Discount rates Class 12 Financial Management, 15.414MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Today Discount rates • Using the CAPM • Estimating beta and the cost of capital Reading • Brealey and Myers, Chapter 9 • Graham and Harvey (2000, p. 1 – 10)MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Review The CAPM Measuring risk A stock’s systematic risk is measured by beta, the slope when the stock return is regressed on the market: Ri = α + β RM + ε Required returns Investors should be compensated for bearing non-diversifiable, beta risk. The required return on a stock is: E[Ri] = rf + βi E[RM – rf] Market risk premium 3MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 The risk-return trade-off 0% 5% 10% 15% 20% 25% Stock's expected return Slope = E[RM] – rf β = 1.5 β = 0.5 β = 0 Market portfolio (β = 1) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Stock's beta 4MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Using the CAPM Valuation NPV = CF0 + CF1 + CF2 CF3 CF4+ + + ...r) (1 r) (1 2 r) (1 3 r) (1 4++ + + Discount rate The rate of return that investors demand on investments with the same level of risk. CAPM Risk = the project’s beta Discount rate = rf + βproject E[RM – rf] 5MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Using the CAPM Practical issues 1: How can we estimate the project’s beta? 2: What is the riskfree rate and the market risk premium? 3: How does debt affect risk and the cost of capital? 4: Additional risk factors? 6MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Example It’s 1979. Southwest Airlines, a growing start-up, has been profitable as the low-cost airline in the Texas market. Southwest is thinking about expanding to other U.S. cities. Management forecasts that the expansion will cost $100 million over the next few years but will lead to strong future growth ($ millions): Year 1977 1978 1979 1980 1981 1982 Sales 49.0 81.1 136.1 213.1 270.4 331.2 NI 7.5 17.0 16.7 28.4 34.2 34.0 NWC 5.1 10.7 12.4 11.1 19.3 CAPX 41.5 45.1 54.5 56.7 79.4 140.2 9.7 Growth is expected to slow to 10% annually after 1982. What cost of capital should Southwest use to evaluate the proposed expansion? 7MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Southwest stock price, 1970 – 1979 $30 25 20 15 10 5 0 Dec-72 Dec-73 Dec-74 Dec-75 Dec-76 Dec-77 Dec-78 Dec-79 8MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Issue 1 How can we estimate the project’s beta? What factors are important? Two approaches Estimate the firm’s beta Estimate the industry’s beta (comparables) How much data? 5 – 10 years of monthly data 9MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Estimating beta 1: Estimate the firm’s beta Advantage If the project has the same risks as the firm (an expansion), this approach measures exactly what we want Disadvantages Generally not very precise (high standard error) Firm’s beta might change over time Can’t be used for projects in a new line of business or for diversified firms 10MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Southwest Is this approach useful for SW? Is the risk (beta) of the expansion likely to be the same as the beta of the firm? Is Southwest’s past beta likely to be a useful guide for the future beta of the project? Southwest, 1973 – 1979 (84 months) RSW = α + βSW RM + εi Estimate: βSW = 1.25 (std error = 0.31); R2 = 0.16 [RM = return on a market index, like S&P 500] 11MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Southwest vs. Total U.S. market return -40% -30% -20% -10% 0% 10% 20% 30% 40% -40% -30% -20% -10% 0% 10% 20% 30% 40% Mkt return SW return Slope = 1.25 12MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Southwest’s beta over time 1973-1977 β = 1.20 1978-1982 β = 1.14 1983-1987 β = 1.06 1988-1992 β = 1.52 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 Mkt return SW return -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 Mkt return SW return -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 Mkt return SW return -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 Mkt return SW return 13MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Estimating beta 2: Estimate the industry’s beta* Advantages Beta estimated more precisely. Appropriate if the project is in a new line of business. Disadvantages Do the firm’s really have the same risk as the project? Do they serve different markets? Do they have more debt? Do they have the same cost stucture? * Estimate the betas of individual firms and then average, or estimate the beta of an industry portfolio. 14MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Southwest Is this approach useful for SW? Is the risk (beta) of the expansion likely to be the same as the beta of other airlines? Airline betas, 1973 – 1979 Airline β Airline β American 1.42 Northwest 1.35 Continental 1.18 United 1.55 Delta 1.30 USAir 1.37 Average = 1.36, standard error of 0.13 15MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Airline industry vs. Total U.S. market return Slope = 1.36 -30% -20% -10% 0% 10% 20% 30% 40% -30% -20% -10% 0% 10% 20% 30% industry return Mkt return Airline 16MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Issue 2 Riskfree rate? rproject = rf + βproject E[RM – rf] Should the riskfree rate be the short-term Tbill rate or the long-term Tbond rate? Match horizons If short-lived project, use Tbill rate If long-lived project, use Tbond rate (say, 10-year) Riskfree rate changes a lot over time 1979: Tbill rate = 9.65%, Tbond rate = 10.39% 2003: Tbill rate = 0.93%, Tbond rate = 4.31% 17MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Interest rates, 1953 – 2001 16% 12% 8% 4% 0% Jun-53 Jan-63 Jun-72 Jan-82 Jun-91 Jan-01 1-yr Tbill 10-yr Tbond 18MIT SLOAN SCHOOL OF MANAGEMENT 15.414 Class 12 Issue 2 Market risk premium? rproject = rf + βproject E[RM – rf] Historical estimates 1872 – 1999: 5.73% (std error = 1.63%) 1926 – 1999: 8.26% (std error = 2.24%) 1963 – 1999: 6.44% (std error = 2.51%) r = DY + g 1872 – 1999: 3.64% (std error = 1.15%) 1872 – 1949: 3.79% (std error = 1.78%) 1950 – 1999: 3.40% (std error = 0.99%) Constant growth model P = gr D − Going forward? My guess, 4 – 6% 19MIT SLOAN SCHOOL