X is negatively correlated to firm’s other assets.

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

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Market Risk

The effect (risk) of the project on a well diversified stock portfolio.

It takes in consideration the stockholders’ other assets (investments).

Depends on project’s and its correlation with the stock market.

Measured by the project’s market beta.

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Variables that Influence a Project’s NPV and IRR

Market Size Selling Price Market Growth Rate Market Share (unit volume sales) Residual Value of Investment Operating/Fixed Costs Investment required

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Sensitivity Analysis

Answers the question “what if” Shows how changes in one variable affects

NPV or IRR. The value of one variable is changed while

holding all other variables constant.

Provides some idea of stand-alone risk.

Provides breakeven information.

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Why is sensitivity analysis useful?

Provides some idea of stand-alone risk.

Identifies dangerous variables.

Provides breakeven information.

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Sensitivity Analysis

Each variable is changed by several percentage points above and below its expected value (while holding the other variables constant).

Then a new NPV is calculated using each of these values.

Finally the set of NPV’s is plotted against the variable that was changed.

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Example

Change fromBase Level

Resulting NPV (000s)

Unit Sales Salvage k

-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

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-30 -20 -10 Base 10 20 30 Value

82

NPV(000s)

Unit Sales

Salvage

k

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Sensitivity Analysis

Slope of the lines in the graphs show how sensitive NPV is to changes in each of the inputs.

The steeper the slope, the more sensitive the NPV is to a change in the variable.

Comparison of 2 projects - the one with the steeper slope (sensitivity lines) would be riskier, because for that project a relatively small error in estimating a variable would produce a large change in the project’s expected NPV.

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Steeper sensitivity lines show greater risk. Small changes result in large declines in NPV.

Unit sales line is steeper than salvage value or k, so for this project, should worry most about accuracy of sales forecast.

Results of Sensitivity Analysis

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Weaknesses ofSensitivity analysis

Does not reflect diversification.

Says nothing about the likelihood of change in a variable, i.e. a steep sales line is not a problem if sales aren’t expected to fall.

Ignores the relationships among variables.

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Scenario Analysis

Considers both the sensitivity of NPV to changes in key variables and identifies the range of possible outcomes under the worst, best, and most likely case.

It considers the impact of simultaneous changes in key variables on the project.

It provides a range of possible outcomes.

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Scenario Analysis

Standard Deviation of NPV:

Coefficient of Variation:CVNPV =

n

iiNPV NPVENPVP

1

2)]([

)(NPVENPV

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Scenario Analysis

The project’s COV can be compared with the COV of the company’s average project to get an idea of the relative riskiness of the project under consideration.

Although scenario analyze can provide useful information about a project’s stand alone risk, it is limited because it only considers a few discrete outcomes (NPVs), even though there can be an infinite amount of possibilities.

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Assume: all variables are known with certainty except unit sales, which could range from 900 to 1,600.

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

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

Scenario Probability NPV(000)

Worst 0.25 $ 15

Base 0.50 82

Best 0.25 148

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If the firm’s 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 project has high risk.

CV measures a project’s stand-alone risk. It does not reflect firm or stockholder diversification.

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Would a project in a firm’s core business likely be highly correlated with the firm’s other assets?

Yes. Economy and customer demand would affect all core products.

But each product would be more or less successful, so correlation < +1.0.

Core projects probably have correlations within a range of +0.5 to +0.9.

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How do correlation and affect a project’s contribution to corporate risk?

If P is relatively high, then project’s corporate risk will be high unless diversification benefits are significant.

If project cash flows are highly correlated with the firm’s aggregate cash flows, then the project’s corporate risk will be high if P is high.

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Would correlation with the economy affect market risk?

Yes.

High correlation increases market risk (beta).

Low correlation lowers it.

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Subjective risk factors should also be considered

A numerical analysis may not capture all of the risk factors inherent in the project.

For example, if the project has the potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate.

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Weaknesses of Scenario Analysis

Only considers a few possible out-comes.Assumes that inputs are perfectly

correlated--all “bad” values occur together and all “good” values occur together.

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

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Monte Carlo Simulation

A computerized version of scenario analysis.

Computer randomly selects a value for each variable and combines these values to determine the NPV/IRR of the project.

The process is repeated many times (1,000 or more) until a probability distribution of the project’s NPVs/IRRs is developed with its own expected value and standard deviation.

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Monte Carlo Simulation

The inputs to a simulation include all of the principal factors affecting the project’s profitability, and the simulation output is a probability distribution of NPVs or IRRs for the project.

