1. © 2009 McGraw-Hill Ryerson Limited 7-1 Chapter 7 Common Stock Valuation CHAPTER OUTLINE Security analysis Security analysis The dividend discount model The dividend discount model The two-stage dividend growth model The two-stage dividend growth model The residual Income Model The residual Income Model Price ratio analysis Price ratio analysis An analysis of McGraw-Hill Company An analysis of McGraw-Hill Company

2. © 2009 McGraw-Hill Ryerson Limited 7-2 Security Analysis Fundamental analysis is a term for studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock. Fundamental analysis is a term for studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock. The basic idea is to identify “undervalued” stocks to buy and “overvalued” stocks to sell. In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst. The basic idea is to identify “undervalued” stocks to buy and “overvalued” stocks to sell. In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst.

3. © 2009 McGraw-Hill Ryerson Limited 7-3 The Dividend Discount Model The Dividend Discount Model (DDM) is a method to estimate the value of a share of stock by discounting all expected future dividend payments. The DDM equation is: The Dividend Discount Model (DDM) is a method to estimate the value of a share of stock by discounting all expected future dividend payments. The DDM equation is: In the DDM equation: In the DDM equation: V(0) = the present value of all future dividends V(0) = the present value of all future dividends D(t) = the dividend to be paid t years from now D(t) = the dividend to be paid t years from now k = the appropriate risk-adjusted discount rate k = the appropriate risk-adjusted discount rate

4. © 2009 McGraw-Hill Ryerson Limited 7-4 Example: The Dividend Discount Model Suppose that a stock will pay three annual dividends of $200 per year, and the appropriate risk-adjusted discount rate, k, is 8%. Suppose that a stock will pay three annual dividends of $200 per year, and the appropriate risk-adjusted discount rate, k, is 8%. In this case, what is the value of the stock today? In this case, what is the value of the stock today?

5. © 2009 McGraw-Hill Ryerson Limited 7-5 The Dividend Discount Model: the Constant Growth Rate Model Assume that the dividends will grow at a constant growth rate g. Assume that the dividends will grow at a constant growth rate g. Then, the dividend next period (t + 1) is: Then, the dividend next period (t + 1) is: In this case, the DDM formula becomes: In this case, the DDM formula becomes:

6. © 2009 McGraw-Hill Ryerson Limited 7-6 Example: The Constant Growth Rate Model Suppose the current dividend is $10, the dividend growth rate is 10%, there will be 20 yearly dividends, and the appropriate discount rate is 8%. What is the value of the stock, based on the constant growth rate model? Suppose the current dividend is $10, the dividend growth rate is 10%, there will be 20 yearly dividends, and the appropriate discount rate is 8%. What is the value of the stock, based on the constant growth rate model?

7. © 2009 McGraw-Hill Ryerson Limited 7-7 The Constant Perpetual Growth Model. Assuming that the dividends will grow forever at a constant growth rate g. Assuming that the dividends will grow forever at a constant growth rate g. In this case, the DDM formula becomes: In this case, the DDM formula becomes:

8. © 2009 McGraw-Hill Ryerson Limited 7-8 Example: Constant Perpetual Growth Model Think about the electric utility industry. Think about the electric utility industry. In mid-year, the dividend paid by the utility company, American Electric Power (AEP), was $1.40. In mid-year, the dividend paid by the utility company, American Electric Power (AEP), was $1.40. Using D(0)=$1.40, k = 7.3%, and g = 1.5%, calculate an estimated value for AEP. Using D(0)=$1.40, k = 7.3%, and g = 1.5%, calculate an estimated value for AEP. Note: the actual mid-year stock price of AEP was $38.80. What are the possible explanations for the difference?

9. © 2009 McGraw-Hill Ryerson Limited 7-9 Estimating the Growth Rate The growth rate in dividends (g) can be estimated in a number of ways. The growth rate in dividends (g) can be estimated in a number of ways. Using the company’s historical average growth rate. Using the company’s historical average growth rate. Using an industry median or average growth rate. Using an industry median or average growth rate. Using the sustainable growth rate. Using the sustainable growth rate.

