1 6 Common Stock Valuation

6-2 Common Stock Valuation Fundamental analysis: Studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock Basic Idea: Find undervalued (“cheap”) stocks to buy Find overvalued (“rich”) stocks to sell or short Three categories of methods: 1.Dividend Discount Models 2.Residual Income Models 3.Price Ratio Models

6-3 The Dividend Discount Model Dividend Discount Model (DDM): Estimates the value of a share of stock by discounting all expected future dividend payments. The basic DDM equation: In the DDM equation: P 0 = the present value of all future dividends D t = the dividend to be paid t years from now k = the appropriate risk-adjusted discount rate

6-4 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%. What is the value of the stock today?

6-5 The Constant Growth Rate Model Assume that the dividends will grow at a constant growth rate g. The dividend next period (t + 1) is: For constant dividend growth, the DDM formula becomes:

6-6 The Constant Growth Rate Model Current dividend = $10 = D(0) Dividend growth rate = 10% = g There will be 20 yearly dividends= T Appropriate discount rate = 8%. = k What is the value of the stock, based on the constant growth rate model?

6-7 The Constant Perpetual Growth Model: “The Gordon Growth Model” Assume dividends will grow forever at a constant growth rate g. For constant perpetual dividend growth, the DDM formula becomes:

6-8 Example: Constant Perpetual Growth Model In 2007, the dividend paid by DTE Energy, Inc. (DTE) was $2.12. Using D 0 =$2.12, k = 6.7%, and g = 2%, calculate an estimated value for DTE: Note: the actual mid-2007 stock price of DTE was $47.81.

6-9 The Dividend Discount Model: Estimating the Growth Rate Three possible sources for g: The company’s historical average growth rate An industry median or average growth rate The sustainable growth rate

6-10 The Historical Average Growth Rate Suppose the Broadway Joe Company paid the following dividends: 2002: $ : $ : $ : $ : $ : $2.20 The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

6-11 Historical Growth Rates Example YearEOY Dividend 2002$ $ $ $ $ $2.20

6-12 Geometric Average Dividend Growth Rate YearEOY Dividend 2002$ $ $ $ $ $2.20 Geometric Average Dividend Growth Rate = 7.96%

6-13 Arithmetic Average Dividend Growth Rate YearEOY Dividend Yearly Growth Rate 2002$ $1.70($1.70-$1.50)/$1.50 =13.33% 2004$1.75($1.75-$1.70)/$1.70 =2.94% 2005$1.80($1.80-$1.75)/$1.75 =2.86% 2006$2.00($2.00-$1.80)/$1.80 =11.11% 2007$2.20($2.20-$2.00)/$2.00 =10% Sum40.24 Arithmetic Average Dividend Growth Rate = 40.24/5 = 8.048%

6-14 The Sustainable Growth Rate Return on Equity (ROE) = Net Income / Equity Payout Ratio = % of earnings paid out as dividends Retention Ratio = % of earnings retained for investment

6-15 Calculating and Using the Sustainable Growth Rate American Electric Power (AEP) in 2007: ROE =10.17% Projected earnings per share = $2.25 Dividend per-share = $1.56 What was AEP’s: Retention rate? Sustainable growth rate? Payout ratio = $1.56 / $2.25 =.693 or 69.3% Retention ratio = 1 –.693 =.307 or 30.7% AEP’s sustainable growth rate =  = = 3.122%

6-16 Calculating and Using the Sustainable Growth Rate What is the value of AEP stock, using the perpetual growth model, and a discount rate of 6.7%? The actual mid-2007 stock price of AEP was $ Using the sustainable growth rate to value the stock gives a reasonably accurate estimate.

6-17 The Two-Stage Dividend Growth Model Assumes a firm will: Grow at a rate g 1 for T years (g 1 may be > k) Then will grow at a rate g 2 < k during a perpetual second stage of growth The Two-Stage Dividend Growth Model formula:

6-18 Using the Two-Stage Dividend Growth Model First Component = Present value of the first T dividends Second Component =Present value of all subsequent dividends First Component Second Component

6-19 Using the Two-Stage Dividend Growth Model MissMolly.com: Current dividend, D 0 = $5, Dividend expected to “shrink” at the rate g 1 = -10% for 5 years (T) But grow at the rate g 2 = 4% forever Discount rate, k = 10% What is the present value of the stock?

6-20 Using the Two-Stage Dividend Growth Model $46.03 =$14.25 present value of the first five dividends plus $31.78 present value of all subsequent dividends

6-21 Using the DDM to Value a Firm Experiencing “Supernormal” Growth Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year. You believe 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.?

