FIN 40153: Advanced Corporate Finance

THE WEIGHTED AVERAGE COST OF CAPITAL

(BASED ON RWJ CHAPTER 13)

The Cost of Capital and Valuation Debt and Equity A company can get cash for investment by retaining

earnings or selling either debt or equity. Does it make any difference how the firm raises

money? What is the proper discount rate when the firm uses both

debt and equity? How do we perform capital budgeting/valuation when

the project has different risk and/or capital structure than the firm as a whole?

Setting the stage

AssetsProduce Cash FlowsThat Create Value

Debt

Equity

CashFlows

The firm’s assets are a portfolio of the debt and equity.Debt and equity just divide up the cash flows (value) of the firm.

The Weighted Average Cost Of Capital(WACC)

• When a firm has both debt and equity in its capital structure, the most frequent recommendation is to base the project discount rate on the weighted average cost of capital (WACC):

)T(1rDE

Dr

DE

EWACC CDE

• where

– E is the market value of the firm’s stock

– D is the market value of the firm’s debt

– rE is the required rate of return on the firm’s stock

– rD is the required before tax rate of return on the firm’s debt

– TC is the firm’s marginal tax rate

Why Is There A Tax Adjustment For Debt?

Consider a firm that has earnings before interest and taxes each period of $1000. Under scenario A, the firm is all equity financed; under scenario B, the firm has issued debt with a face value of $1000 and a coupon rate of 10%. The firm has a 40% marginal tax rate.

Why Is There A Tax Adjustment For Debt?

In A, the firm can distribute a total of $600 to stakeholders. In B, the firm can distribute $100+$540=$640 to stakeholders. The tax shield from debt gives the firm $40 more to distribute. This tax

shield lowers the effective interest payment on debt to $60=$100(1-0.4) or 6% coupon rate.

A B

EBIT $1000 $1000Interest $0 $(100)

______ ______EBT $1000 $900Tax (40%) $(400) $(360)

______ ______Net Inc $600 $540

Calculation of the cost of debt (RDebt)

The before tax cost of debt can be calculated as the yield to maturity (YTM) on the firm’s existing debt. Much debt is not publicly traded, so you do not have the current

price to compute the YTM. YTM is basically the IRR of the debt.

Can also be determined using the current interest rates applicable to bonds of companies with comparable financial structure and bond ratings. Wall Street Journal Moody’s

The after tax cost of debt is the before tax cost of debt multiplied by (1-Tc), where Tc is the firm’s effective marginal tax rate.

Bond Ratings and Bond Yields

So on 3/1/2006 10 year AAA bonds pay 68 basis points higher than 10 year than Treasuries, 4.59% + 0.68% = 5.27%

High Yield Bond Quotes

For Intelsat if the face a corporate tax rate of 35% their after tax cost of debt would be 9.467(1 – 0.35) = 6.154%

Calculation of the cost of equity (rEquity)

The cost of equity can be calculated using the Security Market Line (SML) from the CAPM.

rE= Rf+ (E[RM]- Rf)

Three inputs are required Firm Beta Risk free rate Market risk premium

Applying the CAPM (i) An estimate of the risk free interest rate.

Practitioners tend to favor the current yield on longer-term treasury bonds but adjust according to projects maturity.

Remember to adjust the market risk premium accordingly.

(ii) An estimate of the market risk premium, E(Rm - rf), the extra return investors expect to earn from holding the market instead of the risk-free bond. The theory calls for a forward looking measure (expected) Expectations are not observable. Generally use a historically estimated value.

(iii) An estimate of beta. Is the project or a surrogate for it traded in financial markets? If so, gather data and run an OLS regression.

How To Obtain Beta. Estimate beta from a regression equation.

In practice, generally use last five years of monthly data. Some companies publish beta estimates on a regular basis: Value Line Merrill Lynch Beta Book Internet Finance Websites

What if the company is not publicly traded? Find a comparable company that is traded. Use accounting data (ROE) instead of stock returns Reason it out.

Microsoft Return Versus S&P 500

RMicrosoft

RS&P

Estimating Microsoft’s Beta

Regression Results of Microsoft Return on S&P 500 Return 2001-

2004SUMMARY OUTPUT

Regression StatisticsMultiple R 0.598458926R Square 0.358153086Adjusted R Square 0.34708676Standard Error 0.099420174Observations 60

ANOVAdf SS MS F Significance F

Regression 1 0.319900025 0.319900025 32.36422661 4.41249E-07Residual 58 0.573293522 0.009884371Total 59 0.893193547

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -0.000268979 0.012848137 -0.020935275 0.983369144 -0.025987299 0.025449341 -0.025987299 0.025449341X Variable 1 1.563925441 0.274905499 5.688956548 4.41249E-07 1.013642709 2.114208173 1.013642709 2.114208173

This is Microsoft’s Beta

What Determines Beta?

