1. Lecture 10 Cost of Capital Analysis (cont’d …) Investment Analysis

2. CAPM Method For more than 30 years, financial theorists and practitioners generally have favored the notion that using CAPM is the preferred method to estimate the cost of equity capital. In spite of many criticisms, it is still one of the most widely used models for estimating the cost of equity capital “R e,” especially for larger companies. CAPM is derived from the capital markets. It attempts to provide a measure of market relationships based on the theory of expected returns, if investors diversify their portfolios. As discussed earlier, capital markets divide risk beyond simple maturity risks into two types: – Systematic Risk – Unsystematic Risk CAPM is based solely on quantifying systematic risk because it assumes that prudent investors will eliminate unsystematic risk by holding large, well diversified portfolios. The unsystematic risk attached to a particular company’s stock is eliminated through diversification. Investment Analysis

3. CAPM Method (cont’d …) The primary difference between CAPM and the buildup method is the introduction of market/systematic risk for a specific stock. Market risk is measured by a factor called beta. Beta measures the sensitivity of excess total returns (total returns over the risk-free rate of returns) on any individual security or portfolio of securities to the total excess returns on some measure of the market. Covariance of asset i with Market Portfolio Cov im Beta of an asset i = = Variance of the Market Portfolio σ 2 m Investment Analysis

4. Interpreting Beta Beta > 1.0 when market rates of return move up or down, the rates of return for the subject tend to move in the same direction and with greater magnitude. Example: For a stock with no dividend, if the market is up 10%, the price of a stock with a beta of 1.2 would be expected to be up by 12%. If the market is down by 10%, the price of the same stock would be expected to be down by 12%. Beta = 1.0 Fluctuations in rates of return for the subject tend to equal fluctuations in rates of return for the market. Investment Analysis

5. Interpreting Beta (cont’d ….) Beta < 1.0 When market rates of return move up or down, rates of return for the subject tend to move up or down but to a lesser extent. Example: For a stock with no dividend, if the market is up 10%, the price of a stock with a beta of 0.8 would be expected to be up 8%. Negative beta (very rare) A negative beta simply means that the stock is inversely correlated with the market. Many precious metals and precious metal related stocks are beta negative as their value tends to increase when the general market is down and vice versa. Investment Analysis

6. MCAPM Method CAPM assumes a fully diversified portfolio, it is applied in valuation to assess the value of an investment in a single company. This distinction necessitates inclusion of the specific company risk premium in MCAPM. These differences make CAPM less effective in appraising closely held business interests, particularly of smaller companies. The primary difference between CAPM and buildup model is the introduction of market/systematic risk for a specific stock as a modifier to the general equity risk premium. In CAPM, only systematic or beta risk is rewarded, small company stocks have had returns in excess of those implied by their betas. To overcome these limitations, MCAPM was developed, which includes two additional premiums that add precision to the process of estimating a required rate of return. Investment Analysis

7. MCAPM (cont’d …) MCAPM is expressed as: E(R i ) = R f + B(RP m ) + RP s +RP u Where: E(R i )= Expected rate of return on security I R f = Rate of return on a risk free security B= Beta RP m = General equity risk premium for the market RP s = Risk premium for small size RP u = Risk premium attributable to the specific company/unsystematic risk Investment Analysis

8. Company Specific Risk Factors The notion that the only component of risk that investors care about is market/systematic risk is based on the assumption that all unique or unsystematic risk can be eliminated by holding a perfectly diversified portfolio of risky assets that will, by definition, have a beta of 1.0. Without addressing the validity of that assumption for the public markets here, it is obviously not feasible for investors in closely held companies to hold such a perfectly diversified portfolio that would eliminate all unique risk. Therefore, for the cost of capital for closely held companies, even when using CAPM, we have to consider whether there may be other risk elements that neither the beta factor nor the size premium fully accounts for. If so, an adjustment to the discount rate for unique risk would be appropriate. Investment Analysis

9. Using MCAPM MCAPM is most effective in developing a cost of equity capital when a group of public companies that are reasonable similar to the target can identified. When a population of say three to six similar public companies is available, analyze their operating and financial characteristics and compare them to the target. Assess the systematic risk reflected in their betas considering conditions within that industry or segments of it and then analyze specific company factors. When this information is available, the cost of equity can be computed from the MCAPM with reasonably reliable results. Investment Analysis

10. Arbitrage Pricing Theory (APT) Arbitrage is the practice of taking advantage of a state of imbalance between two markets and thereby making a risk free profit. APT describes the mechanism of arbitrage whereby investors will bring an asset which is mispriced, according o the APT model, back into line with its expected price. Note that under true arbitrage, the investor locks in a guaranteed payoff, whereas under APT arbitrage as described below, the investor locks in a positive expected payoff. APT thus assumes “arbitrage in expectations,” i.e., that arbitrage by investors will bring asset prices back into line with the returns expected by the model. APT holds that the expected return of a financial asset can be modeled as a linear function of various macroeconomic factors, where sensitivity to changes in each factor is represented by a factor specific beta coefficient. Investment Analysis

11. APT (cont’d …) APT along with the CAPM is one of two influential theories on asset pricing. APT differs form CAPM in that it is less restrictive in its assumptions. It allows for an explanatory mode of asset returns. It assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical “market portfolio.” APT model for predicting the behavior and performance of a financial instrument or portfolio is based on the proposition that if the returns of a portfolio of assets can be quantified and described by a factor based structure or model, the expected return of each asset in the portfolio can be described by a linear combination of the factors of the returns of the assets with in the portfolio group. Investment Analysis

12. APT (cont’d …) APT model formula is: E(R i ) = R f + (B 1 K 1 ) + (B 2 K 2 ) + … + (B n K n ) Where: E(R i )=Expected rate of return R f =Rate of return on a risk free security K 1, K 2, K n =Risk premium associated with factor K for the average asset in the market B 1, B 2, B n =Sensitivity of the security i to each risk factor relative to the market average sensitivity to that factor Investment Analysis

13. APT (cont’d …) The general risk factors considered in building a rate through APT, in addition to systematic or market risk, include: Confidence Risk: The unanticipated changes in investors’ willingness to undertake relatively risky investments. It is measured as the difference between the rate of return on relatively risky corporate bonds and the rate of return on government bonds, both with 20 year maturities. Time Horizon Risk: The unanticipated changes in investors’ desired time to payout. It is measured as the difference between the return on 20 year government bonds and 30 day treasury bills. Inflation Risk: A combination of the unexpected components of short and long run inflation rates. Business Cycle Risk: Represents unanticipated changes in the level of real business activity. This component measures whether economic cycles are in the upswing or downswing with each, respectively, adding a positive or negative adjustment to the overall required rate of return. APT mode is not widely used in business valuation assignments for cost of capital determinations due to the unavailability of usable data for the components of the model. Investment Analysis