6-22 Using the DDM to Value a Firm Experiencing “Supernormal” Growth First, calculate the total dividends over the “supernormal” growth period: YearTotal 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

6-23 Using the DDM to Value a Firm Experiencing “Supernormal” Growth 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 = [$ x 1.10] / (0.20 – 0.10) = $

6-24 Using the DDM to Value a Firm Experiencing “Supernormal” Growth The value of the firm today = the present value of $ plus the present value of the dividends paid in the first 3 years:

6-25 Nonconstant growth followed by constant growth k=20% = P 0 g 1 = 30% g 2 = 10% D 0 = P 3 = $ – 0.10 = $

6-26 Discount Rates for Dividend Discount Models Estimate discount rate using the Capital Asset Pricing Model (CAPM ) Discount rate = time value of money + risk premium Time value of money = U.S. T-bill rate Risk Premium = (stock beta x stock market risk premium) T-bill rateReturn on 90-day U.S. T-bills Stock BetaRisk relative to an average stock Stock Market Risk Premium Risk premium for an average stock

6-27 Observations on Dividend Discount Models Constant Perpetual Growth Model: +Simple to compute -Not usable for firms that do not pay dividends -Not usable when g > k -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

6-28 Observations on Dividend Discount Models Two-Stage Dividend Growth Model: +More realistic; accounts for two stages of growth +Usable when g > k in the first stage -Not usable for firms that do not pay dividends -Sensitive to the choice of g and k -k and g may be difficult to estimate accurately

6-29 Residual Income Model (RIM) Value firms that do NOT pay dividends Major Assumption: The Clean Surplus Relationship, or CSR  The change in book value per share is equal to earnings per share minus dividends Mathematically equivalent to the Constant Perpetual Growth Model

6-30 Residual Income Model (RIM) 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 Two equivalent RIM formula :

6-31 The Residual Income Model Where: EPS 1 = Earnings per share at t=0 times (1+g) B 0 = Book value per share at t=0 g = assumed perpetual growth rate k = required return

6-32 Using the Residual Income Model Superior Offshore International, Inc. (DEEP) July 1, 2007—shares selling for $10.94 Using the RIM: EPS 0 =$1.20 DIV = 0 B 0 =$5.886 g = 0.09 k =.13

6-33 The Growth of DEEP Using the information from the previous slide, what growth rate results in a DEEP price of $10.94?

6-34 Price Ratio Analysis Price-earnings ratio (P/E ratio) Price-cash flow ratio (P/CF ratio) Price-sales ratio (P/S ratio) Price-book ratio (P/B ratio)

6-35 Price-Earnings Ratio (P/E) Most popular price ratio Inverse = Earnings Yield (E/P) High P/E Ratio stocks = “Growth Stocks” Expensive relative to earnings Low P/E Ratio stocks = “Value Stocks” Cheap relative to earnings Where: P = Current stock price EPS = Annual earnings per share

6-36 Price-Cash Flow Ratio (P/CF) Where: P = Current stock price CFPS = Current cash flow per share CF = NI + Depreciation P/CF can be more informative than P/E If EPS >> CFPS Poor quality earnings

6-37 Price-Sales Ratio (P/S) Focuses on firm’s ability to generate sales growth Cannot be compared in isolation Industry specific comparisons Where: P = Current stock price SPS = Annual sales per share

6-38 Price-Book Ratio (P/B) Also “Market to Book” P/B  Historical cost vs. Current Market Value > 1.0 = firm has created value < 1.0 = firm worth less than it cost Where: P = Current stock price BVPS = Current book value per share

6-39 Price/Earnings Analysis: Intel Corp. Intel Corp (INTC) - Earnings (P/E) Analysis 5-year average P/E ratio27.30 Current EPS$0.86 EPS growth rate8.5% Expected stock price: = Historical P/E ratio  projected EPS $25.47 =  ($0.86  1.085) Mid-2007 stock price = $24.27

6-40 Price/Cash Flow Analysis: Intel Corp. Intel Corp (INTC) - Cash Flow (P/CF) Analysis 5-year average P/CF ratio14.04 Current CFPS$1.68 CFPS growth rate7.5% Expected stock price: = Historical P/CF ratio  projected CFPS $25.36 =  ($1.68  1.075) Mid-2007 stock price = $24.27

6-41 Price/Sales Analysis, Intel Corp. Intel Corp (INTC) - Sales (P/S) Analysis 5-year average P/S ratio 4.51 Current SPS$6.14 SPS growth rate 7% Expected stock price: = Historical P/S ratio x projected SPS $29.63 = 4.51  ($6.14  1.07) Mid-2007 stock price = $24.27

6-42 Intel Corp: Recap

6-43 The McGraw-Hill Company Analysis

6-44 The McGraw-Hill Company Analysis

6-45 The McGraw-Hill Company Analysis Based on the CAPM: k = 3.1% + (.80  9%) = 10.3% Retention ratio = 1 – $.66/$2.65 =.751 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)

6-46 The McGraw-Hill Company Analysis ( Using the Residual Income Model, I) Assume “today” is January 1, 2008, g = 7.5%, and k = 12.6%. Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below. We use column one and our growth assumption for column three (CSR) of the table below. = 3.05 x = 6.50 x “Plug” = – ( – 6.50)

6-47 The McGraw-Hill Company Analysis ( Using the Residual Income Model, II) Using the CSR assumption: Using Value Line numbers: EPS 1 =$3.45 B 1 =$9.25 B 0 =$6.50; And using the actual change in book value instead of an estimate of the new book value Stock price at the time = $ What can we say?

6-48 The McGraw-Hill Company Analysis, IV

6-49 Useful Internet Sites (the New York Society of Security Analysts) (American Association of Individual Investors) (Economic Value Added) (the home of the Value Line Investment Survey) Websites for some companies analyzed in this chapter:

50 6 Common Stock Valuation