# Copyright 2014 by Diane Scott Docking 1 Stock Valuation Video: How the Market Really works.

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Copyright 2014 by Diane Scott Docking 1 Stock Valuation Video: How the Market Really works

Copyright 2014 by Diane Scott Docking 2 Learning Objectives Understand how to calculate stock returns Understand how stock prices (values) are determined when  dividends grow at a constant rate  dividend growth is nonconstant Identify factors that affect stock prices

Copyright 2014 by Diane Scott Docking 3 Stock Valuation The price of a share of stock is the total value of the company divided by the number of shares outstanding Stock price by itself doesn’t represent firm value  Number of shares outstanding Stock price is determined by the demand and supply for the shares Investors try to value stocks and purchase those that are perceived to be undervalued by the market New information creates re-evaluation

4 Copyright 2014 by Diane Scott Docking Stock Returns The returns on a stock over one period (R t ) can be divided into capital gains and dividend returns: P t = stock price at time t D t = dividends paid over time t – 1 to t (P t – P t – 1 ) / P t – 1 = capital gain over time t – 1 to t D t / P t – 1 = return from dividends paid over time t – 1 to t The returns on a stock over one period (R t ) can be divided into capital gains and dividend returns: P t = stock price at time t D t = dividends paid over time t – 1 to t (P t – P t – 1 ) / P t – 1 = capital gain over time t – 1 to t D t / P t – 1 = return from dividends paid over time t – 1 to t Dividend Yield Capital Gains Rate

Copyright 2014 by Diane Scott Docking 5 Example: Determining Rate of Return Union Corporation currently pays an annual dividend of \$1.00. The current stock price is \$50. At the end of 1 year, the stock price is \$55. What is Union Co.’s annual rate of return on its stock?

Copyright 2014 by Diane Scott Docking 6 Example: Stock Return Calculation Jake buys 10 shares of AVU stock at \$55.10 and sells it 1 year later for \$56.30 after collecting a \$0.30 dividend per share. 1. What is Jake’s pre-tax holding period return?

Copyright 2014 by Diane Scott Docking 7 Example: Stock Return Calculation (cont.) 2. If the dividend is taxed at the ordinary rate = 28% and the capital gains at 15%, what is Jake’s after tax holding period return?

Copyright 2014 by Diane Scott Docking 8 Example: 2 year Stock Return Calculation Jake buys 10 shares of AVU stock at \$55.10 and sells it 2 years later for \$56.30 after collecting a \$0.30 dividend per share per year. 1. What is Jake’s pre-tax holding period return? CF 0 = - \$55.10 CF 1 = \$.30 CF 2 = \$.30 + \$56.30 = \$56.60 Therefore IRR = 1.6246% OR PV = -\$55.10 n = 2 PMT =.30 FV = \$56.30 YTM = 1.6246%

Copyright 2014 by Diane Scott Docking 9 Stock Valuation Methods The Dividend-Discount Model  Estimating Dividends in the Dividend-Discount Model Total Payout and Free Cash Flow Valuation Models Valuation Based on Comparable Firms Valuation Using P/E Ratios Economic Value Added (EVA) Approach Information, Competition, and Stock Prices

Copyright 2014 by Diane Scott Docking 10 Dividend-Discount Model The Dividend-Discount Model  Zero or No growth in dividends, but unlimited life  Zero growth in dividends, but limited life  Constant growth in dividends  Nonconstant growth in dividends

Copyright 2014 by Diane Scott Docking 11 Dividend-Discount Model The price of a stock reflects the present value of the stock's future dividends D 0 = dividend in period 0 expected to remain constant forever r s = discount rate or required rate of return on the stock Zero Growth in Dividends Perpetuity Dividend Model

Copyright 2014 by Diane Scott Docking 12 Example: Zero Dividend Growth Model Joan’s Fabric Corp. pays an annual dividend of \$5.00 per share on its Preferred stock. This dividend is expected to remain constant into the future. The expected rate of return on the stock is 6.50%. What is the current market price of the stock?

Copyright 2014 by Diane Scott Docking 13 Dividend-Discount Model The price of a stock reflects the present value of the stock's future dividends t = period D t = dividend in period t r s = discount rate or required rate of return on the stock Zero Growth in Dividends Non-Perpetuity Dividend Model

Copyright 2014 by Diane Scott Docking 14 Example: 1-period Dividend Growth Model Mary expects Longs Drug Stores to pay an annual dividend of \$.56 per share in the coming year and to trade \$45.50 per share at the end of the year. Investments with equivalent risk to Longs’ stock have an expected return of 6.80% What is the most Mary would pay today for Longs’ stock? What dividend yield and capital gain rate would Mary expect at this price?

