Risk Measurement and the Cost of Capital Byers

Calculating Returns

Risk–Return Tradeoff Two key lessons from capital market history: There is a reward for bearing risk The greater the potential reward, the greater the risk

Percentage Returns It is generally more intuitive to think in terms of percentages than dollar returns Dividend yield = income / beginning price Capital gains yield = (ending price – beginning price) / beginning price Total percentage return = dividend yield + capital gains yield

Percent Return Dividend Yield Capital Gains Yield

Example – Calculating Returns You bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40. What is your dollar return? Dollar return = 1.25 + (40 – 35) = $6.25 What is your percentage return? Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (40 – 35) / 35 = 14.29% Total percentage return = 3.57 + 14.29 = 17.86% You might want to point out that total percentage return is also equal to total dollar return / beginning price. Total percentage return = 6.25 / 35 = 17.86%

Another Example You held 250 shares of Hilton Hotel’s common stock. The company’s share price was $24.11 at the beginning of the year. During the year, the company paid a dividend of $0.16 per share, and ended the year at a price of $34.90. What is the dollar return, the percentage return, the capital gains yield, and the dividend yield for Hilton?

Dollar return = 250 x ($34. 90-$24. 11+$0. 16) = $2,737 Dollar return = 250 x ($34.90-$24.11+$0.16) = $2,737.50 Percent return = ($34.90-$24.11+$0.16)/$24.11 = 45.42% Capital gains yield = ($34.90 - $24.11)/$24.11 = 44.75% Dividend yield = $0.16/$24.11 = 0.66%

U.S. Financial Markets

Year-to-Year Total Returns Large-Company Stock Returns

Year-to-Year Total Returns Small-Company Stock Returns

Year-to-Year Total Returns Long-Term Government Bond & U.S. Treasury Bill Returns

Average Returns: The First Lesson 1926 - 2014 Investment Average Return Large Stocks 12.1% Small Stocks 16.7% Long-term Corporate Bonds 6.4% Long-term Government Bonds 6.1% U.S. Treasury Bills 3.5% Inflation 3.0%

Risk Variance = VAR(R) or σ2 Standard deviation = SD(R) or σ Risk is measured by the dispersion, spread, or volatility of returns Variance = VAR(R) or σ2 Common measure of return dispersion Standard deviation = SD(R) or σ Square root of the variance Same "units" as the average

Example: Using the following returns, calculate the average return, the variance, and the standard deviation for Acme stock. Year Acme 1 10% 2 4 3 - 8 4 13 5 5

Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4. 80% σ2Acme = [(10 – 4 Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4.80% σ2Acme = [(10 – 4.8)2 + (4 – 4.8)2 + (- 8 – 4.8)2 + (13 – 4.8)2 + (5 – 4.8)2 ] / (5 - 1) σ2Acme = 258.8 / 4 = 64.70 σAcme = (64.70)1/2 = 8.04%

Historical Average Returns and Standard Deviation Figure 10.10

Return Variability Review and Concepts Normal distribution: A symmetric frequency distribution The “bell-shaped curve” Completely described by the mean and variance Does a normal distribution describe asset returns?

The Normal Distribution Figure 10.11

The Principle of Diversification Diversification can substantially reduce risk without an equivalent reduction in expected returns Reduces the variability of returns Caused by the offset of worse-than-expected returns from one asset by better-than-expected returns from another Minimum level of risk that cannot be diversified away = systematic portion

Standard Deviations of Annual Portfolio Returns Table 11.7

Portfolio Conclusions As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio - sp falls very slowly after about 20 - 30 stocks are included The lower limit for sp ≈ 20% = sM. Forming well-diversified portfolios can eliminate about half the risk of owning a single stock. 31

Portfolio Diversification Figure 11.1

Total Risk = Stand-Alone Risk Total risk = Systematic risk + Unsystematic risk The standard deviation of returns is a measure of total risk For well-diversified portfolios, unsystematic risk is very small Total risk for a diversified portfolio is essentially equivalent to the systematic risk

Systematic Risk Principle There is a reward for bearing risk There is no reward for bearing risk unnecessarily The expected return (market required return) on an asset depends only on that asset’s systematic or market risk.

Market Risk for Individual Securities The contribution of a security to the overall riskiness of a portfolio Relevant for stocks held in well-diversified portfolios Measured by a stock’s beta coefficient, j Measures the stock’s volatility relative to the market 34

Interpretation of Beta If  = 1.0, stock has average risk If  > 1.0, stock is riskier than average If  < 1.0, stock is less risky than average Beta of the market = 1.0 Beta of a T-Bill = 0 39

Beta Coefficients for Selected Companies Table 11.8

Capital Asset Pricing Model The capital asset pricing model (CAPM) defines the relationship between risk and return E(RA) = Rf + βA [E(RM) – Rf] If an asset’s systematic risk () is known, CAPM can be used to determine its expected return

SML and Equilibrium

Example: Suppose the Treasury bond rate is 6%, the average return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2. According to the CAPM, what should be the required rate of return on Disney stock?

E(RA) = Rf + A(E(RM) – Rf) E(RA) =. 06 + 1. 2 (. 12 -. 06) E(RA) = E(RA) = Rf + A(E(RM) – Rf) E(RA) = .06 + 1.2 (.12 - .06) E(RA) = .132 = 13.2% According to the CAPM, Disney stock should be priced to give a 13.2% return.