Beta is a measure of sensitivity to the market.

Companies with cyclical cash flows will tend to have higher betas.

Higher operating leverage implies higher betas. operating leverage is the ratio of fixed

costs to variable costs. Higher financial leverage also means higher

equity beta.

The Market Risk Premium

The market risk premium measures the additional return that an investor needs to hold risky assets (i.e. stocks) rather than risk-free assets (treasuries).

The Market Risk Premium is defined as:

Ideally, the MRP would be based on expectations of investors about the future. However, expectations are not observable.

We can observe what has actually happened based on historical data.

]R][E[R FM

The Market Risk Premium (Excess Returns) Excess Returns

The difference between the average return for an investment and the average return for a risk-free asset

The extra return earned for holding a risky investment

For U.S. data from 1928 to 2007

The Market Risk Premium

Recall that the standard deviation of returns on the S&P 500 is approximately 20% per year.

If we use data from 1928-2007 we have 80 years of data. The standard error of the risk premium estimate is about

0.20/sqrt(80)=0.022 This implies that our estimate of the risk premium is not very

precise. The 95% confidence interval is: 0.078 ± 2 x 0.022 The risk premium is between 3.3% and 12.2% Note that these calculations assume that the process generating

stock returns is stationary over time. What if it is not?

The Market Risk Premium

Should we use a longer sample? Some researchers have now been able to get U.S. stock return data

back to the early 1800s. See for example “Stocks for the Long Run” by Jeremy Siegel http://www.wharton.edu/research/1998.html

Also, do we want to create our sample estimate using only data from U.S. markets?

The U.S. “won” the major wars, avoided communism or other major social upheaval. Could the U.S. market outcomes reflect what was expected, plus a “bonus” for doing so well?

Lets look at some data from “A Century of Global Stock Market Returns” provided by William Goetzmann, Yale University.

]R][E[R FM

•

0 20 40 60 80 100

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

US

Canada

Austria

Belgium

Denmark Finland

France

Germany*

Ireland

Italy

Netherlands

Norway

Portugal*

Spain

Sweden Switzerland

UK

Czechoslovakia

Greece

Hungary

Poland

Australia

New Zealand

Japan*

India

Pakistan

Philippines

Argentina*

Brazil

Mexico

Chile*

Colombia

Peru*

Uruguay

Venezuela

Egypt

Israel

South Africa

Years of Existence since 1921 (* indicates a long-term break)

Percent

Fig.1. Real Returns on Global Stock MarketsSorted by Years of Existence: 1921-1996

The US is clearly not typical

Country Risk Premiums

How do estimates of the market risk premium change?

If we add additional years to the sample using the Siegel data it suggests a risk premium relative to short-term treasuries of perhaps 6% per year (compared to 7.78%).

The Goetzmann data suggest that the average U.S. stock return exceeds average world returns by about 2% per year.

These findings suggest estimates of: 6.0% relative to short-term treasuries. 4.5% relative to long-term treasuries .

Finally, might the risk premium change over time -- higher at some points, lower at others? If the risk premium is not stationary then using a longer sample will

not provide an accurate estimate of current expectations. But using only recent data increases the estimation error.

Betas and Leverage

• We noted earlier that the beta of a portfolio is the average of the component betas. Also, we can think of the firm’s assets as a portfolio of the debt and equity claims. From these insights it follows that:

DebtEquityAssets DE

D

DE

E

• Where E is the market value of the stock (equity) and D is the Where E is the market value of the stock (equity) and D is the market value of debt (borrowings).market value of debt (borrowings).

Risk of Debt and Equity

AssetsProduce Cash FlowsThat Create Value

(Asset Beta)

Debt(Debt Beta)

Equity(Equity Beta)

CashFlows

The firm’s assets are a portfolio of the debt and equity.Debt and equity just divide up the cash flows (value) of the firm.

Beta and Leverage This formula can be used to find the asset beta given the equity

and debt betas or to find the equity beta, given the asset and debt betas. Rearranging the formula gives:

Note that the equity beta increases as leverage (D/E) increases. It is often assumed that the debt has a zero beta (a big

simplification). Then:

)( DebtAssetsAssetsEquity ED

DEE

EquityAssets

ED

AssetsEquity 1

Beta and Leverage This formula can be used to find the asset beta given the equity

and debt betas or to find the equity beta, given the asset and debt betas.

For firms with risky debt (i.e., below investment grade), in practice it is often assumed that the debt beta is 0.25 to 0.30.

)( DebtAssetsAssetsEquity ED

DebtEquityAssets DED

DEE

Adjusting beta for different capital structures

Example: Gamma airlines’ equity beta is observed to be 1.31. It’s equity is worth 25.0 million while its debt is worth 15.0 million. What is the beta of the underlying assets assuming a debt beta of zero?

Note: The asset beta is always less than or equal to the equity beta.