10. 7-10 The Historical Average Growth Rate Suppose the Kiwi Company paid the following dividends: Suppose the Kiwi Company paid the following dividends: 2000: $1.502003: $1.80 2000: $1.502003: $1.80 2001: $1.702004: $2.00 2001: $1.702004: $2.00 2002: $1.752005: $2.20 2002: $1.752005: $2.20 The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages. The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

11. © 2009 McGraw-Hill Ryerson Limited 7-11 The Sustainable Growth Rate Return on Equity (ROE) = Net Income / Equity Return on Equity (ROE) = Net Income / Equity Payout Ratio = Proportion of earnings paid out as dividends Payout Ratio = Proportion of earnings paid out as dividends Retention Ratio = Proportion of earnings retained for investment Retention Ratio = Proportion of earnings retained for investment

12. © 2009 McGraw-Hill Ryerson Limited 7-12 Example: Calculating and Using the Sustainable Growth Rate In 2005, American Electric Power (AEP) had an ROE of 14.59%, projected earnings per share of $2.94, and a per-share dividend of $1.40. What was AEP’s: Retention rate? Retention rate? Sustainable growth rate? Sustainable growth rate? Payout ratio = $1.40 / $2.94 =.476 Payout ratio = $1.40 / $2.94 =.476 So, retention ratio = 1 –.476 =.524 or 52.4% So, retention ratio = 1 –.476 =.524 or 52.4% Therefore, AEP’s sustainable growth rate =.1459  52.4% = 7.645% Therefore, AEP’s sustainable growth rate =.1459  52.4% = 7.645%

13. © 2009 McGraw-Hill Ryerson Limited 7-13 Example: Calculating and Using the Sustainable Growth Rate What is the value of AEP stock, using the perpetual growth model, and a discount rate of 7.3%? What is the value of AEP stock, using the perpetual growth model, and a discount rate of 7.3%? Recall the actual mid-year stock price of AEP was $38.80. Recall the actual mid-year stock price of AEP was $38.80. Clearly, there is something wrong because we have a negative price. What causes this negative price? Clearly, there is something wrong because we have a negative price. What causes this negative price? Suppose the discount rate is appropriate. What can we say about g? Suppose the discount rate is appropriate. What can we say about g?

14. © 2009 McGraw-Hill Ryerson Limited 7-14 The Two-Stage Dividend Growth Model The two-stage dividend growth model assumes that a firm will initially grow at a rate g 1 for T years, and thereafter grow at a rate g 2 < k during a perpetual second stage of growth. The two-stage dividend growth model assumes that a firm will initially grow at a rate g 1 for T years, and thereafter grow at a rate g 2 < k during a perpetual second stage of growth. The Two-Stage Dividend Growth Model formula is: The Two-Stage Dividend Growth Model formula is: Although the formula looks complicated, think of it as two parts: Although the formula looks complicated, think of it as two parts: Part 1 is the present value of the first T dividends (it is the same formula we used for the constant growth model). Part 1 is the present value of the first T dividends (it is the same formula we used for the constant growth model). Part 2 is the present value of all subsequent dividends. Part 2 is the present value of all subsequent dividends.

15. 7-15 Two-Stage Dividend Growth Model The total value of $46.03 is the sum of a $14.25 present value of the first five dividends, plus a $31.78 present value of all subsequent dividends. The total value of $46.03 is the sum of a $14.25 present value of the first five dividends, plus a $31.78 present value of all subsequent dividends. So, suppose Molly.com has D(0) = $5, which is expected to “shrink” at the rate g 1 = -10% for 5 years, but grow at the rate g 2 = 4% forever. With a discount rate of k = 10%, what is the present value of the stock?

16. 7-16 Example of supernormal growth Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year. You believe that this rate will last for only three more years. Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year. You believe that this rate will last for only three more years. Then, you think the rate will drop to 10% per year. Total dividends just paid were $5 million. The required rate of return is 20%. What is the total value of Chain Reaction, Inc.? Then, you think the rate will drop to 10% per year. Total dividends just paid were $5 million. The required rate of return is 20%. What is the total value of Chain Reaction, Inc.? First, calculate the total dividends over the “supernormal” growth period: First, calculate the total dividends over the “supernormal” growth period: Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as: V(3) = [D(3) x (1 + g)] / (k – g) V(3) = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835 Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as: V(3) = [D(3) x (1 + g)] / (k – g) V(3) = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835 Year Total Dividend: (in $millions) 1 $5.00 x 1.30 = $6.50 2 $6.50 x 1.30 = $8.45 3 $8.45 x 1.30 = $10.985

17. 7-17 Example of supernormal growth Therefore, to determine the present value of the firm today, we need the present value of $120.835 and the present value of the dividends paid in the first 3 years: Therefore, to determine the present value of the firm today, we need the present value of $120.835 and the present value of the dividends paid in the first 3 years:

18. © 2009 McGraw-Hill Ryerson Limited 7-18 Discount Rates The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ). The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ). We will discuss the CAPM in a later chapter. We will discuss the CAPM in a later chapter. However, we can estimate the discount rate for a stock using the following formula: However, we can estimate the discount rate for a stock using the following formula: Discount rate = time value of money + risk premium Discount rate = time value of money + risk premium = T-bill rate + (stock beta x stock market risk premium) T-bill rate:return on 90-day T-bills Stock Beta: Risk relative to an average stock Stock Market Risk Premium: Risk premium for an average stock

19. © 2009 McGraw-Hill Ryerson Limited 7-19 Dividend Discount Models Constant Perpetual Growth Model: Simple to compute Not usable for firms that do not pay dividends Not usable when g > k Is sensitive to the choice of g and k k and g may be difficult to estimate accurately. Constant perpetual growth is often an unrealistic assumption.

20. © 2009 McGraw-Hill Ryerson Limited 7-20 Dividend Discount Models Two-Stage Dividend Growth Model: More realistic in that it accounts for two stages of growth Usable when g > k in the first stage Not usable for firms that do not pay dividends Is sensitive to the choice of g and k k and g may be difficult to estimate accurately.

21. © 2009 McGraw-Hill Ryerson Limited 7-21 Residual Income Model (RIM) We have valued only companies that pay dividends. We have valued only companies that pay dividends. But, there are many companies that do not pay dividends. But, there are many companies that do not pay dividends. What about them? What about them? It turns out that there is an elegant way to value these companies, too. It turns out that there is an elegant way to value these companies, too. The model is called the Residual Income Model (RIM). The model is called the Residual Income Model (RIM). Major Assumption (known as the Clean Surplus Relationship, or CSR): The change in book value per share is equal to earnings per share minus dividends. Major Assumption (known as the Clean Surplus Relationship, or CSR): The change in book value per share is equal to earnings per share minus dividends.

22. © 2009 McGraw-Hill Ryerson Limited 7-22 Residual Income Model (RIM) Inputs needed: Inputs needed: Earnings per share at time 0, EPS 0 Earnings per share at time 0, EPS 0 Book value per share at time 0, B 0 Book value per share at time 0, B 0 Earnings growth rate, g Earnings growth rate, g Discount rate, k Discount rate, k There are two equivalent formulas for the Residual Income Model: There are two equivalent formulas for the Residual Income Model: BTW, it turns out that the RIM is mathematically the same as the constant perpetual growth model.

23. © 2009 McGraw-Hill Ryerson Limited 7-23 Using the Residual Income Model. National Beverage Corporation (FIZ) National Beverage Corporation (FIZ) It is July 1, 2005—shares are selling in the market for $7.98. It is July 1, 2005—shares are selling in the market for $7.98. Using the RIM: Using the RIM: EPS 0 =$0.47 EPS 0 =$0.47 DIV = 0 DIV = 0 B 0 =$4.271 B 0 =$4.271 g = 0.09 g = 0.09 K =.103 K =.103 What can we say about the market price of FIZ?

24. 7-24 The Growth of FIZ Using the information from the previous slide, what growth rate results in a FIZ price of $7.98? Using the information from the previous slide, what growth rate results in a FIZ price of $7.98?

25. 7-25 Price Ratio Analysis Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income. Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income. Earnings and cash flows that are far from each other may be a signal of poor quality earnings. Earnings and cash flows that are far from each other may be a signal of poor quality earnings. Price-earnings ratio (P/E ratio) Price-earnings ratio (P/E ratio) Current stock price divided by annual earnings per share (EPS) Current stock price divided by annual earnings per share (EPS) Earnings yield Earnings yield Inverse of the P/E ratio: earnings divided by price (E/P) Inverse of the P/E ratio: earnings divided by price (E/P) High-P/E stocks are often referred to as growth stocks, while low- P/E stocks are often referred to as value stocks. High-P/E stocks are often referred to as growth stocks, while low- P/E stocks are often referred to as value stocks. Price-cash flow ratio (P/CF ratio) Price-cash flow ratio (P/CF ratio) Current stock price divided by current cash flow per share Current stock price divided by current cash flow per share In this context, cash flow is usually taken to be net income plus depreciation. In this context, cash flow is usually taken to be net income plus depreciation.

