Module 3. WACC as a measure of risk. Evaluating WACC
Cost of Capital
The Cost of Capital is the rate of return a firm has to pay on capital it bo
ows. The Cost of Capital is the appropriate required rate of return while calculating NPV, or the rate that the IRR must exceed for a project to be accepted. Why? Because if the rate of return on a project exceeds the rate of return that the firm must pay on the capital bo
owed, then the firm can repay and have something left for itself, that is positive NPV. Of course, we must accurately account for all costs. A firm may have made investments like resources it already owns, in which case the firm not only needs to repay capital bo
owed, but also in NPV and IRR calculations the opportunity costs of resources owned for the firm need to be taken into account.
At the beginning we will examine the issues in estimating cost of capital. As a firm will have capital from multiple sources, the cost of capital becomes the Weighted Average Cost of Capital (WACC). The true measure of the net amount of return paid by the firm on all bo
owed capital is WACC.
The calculations of WACC first requires the calculation of the cost of individual sources of capital like debt, equity, retained earnings, prefe
ed stocks etc.
CAPM (Capital Asset Pricing Model) is a theory of discount rates (costs of capital). The essential idea behind CAPM is that investors can get rid of firm-specific risk by diversification. That implies that they care only about systematic (economy-wide) risk. For example, the risk that the product of a firm may fail as it is inferior to its competitors is a firm specific risk, whereas the risk that a firm will have low sales because the economy moves into a recession is a systematic risk. Beta is a measure of systematic risk. The risk premium equals the excess rate of return (discount rate) that a risky asset earns over the riskless rate. According to CAPM the risk premium equals beta multiplied by market risk premium (which is common to all assets).
Defining WACC
• WACC is defined as the average of the estimated required rates of return for the firm’s interest-bearing debt (kd), prefe
ed stock (kp), and common equity (ke). The weights used for each source of funds are equal to the proportions in which funds are raised.
– Note that the cost of debt financing is adjusted downward to reflect the interest tax-shield.
Steps in a WACC
• Step 1. Estimate capital structure and determine the weights of each component: wd, wp, we.
• Step 2. Estimate the opportunity cost of each of the sources of financing: kd, kp, ke, and adjust for the effects of taxes where appropriate.
• Step 3. Calculate WACC by computing a weighted average of the estimated after-tax costs of capital sources used by the firm.
Estimation Issues
• Use market weights.
• Use market-based opportunity costs.
– Costs should reflect the cu
ent required rates of return, rather than historical rates.
• Use forward-looking weights and opportunity costs.
– WACC assumes constant capital structure, if this does not exist (i.e. LBO) analyst should apply APV model.
Estimating WACC
• The connection of the WACC to the discounted cash flow (DCF) estimate of firm value is:
1) Evaluate the Firm’s Capital Structure Weights. βE
• We must determine the weights that are to be used for the components of the firm’s capital structure.
• Represented by the fraction of the firm’s invested capital contributed by each of the sources of capital
– Market value of interest-bearing debt, prefe
ed equity, and common equity
2) Estimate the Cost of Debt, Prefe
ed & Common Equity
• Cost of Debt (kd)
– We use yield to maturity (YTM) on publicly-traded bonds or the risk-free rate plus a default spread given actual (or projected) debt rating
• Cost of Prefe
ed (kp)
– Prefe
ed generally pays a constant dividend every period (perpetuity), so we take the perpetuity formula, rea
ange and solve for kp
• Cost of Common Equity (ke)
– We use CAPM methods or DCF approach
3) Weight the different costs by the fractions in total financing to get WACC.
Cost of Debt Capital kd
• Use yield to maturity (YTM) on publicly-traded bonds
– Risk-free rate plus default spread given actual (or projected) debt rating
• If debt is not publicly-traded, analyst should estimate Kd using the YTM on a portfolio of bonds with similar credit ratings and maturity
– Reuters provides average spreads to Treasury data that is updated daily and cross-categorized by both default rating (Moody’s, S&P, Fitch) and years to maturity
• 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);
Cost of Prefe
ed Equity (Kp)
• The cost of straight (nonconvertible) prefe
ed stock can be calculated:
• Using the prefe
ed dividend and observed price of prefe
ed stock, we can infer required rate of return:
Cost of Common Equity (Ke)
• Ke is the most difficult estimate; it is the rate of return investors expect from investing in the firm’s stock
– Common shareholders are the residual claimants of the firm’s earnings, there is no promised or pre-specified return based on a financial contract
– Returns are based on cash distributions (i.e., dividends and cash proceeds from the sale of the stock)
• Estimation Approaches:
– Asset pricing models - variants of Capital Asset Pricing Model (CAPM)
– Discounted cash flow approach
Traditional CAPM
• CAPM may be used to estimate a company’s Ke based on the risk-free rate plus a premium for equity risk.
