5. Cost of Equity (48 points, 8 points each) You want to calculate a reasonable cost of equity for your firm. To do so, you have decided to rely on the CAPM. You have decided to use long-term government bonds as your benchmark for the risk- free rate. These bonds earned a return of 8% in the most recent year and currently carry a yield-to-maturity of 5%. You have compiled market rates of return and risk-free rates of return (i.e., one-month T-bills) over the last eight decades: Risk Real Premium Return Asset Class Mean (vs. T-Bills) (vs. Inflation) Min. Median Max. Std. Dev. Small Company Stocks 15.3 11.9 12.3 -50.2 17.5 124.7 30.0 Common Stocks 11.9 8.5 8.9 43.4 13.7 54.0 19.8 Long-Term Corp. Bonds 6.2 2.9 3.3 4.8 42.6 8.4 Long-Term Gov't Bonds 5.9 2.5 2.9 - 14.9 3.7 40.4 9.8 Intermediate Gov't Bonds 5.2 1.8 2.2 -5.1 29.1 5.6 US Treasury Bills 3.4 0.4 0.0 3.0 14.7 3.1 Inflation 3.0 -10.3 2.7 18.1 4.0 -8.1 3.5 Finally, you have regressed the firm's return on the market return using the last 60 months of available data and obtained the following results: Variable Intercept Market return Coef. 0.04 1.57 Std. Error 0.011 0.30 The R-squared from this regression is 16%. A. Using long-term government bonds as your risk-free benchmark, what is your estimate of the risk-free rate of return? Explain. B. What is your estimate of the market risk premium? Explain. C. What is your estimate of the firm's beta? What other data would you want to analyze to assess the reasonableness of your beta estimate? D. Calculate an approximate 95% confidence interval for your beta estimate. How precise is your estimated beta? E. What is your estimate of the firm's cost of equity? F. Should you use this cost of equity to evaluate new investment projects? Why or why not? 5. Cost of Equity (48 points, 8 points each) You want to calculate a reasonable cost of equity for your firm. To do so, you have decided to rely on the CAPM. You have decided to use long-term government bonds as your benchmark for the risk- free rate. These bonds earned a return of 8% in the most recent year and currently carry a yield-to-maturity of 5%. You have compiled market rates of return and risk-free rates of return (i.e., one-month T-bills) over the last eight decades: Risk Real Premium Return Asset Class Mean (vs. T-Bills) (vs. Inflation) Min. Median Max. Std. Dev. Small Company Stocks 15.3 11.9 12.3 -50.2 17.5 124.7 30.0 Common Stocks 11.9 8.5 8.9 43.4 13.7 54.0 19.8 Long-Term Corp. Bonds 6.2 2.9 3.3 4.8 42.6 8.4 Long-Term Gov't Bonds 5.9 2.5 2.9 - 14.9 3.7 40.4 9.8 Intermediate Gov't Bonds 5.2 1.8 2.2 -5.1 29.1 5.6 US Treasury Bills 3.4 0.4 0.0 3.0 14.7 3.1 Inflation 3.0 -10.3 2.7 18.1 4.0 -8.1 3.5 Finally, you have regressed the firm's return on the market return using the last 60 months of available data and obtained the following results: Variable Intercept Market return Coef. 0.04 1.57 Std. Error 0.011 0.30 The R-squared from this regression is 16%. A. Using long-term government bonds as your risk-free benchmark, what is your estimate of the risk-free rate of return? Explain. B. What is your estimate of the market risk premium? Explain. C. What is your estimate of the firm's beta? What other data would you want to analyze to assess the reasonableness of your beta estimate? D. Calculate an approximate 95% confidence interval for your beta estimate. How precise is your estimated beta? E. What is your estimate of the firm's cost of equity? F. Should you use this cost of equity to evaluate new investment projects? Why or why not