The project is accepted if the decision maker feels that enough of the distribution lies above the normal cutoff criteria (NPV >0) or (IRR> Required Rate of Return).

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Simulation Results (1000 trials)

Units Price NPVMean 1260 $202 $95,914St. Dev. 201 $18 $59,875CV 0.62 Max 1883 $248 $353,238 Min 685 $163 ($45,713)Prob NPV>0 97%

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Interpreting the Results

Inputs are consistent with specified distributions. Units: Mean = 1260, St. Dev. = 201. Price: Min = $163, Mean = $202, Max

= $248. Mean NPV = $95,914. Low probability

of negative NPV (100% - 97% = 3%).

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Histogram of Results

-$60,000 $45,000 $150,000 $255,000 $360,000

NPV ($)

Probability

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0 E(NPV) NPV

Probability Density

Also gives NPV, CVNPV, probability of NPV > 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

xx xx 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 x x x x x

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Advantages of Monte Carlo Simulation

Reflects the probability distributions of each input.

Shows range of NPVs, the expected NPV, NPV, and CVNPV.

Gives an intuitive graph of the risk situation.

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Weaknesses of simulation

Difficult to specify probability distributions and correlations.

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

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Project Risk Analysis

Sensitivity, scenario, and simulation analyses do not provide a decision rule. They do not indicate whether a project’s expected return is sufficient to compensate for its risk.

Sensitivity, scenario, and simulation analyses also ignore diversification. As a result, they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting.

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Risk Adjusted Discount Rate Calculate the NPV of a project, using a

discount rate that has been adjusted for the riskiness of the project.

Risk premiums applied to individual projects are chosen in a subjective manner.

Projects assigned to risk classes and then the same discount rate is assigned to all projects in each class.

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Cost of Capital

Capital : amount of money raised by a corporation from creditors and investors through the issuance of bonds (debt), preferred stock, and/or common stock.

Cost: the rate of return required by investors and creditors who supply capital to the firm, or

The cost to the corporation of raising funds from investors and/or creditors, or

The minimum rate of return required on new investments undertaken by the firm.

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Capital Structure

The proportion of a firm’s total assets financed by debt, preferred stock, and common stock.

Component cost - the required rate of return on each source of capital (debt, preferred stock, common stock)

Target Capital Structure - percentages are set for different financing sources.

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Weighted Average Cost of Capital (WACC)

The average (after-tax) cost of the sources of capital weighted by the proportion of each component in the firm’s capital structure.

EVA - firms create value if their income exceeds the cost of capital used to finance their operations.

For a project to be accepted, it must generate a return greater than its WACC.

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WACC

The WACC is based on the weighted costs of the individual components of capital. The weights are equal to the proportion of each of the components in the target capital structure.

The appropriate component costs to use are the marginal costs or the costs associated with the next dollar of capital to be raised. These may differ from the historical costs of capital raised in the past.

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Marginal Cost of Capital

The primary objective of managers is to maximize shareholder value. To do this managers must select projects that are expected to earn more than the firm’s cost of capital.

To evaluate a project that requires raising and investing new capital, managers must compare the marginal cost of capital to the project’s expected return.

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Cost of Debt

The after-tax cost of debt is used in the calculation of WACC because of the tax savings that result from the deductibility of interest.

kd = ( 1- Tax rate)

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Component Cost of Debt

Interest is tax deductible, so the after tax (AT) cost of debt is:

rd AT = rd BT(1 - T)

= 10%(1 - 0.40) = 6%.

Use the nominal rate.

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Cost of Preferred Stock

The rate of return investors require on the firm’s preferred stock adjusted for flotation costs.

kps = Dps/Pn

Because of the non-deductibility of preferred stock dividends, the cost of preferred stock is higher than that of debt. As a result, firms prefer to issue debt rather than from preferred stock.

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Cost of Preferred Stock

PP = $113.10; 10%Q; Par = $100; F = $2

%.0.9090.010.111$

10$

00.2$10.113$

100$ 1.0

n

psps P

Dr

Use this formula:

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Picture of Preferred Stock

2.50 2.50

0 1 2rps = ?

-111.1

...

2.50

.50.2$

10.111$PerPer

Q

rr

D

%.9)4%(25.2 %;25.210.111$

50.2$)( NompsPer rr

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Cost of Common Stock (ks)

The rate of return required by investors in the firm’s common stock.

Equity capital can be raised internally through retained earnings or through the sale of new common.

