Chapter 6 Mc GrawHillIrwin Common Stock Valuation Copyright

Chapter 6 Mc. Graw-Hill/Irwin Common Stock Valuation Copyright © 2012 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Security Analysis: Be Careful Out There • 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. 6 -2

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 basic DDM equation is: • In the DDM equation: – P 0 = the present value of all future dividends – Dt = the dividend to be paid t years from now – k = the appropriate risk-adjusted discount rate 6 -3

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%. • In this case, what is the value of the stock today? 6 -4

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? 6 -5

The Dividend Discount Model: the Constant Perpetual Growth Model • Assuming that the dividends will grow forever at a constant growth rate g. • For constant perpetual dividend growth, the DDM formula becomes: 6 -6

Example: Constant Perpetual Growth Model • Think about the electric utility industry. • In 2009, the dividend paid by the utility company, DTE Energy Co. (DTE), was $2. 12. • Using D 0 =$2. 12, k = 5. 75%, and g = 2%, calculate an estimated value for DTE. Note: the actual mid-2009 stock price of DTE was $40. 29. What are the possible explanations for the difference? 6 -7

The Dividend Discount Model: Estimating the Growth Rate • The growth rate in dividends (g) can be estimated in a number of ways: – Using the company’s historical average growth rate. – Using an industry median or average growth rate. – Using the sustainable growth rate. 6 -8

The Historical Average Growth Rate • Suppose the Broadway Joe Company paid the following dividends: – 2005: $1. 50 – 2006: $1. 70 – 2007: $1. 75 • 2008: $1. 80 2009: $2. 00 2010: $2. 20 The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages. 6 -9

The Sustainable Growth Rate • Return on Equity (ROE) = Net Income / Equity • Payout Ratio = Proportion of earnings paid out as dividends • Retention Ratio = Proportion of earnings retained for investment 6 -10

Example: Calculating and Using the Sustainable Growth Rate • In 2009, American Electric Power (AEP) had an ROE of 10%, projected earnings per share of $2. 90, and a pershare dividend of $1. 64. What was AEP’s: – Retention rate? – Sustainable growth rate? • Payout ratio = $1. 64 / $2. 90 =. 566 or 56. 6% • So, retention ratio = 1 –. 566 =. 434 or 43. 4% • Therefore, AEP’s sustainable growth rate =. 10 . 434 =. 0434, or 4. 34% 6 -11

Example: Calculating and Using the Sustainable Growth Rate, Cont. • What is the value of AEP stock using the perpetual growth model and a discount rate of 5. 75%? • The actual late-2009 stock price of AEP was $31. 83. • In this case, using the sustainable growth rate to value the stock gives a reasonably poor estimate. • What can we say about g and k in this example? 6 -12

Analyzing ROE • To estimate a sustainable growth rate, you need the (relatively stable) dividend payout ratio and ROE. • Changes in sustainable growth rate likely stem from changes in ROE. • The Du. Pont formula separates ROE into three parts (profit margin, asset turnover, equity multiplier) • Managers can increase the sustainable growth rate by: – – Decreasing the dividend payout ratio Increasing profitability (Net Income / Sales) Increasing asset efficiency (Sales / Assets) Increasing debt (Assets / Equity) 6 -13

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, it will grow at a rate g 2 < k during a perpetual second stage of growth. • The Two-Stage Dividend Growth Model formula is: 6 -14

Using the Two-Stage Dividend Growth Model, I. • 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 2 is the present value of all subsequent dividends. • So, suppose Miss. Molly. com has a current dividend of 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? 6 -15

Using the Two-Stage Dividend Growth Model, II. • 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. 6 -16

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, I. • 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. ? 6 -17

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, II. • First, calculate the total dividends over the “supernormal” growth period: 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 • Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as: P 3 = [D 3 x (1 + g)] / (k – g) P 3 = [$10. 985 x 1. 10] / (0. 20 – 0. 10) = $120. 835 6 -18

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, III. • 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: If there are 20 million shares outstanding, the price per share is $4. 38. 6 -19

The H-Model, I. • For Chain Reaction, Inc. , we assumed a supernormal growth rate of 30 percent per year for three years, and then growth at a perpetual 10 percent. • The growth rate is more likely to start at a high level and then fall over time until reaching its perpetual level. • Many possible ways to assume how the growth rate declines • A popular way is the H-model: which assumes a linear growth rate decline 6 -20

The H-Model, II. • Let’s revisit Chain Reaction, Inc. – Suppose the growth rate begins at 30% and reaches 10% in year 4 and beyond. – Using the H-model, we would assume that the company’s growth rate would decline by 20% from the end of year 1 to the beginning of year 4. • If we assume a linear decline: – the growth rate falls by 6. 67% per year (20%/3 years). – Growth estimates would be: 30%, 23. 33%, 16. 66%, and 10% • Using these growth estimates, you will find that the firm value is $75. 93 million, or $3. 80 per share. • The value is lower than before because of the lower growth rates in years 2 and 3. 6 -21

Discount Rates for Dividend Discount Models • 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. • However, we can estimate the discount rate for a stock using this formula: Discount rate = time value of money + risk premium = U. S. T-bill Rate + (Stock Beta x Stock Market Risk Premium) T-bill Rate: return on 90 -day U. S. T-bills Stock Beta: risk relative to an average stock Stock Market Risk risk premium for an average stock Premium: 6 -22

Observations on Dividend Discount Models, I. 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. 6 -23

