Dividend Discount and Gordon Growth Models

• The following statements relate to the dividend discount model

Dividend Discount Model

• The dividend discount model can still be used to value the dividends that the company will pay after the high growth eases.
• Stock valuation depends on the assumptions made about expected future growth and risk
• The dividend discount model will find more undervalued stocks only if the stock market falls more than merited by changes in the fundamentals
• Portfolios of stocks that are undervalued using the dividend discount model seem to earn excess returns over long time periods
• The dividend discount model is biased towards stocks that pay out dividends.

Gordon Growth Model Analysis

• The analyst complains that the Gordon Growth Model yields absurd results
• 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
• 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
• An upper limit on how high growth rates can go operates as a constraint in the model
• Smoothing effect cannot have a large effect on the value estimate obtained from the model in present value terms
• The Gordon Growth Model requires that, in the long term, the growth rate for a firm maintain stability and be close to the growth rate in the economy
• Cyclical firms, which maintain an average growth rate close to a stable rate, cyclical ups and downs notwithstanding, can be valued using the Gordon Growth Model

Ameritech Corporation Dividend Valuation

• In 1992, Ameritech Corporation paid dividends per share of $3.56
• 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%
• Cost of Equity = 6.25% + 0.90 * 5.5% = 11.20%
• Value Per Share = $3.56 * 1.055/(.1120 - .055) = $65.89
• If the stock is trading for $80 per share, one would solve for g. (growth rate in dividends)
• $3.56 (1 + g)/(.1120 - g) = $80
• g = (80*.112 - 3.56)/(80+ 3.56) = 6.46%

Factors in Estimating Growth Rate

• A key input for the Gordon Growth Model is the expected growth rate in dividends over the long term
• An increase in the inflation rate 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
• A rapidly growing economy should affect the estimation of a stable growth rate and a much higher stable growth rate can be used for firms in economies which are growing rapidly
• 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 three-stage growth model can be used to value the stock

Newell Corporation Stock Price Evaluation

• Newell Corporation reported earnings per share of $2.10 in 1993, on which it paid dividends per share of $0.69
• Earnings are expected to grow 15% a year from 1994 to 1998, during which period the dividend payout ratio is expected to remain unchanged
• After 1998, 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 1998
• The treasury bond rate is 6.25%
• Expected Earnings Per Share in 1999 = $2.10 * 1.155 * 1.06 = $4.48
• Expected Dividends Per Share in 1999 = $4.48 * 0.65 = $2.91
• Cost Of Equity After 1999 = 6.25% + 1.1 * 5.5% = 12.30%
• Expected Price at the End of 1998 = Expected DPS in 1999/(ke, 1999 - g) = $2.91/(.1230 - .06) = $46.19

Church & Dwight Valuation

• Church & Dwight, reported earnings per share of $1.50 in 1993 and paid dividends per share of $0.42
• In 1993, 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% and the treasury bond rate is 7%
• Retention Ratio = 1 - Payout Ratio = 1 - 0.42/1.50 = 72%
• Return on Assets must be calculated
• Return on Assets = (Net Income + Int Exp (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, one can calculate a much more simplified Return on Equity
• Return on Equity = 30/160 = .1875
• Expected Growth Rate = 0.72 * .1875 = 13.5%
• Expected payout ratio after 1998 = 1 - g/[ROC + D/E (ROC - i (1-t))] = 1 - .06/(.125+.25(.125 - .07(1-.385)) = 0.5876
• Unlevered Beta = 0.85/(1 + (1 - 0.385) * 0.05) = 0.8246
• Beta After 1998 = 0.8246* (1 + (1 - 0.385) * 0.25) = 0.95
• Cost of Equity in 1999 is 12.23%
• Expected Dividend in 1999 = ($1.50 * 1.1355 * 1.06) * 0.5876 = $1.76
• Expected Price at End of 1998 = $1.76/(.1223 - .06) = $28.25
• 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

Explore the Dividend Discount Model (DDM) and Gordon Growth Model for stock valuation. Understand the impact of growth and risk assumptions on stock valuation. The DDM is biased towards dividend-paying stocks and may not be suitable for companies with zero dividends.