Αρτίκης Γ. Παναγιώτης Κόστος Κεφαλαίου Estimating Inputs: Discount Rates Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation. At an intuitive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted. Equity versus Firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital. Currency: The currency in which the cash flows are estimated should also be the currency in which the discount rate is estimated. Nominal versus Real: If the cash flows being discounted are nominal cash flows (i.e., reflect expected inflation), the discount rate should be nominal. Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 2 1
The CAPM: Cost of Equity Cost of Equity = R f + Beta * [ E(R m ) R f ] where, R f = Riskfree rate E(R m ) = Expected Return on the Market Index (Diversified Portfolio) In practice, Short term government security rates are used as risk free rates Betas are estimated by regressing stock returns against market returns Historical risk premiums are used for the risk premium Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 3 Short term Governments are not riskfree On a riskfree asset, the actual return is equal to the expected return. Therefore, there is no variance around the expected return. For an investment to be riskfree, then, it has to have: No default risk No reinvestment risk Thus, the riskfree rates in valuation will depend upon when the cash flow is expected to occur and will vary across time. A simpler approach is to match the duration of the analysis (generally long term) to the duration of the riskfree rate (also long term). Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 4 2
Estimating Beta Historical Market Beta The standard procedure for estimating betas is to regress stock returns (R j ) against market returns (R m ): R j = a + b R m where a is the intercept and b is the slope of the regression. The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. This beta has three problems: It has high standard error It reflects 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. Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 5 Estimating Beta Historical Market Beta Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 6 3
Estimating Beta Historical Market Beta R ( t) α + β R ( t) e ( t) HP = HP HP S& P500 + HP Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 7 Estimating Beta Historical Market Beta Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 8 4
Determinants of Betas Product or Service: The beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market. Cyclical companies have higher betas than non-cyclical firms Firms which sell more discretionary products will have higher betas than firms that sell less discretionary products Operating Leverage: The greater the proportion of fixed costs in the cost structure of a business, the higher the beta will be of that business. This is because higher fixed costs increase your exposure to all risk, including market risk. Financial Leverage: The more debt a firm takes on, the higher the beta will be of the equity in that business. Debt creates a fixed cost, interest expenses, that increases exposure to market risk. Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 9 Equity Betas and Leverage The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio: β L = β u [ 1+ (1-t) (D/E) ] where β L = Levered or Equity Beta β u = Unlevered Beta (Asset Beta) t = Corporate marginal tax rate D = Market Value of Debt E = Market Value of Equity Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 10 5
Equity Betas and Leverage Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 11 Equity Betas and Leverage Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 12 6
Business Betas & Operating Leverage The business beta alone can be written as a function of the unlevered beta and the operating leverage as measured by the ratio of fixed to variable costs: β business = β u / [1 + (Fixed Costs/Variable Costs)] β business = β u / [1 + (% Change EBIT / % Change Revenues)] Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 13 You would like to estimate the beta coefficient for «Van» company, which is not listed, and operates in the apparel shoe industry. The company has a: fixed to variable cost ratio of 31.16%, debt to equity ration of 9.41% and tax rate of 34.06%. Collect a group of publicly traded comparable firms, preferably in the same line of business, but more generally, affected by the same economic forces that affect the firm being valued. A Simple Test: To see if the group of comparable firms is truly comparable, estimate a correlation between the revenues or operating income of the comparable firms and the firm being valued. If it is high (and positive), of course, you have comparable firms. Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 14 7
Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 15 Estimate the average market value debt-equity ratio and tax rate of the comparable firms, and calculate the industry average unlevered beta: β u = β L / [1 + (1 t) (Industry Average D/E)] Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 16 8
Estimate the average fixed costs to variable costs ratio of the comparable firms and calculate the industry average business beta: β business = β u / [1 + (Fixed Costs/Variable Costs)] Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 17 Use the private firms fixed cost to variable cost ratio to estimate the unlevered beta of the firm: Private firm β u = β business x [1 + (Fixed Costs/Variable Costs)] Estimate a optimal debt ratio for the private firm, based upon its operating income and cost of capital and calculate the levered beta for the private firm: Levered β private firm = β u [1 + (1 - t) (Optimal D/E)] Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 18 9
Comparable Firms Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 19 Everyone uses historical premiums, but.. Cost of Equity = R f + Beta * [ E(R m ) R f ] The historical premium is the premium that stocks have historically earned over riskless securities. Practitioners never seem to agree on the premium; it is sensitive to How far back you go in history Whether you use T.bill rates or T.Bond rates Whether you use geometric or arithmetic averages. Arithmetic Average Geometric Average Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds 1928-2016 7.96% 6.24% 6.11% 4.62% Std Error 2.12% 2.26% 1967-2016 6.57% 4.37% 5.25% 3.42% Std Error 2.39% 2.72% 2007-2016 7.90% 3.62% 6.15% 2.30% Std Error 6.06% 8.63% Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 20 10
Βιβλιογραφία Αρτίκης Π., «Διαχείριση Αξίας και Κινδύνου» Κεφάλαιο 11 Π. Γ. Αρτίκης - Κόστος Κεφαλαίου 21 11