DCF Practice Questions (Part 5) V: DIVIDEND DISCOUNT MODELS

Question 8 - The Three-Stage Dividend Discount Model Medtronic Inc., the world's largest manufacturer of implantable biomedical devices, reported earnings per share in 2004 of $3.95, and paid dividends per share of $0.68. Its earnings are expected to grow 16% from 2005 to 2009, but the growth rate is expected to decline each year after that to a stable growth rate of 6% in 2014. The payout ratio is expected to remain unchanged from 2005 to 2009, after which it will increase each year to reach 60% in steady state. The stock is expected to have a beta of 1.25 from 2005 to 2009, after which the beta will decline each year to reach 1.00 by the time the firm becomes stable. (The Treasury bond rate is 6.25 %.) A. Assuming that the growth rate declines linearly (and the payout ratio increases linearly) from 2010 to 2014, estimate the dividends per share each year from 2005 to 2014. B. Estimate the expected price at the end of 2014. C. Estimate the value per share, using the three-stage dividend discount model.

A. Period EPS DPS 1 $4.58 $0.79 2 $5.32 $0.92 3 $6.17 $1.07 4 $7.15 $1.21 5 $8.30 $1.43 6 $9.46 $2.35 7 $10.59 $3.56 8 $11.65 $4.94 9 $12.58 $6.44 10 $13.34 $8.00 B. Expected Price at End of 2014 = ($13.34 * 1.06 * 0.60)/(.1175 - .06) = $147.54 (Cost of Equity = 6.25% = 5.5% = 11.75%) C. PV of Dividends - High Growth = $3.67 PV of Dividends - Transition = $9.10 PV of Terminal Price = $44.59 Value Per Share = $57.36

Question 2 - Gordon Growth Model: Concepts An analyst complains that the Gordon Growth Model yields absurd results. He presents several problems that he has had with the model. Respond to each of these comments. A. The model values stocks which do not pay dividends at zero. B. The model sometimes yields negative values for stocks, when growth rates exceed the discount rate. C. The model yields absurdly high values for other stocks, where the discount rate is very close to the growth rate. D. No firm raises dividends by a fixed percent every year. The model's assumption is unrealistic and the values obtained from it will not hold. E. Since cyclical firms have earnings which go up and down, based upon economic conditions, the model can never be used to value a cyclical firm.

A. A stock that pays no dividends is not a stable stock. The Gordon Growth model is not designed to value such a stock. If a company with stable growth insists on not paying dividends, but retains the FCFE, this FCFE can be used in the Gordon Growth model as the dividend. B. A stable stock cannot have a growth rate greater than the discount rate, because no company can grow much faster than the economy in which it operates in the Gordon Growth Model. This upper limit on how high growth rates can go operates as a constraint in the model. C. This should not happen for a stable stock, for the same reasons stated above. D. It is true that the model smooths out growth rates in dividends. In present value terms, though, this smoothing effect cannot have a large effect on the value estimate obtained from the model. E. The model requires that, in the long term, the growth rate for a firm is stable (close to the growth rate in the economy). Thus, cyclical firms, which maintain an average growth rate close to a stable rate, cyclical ups and downs notwithstanding, can be valued using this model.

*Question 7 - The H Model Oneida Inc. the world's largest producer of stainless steel and silver plated flatware, reported earnings per share of $0.80 in 2008, and paid dividends per share of $0.48 in that year. The firm is expected to report earnings growth of 25% in 2009, after which the growth rate is expected to decline linearly over the following six years to 7% in 2014. The stock is expected to have a beta of 0.85. (The Treasury bond rate is 6.25 %.) A. Estimate the value of stable growth, using the H Model. B. Estimate the value of extraordinary growth, using the H Model. C. What are the assumptions about dividend payout in the H Model?

A. Cost of Equity = 6.25% + 0.85 * 5.5% = 10.93% Value of Stable Growth = $0.48 * 1.07/(.1093 - .07) = $13.07 B. Value of Extraordinary Growth = $0.48 * (6/2) * (.25 - .07)/(.1093 - .07) = $6.60 C. The payout ratio is assumed to remain unchanged as the growth rate changes. The payout ratio in this case is assumed to remain at 60% (0.48/0.80).