Cost of Capital Basics The cost to a firm for capital funding = the return to the providers of those funds A firm must earn at least the required return to compensate investors for the financing they have provided The required return is the same as the appropriate discount rate

Three basic sources of financing: Equity Debt Preferred stock (sometimes) We need to find the cost of each of these sources

Cost of Equity - Dividend growth model - SML or CAPM The cost of equity is the return required by equity investors given the risk of the cash flows from the firm Two major methods for determining the cost of equity - Dividend growth model - SML or CAPM

The Dividend Growth Model Approach Start with the dividend growth model formula and rearrange to solve for RE

Example: Dividend Growth Model Your company is expected to pay a dividend of $4.40 per share next year. (D1) Dividends have grown at a steady rate of 5.1% per year and the market expects that to continue. (g) The current stock price is $50. (P0) What is the cost of equity?

The SML Approach Use the following information to compute the cost of equity Risk-free rate, Rf Market risk premium, E(RM) – Rf Systematic risk of asset, 

Example: SML Company’s equity beta = 1.2 Current risk-free rate = 7% Expected market risk premium = 6% What is the cost of equity capital?

Example: Cost of Equity Data: Beta = 1.5 Market risk premium = 9% Current risk-free rate = 6%. Analysts’ estimates of growth = 6% per year Last dividend = $2. Currently stock price =$15.65 Using SML: RE = 6% + 1.5(9%) = 19.5% Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55%

Cost of Debt The cost of debt = the required return on a company’s debt Method 1 = Compute the yield to maturity on existing debt Method 2 = Use estimates of current rates based on the bond rating expected on new debt The cost of debt is NOT the coupon rate

Calculating the Cost of Debt: Example A firm sold a 20-year bond issue 5 years ago. The bond has a 7.5% annual coupon and a $1,000 face value. If the current market price of the bond is $878.25 and the tax rate is 40%, what is the after-tax cost of debt?

Cost of Debt for our firm 30 N -1253.72 PV 1000 FV 60 PMT CPT I/Y 4.45% YTM = 4.45%*2 = 8.9% Current bond issue: 15 years to maturity Coupon rate = 12% Coupons paid semiannually Currently bond price = $1,253.72

Component Cost of Debt Use the YTM on the firm’s debt Interest is tax deductible, so the after-tax (AT) cost of debt is: If the corporate tax rate = 40%:

Some More Examples of the Cost of Debt Yield-to-Maturity Approach Consider a company that has debt outstanding that has a coupon rate of 5%, 10 years to maturity, and is quoted at $980. What is the after-tax cost of debt if the marginal tax rate is 40%? Assume semi-annual interest. Solution: rd = 0.0526 (1 – 0.4) = 3.156% The cost of debt capital is 3.156% Debt-Rating Approach Consider a company that has nontraded $100 million of debt outstanding that has a debt-rating of AA. The yield on AA debt is currently 6.2%. What is the after-tax cost of debt if the marginal tax rate is 40%? Solution: rd = 0.062 (1 – 0.4) = 3.72% The cost of debt capital is 3.72% LOS: Calculate and interpret the cost of fixed rate debt capital using the yield-to-maturity approach and the debt-rating approach. Pages 135–138 Example: Cost of Debt Yield to maturity PMT = 2.5 N = 20 PV = 98 FV = 100 Solve for I, then multiple by 2 → YTM = 5.26% Debt-Rating approach The yield is the yield for similarly rated bonds.

Cost of Preferred Stock Preferred pays a constant dividend every period Dividends expected to be paid forever Preferred stock is a perpetuity Example: Preferred annual dividend = $10 Current stock price = $111.10 RP = 10 / 111.10 = 9%

Weighted Average Cost of Capital Use the individual costs of capital to compute a weighted average cost of capital for the firm This “average” = the required return on the firm’s assets, based on the market’s perception of the risk of those assets The weights are determined by how much of each type of financing is used

Determining the Weights for the WACC Weights = percentages of the firm that will be financed by each component Try to use the target weights, if possible If not available, use market values

Capital Structure Weights Notation E = market value of equity = # outstanding shares times price per share D = market value of debt = # outstanding bonds times bond price V = market value of the firm = D + E Weights E/V = percent financed with equity D/V = percent financed with debt

WACC = (E/V) x RE + (P/V) x RP + (D/V) x RD x (1- TC) Where: (E/V) = % of common equity in capital structure (P/V) = % of preferred stock in capital structure (D/V) = % of debt in capital structure RE = firm’s cost of equity RP = firm’s cost of preferred stock RD = firm’s cost of debt TC = firm’s corporate tax rate Weights Component costs

Estimating Weights Given: Weights: Component Values: Stock price = $50 3m shares common stock $25m preferred stock $75m debt 40% Tax rate Component Values: VE = $50 x (3 m) = $150m VP = $25m VD = $75m VF = $150+$25+$75=$250m Weights: E/V = $150/$250 = 0.6 (60%) P/V = $25/$250 = 0.1 (10%) D/V = $75/$250 = 0.3 (30%)

WACC Component Weight Required Return Debt (before tax) 0.30 8.9% Preferred Stock 0.10 9% Common equity 0.60 14.1% WACC = E/V x RE + P/V x RP + D/V x RD (1- TC) WACC = 0.6(14.1%)+0.1(9%) +0.3(8.9%)(1-.40) WACC = 8.46% + 0.9% + 1.60% = 12.2%

A note on converting debt ratios and D/E ratios

Should the company use the composite WACC as the hurdle rate for each of its projects? NO! The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk. Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.

Divisional and Project Costs of Capital There will clearly be situations in which the cash flows under consideration have risks that are distinctly different from those of the overall firm. What do we do?

The Pure Play Approach The use of a WACC that is appropriate for a particular project based on the cost of capital of similar publicly traded companies Can be difficult to find

The Subjective Approach Use judgment to adjust the WACC up or down depending on the risk of the project Example: