DCF- Cost of Capital IIEstimating Beta

Historical beta: advantages

• Firm’s historical βe

• Estimated by regressing the firm’s excess stock returns on the excess returns of a market portfolio, where excess returns are defined as the returns in excess of the risk-free return

• Analysts typically estimate using historical returns

• We must ensure this accurately reflects the relationship between risk and return in the future

Historical beta has two problems:

1. It has high standard error (low t stat)

2. It reflects the past, not the current status

• the firm’s business mix over the period of the regression, not the current mix

• It reflects the firm’s average financial leverage over the period rather than the current leverage.

• Example: real estate

Historical beta: disadvantages

Problems with CAPM

• Academic research has failed to find a significant cross-sectional relation between the beta estimates of stocks and their future rates of return.

• Firm characteristics, like market capitalization and book-to-market ratios, provide much better predictions of future returns than do betas.

• Proposed modifications of CAPM – i.e. size premium

• Ibbotson Associates, divides firms into discrete groups based on the total market value of their equity (the following is based on the 2013 Ibbotson NYSE Decile-Size Premium Data):

• Large-cap: firms with market value of equity above $7.687B - no size premium.

• Mid-cap: firms with market value of equity between $7.687B and $1.912B – apply size premium of 1.12%.

• Low-cap: firms with market value of equity between $1.912B and $5141M – apply size premium of 1.85%

• Micro-cap: firms with market value of equity below $514M - apply size premium of 3.81%.

Which company has a higher beta?

• The Mcdonald (MCD)

• Equity Market Capitalization as of 1/2/2015: 89.38B (Large-cap)

• MCD required return – cost of equity

Risk Free Rate (10-year T-Bond Yield) as of 1/2/2015 2.24%

MCD Beta (Finance.yahoo.com) 0.58

Equity Risk Premium (assumed) 5.20%

Large-Cap Premium 0.0%

• Kmcd = 2.24% + 0.58*5.20% + 0 = 6.50%

• The Shakeshack (SHAK)

• Equity Market Capitalization as of 1/2/2015: 1.63B (low-cap)

• CAKE Required Return – Cost of Equity (Ke):

Risk Free Rate (10-year T-Bond Yield) as of 1/2/2015 2.24%

SHAK Beta (Finance.yahoo.com) 1.78

Equity Risk Premium (assumed) 5.20%

low-Cap Premium 1.85%

KSHAK = 2.24% + 1.78 * 5.20% + 1.85% = 13.31%

Size Premium Examples

Factor models:

• Another approach to estimate ke is through the use of multifactor risk models that capture the risk of investments with multiple betas and factor risk premiums.

• Risk factors:

• Macroeconomic variables: changes in interest rates, inflation, or GDP

• Factor portfolios

• The Fama-French three-factor model is the most widely used

• It attempts to capture the determinants of equity returns using three risk premiums:

• The equity risk premium of the CAPM

• A size risk premium: SMB (small minus big) – return on small cap portfolio minus return on large cap portfolio

• A risk premium related to the relative value of the firm when compared to its book value (historical cost-based value): HML (high minus low)

Fama-French example: AppleThe resulting estimate of Apple’s ke is 5.98%, which is very different from the 7.1% we obtained using the standard CAPM

Apple Inc.

The resulting estimate of Apple’s ke is 5.98%, which is very different from the 7.1% we obtained using the standard CAPM.

Should we use CAPM or Fama-French?

• Which model provides a better estimate of the cost of equity?

• Which model better explains the historical returns?

• Are these factors robust?

• In practice, CAPM is preferred as its theory is the most robust.

• Size and value in China

Don’t like the fundamental assumptions about CAPM

• Logic: risk needs to be rewarded (there is a price of risk)

• Assumption 1: Investors are diversified

• Assumption 2: The risk premium is reflected in the market price.

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Don’t like the diversified investor focus, but okay with price-based measures

1. Relative Standard Deviation• Relative Volatility = Std dev of Stock/ Average Std dev across all stocks• Captures all risk, rather than just market risk

2. Proxy Models• Look at historical returns on all stocks and look for variables that

explain differences in returns. • You are, in effect, running multiple regressions with returns on

individual stocks as the dependent variable and fundamentals about these stocks as independent variables.

• This approach started with market cap (the small cap effect) and over the last two decades has added other variables (momentum, liquidity etc.)

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Don’t like the price-based approach..

1. Accounting risk measures: To the extent that you don’t trust market-priced based measures of risk, you could compute relative risk measures based on

• Accounting earnings volatility: Compute an accounting beta or relative volatility

• Balance sheet ratios: You could compute a risk score based upon accounting ratios like debt ratios or cash holdings

2. Potential Problems with Accounting Beta:1. Accounting earnings tend to be smoothed out, resulting in biased

beta for risky firms2. Accounting earnings are affected by changes in depreciation or

inventory method3. Quarterly reports results in fewer observations and thus high std

error.