Question 3 - Gordon Growth Model Ameritech Corporation paid dividends per share of $3.56 in 2012, and dividends are expected to grow 5.5% a year forever. The stock has a beta of 0.90, and the Treasury bond rate is 6.25%. A. What is the value per share, using the Gordon Growth Model? B. The stock is trading for $80 per share. What would the growth rate in dividends have to be to justify this price? Question 4 - Growth Rate in the Gordon Growth

A. Cost of Equity = 6.25% + 0.90 * 5.5% = 11.20% Value Per Share = $3.56 * 1.055/ (.1120 - .055) = $65.89 B. $3.56 (1 + g)/ (.1120 - g) = $80 Solving for g, g = (80 * .112 - 3.56)/ (80 + 3.56) = 6.46%

Question 5 - Two-Stage Dividend Discount Model: Basics Newell Corporation, a manufacturer of do-it-yourself hardware and housewares, reported earnings per share of $2.10 in 2009, on which it paid dividends per share of $0.69. Earnings are expected to grow 15% a year from 2010 to 2014, during which period the dividend payout ratio is expected to remain unchanged. After 2014, the earnings growth rate is expected to drop to a stable 6%, and the payout ratio is expected to increase to 65% of earnings. The firm has a beta of 1.40 currently, and it is expected to have a beta of 1.10 after 2014. The Treasury bond rate is 6.25%. A. What is the expected price of the stock at the end of 2014? B. What is the value of the stock, using the two-stage dividend discount model?

A. Expected Earnings per Share in 2015 = $2.10 * 1.155 * 1.06 = $4.48 Expected Dividends per Share in 2015 = $4.48 * 0.65 = $2.91 Cost of Equity post 2015 = 6.25% + 1.1 * 5.5% = 12.30% Expected Price at the End of 2014 = Expected DPS in 2015/ (ke, 2015 - g) = $2.91/ (.1230 - .06) = $46.19 B. Year EPS DPS 2010 $2.42 $0.79 2011 $2.78 $0.91 2012 $3.19 $1.05 2013 $3.67 $1.21 2014 $4.22 $1.39 $46.19 Cost of Equity = 6.25% + 1.40 * 5.5% = 13.95% PV of Dividends and Terminal Price (@ 13.95%) = $27.59

Question 1 - Uses of the Dividend Discount Model Respond true or false to the following statements relating to the dividend discount model. A. The dividend discount model cannot be used to value a high growth company that pays no dividends. B. The dividend discount model will undervalue stocks, because it is too conservative. C. The dividend discount model will find more undervalued stocks, when the overall stock market is depressed. D. Stocks that are undervalued using the dividend discount model have generally made significant positive excess returns over long periods (five years or more). E. Stocks which pay high dividends and have low price/earnings ratios are more likely to come out as undervalued using the dividend discount model.

A. False. The dividend discount model can still be used to value the dividends that the company will pay after the high growth eases. B. False. It depends upon the assumptions made about expected future growth and risk. C. False. This will be true only if the stock market falls more than merited by changes in the fundamentals (such as growth and cash flows). D. True. Portfolios of stocks that are undervalued using the dividend discount model seem to earn excess returns over long time periods. E. True. The model is biased towards these stocks because of its emphasis on dividends.