819.031.11525

25

Assets

Points to Note Regarding Beta and Leverage

If the firm uses no debt (D=0) the equity beta and the asset beta are equal.

If the firm uses debt, the equity beta is increased relative to the asset beta:

implies:

(1) equity holders will require a higher rate of return, (2) when comparable firms are used to estimate beta, allowances for

differing capital structures will be required.

ED

AssetsEquity 1

How to use the set of tools developed here to select discount rates for capital budgeting.

The cost of capital for each project should reflect the systematic risk of that project and the capital structure of the firm (or division) taking the project. So, Select a publicly traded company that is comparable in terms of

the risk of the underlying business (i.e., the asset beta). Obtain the unlevered (asset) beta of the comparable. Obtain the corresponding project equity beta for your firm,

reflecting your firm’s capital structure. Obtain the cost of equity and cost of debt for this project reflecting

your firm’s capital structure. Calculate the WACC for the project and perform NPV analysis

based on the expected cash flows with no leverage.

EXAMPLEThe Story For BK Industries

Remember BK Industries has been producing publishing equipment for some time now and the CEO believes that he has stumbled upon a valuable product innovation that embeds new features in text editing systems. BK’s cost advantages and vast skill in marketing mean it would be difficult for competitors to undertake such a project.

BK IndustriesIncremental Cash Flows

Suppose that BK forecasts the following cash flows from operating a text editing business ($ millions).

Year 0 Year 1 Year 2 Year 3 Year 4 Year5

-26.00 3.98 5.42 6.69 5.99 22.46

BK Industries Net Present Value (NPV)

BK has estimated its company cost of capital to be 10%. What is the NPV of the text editing business?

NPV (@ r=10%) =

-26.00 + 3.98/(1.10) + 5.42/(1.10)2 + 6.69/(1.10)3 +

5.99/(1.10)4 + 22.46/(1.10)5 = $5.159 Million

The NPV is greater than zero, so BK should proceed with the project.

Example: BK Industries Revisited

Suppose that BK Industries is a conglomerate company with operations in a number of other products lines with no text editing business. Also suppose BK’s current equity beta is 1.0. BK has and will maintain a debt/equity ratio of 1.0. Can we use the company cost of capital to

value the text editing project? Latec Inc. is a firm that makes only text editing

systems. Latec’s equity beta is 1.35. Latec has a debt to equity ratio of 0.75.

Delevered Betas with debt/equity ratios

• The formulas for obtaining asset betas from equity betas and vice versa provided earlier required dollars values for debt (D) and equity (E). What if you are only given the leverage ratio, L = D/E? The formulas are restated as:

EquityAssets L

1

1

)1( LAssetsEquity

Delever Latec’s Beta to obtain the Beta of text-editing assets:

• Latec has L =0.75and an equity beta of 1.35.

77.035.175.01

1

Assets

Relever the asset Beta to reflect BK’s capital structure:

54.11177.0 Equity

Recalling that BK will keep its debt/equity ratio equal to one, we can get:

This is the beta for a BK equity position in a text editing asset.Why is this equity beta greater than Latec’s?

BK Industries, Cont. Assume that the risk free rate is 8% and that BK’s cost of debt

is also 8%. The market risk premium is 7% and the marginal tax rate is 45%. The required return on BK’s equity is:

The weighted average cost of capital for the text editing venture (using the fact that D/E = 1 here) is:

%59.11 )45.01%(81+1

1%78.18

1+1

1=

)1(

CDE TrDE

Dr

DE

EWACC

%78.18%754.1%8)][( FMFequity RRERr

Finally, we can evaluate the NPV of the text editing venture using the WACC that reflects the risk associated with this particular business.

The NPV of the text editing project is -$21,329

Notice that the selected discount rate of 11.59% reflects:

The risk (beta) of text editing businesses, not BK’s existing The risk (beta) of text editing businesses, not BK’s existing businesses.businesses.

BK’s capital structure, not that of the surrogate firm.BK’s capital structure, not that of the surrogate firm.

COMPANY COST OF CAPITAL ANDPROJECT COST OF CAPITAL

Required return

Project beta

Company cost of capital

required return on projectSecurity market line showing

Average betaof firm's assets

Risky ProjectSafe Project

Some Common Errors to Avoid Using book value weights in the WACC.

The weights should be based on market values The weights should reflect the firm’s target

capital structure.

Using incorrect leverage ratios for levering and unlevering betas and computing WACC. D/E versus D/(D+E). Know which one you are using.

Some Common Errors to Avoid Subtracting the current risk-free rate from the

historical average market return to get the market-risk-premium. The MRP estimate should be based on the difference

between the historical average of the market return and the historical average return on the risk-free bond.

The current risk-free rate is used for the stand-alone Rf if the SML equation.

]R][E[RR]E[R FMiFi

Current-ValueHistorical difference between return on the market and return on the risk-free bond