Chapter Common Stock Valuation McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Common Stock Valuation • Our goal in this chapter is to examine the methods commonly used by financial analysts to assess the economic value of common stocks. • These methods are grouped into three categories: – Dividend discount models – Residual Income models – Price ratio models 6-2 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. 6-3 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 basic DDM equation is: D(1) D(2) D(3) D(T) V(0) = + 2 + 3 + L T ()1+ k ()1+ k ()1+ k ()1+ k • In the DDM equation: – V(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%. • In this case, what is the value of the stock today? D(1) D(2) D(3) V(0) = + + ()1+ k ()1+ k 2 ()1+ k 3 $200 $200 $200 V(0) = + + = $515.42 ()1+ 0.08 ()1+ 0.08 2 ()1+ 0.08 3 6-5 The Dividend Discount Model: the Constant Growth Rate Model • Assume that the dividends will grow at a constant growth rate g. The dividend next period (t + 1) is: D()t + 1 = D(t)× (1 + g) So, D(2) = D(1) × (1 + g) = D(0) × (1 + g) × (1 + g) • For constant dividend growth, the DDM formula becomes: T D(0)(1+ g) ⎡ ⎛1+ g ⎞ ⎤ V(0) = ⎢1− ⎜ ⎟ ⎥ if k ≠ g k − g ⎣⎢ ⎝1+ k ⎠ ⎦⎥ V(0) = T ×D(0) if k = g 6-6 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? T D(0)(1+ g) ⎡ ⎛1+ g ⎞ ⎤ V(0) = ⎢1− ⎜ ⎟ ⎥ if k ≠ g k − g ⎣⎢ ⎝1+ k ⎠ ⎦⎥ 20 $10 × ()1.10 ⎡ ⎛1.10 ⎞ ⎤ V()0 = ⎢1− ⎜ ⎟ ⎥ = $243.86 .08 −.10 ⎣⎢ ⎝1.08 ⎠ ⎦⎥ 6-7 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: D()0 × (1+ g) D(1) V()0 = = (Important : g < k) k − g k − g 6-8 Example: Constant Perpetual Growth Model • Think about the electric utility industry. • In mid-2005, 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 DTE. $1.40 × (1.015) V()0 = = $24.50 .073 −.015 Note: the actual mid-2005 stock price of AEP was $38.80. What are the possible explanations for the difference? 6-9 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. 6-10 The Historical Average Growth Rate • Suppose the Kiwi Company paid the following dividends: – 2000: $1.50 2003: $1.80 – 2001: $1.70 2004: $2.00 – 2002: $1.75 2005: $2.20 • The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages. Year: Dividend: Pct. Chg: 2005 $2.20 10.00% 2004 $2.00 11.11% 2003 $1.80 2.86% Grown at 2002 $1.75 2.94% Year: 7.96%: 2001 $1.70 13.33% 2000 $1.50 2000 $1.50 2001 $1.62 2002 $1.75 Arithmetic Average: 8.05% 2003 $1.89 2004 $2.04 Geometric Average: 7.96% 2005 $2.20 6-11 The Sustainable Growth Rate Sustainable Growth Rate = ROE × Retention Ratio = ROE × (1 - Payout Ratio) • Return on Equity (ROE) = Net Income / Equity • Payout Ratio = Proportion of earnings paid out as dividends • Retention Ratio = Proportion of earnings retained for investment 6-12 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? – Sustainable growth rate? • Payout ratio = $1.40 / $2.94 = .476 • So, retention ratio = 1 – .476 = .524 or 52.4% • Therefore, AEP’s sustainable growth rate = .1459 × 52.4% = 7.645% 6-13 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 7.3%? • Recall the actual mid-2005 stock price of AEP was $38.80. $1.40 × (1.07645) V()0 = = −$436.82 << $38.80 .073 −.07645 • 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? 6-14 The Two-Stage Dividend Growth Model • The two-stage dividend growth model assumes that a firm will initially grow at a rate g1 for T years, and thereafter grow at a rate g2 < k during a perpetual second stage of growth. • The Two-Stage Dividend Growth Model formula is: T T D(0)(1+ g ) ⎡ ⎛ 1+ g ⎞ ⎤ ⎛ 1+ g ⎞ D(0)(1+ g ) V(0) = 1 ⎢1− ⎜ 1 ⎟ ⎥ + ⎜ 1 ⎟ 2 k − g1 ⎣⎢ ⎝ 1+ k ⎠ ⎦⎥ ⎝ 1+ k ⎠ k − g2 6-15 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 MissMolly.com has a current dividend of D(0) = $5, which is expected to “shrink” at the rate g1 -- 10% for 5 years, but grow at the rate g2 = 4% forever. • With a discount rate of k = 10%, what is the present value of the stock? 6-16 Using the Two-Stage Dividend Growth Model, II. T T D(0)(1+ g ) ⎡ ⎛1+ g ⎞ ⎤ ⎛1+ g ⎞ D(0)(1+ g ) V(0) = 1 ⎢1− ⎜ 1 ⎟ ⎥ + ⎜ 1 ⎟ 2 k − g 1+ k 1+ k k − g 1 ⎣⎢ ⎝ ⎠ ⎦⎥ ⎝ ⎠ 2 5 5 $5.00(0.90) ⎡ ⎛ 0.90 ⎞ ⎤ ⎛ 0.90 ⎞ $5.00(1+ 0.04) V(0) = ⎢1− ⎜ ⎟ ⎥ + ⎜ ⎟ 0.10 − (−0.10) ⎣⎢ ⎝1+ 0.10 ⎠ ⎦⎥ ⎝1+ 0.10 ⎠ 0.10 − 0.04 = $14.25 + $31.78 = $46.03. • 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. 6-17 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.? 6-18 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: V(3) = [D(3) x (1 + g)] / (k – g) V(3) = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835 6-19 Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, III. • 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: D(1) D(2) D(3) V(3) V(0) = + + + ()1+ k ()1+ k 2 ()1+ k 3 ()1+ k 3 $6.50 $8.45 $10.985 $120.835 V(0) = + + + ()1+ 0.20 ()1+ 0.20 2 ()1+ 0.20 3 ()1+ 0.20 3 = $5.42 + $5.87 + $6.36 + $69.93 = $87.58 million. 6-20 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 Premium: risk premium for an average stock 6-21 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.