• To understand the relation between risk and return it is useful to decompose the risk associated with an investment into two components:
– Systematic risk or nondiversifiable risk
– Nonsystematic risk or diversifiable risk
Systematic Risk
• Systematic risk or nondiversifiable risk
– Variability that contributes to the risk of a diversified portfolio
– Examples: market factors such as changes in interest rates and energy prices that influence almost all stocks.
– The logic of the CAPM suggests that stocks that are very sensitive to these sources of risk should have high required rates of return, since these stocks contribute more to the variability of diversified portfolios.
Nonsystematic risk
• Nonsystematic risk or diversifiable risk
– Variability that does not contribute to the risk of a diversified portfolio.
– Examples: random firm-specific events such as lawsuits, product defects, and various technical innovations.
– These sources of risk should have almost no effect on required rates of return because they contribute very little to the overall variability of diversified portfolios.
• “Risk-adjusted return” CAPM takes into account beta, the risk free rate, and the expected return on the market. It is also the equation for the Security Market Line:
Ke and the risk-free rate: Krf
• In the U.S. the risk-free rate of interest can be estimated by using a U.S. Treasury Rate
– Long-term XXXXXXXXXXyear)
– Intermediate-term
– Short-term
• It should be consistent with the market risk premium assumption, and ideally matches the useful economic life of the asset to be valued.
KE and the βE:
• The firm’s βE represents the sensitivity of its equity returns to variations in the rates of return on the overall market portfolio.
– If the value of the market portfolio of risky investments outperforms Treasury bonds by 10% during a particular month, then a stock with a beta coefficient of 1.25 would expect to outperform Treasury bonds by 12.5%.
Alternatives for βE:
• Firm’s historical or predicted
– 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
• Beta estimate based on betas of comparable firms
– Publicly-traded peers selected by business mix and relative risk
– Involves adjustments for differences in capital structure
– Involves “unlevering” the betas for each of the sample firms to remove the influence of capital structure
– The average ?Unlevered are “relevered” to reflect the capital structure of the target firm
– Prefe
ed estimation method for privately-held firms
The Equity Beta
• Factors favoring historical company beta
– Using cu
ent capital structure in developing weights
– No change expected in business mix
• Factors favoring historical industry beta
– Change in business mix expected
– Firm in Chapter 11
– Firm betas vary substantially by source
– Firm not publicly-traded
• Factors favoring forecasted beta
– Using future weights, not historical weights to estimate WACC
– Projecting change in business mix
• Time Frame for measurement of beta
– A longer time frame (5 years) smoothes out i
egularities in the market, which may be present over shorter periods of time.
– A shorter period (2 years) may be more appropriate for companies in dynamic, high growth industries or for recently restructured companies.
– Typically at least 3 years is used to capture statistically significant return experience.
Ke and the expected equity risk premium: (Km – Krf)
• Equity risk premium is an estimate of excess returns above the risk-free rate.
• The discount rate must reflect the opportunity cost of capital, which is in turn determined by the rate of return associated with investing in other risky investments.
• If one believes that the stock market will generate high returns over the next 10 years, then the required rate of return on a firm’s stock will also be quite high.
– Cu
ent equity risk premium forecasts can be as low as 3%.
– 5% is commonly used in practice.
• Historical equity risk premium
– Many analysts use history as a guide to estimate the future market return premium. I
otson Associates calculates historical risk premiums over several time periods.
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
• I
otson Associates, divides firms into discrete groups based on the total market value of their equity (the following is based on the 2005 I
otson NYSE Decile-Size Premium Data):
– Largecap: firms with market value of equity above $4.794B - no size premium.
– Mid-cap: firms with market value of equity between $4.794B and $1.167B – apply size premium of 0.91%.
– Low-cap: firms with market value of equity between $1.167B and $331M – apply size premium of 1.70%
– Micro-cap: firms with market value of equity below $331M - apply size premium of 4.01%.
Estimating Required Rates of Return for Projects
We will next go deeper into the issue of the rate of discount to be used by a firm to judge a project. In the last session