The cost of retained earnings is the opportunity cost, i.e. the return that investments could earn in alternative investments.

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Cost of Common Stock (ks)

Funds generated through earnings can either be paid out as dividends or retained to be reinvest them in the firm.

If the funds are paid out as dividends, stockholders can reinvest these dividends elsewhere to earn an appropriate rate of return.

The cost of internal equity to the firm is less than the cost of new common stock, because the sale of new stock requires the payment of flotation costs.

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Two ways to determine the

cost of equity, ks:

1. Capital Asset Pricing Model

ks = kRF + (kM - kRF)b

= kRF + (RPM)b.

2. Dividend Growth Model

ks = D1/P0 + g

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Capital Asset Pricing Model

The rate of return investors require on the firm’s common stock is a function of the risk free rate (kRF – Treasury Bond rate), the market risk premium, and the firm’s beta.

rs = rRF + (RPM )bi

Equity/Market Risk Premium: RPM = (rM - kRF) The additional return that investors require to

invest in risky equities.

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Estimating Beta

Run a regression with returns of the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.

Historical beta: based on the past relationship between a stock’s return and the returns of the market portfolio.

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Cost of equity based on the CAPM

rRF = 7%, RPM = 6%, b = 1.2

rs = rRF + (rM - rRF )b.= 7.0% + (6.0%)1.2 =

14.2%.

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Dividend Growth Model

ks = D1/P0 + g

D1 - dividend to be paid next year

P0 - current price of the stock

g - expected growth rate of dividendsg = (Retention Rate)(ROE) org = (1- Payout Ratio)(ROE)

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Dividend Growth Model Future dividends are assumed to grow

at a constant rate. Payout ratio - the proportion of

earnings (net income) paid out in the form of dividends.

Retention rate - the proportion of earnings not paid out as dividends (i.e. retained and reinvested in the firm).

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What’s the DCF cost of equity, rs?Given: D0 = $4.19;P0 = $50; g = 5%.

g

P

gDg

P

Drs

0

0

0

1 1

$4. .

$50.

. .

.

19 1050 05

0 088 0 05

13 8%.

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Weighted Average Cost of Capital

WACC = wdkd(1-T) + wpskps+ wceks

Represents the average cost of each new or marginal dollar of capital supplied.

Percentage capital components (wd, wps, wce) are based on accounting book values, current market values of the components, or the targeted capital structure.

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Determining WACC

1) Calculate the cost of capital for each individual component.

kd = ( 1- Tax rate),

kps = Dps/Pn

ks = D1/P0 + g

2) Compute the weighted (marginal) cost of capital for each increment of capital raised.

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Factors Affecting WACC

Interest Rates Market Risk Premium Tax Rates Capital Structure Policy Dividend Policy Investment Policy

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Estimating Project Risk

The (marginal) cost of capital is a function of project’s risk.

The firm’s WACC is closely related to the degree of risk associated with new investments, existing assets, and the firm’s capital structure.

The 3 risks associated with a project are:1. Stand-alone risk2. Corporate or with-in firm risk3. Market or beta risk

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Divisional Beta

Security Market Line - expresses the risk return trade-off:

ks = kRF + (kM - kRF)bi

bi - the beta of a division.

ks - required rate of return on the division’s

investment.

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Estimating Project Risk

Stand Alone risk - the project’s diversifiable risk. It is measured by the variability of the project’s expected returns.

Corporate/Within Firm Risk - the project’s contribution to the firm’s overall risk (the fact that the project represents only one of the firm’s portfolio of assets. It is measured by the project’s impact on uncertainty about the firm’s future earnings.

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Estimating Project Risk

Market/Beta Risk - project's risk as viewed by the a well diversified stockholder who recognizes that the project is only one of the firm’s assets and that the firm’s tock is but one part of the investor’s total portfolio.

Measures by the project’s impact on the firm’s beta.

Market Risk directly affects the stock prices.

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CAPM and Project Risk

Using the CAPM to estimate a project’s risk adjusted cost of capital:

kproject = kRF + (kM - kRF)bproject

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Capital Asset Pricing Model

Market (systematic) risk is the only relevant risk for capital budgeting purposes.

Firm can be viewed as a portfolio of assets, each having its own beta.

The beta of a firm is the weighted average betas of its individual assets.

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Mistakes in Estimating WACC Using the current cost of debt instead of

the interest rate on new debt. Using the historical average rate return on

stocks instead of the current expected rate of return on stocks to estimate the risk premium.

If the targeted capital structure is unknown use the market values to obtain the weights.