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Determinants of Betas & Relative Risk

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In an ideally world, steps to estimate beta

Adjusting for operating leverage…

• Within any business, firms with lower fixed costs (as a percentage of total costs) should have lower unlevered betas. If you can compute fixed and variable costs for each firm in a sector, you can break down the unlevered beta into business and operating leverage components.

• Unlevered beta = Pure business beta * (1 + (Fixed costs/ Variable costs))

• The biggest problem with doing this is informational. It is difficult to get information on fixed and variable costs for individual firms.

• In practice, we tend to assume that the operating leverage of firms within a business are similar and use the same unlevered beta for every firm.

Adjusting for financial leverage…

• Conventional approach: The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio

L = u (1+ ((1-t)D/E))

In some versions, the tax effect is ignored and there is no (1-t) in the equation.

• What have we assumed in deriving above equation?

• Debt Adjusted Approach: If debt carries market risk and you can estimate the beta of debt, you can estimate the levered beta as follows:

L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)

While the latter is more realistic, estimating betas for debt can be difficult to do.

Bottom-up Betas18

Why bottom-up betas?

• The standard error in a bottom-up beta will be significantly lower than the standard error in a single regression beta. Roughly speaking, the standard error of a bottom-up beta estimate can be written as follows:

Std error of bottom-up beta =

• The bottom-up beta can be adjusted to reflect changes in the firm’s business mix and financial leverage. Regression betas reflect the past.

• You can estimate bottom-up betas even when you do not have historical stock prices. This is the case with initial public offerings, private businesses or divisions of companies.

 

Average Std Error across Betas

Number of firms in sample

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Estimating Bottom Up Betas & Costs of Equity: A Mining Company (Vale)

Business Sample

Sample

size

Unleveredbeta

ofbusiness Revenues

PeerGroup

EV/Sales

Valueof

Business

Proportionof

Vale

Metals&Mining

Globalfirmsinmetals&

mining,Marketcap>$1billion 48 0.86 $9,013 1.97 $17,739 16.65%

IronOre Globalfirmsinironore 78 0.83 $32,717 2.48 $81,188 76.20%

FertilizersGlobalspecialtychemicalfirms 693 0.99 $3,777 1.52 $5,741 5.39%

LogisticsGlobaltransportationfirms 223 0.75 $1,644 1.14 $1,874 1.76%

ValeOperations 0.8440 $47,151 $106,543 100.00%

Brazil Company Embraer’s Bottom-up Beta

Business Unlevered Beta D/E Ratio Levered betaAerospace 0.95 18.95% 1.07

• Levered Beta= Unlevered Beta ( 1 + (1- tax rate) (D/E Ratio)= 0.95 ( 1 + (1-.34) (.1895)) = 1.07

• Question: Can an unlevered beta estimated using U.S. companies be used to estimate the beta for a Chinese/Brazil company?

a. Yesb. No

What concerns would you have in making this assumption?

Gross Debt versus Net Debt Approaches

• Taking the difference between debt and cash (net debt) when computing debt ratios would arrive at very different values.

• For Embraer, using the gross debt ratio• Gross D/E Ratio for Embraer = 1953/11,042 = 18.95%

• Levered Beta using Gross Debt ratio = 1.07

• Using the net debt ratio, we get• Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity

= (1953-2320)/ 11,042 = -3.32%• Levered Beta using Net Debt Ratio = 0.95 (1 + (1-.34) (-.0332)) = 0.93

• The cost of Equity using net debt levered beta for Embraer will be much lower than with the gross debt approach. The cost of capital for Embraer will even out (partially) since the debt ratio used in the cost of capital equation will now be a net debt ratio rather than a gross debt ratio.

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Division Beta Market Value

Personal Computers

1.60 $100 million

Software 2.00 $150 million

Computer Mainframes

1.20 $250 million

You have been asked to estimate the beta of a high-technology firm which

has three divisions with the following characteristics

Exercise

A. What is the beta of the equity of the firm?

B. What would happen to the beta of equity if the firm divested itself of its software

business?

C. If you were asked to value the software business for the divestiture, which beta would

you use in your valuation?

The Cost of Equity: A Recap24

Exercise (tax rate = 0)

The CFO of Sterling Chemical is interested in evaluating the cost of equity capital for his firm. However, Sterling uses very little debt in its capital structure (the firm’s debt-to-equity capitalization ratio is only 20%), while larger chemical firms use substantially higher amounts of debt. The following table shows the levered equity betas, debt-to-equity ratios, and debt betas for three of the largest chemical firms:

a. Use the information given above to estimate the unlevered equity betas for each of

the companies.

b. If Sterling’s debt-to-equity capitalization ratio is .20 and its debt beta is .30, what is

your estimate of the firm’s levered equity beta?

Cost of Debt

Cost of Debt Capital (Book vs market)

• You are assuming the cost of debt, to use in the cost of capital, for a firm:

• The firm has $1 billion in bank loans outstanding, carrying an interest rate of 4% and a remaining maturity of 8 years. The current risk free is 5% and you anticipate that your default spread to borrow long term is 2%. What is the pre-tax cost of debt for this firm?• 4%

• 5%

• 7%

• 5.5%

• 6%

• None of above

Debt Ratio

• The firm has a market value of equity of $1 billion and you are computing the debt to capital ratio D/(D+E) for the firm. What is the debt to capital ratio?

• 50%

• >50%

• <50%

Cost of Debt

• The cost of debt is the rate at which you can borrow at currently.

• It reflect • Default risk of the firm

• The level of interest rate in the market

• Looking up the yield to maturity on a bond outstanding from the firm. Problem is very few firms have long term bonds that are liquid and widely traded.

• Use rating to calculate default spread.

Cost of Debt Capital

• For debt with default risk, the expected cash flows must reflect the probability of default (Pb) and the recovery rate (Re) on the debt in the event of default.

• Cost of Debt Capital is after-tax: kd (1-t)

The probability of default Pb: promised yield (YTM) vs expected return

(kd)

Estimating the Cost of Debt• When in trouble (either because you have no ratings or multiple

ratings for a firm), estimate a synthetic rating for your firm and the cost of debt based upon that rating.

• Idea: sorting on observables

• Example: sort using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio

Interest Coverage Ratio = EBIT / Interest Expenses

Suppose for Embraer, the interest coverage ratio is 3.56.

Interest Coverage Ratios, Ratings and Default Spreads: 2004

Based on the interest coverage ratio of 3.56, the synthetic rating for Embraer is A-, giving it a default spread of 1.00%

Synthetic Ratings: Some Caveats

• The relationship between interest coverage ratios and ratings, developed using US companies, tends to travel well, as long as we are analyzing large manufacturing firms in markets with interest rates close to the US interest rate

• They are more problematic when looking at smaller companies in markets with higher interest rates than the US.

• One way to adjust for this difference is modify the interest coverage ratio table to reflect interest rate differences (For instances, if interest rates in an emerging market are twice as high as rates in the US, halve the interest coverage ratio), i.e., normalization.

Cost of Preferred Equity (Kp)

• A straight (i.e., nonconvertible) preferred stock pays the holder a fixed dividend each period (quarterly) forever

• The cost of straight (nonconvertible) preferred stock can be calculated:

• Using the preferred dividend and observed price of preferred stock, we can infer required rate of return:

Kp Example: Alabama Power Company

• To illustrate, consider the preferred shares issued by Alabama Power Company (ALP-PP), which pay a 5.3% annual dividend on a $25.00 par value, or $1.33 per share. On February 26, 2014, these preferred shares were selling for $24.96 per share. Consequently, investors require a 5.33% return on these shares, calculated as follows:

Subsidized Debt

• Assume that the government lends money to Company A at a subsidized interest rate (say 6%), In computing the cost of Capital, should we use the cost of debt based upon subsidized cost of debt?

• A. The subsidized cost of debt, this is what you are paying for

• B. The fair cost 9%. This is what the company should require its cost to cover

• C. A number in the middle

Weights for the cost of capital calculation

• In computing the cost of capital for a publicly traded firm, the general rule for computing weights for debt and equity is that you use the market value weights (and not book value weights) . Why?

• A. Because the market is usually right

• B. Because market values are easy to obtain

• C. Because book values of debt and equity are meaningless

• D. None of the above

Dealing with hybrids

• When dealing with hybrids (convertible bonds, for instance), break the security down into debt and equity and allocate the amounts accordingly. Thus, if a firm has $125 million in convertible debt outstanding, break the $125 million into straight debt and conversion option. The conversion option is equity.

Example

• Assume that the firm you are analyzing has $125 million in face value of convertible debt with a stated interest rate of 4%, a 10-year maturity and a market value of $140 million. If the firm has a bond rating of A and the interest rate on A – rated bond is 8%. You can break down the value of the convertible bond into • Straight debt

• （4% of $125 million)(PV of annuity, 10 years, 8%) + 125/(1.08^10) = $ 91.45 million

• Equity• $140 - $91.45 = $48.55

• The debt portion get added to the debt and the option portion get added to the equity.