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FIN 501 (31)
Chapter 7

# Chapter 7.docx

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School
Department
Finance
Course
FIN 501
Professor
Edward Blinder
Semester
Summer

Description
Chapter 7: Common Stock Valuation  7.1 Security Analysis:  Fundamental Analysis: examination of a firm’s accounting statements and other financial and economic information to assess the economic value of a company’s stock  Numbers such as a company’s earnings per share, cash flow, book equity value, and sales are often called fundamentals because they describe, on a basic level, a specific firm’s operations and profits (or lack of profits)  7.2 The Dividend Discount Model:  A 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  Dividend Discount Model (DDM): method of estimating the value of a share of stock as the present value of all expected future dividend payments (where dividends are adjusted for risk and the time value of money)  For example, suppose a company pays a dividend at the end of the year. - Let D(t) denote a dividend to be paid t years from now - Let V(0) represent the present value of the future dividend steam - Let k denote the appropriate risk-adjusted discount rate - Using the dividend discount mode, the present value of a share of this company’s stock is measured as this sum of discounted future dividends: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) - Assumes that the last dividend is paid T years from now, where the value of T depends on the specific valuation problem considered  Constant Dividend Growth Rate Model: a version of the dividend discount model that assumes a constant dividend growth rate - Letting a constant growth rate be denoted by g, then successive annual dividends are stated as: ( ) ( )( ) - If the number of dividends to be paid is large, calculating the present value of each dividend separately is tedious and possibly prone to error - Fortunately, if the growth rate is constant, some simplified expressions are available to handle certain special cases - The present value of the next T dividends, that is, D(1) through D(T), can be calculated using this: ( ) ( )( ) [ ( ( )) ] ( ) - Requires that the growth rate and the discount rate does not equal to each other ( ), since this requires division to be zero - When the growth rate is equal to the discount rate, that is, k=g, the effects of growth and discounting cancel exactly, and the present value V(0) is simply the number of payments T times the current dividend D(0): ( ) ( )  Constant Perpetual Growth: - Where a firm will pay dividends that grow at the constant rate g forever - 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 - Constant perpetual growth model: ( )( ) ( ) ( ) - Since D(0)(1+g)= D(1), we could also write the constant perpetual growth model as: ( ) ( ) ( )  Applications of the Constant Perpetual Growth Model: - The constant perpetual growth model can be usefully applied only to companies with a history of relatively stable earnings and dividend growth expected to continue into the distant future  Historical Growth Rates: - In the constant growth model, a company’s historical average dividend growth rate is frequently taken as an estimate of future’s dividend growth - There are two ways to calculate a historical growth rate yourself: 1. Geometric Average Dividend Growth Rate: a dividend growth rate based on a geometric average of historical dividends ( ) ⁄ [ ] ( ) D(0) is the earliest dividend and D(N) is the latest dividend to be used. 2. Arithmetic Average Dividend Growth Rate: a dividend growth rate based on an arithmetic average of historical dividends o We first calculate each year’s dividend growth rate separately and then calculate an arithmetic average of these annual growth rates o Example on page 195  The Sustainable Growth Rate: - It is necessary to come up with an estimate of g, the growth rate in dividends - In our previous discussions, we described two ways to do this: (1) using the company’s historic average growth rate or (2) using an industry median or average growth rate - We now describe a third way, know as the sustainable growth rate: a dividend growth rate that can be sustained by a company’s 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 - If we let D stand for dividends and EPS stand for earnings per share, then the payout ratio is: - The Retention Ratio: ( ) - Return on equity is commonly computed using an accounting-based performance measure and is calculated as a firm’s net income dividend by stockholders’ equity: ( ) - Common problems with sustainable growth rates is that they are sensitive to year-to-year fluctuations in earnings - Security analysts routinely adjust sustainable growth rate estimates to smooth out the effects of earning variations  7.3 The Two-Stage Dividend Growth Model:  Two-stage dividend growth model: dividend model that assumes a firm will temporarily grow at a rate different from its long-term growth rate  Assumes that a firm will initially grow at a rate during a first stage of growth lasting T years and thereafter grow at a rate during a perpetual second stage of growth  The present value formula for the two-stage dividend growth model is stated as follows: ( )( ) ( )( ) ( ) [ ( ) ] ( ) ( ) - The first term on the right-hand side measures the present value of the first T dividends and is the same expression we used earlier for the constant growth model - The second term then measures the present value of all subsequent dividends  The two-stage formula requires that the second-stage growth rate be strictly less than the discount rate, that is,  However, the first- stage growth rate can be greater, smaller, or equal to the discount rate  In the special case where the first-stage growth rate is equal to the discount rate, that is, , the two- stage formula reduces to this form: ( )( ) ( ) ( )  The last case we consider is non-constant growth in the first stage  Using the dividend growth model, we can say that the price in 4 years will be: ( ) ( ) ( ) ( ) ( ) ( ) ( )  We can now calculate the total value of the stock as the present value of the first three dividends plus the present value of the price at Time 3, V(3): total value of the stock today
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