Observations on Dividend Discount Models, II. 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. 6 -24

Residual Income Model (RIM), I. • We have valued only companies that pay dividends. – But, there are many companies that do not pay dividends. – What about them? – It turns out that there is an elegant way to value these companies, too. • 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. 6 -25

Residual Income Model (RIM), II. • Inputs needed: – – Earnings per share at time 0, EPS 0 Book value per share at time 0, B 0 Earnings growth rate, g Discount rate, k • 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. 6 -26

Using the Residual Income Model • Duckwall—Alco Stores, Inc. (DUCK) • It is July 1, 2010—shares are selling in the market for $10. 94. • Using the RIM: – – – EPS 0 = $1. 20 DIV = 0 B 0 = $5. 886 g = 0. 09 k =. 13 • What can we say about the market price of DUCK? 6 -27

The Growth of DUCK • Using the information from the previous slide, what growth rate results in a DUCK price of $10. 94? 6 -28

Free Cash Flow, I. • We can value companies that do not pay dividends using the residual income model. • Note: We assume positive earnings when we use the residual income model. • But, there are companies that do not pay dividends and have negative earnings. • Negative earnings = little value? – We calculate earnings based on accounting rules and tax codes. – It is possible that a company has: • negative earnings • positive cash flows • a positive value. 6 -29

Free Cash Flow, II. • Depreciation—the key to understand how a company can have negative earnings and positive cash flows • Depreciation reduces earnings because it is counted as an expense (more expenses = lower taxes paid). • Most stock analysts, however, use a relatively simple formula to calculate Free Cash Flow, FCF: FCF = Net Income + Depreciation – Capital Spending • We can see that it is possible for: Net Income < 0 and FCF > 0 • Depreciation and Capital Spending matter in FCF. 6 -30

DDMs Versus FCF • The DDMs calculate a value of the equity only. – DDMs use dividends, a cash flow only to equity holders – DDMs use the CAPM to estimate required return – DDMs use an equity beta to account for risk • Using the FCF model, we calculate a value for the firm. – Free cash flow can be paid to debt holders and to stockholders. – We can still calculate the value of equity using FCF • Calculate the value of the entire firm • Subtract out the value of debt – We need a beta for assets, not the equity, to account for risk 6 -31

Asset Betas • Asset betas measure the risk of the company’s industry. – Firms in an industry should have about the same asset betas. – Their equity betas, however, could be quite different. • Investors can increase portfolio risk by using margin (i. e. , borrowing money to buy stock). • A business can increase risk by using debt. • So, to value the company, we must “convert” reported equity betas into asset betas by adjusting for leverage. • The following conversion formula is widely used: • What happens when a firm has no debt? tax rate. 6 -32

The FCF Approach, Example • Inputs – An estimate of FCF: • Net Income • Depreciation • Capital Expenditures – – – The growth rate of FCF The proper discount rate Tax rate Debt/Equity ratio Equity beta • Calculate value using a “DDM” formula • “DDM” because we are using FCF, not dividends. 6 -33

Valuing Landon Air: A New Airline • An estimate of FCF: – – – – Net Income: $25 million Depreciation: $10 million Capital Expenditures: $3 million Growth rate of FCF: 3% Tax rate: 35% Debt/Equity ratio: . 40 Equity beta: 1. 2 Assume: No dividends Risk-free rate = 4% Market risk premium = 7% • Asset Beta: 1. 2 = BAsset x [1+. 4 x (1 -. 35)] 1. 2 = BAsset x 1. 26 BAsset = 0. 95 • The proper discount rate: k = 4. 00 + (7. 00 × 0. 95) = 10. 65% 6 -34

Price Ratio Analysis, I. • Price-earnings ratio (P/E ratio) – Current stock price divided by annual earnings per share (EPS) • Earnings yield – 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. 6 -35

Price Ratio Analysis, II. • Price-cash flow ratio (P/CF ratio) – Current stock price divided by current cash flow per share – In this context, cash flow is usually taken to be net income plus depreciation. • 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. 6 -36

Price Ratio Analysis, III. • Price-sales ratio (P/S ratio) – 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. • Price-book ratio (P/B ratio) – 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. 6 -37

Price/Earnings Analysis, Intel Corp (INTC) - Earnings (P/E) Analysis 5 -year average P/E ratio Current EPS growth rate 20. 96 $. 92 8. 5% Expected stock price = historical P/E ratio projected EPS $20. 92 = 20. 96 ($. 92 1. 085) Late-2009 stock price = $19. 40 6 -38

Price/Cash Flow Analysis, Intel Corp (INTC) - Cash Flow (P/CF) Analysis 5 -year average P/CF ratio Current CFPS growth rate 10. 85 $1. 74 7. 5% Expected stock price = historical P/CF ratio projected CFPS $20. 29 = 10. 85 ($1. 74 1. 075) Late-2009 stock price = $19. 40 6 -39

Price/Sales Analysis, Intel Corp (INTC) - Sales (P/S) Analysis 5 -year average P/S ratio Current SPS growth rate 3. 14 $6. 76 7% Expected stock price = historical P/S ratio projected SPS $22. 71 = 3. 14 ($6. 76 1. 07) Late-2009 stock price = $19. 40 6 -40

The Mc. Graw-Hill Company Analysis, IV. 6 -41

Useful Internet Sites • • • www. nyssa. org (The New York Society of Security Analysts) www. aaii. com (The American Association of Individual Investors) www. valueline. com (the home of the Value Line Investment Survey) 6 -42