Cost of Capital Estimation

Methods for Benchmarking the Cost of Equity Capital Capital Asset Pricing Model using beta from a regression analysis (top-down method) Capital Asset Pricing Model weighting beta estimates for individual divisions using industry betas (bottom-up method) Implied Cost of Equity using stock valuation model, given stock price and expected growth rates

Only Systematic Risk is Priced in the Capital Asset Pricing Model The key result of the CAPM is that the relevant risk of any asset is the risk that it adds to the market portfolio—the systematic risk Systematic risk is exposure to market factors that affect all securities to a greater or lesser degree (e.g. inflation, GDP growth, interest rates, political events, etc.) In well diversified portfolios exposure to firm-specific (unsystematic) events is diversified away (e.g. management changes, product announcements, litigation, etc.) The systematic risk is measured by the security’s co-movement with a broadly diversified portfolio

Risk measures Standard deviation (stdev) Covariance (covar.s)   Standard deviation (stdev) Covariance (covar.s) Correlation Coefficient (correl) The standardization confines the ρ to values between –1 and +1

Portfolio standard deviation for a two-security portfolio:

Two-Security Portfolio Variance-Covariance Matrix The two-security portfolio  contains two covariance (market risk) terms and two variance (stand-alone risk) terms 2A CovA.B CovB.A 2B

Three-Security Portfolio Variance-Covariance Matrix 2A CovA.B CovA.C CovB.A 2B CovB,C CovC,A CovC.B 2C

Standard deviation and risk The standard deviation of a single security includes both systematic and unsystematic risk For well diversified portfolios, the standard deviation includes systematic risk only

Efficient Portfolios Combining assets with less than perfect correlation improves portfolio efficiency by reducing unsystematic risk An efficient portfolio is one that offers: the most return for a given amount of risk, or the least risk for a give amount of return. The collection of efficient portfolios is called the efficient frontier

See two-security example Expected Portfolio Return, E(Rp) Efficient Frontier Risk, p See two-security example

Capital Asset Pricing Model The CAPM is an equilibrium model that specifies a linear relationship between risk and required rate of return for assets held in well-diversified portfolios.

Adding a risk-free security When a risk-free security with return rRF is added, investors can create portfolios that combine this security with a portfolio of risky securities. Since the risk-free asset has zero variance, its covariance is also zero Thus the standard deviation of a 2-security portfolio of the risk-free asset and the market portfolio, M, is: wmσm

What impact does rRF have on the efficient frontier? Both the standard deviation and expected return are linear functions of the weights wrf and wm The straight line connecting rRF with M (market), the tangency point between the line and the old efficient frontier, becomes the new efficient frontier.

New Efficient Frontier Efficient Frontier with a Risk-Free Asset Expected Return, rp M ^ rM . The Capital Market Line (CML): New Efficient Frontier rRF M Risk, p

^ rM - rRF ^ rp = rRF + p. M p is determined by selecting weights on: the risk-free security (wrf) the market portfolio (wm)

The Security Market Line (SML) The equation for the Security Market Line, the principal result of the Capital Asset Pricing Model, gives the risk/return relationship for individual securities. Substitute the contribution of an individual security’s risk to the market portfolio standard deviation, ρi,mσi , for σp:

Beta  

Beta intuition Beta is simply a measure of relative systematic risk, or relative exposure to the economic variables that drive market returns. For example, a security with a beta of 1.20 exhibits 20 percent more variability in response to market returns as compared with a typical security.

Result of the CAPM SML: Expected return for stocks includes a risk-free component a risky component as determined by a risk premium for the average stock, known as the ‘market risk premium’, (rm - rrf) and the beta of the individual stock, which measures the degree of market risk exposure for the individual security The expected (required) return on the stock is the issuing company’s cost of Equity

Security Markey Line Expected return on market = Rm - Rrf Based on the example in the book. Point out that there is a linear relationship between beta and expected return. Ask if the students remember the form of the equation for a line. Y = mx + b E(R) = slope (Beta) + y-intercept The y-intercept is = the risk-free rate, so all we need is the slope Risk-free rate

Which security has more unsystematic risk? Std. Deviation Beta Security A 20% 1.25 Security B 30% 0.95 Which security has more unsystematic risk? Which security has more systematic risk? Which security should have the higher required return?

Estimating the CAPM Inputs The beta of the security The expected market risk premium The current risk-free rate

Estimating Beta (top-down approach) Standard approach is to regress stock returns against those of a broad market index, where the slope of the regression line is the beta coefficient: most services use either 5 years (monthly returns) or 2-3 years (weekly) regressed on the S&P 500 A 5-year interval insures against possible aberrant shocks to the beta due to unusual short-term events A shorter interval may better reflect the company’s current risk profile if its business or operating environment have changed Many services adjust beta toward 1.0 Example: Adj. Beta = 0.67*beta + 0.33*1.0

Bottom-up Betas The beta of a portfolio is a market-value weighted average of the betas of the assets comprising the portfolio the beta of a firm is a weighted average of the individual divisions or projects in which the firm invests A bottom-up beta estimates beta for each of the divisions using industry betas, and uses a weighted average of these division betas to estimate the corporate beta

Advantages of Bottom-up Betas Since the procedure involves averaging across several regression betas, the estimation error is lower, and the estimates are more stable The bottom-up beta may provide a better estimate of the true beta when the firm has reorganized or restructured itself substantially during the period of the regression Weight the division betas based on the current mix Division betas are required to make investment decisions

Division Cost of Capital The firm’s overall cost of capital cannot be applied to individual divisions or projects when there are differences in risk: 1) operating (business) risk; 2) financial risk

Operating Risk Variability in Earnings Before Interest and Taxes Two sources: 1) Industry Effects on sales Cyclical companies have higher business risk than non-cyclical firms Firms which sell more high-cost and discretionary products will have higher business risk 2) Operating leverage effects: Operating leverage refers to the proportion of the total costs of the firm that are fixed. Other things equal, higher operating leverage results in greater earnings variability Operating leverage measure = % Change in EBIT / % Change in Revenues

Operating Leverage Revenue 100 200 300 Variable costs (20%) (20) (40) (60) Fixed costs (100) EBIT 60 140 Variable costs (50%) (50) (150) 10 110

Financial Risk As firms borrow, they create fixed costs (interest payments) that make their earnings to equity investors more volatile This increased earnings volatility increases the equity Beta As more variance is added, and some fraction of this variance is correlated with markets, beta increases

The Pure-Play approach to Beta estimation The typical approach is to find publicly traded ‘pure play’ companies operating primarily in division’s business Can expand to customers and suppliers if difficult to find companies They should have levels of operating risk (EBIT variance) that are comparable to that of the division since they are in the same industry Their levels of financial risk, however, will vary due to differences in financing choice

The Pure-Play approach to Beta estimation Process for dealing with financial leverage differences: Unlever the betas of the pure-play firms removes the effects of their debt-equity mix on beta Take an average of these unlevered betas Relever the betas at the division’s target debt-to-stock ratio

The Cost of Equity at Different Levels of Debt: Hamada’s Equation bL = bU [1 + (1 - t)(D/S)] bU is the beta of a firm when it has no debt (the unlevered beta) Use this equation to unlever the observed pure play betas (bL’s), then average the resulting bU’s Use the debt-stock mix (D/S) and marginal tax rates (t) of these companies to unlever Divide bL by term in brackets Relever average unlevered beta at the division’s target capital structure (D/S) and marginal tax rate (t) Multiply resulting average bU by term in brackets Plug relevered beta into CAPM to yield rs See AOL example

Levered Beta Calculation Division's target capital structure (D/S) = 0.6 Tax Rate = 40% Pure Play Actual Market Value Market Value Unlevered Company Beta (bL) Debt Equity D/S Beta (bu) A 0.8 1000 1.00 0.50 B 1.2 800 500 1.60 0.61 C 0.6 1500 2000 0.75 0.41 Average 0.51 Levered beta = .51[1+(1-.4)*.6] Result 0.69

Second CAPM Input: The Market Risk Premium The equity market risk premium is the premium that investors demand for investing in an average risk investment, above the risk-free rate, (rm – rrf) The expected rate of return on the average stock minus the risk-free rate at any point in time.

Approaches to Estimating the Market Risk Premium Assume that the actual premium delivered over long time periods is equal to the expected premium - i.e., use historical data Estimate the implied premium using today’s security prices and expected growth in earnings Forecasts future stock returns based on fundamentals: payouts, multiples and growth Survey data

The Historical Risk Premium Approach Defines a time period for the estimation Calculates the difference between average returns on a stock index and average returns on a riskless security during the period Uses the difference as a premium looking forward

The Historical Risk Premium Approach The limitations of this approach are: Assumes that the risk aversion of investors has not changed in a systematic way across time. (The risk aversion may change from year to year, but it reverts back to historical averages) Assumes that the riskiness of the “risky” portfolio (stock index) has not changed in a systematic way across time. Strange results, since after periods of high returns, you conclude that investors have become risk averse, when the opposite is probably true.

Risk Premium Based on Forecasted Fundamentals R = PAYOUT * E/P + G ≈ 7.5% ≈ 50% 7% ≈ 4% (a P/E of 14) (2 real + 2 inflation) Use P/E ratio to determine earnings yield, multiply by payout which includes dividends and repurchases Add an expected LT growth rate for earnings to arrive at 7.5% forecast yield for large stocks (S&P 500) Subtracting long-term Treasury yield of 1.8% yields an estimated risk premium of 5.7%

Implied Market Risk Premiums

2011 survey data on the Market Risk Premium

Third CAPM Input: The Risk-free Rate U.S. Treasuries are used as the risk-free rate While open to debate, most favor using a long-term Treasury rate for the following reasons: The LT rate reflects an average of future expected short-term rates over the life of the investment The LT rate is much more stable than ST rates The cash flows underlying stocks are long-lived The 10-year Treasury is commonly used The Treasury rates can be found on: http://www.bloomberg.com/markets/rates/index.html

Implied Cost of Equity as another benchmark As an alternative to the CAPM approach, bottom-up or top-down, for corporate finance purposes the cost of Equity can be estimated using the stock price and expected growth in Free Cash Flow to Equity Constant growth version: Since stock price and consensus analyst growth forecasts are known, the company can back into an implied cost of Equity by solving for ‘r’ using a stock valuation model.

Advantages of Implied Cost Market-based measure Do not have to estimate beta Do not have to estimate market risk premium These assumptions are implicit in the market’s valuation

Weighted Average Cost of Capital The overall required rate of return % on Invested Capital (Debt + Stock) WACC = (D/V)rd(1-T) + (S/V)rs rd = % weighted average yield-to-maturity on debt rs = % required return on stock (cost of Equity) D = $Debt market value S = $Stock market value T = % tax rate V = $Enterprise value = D + S

Key Terms Capital Asset Pricing Model Systematic risk Beta (unlevered and levered) Market risk premium Operating risk Financial risk