Copyright 2014 by Diane Scott Docking 15 Example: 1-period Dividend Growth Model What is the most Mary would pay today for Longs’ stock? What dividend yield and capital gain rate would Mary expect at this price? At this price, Longs’ dividend yield is Div 1 /P 0 = 0.56/43.13 = 1.30%. The expected capital gain is \$45.50 - \$43.13 = \$2.37 per share, for a capital gain rate of 2.37/43.13 = 5.50%. Total return is 1.30% + 5.50% = 6.80%

Copyright 2014 by Diane Scott Docking 16 Example: Multiyear Dividend Growth Model Suppose Mary plans to hold the stock for two years. She expects the price to be \$45.50 at the end of two years. Mary would receive dividends in both year 1 and year 2 before selling the stock, as shown in the following timeline: What is the most Mary would pay today for Longs’ stock?

Copyright 2014 by Diane Scott Docking 17 Example: Multi-year Dividend Growth Model What is the most Mary would pay today for Longs’ stock?

Copyright 2014 by Diane Scott Docking 18 Dividend-Discount Model The price of a stock reflects the present value of the stock's future dividends t = period D t = dividend in period t r s = discount rate g = the nominal growth rate of earnings over time. Constant Dividend Growth Model

Copyright 2014 by Diane Scott Docking 19 Example 1: Constant Dividend Growth Model Consolidated Edison, Inc. (Con Edison), is a regulated utility company that services the New York City area. Suppose Con Edison just paid \$2.30 per share in dividends. Its equity cost of capital is 7% and dividends are expected to grow by 2% per year in the future. What is the current value of Con Edison’s stock?

Copyright 2014 by Diane Scott Docking 20 Example 1: Constant Dividend Growth Model What is the current value of Con Edison’s stock?

Copyright 2014 by Diane Scott Docking 21 Example 2: Constant Dividend Growth Model Suppose Johnson & Johnson plans to pay \$2.85 per share in dividends in the coming year. Its equity cost of capital is 9% and dividends are expected to grow by 3% per year in the future. What is the estimated value of Johnson & Johnson’s stock?

Copyright 2014 by Diane Scott Docking 22 Example 1: Constant Dividend Growth Model What is the current value of Johnson & Johnson’s stock?

Copyright 2014 by Diane Scott Docking 23 Dividend-Discount Model Firms experience different growth rates: supernormal growth ( g s ) and normal growth ( g ). A 4-step process to calculate current price 1. Find the PV ( P 0 ’ ) of the dividends during the period of supernormal growth ( g s ). 2. Find the price of the stock at the end of the supernormal growth period ( n ), when normal growth ( g ) begins using the constant dividends growth model. NonConstant Dividend Growth Model

Copyright 2014 by Diane Scott Docking 24 Dividend-Discount Model Firms experience different growth rates: supernormal growth ( g s ) and normal growth ( g ). A 4-step process to calculate current price 1. Find the PV ( P 0 ’ ) of the dividends during the period of supernormal growth ( g s ). 2. Find the price of the stock at the end of the supernormal growth period ( n ), when normal growth ( g ) begins using the constant dividends growth model. NonConstant Dividend Growth Model

Copyright 2014 by Diane Scott Docking 25 Dividend-Discount Model A 4-step process to calculate current price 3. Discount this price ( P n ) back to time 0 ( P 0 ” ). 4. Add the two components of the stock price together. NonConstant Dividend Growth Model

Copyright 2014 by Diane Scott Docking 26 Example: Valuing a Firm with Two Different Growth Rates Up and Away Corp. is expected to experience supernormal growth of 30% per year for the next 3 years. After that, the growth rate is expected to drop to 5% for the remainder of the firm’s life. Up and Away’s dividend at the end of last year of \$1.60 per share. The firm’s cost of capital is 20%. What is the value of the firm’s stock?

