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Chapter 7

# Chapter 7 Detailed Note.docx

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Chapter #7 - Stock Valuation 7.1 – Common Stock Valuation  Our goal commonly used by financial analysts to assess the economic value of common stocks.  These methods are grouped into four categories:  Dividend discount models  Residual Income model  Free Cash Flow model  Price ratio models 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. 7.2 – The Dividend Discount Model  the fundamental principle of finance holds that the economic value of a security is properly measured by the sum of its future cash flows, where the cash flows are adjusted for risk and the time value of money.  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: D1 D2 D3 DT P0= 1+k + 2+ 3+ T ( ) (+k) ( 1+k) (1+k)  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 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? P = D1 + D2 + D3 0 (+k) (+k)2(1+k) P0= \$200 + \$2002+ \$2003=\$515.42 (+0.0) (+0.) (1+0.0) Constant Perpetual Growth  Constant Perpetual Growth Model – a version of the dividend discount model in which dividends grow forever at a constant rate, and the growth rate is strictly less than the discount rate  Assuming that the dividends will grow forever at a constant growth rate D0× (+g) D1 P0= k−g =k−g (Important: g< k)  The formula is not valid because the perpetual dividend growth rate greater than a discount rate implies an infinite value since the present value of the dividends keeps getting bigger and bigger 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 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 \$2.12×(1.0) P0= =\$57.66 .0575−.02 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? D (1+g) 1+gT P0= 0 1− ÷  k −g  1+k  20 \$10×(1.)0 1.10  P0= .08−.101−1.08 =\$243.86   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. The Historical Average Growth Rate  Geometric Average Dividend Growth Rate – a dividend growth rate based on a geometric average of historical dividends  Arithmetic Average Dividend Growth Rate – a dividend growth rate based on an arithmetic average of historical dividends  Both have different results – geometric approach is preferred  Suppose the Broadway Joe Company paid the following dividends:  2005: \$1.50 2008: \$1.80  2006: \$1.70 2009: \$2.00  2007: \$1.75 2010: \$2.20  The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages. Year: Dividend:Pct. Chg: 2010 \$2.20 10.00% 2009 \$2.00 11.11% 2008 \$1.80 2.86% Grown at 2007 \$1.75 2.94% Year: 7.96%: 2006 \$1.70 13.33% 2005 \$1.50 2005 \$1.50 2006 \$1.62 2007 \$1.75 Arithmetic Aver8.05% 2008 \$1.89 2009 \$2.04 Geometric Avera7.96% 2010 \$2.20 The Sustainable Growth Rate Sustainable Growth Rate = ROE × Retention Ratio = ROE × (1 - Payout Ratio)  Sustainable Growth Rate – a dividend growth rate that can be sustained by a company’s earnings  Limitation of the constant perpetual growth model is that it should be applied only to companies with stable dividend and earnings growth  A company’s earnings can be paid out as dividends to its shareholders or kept as retained earnings  Retained Earnings – earnings retained within the firm to finance growth  Payout Ratio – proportion of earnings paid out as dividends  Retention ratio – proportion of earnings retained for reinvestment  Return on Equity (ROE) = Net Income / Equity  A common problem with SGR is that they are sensitive to year-to-year fluctuations in earnings  Security analysts routinely adjust SGR estimates to smooth out the effects of earnings variations 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 per- share dividend of \$1.64. What was AEP’s:  Retention rate?  Sustainable growth rate?  Payout ratio = \$1.64 / \$2.90 = .566 or 56.6%  Retention ratio = 1 – .566 = .434 or 43.4%  Therefore, AEP’s sustainable growth rate = .10 ´ .434 = .0434, or 4.34% 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 5.75%? \$1.64×(1.04)4 P0= .0575−.0434=\$121.36  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. 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 DuPont formula separates ROE into three parts (profit margin, asset turnover, equity multiplier) Net Income Net IncomeSales Assets =ROE = × × Equity Sales Assets Equity  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) 7.3 - The Two-Stage Dividend Growth Model  The two-stage dividend growth model - assumes that a firm will initially grow at a rate g for T years, and 1 thereafter, it will grow at a 2ate g < k during a perpetual second stage of growth.  The Two-Stage Dividend Growth Model formula is: T T D0(1+g1) 1+g 1 1+g1 D 01+g 2 P0= 1− ÷+  ÷ k−g1  1+k  1+k  k−g 2 Using the Two-Stage Dividend Growth Model  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.  Suppose MissMolly.com has a current dividend of D0= \$5, which is expected to shrink at the rate1 g = 10%, for 5 years but grow at the ra2e, g = 4%, forever.  With a discount rate of k = 10%, what is the present value of the stock? D (1+g ) 1+g  1+g  D (1+g ) P0= 0 1 − 1÷+ 1÷ 0 2 k−g1  1+k  1+k  k−g2  5 5 P0= \$5.00(0.9− 0.90 ÷+ 0.90÷ \$5.00(1+0.04) 0.10−(−0.1) 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. Example: 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 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.? First, calculate the total dividends over the “supernormal” growth period: Yea Total Dividend: (in r \$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: P3= [D3x (1 + g)] / (k – g) P3= [\$10.985 x 1.10] / (0.20 – 0.10) = \$120.835  To determine t
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