26. © 2009 McGraw-Hill Ryerson Limited 7-26 Price Ratio Analysis Price-sales ratio (P/S ratio) Price-sales ratio (P/S ratio) Current stock price divided by annual sales per share Current stock price divided by annual sales per share A high P/S ratio suggests high sales growth, while a low P/S ratio suggests sluggish sales growth. A high P/S ratio suggests high sales growth, while a low P/S ratio suggests sluggish sales growth. Price-book ratio (P/B ratio) Price-book ratio (P/B ratio) Market value of a company’s common stock divided by its book (accounting) value of equity Market value of a company’s common stock divided by its book (accounting) value of equity A ratio bigger than 1.0 indicates that the firm is creating value for its stockholders. A ratio bigger than 1.0 indicates that the firm is creating value for its stockholders.

27. © 2009 McGraw-Hill Ryerson Limited 7-27 Price/Earnings Analysis, Intel Corp. Intel Corp (INTC) - Earnings (P/E) Analysis Intel Corp (INTC) - Earnings (P/E) Analysis P/EP/CFP/S 5-year average Price ratio37.3019.756.77 Current EPS, CFPS, SPS$1.16$1.94$5.47 EPS, CFPS, SPS growth rate17.5%13.50%10.50% Expected stock price = historical Price ratio  projected EPS,CFPS,SPS $50.84 =37.30  ($1.16  1.175) $43.49 = 19.75  ($1.94  1.135) $40.92 = 6.77  ($5.47  1.105) Mid-2005 stock price =$26.50

28. 7-28 The McGraw-Hill Company Analysis Figure 7.2 The next few slides contain a financial analysis of the McGraw-Hill Company, using data from the Value Line Investment Survey.

29. © 2009 McGraw-Hill Ryerson Limited 7-29 The McGraw-Hill Company Analysis Based on the CAPM, k = 3.1% + (.80  9%) = 10.3% Based on the CAPM, k = 3.1% + (.80  9%) = 10.3% Retention ratio = 1 – $.66/$2.65 =.751 Retention ratio = 1 – $.66/$2.65 =.751 Sustainable g =.751  23% = 17.27% Sustainable g =.751  23% = 17.27% Because g > k, the constant growth rate model cannot be used. (We would get a value of -$11.10 per share) Because g > k, the constant growth rate model cannot be used. (We would get a value of -$11.10 per share)

30. © 2009 McGraw-Hill Ryerson Limited 7-30 The McGraw-Hill Company Analysis (Using the Residual Income Model) Let’s assume that “today” is January 1, 2005, g = 7%, and k = 10.3%. Let’s assume that “today” is January 1, 2005, g = 7%, and k = 10.3%. Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below. Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below. 2005 (time 0) 2006 (VL) 2006 (CSR) Beginning BV per share NA9.459.45 EPS2.252.652.4075 DIV0.660.661.7460 Ending BV per share 9.4511.5010.1115

31. 7-31 The McGraw-Hill Company Analysis Using the CSR assumption: Using the CSR assumption: Using Value Line numbers for EPS 1 =$2.65, B 1 =$11.50 B 0 =$9.45; and using the actual change in book value instead of an estimate of the new book value, (i.e., B 1 -B 0 is = B 0 x k) Using Value Line numbers for EPS 1 =$2.65, B 1 =$11.50 B 0 =$9.45; and using the actual change in book value instead of an estimate of the new book value, (i.e., B 1 -B 0 is = B 0 x k) Stock price at the time = $47.04. What can we say?

32. © 2009 McGraw-Hill Ryerson Limited 7-32 The McGraw-Hill Company Analysis Table 7.4 Quick calculations used: P/CF = P/E  EPS/CFPS P/S = P/E  EPS/SPS

33. © 2009 McGraw-Hill Ryerson Limited 7-33 Useful Internet Sites www.nyssa.org (the New York Society of Security Analysts) www.nyssa.org (the New York Society of Security Analysts) www.nyssa.org www.valueline.com (the home of the Value Line Investment Survey) www.valueline.com (the home of the Value Line Investment Survey) www.valueline.com Websites for the companies analyzed in this chapter: Websites for the companies analyzed in this chapter: www.aep.com www.aep.com www.aep.com www.americanexpress.com www.americanexpress.com www.americanexpress.com www.pepsico.com www.pepsico.com www.pepsico.com www.starbucks.com www.starbucks.com www.starbucks.com www.sears.com www.sears.com www.sears.com www.intel.com www.intel.com www.intel.com www.disney.go.com www.disney.go.com www.disney.go.com www.mcgraw-hill.com www.mcgraw-hill.com www.mcgraw-hill.com