Copyright 2014 by Diane Scott Docking 27 Example: Valuing a Firm with Two Different Growth Rates Given: D 0 = \$1.60; r s = 20%; g s = 30%; g = 5%; n = 3 years 1. Find the PV ( P 0 ’ ) of the dividends during the period of supernormal growth ( g s ). tDividend÷ (1.20) t =PV 1\$1.60(1.30) 1 = \$2.0800÷ (1.20) 1 =\$1.7333 2\$1.60(1.30) 2 = \$2.7040÷ (1.20) 2 =\$1.8778 3\$1.60(1.30) 3 = \$3.5152÷ (1.20) 3 =\$2.0341 ∑ =\$5.6452= \$5.65 =

Copyright 2014 by Diane Scott Docking 28 Example: Valuing a Firm with Two Different Growth Rates 2. Find the price of the stock at the end of the supernormal growth period ( n ), when normal growth ( g ) begins using the constant dividends growth model.

Copyright 2014 by Diane Scott Docking 29 Example: Valuing a Firm with Two Different Growth Rates 3. Discount this price ( P n ) back to time 0 ( P 0 ” ). 4. Add the two components of the stock price together.

Copyright 2014 by Diane Scott Docking 30 Example: Comparing Dividend-Growth Models Jake is considering buying Polo stock which is currently priced at \$62 per share. Polo paid a dividend at the end of last year of \$2.50 per share. Jake’s required rate of return is 5%. Should Jake buy the stock, assuming: 1. The dividend is expected to continue into the foreseeable future? 2. The dividend is expected to grow at a constant rate of 1% into the foreseeable future? 3. The dividend is expected to grow at a rate of 3% for the next 4 years and then at a rate of 1% thereafter?

Copyright 2014 by Diane Scott Docking 31 Example: Comparing Dividend-Growth Models 1. The dividend is expected to continue into the foreseeable future? Do NOT Buy. Priced too high.

Copyright 2014 by Diane Scott Docking 32 Example: Comparing Dividend-Growth Models 2. The dividend is expected to grow at a constant rate of 1% into the foreseeable future? Yes buy. Priced too low

Copyright 2014 by Diane Scott Docking 33 Example: Comparing Dividend-Growth Models 3. The dividend is expected to grow at a rate of 3% for the next 4 years and then at a rate of 1% thereafter? Given: D 0 = \$2.50; r s = 5%; g s = 3%; g = 1%; n = 4years Step 1: Find the PV ( P 0 ’ ) of the dividends during the period of supernormal growth ( g s ). tDividend÷ (1.05) t =PV 1\$2.50(1.03) 1 = \$2.575÷ (1.05) 1 =\$2.4524 2\$2.50(1.03) 2 = \$2.6523÷ (1.05) 2 =\$2.4057 3\$2.50(1.03) 3 = \$2.7318÷ (1.05) 3 =\$2.3598 4\$2.50(1.03) 4 = \$2.8138÷ (1.05) 4 =\$2.3149 ∑ =\$9.5328= \$9.53 =

Copyright 2014 by Diane Scott Docking 34 Example: Comparing Dividend-Growth Models 2. Find the price of the stock at the end of the supernormal growth period ( n ), when normal growth ( g ) begins using the constant dividends growth model.

Copyright 2014 by Diane Scott Docking 35 Example: Comparing Dividend-Growth Models 3. Discount this price ( P n ) back to time 0 ( P 0 ” ). 4. Add the two components of the stock price together. Yes buy. Priced too low

Copyright 2014 by Diane Scott Docking 36 Dividends Versus Return and Growth For another interpretation, note that we can rearrange the constant dividend growth model equation as follows: Solving for r s : Solving for g : or

Copyright 2014 by Diane Scott Docking 37 Example: Solving for Investment Return Carson Co. recently paid a \$1.20 dividend. The dividend is expected to grow at a 2% rate. At a current stock price of \$36.35, what return are shareholders expecting? Solve for r s :

Copyright 2014 by Diane Scott Docking 38 Example: Solving for Growth Rate Flintstone Co. recently paid a \$1.10 dividend. The current stock price of the company is \$46.27 and investors expect a 6% return. What is the expected future growth rate in dividends. Solving for g :

Copyright 2014 by Diane Scott Docking 39 Limitations of Dividend-Discount Model We cannot use the constant dividend growth model to value the stock of the following types of firms:  Firms that pay no dividends  Firms whose growth rate continues to change over time until they mature There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model

Copyright 2014 by Diane Scott Docking 40 Limitations of Dividend-Discount Model We cannot use the constant dividend growth model to value the stock of such a firm for two reasons:  These firms often pay no dividends when they are young  Their growth rate continues to change over time until they mature There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model

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