# Homework Solutions - Lecture 2

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1 Homework Solutions - Lecture 2 1. The value of the S&P 500 index is and the treasury rate is 3.43%. In a typical year, stock repurchases increase the average payout ratio on S&P 500 stocks to over 4%. a. Calculate the implied equity premium assuming the dividend yield in the most recent year was 4% of the current index value and dividends are expected to grow at a constant rate of 5% annually. How does this implied premium compare to the value we calculated when ignoring repurchases? Div = (.04)(1.05) = Div1 R = g + =.05 + CurrentValue = = 9.20% Implied Risk Premium = = 5.77% All of the values in this problem are the same as the problem we did in class except the dividend yield. Because the current value of the index ( ) does not change, but the forecasted dividends here are higher, the implied premium is higher than the one we calculated in class. b. Calculate the implied equity premium assuming the dividend yield in the most recent year was 4% of the current index value, dividends are expected to grow at an annual rate of 10% for the next five years, and at a constant rate of 5% thereafter (Hint: you can use the solver function in excel). How does this implied premium compare to the value we calculated when ignoring repurchases? Here you will need to use the Solver function in excel. Specifically, you should solve for the required return that sets the present value of future dividends equal to the current index value. Div = (.04)(1.10) = = /( R.05) + 5 R = 10.20% Implied Risk Premium = = 6.77% Again, all of the values in this problem are the same as the problem we did in class except the dividend yield. Because the current value of the index ( ) does not change, but the forecasted dividends here are higher, the implied premium is higher than the one we calculated in class.

3 3. In 1995, Time Warner Inc. had a Beta of Part of the reason for this high Beta was the debt left over from the leveraged buyout of Time by Warner in 1989, which amounted to \$10 billion in The market value of equity at Time Warner in 1995 was also \$10 billion. The marginal tax rate was 40%. a) Using the formula for leveraging a beta that includes tax effects (to account for the extremely high and changing leverage), we get: E 10 β u = β e = 1.61 = D(1 T ) + E 10(1.4) + 10 b) The debt/equity ratio in 1995 was 10/10 = 1.0. If the debt ratio goes from 1.0 in 1995, to 0.9 in 1996, and 0.8 in 1997, the levered betas for 1996 and 1997 would equal: D(1 T ) β e = β u 1 + = = E ( +.9(1.4)) D(1 T ) β e = β u 1 + = = E ( +.8(1.4))

5 5. Synthetic Debt Ratings: c. The following information was taken from the income statement and balance sheet of a real firm. Use this information to calculate the EBITDA-to-interest ratio, the Debt-to-EBITDA ratio, the Debt-to-Capital ratio, and the Return on Capital. Based on the values you calculate, use the S&P Ratings Guide on the attached page to estimate a synthetic debt rating for this firm. EBIT = \$5,839 EBITDA = \$7,455 Interest Expense = \$530 Total Debt = \$9,749 Stockholder s Equity = \$18,889 Tax Rate = 36.7% EBITDA Interest Debt EBITDA = 7455 = = = Debt Capital 9749 = = 34.04% (1.367) ROC = = 12.91% Based on these ratios, the firm is roughly similar to other firms in the low A or high BBB ratings categories. d. The firm described above has significant operating leases. The notes to the financial statements show that the firm s operating lease expenses during the period were \$823, of which \$289 is estimated to be interest expense. In addition, you calculate the debt value of operating leases to be \$5,927. Recalculate the ratios above incorporating this new information. Based on these corrected values, use the S&P Ratings Guide to estimate a revised synthetic debt rating for this firm. EBIT = \$5, = \$6,128 EBITDA = \$7, = \$8,278 Interest Expense = = \$819 Total Debt = 9, ,927 = \$15,676 Stockholder s Equity = \$18,889 Tax Rate = 36.7% EBITDA Interest Debt EBITDA = 8278 = = = Debt Capital = = 45.35% (1.367) ROC = = 11.22% Based on these revised ratios, the firm appears to fall at the middle or high end of BBB rated firms (or the very low end of A rated firms). Note that I assume the operating lease expense of \$823 is a combination of interest expense and depreciation.

6 Question 4 Regression Output: SUMMARY OUTPUT Regression Statistics R Square Observations 60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept X Variable y = x R² = Nike Return 20.00% 15.00% 10.00% 5.00% 0.00% % % % -5.00% 0.00% 5.00% 10.00% 15.00% -5.00% % % %

7

8 Question 4 Nike Operating Lease Information: Inputs: 5/31/2011 5/31/2010 5/31/2009 Cost of Debt 4.09% 4.09% 4.09% Round Annuity Length? (1=yes, 0=no) Operating Lease Commitments (mil) 2013 (or year +1) \$374.0 \$334.0 \$ (or year +2) \$310.0 \$264.0 \$ (or year +3) \$253.0 \$220.0 \$ (or year +4) \$198.0 \$177.0 \$ (or year +5) \$174.0 \$148.0 \$168.6 >2017 (after year ) \$535.0 \$466.0 \$588.5 Total \$1,844.0 \$1,609.0 \$1,797.8 Estimation (based on yr 5 pymt): Year 5 payment \$174.0 \$148.0 \$168.6 Annuity yrs PV of Lease Pmts \$1,584.5 \$1, ,529.0

9 Question 4 Nike Employee Stock Options Valuation: Employee Options at Nike updated 2011 Black-Scholes Option Pricing Model Inputs: Black-Scholes Option Pricing Model (with dilution) Inputs (with dilution effects): Stock Price (S) \$84.45 Stock Price (S) \$84.45 Strike Price (X) \$51.29 Strike Price (X) \$51.29 Volatility (σ) 31.50% Volatility (σ) 31.50% Risk-free Rate 3.05% 1.70% Risk-free Rate 3.05% Time to expiration (T) 6.00 yrs Time to expiration (T) 6.00 yrs Dividend Yield 1.60% Dividend Yield 1.60% # of Options (mil) 35 # of Options (mil) 35 # Shares Outstanding (mil) 468 # Shares Outstanding (mil) 468 Output: Output: Adjusted S (dilution) \$81.16 D D D D N(D1) N(D1) N(D2) N(D2) Call Price \$39.47 Call Price \$36.87 Put Price \$5.46 Put Price \$5.86 Value of Call Options (mil) \$1, Value of Call Options (mil) \$1, After-tax Option Value (mil) \$ After-tax Option Value (mil) \$817.38

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