Class #13: Risk 1 “Cost of Capital” 15.535 - Class #13 1Road Map: Where do things fit? • Valuation Fundamentals: – DCF Analysis – Comparative Analysis – Abnormal Earnings Valuation – Cash Flow Analysis • Where Now? – Properly calculating cost of capital: • Equity (CAPM, 3-Factor Model, Implied Cost of Capital) • Cost of Capital: International Companies • Debt • Enterprise 15.535 - Class #13 2Approaches to Calculating Equity Cost of Capital (Discount Rate) • CAPM – based on historical information – What if risk has changed? – Recent change in capital structure? • Application: – Discounting the cash flows (earnings) available to equityholders. – Which cashflows? Answer: The FCF’s after all other parties have been paid (lenders, taxes, etc) 15.535 - Class #13 3Calculation of CAPM discount rate • CAPM: E( R ) = Rf+ E*(Rm-Rf) – Expected return is increasing in systematic risk! – What is “Beta”? • Cov( Rstock,Rmarket –Rf )/Var( Rmarket –Rf ) • Usually = Cov( Rstock,Rmarket)/Var( Rmarket) • Think of it as “Co-wiggling” • According to this model, why does the systematic risk only matter? 15.535 - Class #13 4Where do we get the information? • Where do we get Beta? – KEY ISSUE! This is an estimate from historical data – Estimation period is typically 60 months – Why not longer? Why not shorter? – Sources: Bloomberg, Analysts, Yahoo! Finance, or estimate it yourself! • Where do we get RF? – Federal Reserve Bank of St. Louis: research.stlouisfed.org/fred/data/irates.html 15.535 - Class #13 5Example of CAPM Calculation: • What is Equity Cost of Capital for Microsoft? • Beta = 1.49 • Rf = 4.87% (20 year treasury bond) •(Rm –Rf) = 7.95% • E( R ) = Rf+ E*(Rm-Rf) = 4.87% + 1.49*(7.95%) =16.7% 15.535 - Class #13 6Is the CAPM correct? • Facts: Even after accounting for Beta risk: – Small stocks tend to have higher returns than big stocks. – Firms with high B/M ratios have higher returns. • Maybe the CAPM is a not perfect model: – Other sources of risk beyond single risk factor? – Maybe small stocks have greater systematic risk? • Is there a “size risk factor”? – Are firms that are near financial distress riskier? • Is there a financial distress factor? 15.535 - Class #13 7The Fama-French 3-factor model • Origins: – Fama and French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, for a complete description. • An “extension” of the CAPM: –Rstock =Rf + E*(Rm-Rf) +ESIZE*(RSMB) + EBM*(RHML) – Every stock has different market E, ESIZE, EBM • Where do we get (Rm-Rf), RSMB, RHML? – Homepage of Professor Ken French: • http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ data_library.html 15.535 - Class #13 8Fama-French Factor Returns • What are long-run average values of these factors? • Long-run average (Rm-Rf) = 7.95% per year • Long-run average RSMB = 3.32% per year • Long-run average RHML = 5.05% per year 15.535 - Class #13 9Example Calculation of 3-factor Cost of Capital • Microsoft: – Market Beta = 0.98 – Size Beta = -0.40 (!) – HML Beta = -1.24 (!) •Rstock=Rf+ E*(Rm-Rf) +ESIZE*(RSMB) + EBM*(RHML) = 4.87%+0.98*7.95%+(-0.4)*3.32%+ (-1.24)*5.05% = 5.1% !!!!! 15.535 - Class #13 10Implied Cost of Capital • Let’s assume that the stock market has set the stock price correctly. • Can we use this price information (plus information about future cashflows/earnings) to obtain a estimate of the “implied” cost of equity capital? • Use Discounted FCF formula: –P0 = CF1/(1+r) + CF2/(1+r)2 + CF3/[(r-g)(1+r)2] 15.535 - Class #13 11Example of Implied Cost of Capital Calculation • Microsoft: – Earnings per share 2003: $1.02/share – Earnings per share 2004: $1.08/share – 5-year growth rate: 15% – Current Stock Price = $24.25/share – Use standard DCF model (see handout): • P0 = CF1/(1+r) + CF2/(1+r)2 + CF3/[(r-g)(1+r)2] 15.535 - Class #13 12Example of Implied Cost of Capital Calculation: • Can also use the Residual Income Valuation Model (EBO Model, abnormal earnings model) –P0 = BV0 + AE1/(1+r) + AE2/(1+r)2 + … – Key is the terminal value 15.535 - Class #13 13International Cost of Capital Models • World CAPM or Multifactor Model (Sharpe-Ross) – World CAPM: -Rf -Rf)•Rstock = E*(Rworld d is a world index (ie MSCI World Index), E uses R•Rworl world • Segmented/Integrated CAPM (Bekaert-Harvey) • Credit Rating (Erb-Harvey-Viskanta) • Country Spread Model 15.535 - Class #13 14International Cost of Capital: Segmented/Integrated CAPM • Developed by Bekaert and Harvey (1995) – If country’s stock market is integrated with rest of world, then World CAPM holds: -Rf -Rf)•Rstock = E*(Rworld d is a world index (ie Morgan Stanley Capital World Index)•Rworl • http://www.msci.com/equity/index.html • E calculation is based on uses Rworld – If country’s stock market is segmented from the rest of world, then local CAPM holds: •Rstock -Rf = E*(Rcountry -Rf ) •Rcountry is a country’s stock index, E uses Rcountry – If country is going through process of integration, a combination of two holds. 15.535 - Class #13 15International Cost of Capital: Segmented/Integrated CAPM • Expected return is related to both covariance with world and local indices • Weights (world versus local beta) determined by proxy for degree of integration (like size of trade sector & ratio of stock market capitalization to total GDP) • Downside: – Hard to implement – Only appropriate for countries with equity markets. 15.535 - Class #13 16International Cost of Capital: Credit Rating Model • Developed by Erb, Harvey, and Viskanta • Uses country credit rating as a measure of systematic risk: –“Institutional Investor” magazine has rankings of country credit risk on scale of 0-100. – Run regression: Rcountyr = D+ E*Risk Rank – Estimate “average” cost-of capital in each country. – Can use in 136 countries (even countries without equity markets). – Impressive fit to the data. • Assumes country credit rating is a good measure of risk – Political risk, expropriation risk, exchange rate controls and volatility, etc. 15.535 - Class #13 17International Cost of Capital: Country Spread Model (Goldman Model) • Can be used for individual stocks • Steps: R – Estimate foreign company