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- 1. Stock Valuation Gordon Growth Model Mila Getmansky Sherman
- 2. Approaches to Valuation <ul><li>1. Discounted Cash Flow Valuation </li></ul><ul><ul><li>The value of an asset is the sum of the discounted cash flows. </li></ul></ul><ul><li>2. Contingent Claim Valuation </li></ul><ul><ul><li>A contingent claim can be replicated and, thus, priced using other traded assets whose prices are known. </li></ul></ul><ul><li>3. Relative Valuation </li></ul><ul><ul><li>A company may be priced by comparing its price to another company that has similar characteristics (P/E, Price/Book, etc.) </li></ul></ul>
- 3. Discounted Cash Flow (DCF) <ul><li>What is the net value today of a series of future cash flows? </li></ul><ul><li>Examples: </li></ul><ul><ul><li>Stock: What is the value of a stock that is expected to give a certain amount of dividend every year? </li></ul></ul><ul><ul><li>Bond: what is the value of a bond that gives a certain amount of coupon and principal payments? </li></ul></ul><ul><ul><li>Company: What is the value of the firm as a whole (including the value of equity, debt, and any other securities, like convertible bonds, used to finance the firm)? </li></ul></ul>
- 4. Use Appropriate Discount Rate <ul><li>Stock </li></ul><ul><ul><li>Cost of equity, r E (Obtain r E using Gordon-growth model or CAPM) </li></ul></ul><ul><li>Bond </li></ul><ul><ul><li>Cost of bond, r D (spot rate) </li></ul></ul><ul><li>Company </li></ul><ul><ul><li>WACC (Weighted Average Cost of Capital) WACC=r E E/(E+D)+r D (1-T c )D/(E+D) </li></ul></ul>
- 5. Discount Rate <ul><li>Synonyms: Discount rate, cost of capital, opportunity rate, interest rate </li></ul>
- 6. Assumptions Underlying the Gordon Growth (Dividend) Model <ul><li>1. Stable business : The firm is not expected to change its operations, or move into a different business. </li></ul><ul><li>2. Steady growth : We may assume that the firm (dividends, FCFE) will grow at a constant growth rate, g , year after year. </li></ul><ul><li>3. Stable financial leverage: A change in capital financial leverage would change the cost of equity capital. Stable business + Stable financial leverage => cost of equity capital, r E , is constant. </li></ul><ul><li>4. Dividend and FCFE : All of the firm’s free cash flow is paid out as dividends. </li></ul>
- 7. The Gordon Growth Model <ul><li>With the additional assumption that the firm is expected to live forever, we can write the current stock price, P, as: </li></ul><ul><li>P = D 1 /(r E -g) </li></ul><ul><li>D 1 is the expected dividend in the next period. </li></ul><ul><li>g is the expected growth in dividends. </li></ul><ul><li>r E is the cost of equity . This is required rate of return required by shareholders for investing in the stock. </li></ul>
- 8. An Example Consolidated Edison <ul><li>Consolidated Edison is a utilities/energy company. Its ticker symbol is ED. It fits our assumptions for the application of the Gordon Growth Model. </li></ul><ul><li>It is in a stable business. On their website, they write as a description of the corporate strategy: </li></ul><ul><ul><li>“ The guiding principle of Con Edison's corporate strategy has been, and continues to be, to deliver shareholder value by focusing on what we do best - providing safe, reliable energy to our millions of customers in the Northeast. At Con Edison, we don't have to go back to basics - we never left the basics.” </li></ul></ul><ul><li>Its growth in dividends is stable at about 0.9% per year. </li></ul>
- 9. ConEd Quarterly Dividend History
- 10. An Example Consolidated Edison <ul><li>Next, we need to check if its financial leverage is stable. </li></ul><ul><li>To compute the financial leverage, we need market values of debt and equity. </li></ul><ul><li>The market value of debt is usually difficult to get (unless the long-term debt comprises of traded bonds). So instead, we will assume that the book value of debt is close to the market value of debt. </li></ul><ul><li>The market value of equity can be estimated using the price and the number of shares outstanding. </li></ul><ul><ul><li>If you are using Yahoo, you may have to go back and adjust for splits, as Yahoo reports the prices after adjustment for splits. </li></ul></ul>
- 11. ConEd’s Financial Leverage
- 12. ConEd’s Financial Leverage <ul><li>The graph suggests that the financial leverage has been relatively steady and changed a little within a small bound. </li></ul><ul><li>We may thus assume it to be constant. </li></ul>
- 13. CAPM <ul><li>The CAPM states that, given the beta of the stock, the required return is: </li></ul><ul><li>r E = r F + (beta) x (Market Risk Premium) </li></ul><ul><li>r E = required return on stock </li></ul><ul><li>r F = riskfree rate </li></ul><ul><li>Market Risk Premium = ( r M – r F ), where r M is the required return on the market portfolio. The market portfolio may be proxied by a large diversified index like the S&P 500. </li></ul><ul><li>The beta may be estimated from historical data by a regression of the stock return on the market return. </li></ul>
- 14. Estimating Beta (1/3) <ul><li>The beta is the slope of the regression of the returns of the stock on the returns on the market. </li></ul><ul><li>To estimate the beta, you can use historical returns of both the market and the stock. </li></ul><ul><ul><li>Usually, we will use the S&P 500 as a proxy for the market. </li></ul></ul><ul><li>The amount of data you use requires making a tradeoff. The more the data, the more accurate your estimate. But the longer you go back in history, the more stale the data. </li></ul><ul><li>A reasonable compromise is as follows: </li></ul><ul><ul><li>If you use monthly data, then use 3-5 years of history. Three years is good. </li></ul></ul><ul><ul><li>If you use weekly data, use about one year of history. </li></ul></ul>
- 15. Estimating Beta (2/3) <ul><li>Estimate of beta for ED from 7-year of monthly data = 0. </li></ul><ul><ul><li>The exact estimate is –0.05, but this estimate is not significant (standard error is 0.13 and t-Stat is -0.35). </li></ul></ul><ul><li>The beta is also available on the Yahoo website, but its better to compute your own as you know precisely the assumptions you have made. But you may use this when you need a quick estimate. </li></ul><ul><ul><li>The Yahoo beta; however, is 0.28. This estimate can be insignificant; however, no significance measure is given. </li></ul></ul>
- 16. Estimating Beta (3/3) Output from Excel
- 17. The Market Risk Premium <ul><li>Next, we have to use an estimate of the market risk premium. For this, we can look at the historical returns of the S&P 500 (excess over the riskfree rate, Rm-Rf). </li></ul><ul><li>The estimate of the market risk premium is sensitive to: </li></ul><ul><ul><li>The length of history you use to estimate the risk premium </li></ul></ul><ul><ul><li>The type of averaging – geometric or arithmetic averaging. </li></ul></ul><ul><ul><li>Whether your consider excess returns over the 3-month treasury bill or the 30-year treasury bond. </li></ul></ul>
- 18. The Market Risk Premium Cont. <ul><li>Because we expect the stock to be of infinite life, we will use the 30-year bond rate as our proxy for the risk-free rate. </li></ul><ul><ul><li>The 30-year rate is currently at about 5% (12/2006). </li></ul></ul><ul><li>The geometric average market risk premium is about 5% (Stocks, Bonds, Bills and Inflation, 2005 Yearbook, Ibbotson Associates, Chicago.) </li></ul><ul><li>The geometric average more closely matches the actual holding-period returns of an investor. So we will use the geometric average as an estimate. </li></ul>
- 19. Estimate of Required Return for ED <ul><li>Now, we can use the riskfree rate, and our estimates of the beta and MRP to estimate the cost of equity capital for ED. </li></ul><ul><li>r E = r F + beta x (MRP) = 5% + 0 x 5% = 5%. </li></ul>
- 20. Estimate of Stock Price <ul><li>The current annual dividend for ED is $2.30 (D 0 ). Note, it is per share. </li></ul><ul><li>The growth rate for dividends over the last few years is approximately 0.9%. </li></ul><ul><li>Applying the Gordon Growth Model, </li></ul><ul><li>P = 2.30x(1+0.009)/(0.05-0.009) = $56.60. </li></ul>
- 21. Is this reasonable? <ul><li>Growth rate: Can the firm sustain the historical growth rate in earnings? Earnings have been declining…the 2004 earnings per share were $2.28, compared with 2003, 2002 and 2001 of 2.37, 3.14 and 3.22, respectively. However, in 2005 and 2006 they increased to $2.89 and $2.94 respectively. </li></ul><ul><li>The dividend payout ratio (DPS/EPS) has increased over this period from 0.68 (in 2001) to 0.94 in 2004, but then declined to 78% in 2006. </li></ul><ul><li>Was all of the dividend paid in 2006 really “free cash flow”? Or is the true free cash flow to equity lower? [Check the cash flow statement of 2006] </li></ul>

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