Question 6 - Two-Stage Dividend Discount Model: Estimating Terminal Payout Ratio Church & Dwight, a large producer of sodium bicarbonate, reported earnings per share of $1.50 in 2009 and paid dividends per share of $0.42. In 2009, the firm also reported the following: Net Income = $30 million Interest Expense = $0.8 million Book Value of Debt = $7.6 million Book Value of Equity = $160 million The firm faced a corporate tax rate of 38.5%. (The market value debt-to -equity ratio is 5 %.) The Treasury bond rate is 7%. The firm expects to maintain these financial fundamentals from 2010 to 2014, after which it is expected to become a stable firm, with an earnings growth rate of 6%. The firm's financial characteristics will approach industry averages after 2014. The industry averages are as follows: Return on Assets = 12.5% Debt/Equity Ratio = 25% Interest Rate on Debt = 7% Church and Dwight had a beta of 0.85 in 2009, and the unlevered beta is not expected to change over time. A. What is the expected growth rate in earnings, based upon fundamentals, for the high-growth period (2010 to 2014)? B. What is the expected payout ratio after 2014? C. What is the expected beta after 2014? D. What is the expected price at the end of 2014? E. What is the value of the stock, using the two-stage dividend discount model? *F. How much of this value can be attributed to extraordinary growth? To stable growth?

A. Retention Ratio = 1 - Payout Ratio = 1 - 0.42/1.50 = 72% Return on Assets = (Net Income + Interest Expense (1-t))/(BV of Debt + BV of Equity) = (30 + 0.8 * (1 - 0.385))/ (7.6 + 160) = 18.19% Debt/Equity Ratio = 7.6/160 = .0475 Interest Rate on Debt = 0.8/7.6 = 10.53% Expected Growth Rate = 0.72 [.1819 + .0475 (.1819 - .1053 * (1 - 0.385))] = 13.5% Alternatively, and much more simply, Return on Equity = 30/160 = .1875 Expected Growth Rate = 0.72 * .1875 = 13.5% B. Expected payout ratio after 2014: = 1 - g/ [ROC + D/E (ROC - i (1-t))] = 1 - .06/(.125+.25(.125 - .07(1-.385)) = 0.5876 C. Beta in 2009 = 0.85 Unlevered Beta = 0.85/ (1 + (1 - 0.385) * 0.05) = 0.8246 Beta after 2014 = 0.8246 * (1 + (1 - 0.385) * 0.25) = 0.95 D. Cost of Equity in 2015 = 7% + 0.95 * 5.5% = 12.23% Expected Dividend in 2015 = ($1.50 * 1.1355 * 1.06) * 0.5876 = $1.76 Expected Price at End of 2014 = $1.76/(.1223 - .06) = $28.25 E. Year EPS DPS 2010 $1.70 $0.48 2011 $1.93 $0.54 2012 $2.19 $0.61 2013 $2.49 $0.70 2014 $2.83 $0.79 $28.25 Cost of Equity = 7% + 0.85 * 5.5% = 11.68% PV of Dividends and Terminal Price (@ 11.68%) = $18.47 F. Total Value per Share = $18.47 Value Per Share Using Gordon Growth Model = $1.50 * 1.06 * 0.5876/(.1223 - .06) = $15.00 Value Per Share With No Growth = $1.50 * 0.5876/.1223 = $7.21 Value of Extraordinary Growth = $18.47 - $15.00 = $3.47 Value of Stable Growth = $15.00 - $7.21 = $7.79

Question 4 - Growth Rate in the Gordon Growth Model A key input for the Gordon Growth Model is the expected growth rate in dividends over the long term. How, if at all, would you factor in the following considerations in estimating this growth rate? A. There is an increase in the inflation rate. B. The economy in which the firm operates is growing very rapidly. C. The growth potential of the industry in which the firm operates is very high. D. The current management of the firm is of very high quality.

A. This should increase both the cost of equity (by raising interest rates) and the nominal growth rate. Whether the increase will be the same in both variables will depend in large part on whether an increase in inflation will adversely impact real economic growth. B. This should affect the estimation of a stable growth rate. A much higher stable growth rate can be used for firms in economies which are growing rapidly. C. An analyst has very limited flexibility when it comes to using the Gordon Growth model in estimating growth. If the growth potential of the industry in which the firm operates is very high, a growth rate slightly higher (1 to 2%) than the growth rate in the economy can be used as a stable growth rate. Alternatively, a two-stage or threestage growth model can be used to value the stock. D. Same as the answer to 3.