Constant-growth dividend discount model

EIFM Seminar 10 – week commencing Dec 13th 2021

Question 1: At Litchfield Chemical Corp., a director of the company said that the use of dividend discount models by investors is “proof” that the higher the dividend, the higher the stock price.

a. Using a constant-growth dividend discount model as a basis of reference, evaluate the directors’ statement.

b. Explain how an increase in dividend payout would affect each of the following (holding all other factors constant):

i. Sustainable growth rate.

ii. Growth in book value.


a. This director is confused. In the context of the constant growth model

[i.e., P0 = D1/(k – g)], it is true that price is higher when dividends are higher holding everything else including dividend growth constant. But everything else will not be constant. If the firm increases the dividend payout rate, the growth rate g will fall, and stock price will not necessarily rise. In fact, if ROE > k, price will fall.


(i) An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate

(i.e. ROE plowback) will fall as plowback ratio falls.

(ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason — less funds are reinvested in the firm.



Question 2: Low Tech Chip Company is expected to have EPS in the coming year of $2.50. The expected ROE is 14%. An appropriate required return on the stock is 11%. If the firm has a dividend payout ratio of 40%, what is the intrinsic value of the stock?  


Question 3: Discuss the relationships between the required rate of return on a stock, the firm’s return on equity, the plowback rate, the growth rate, and the value of the firm.

Answer: If the firm earns more on retained earnings (equity) than the firm’s cost of equity capital (required rate of return), the value of the firm’s stock increases; therefore, the firm should retain more earnings, which will increase the growth rate and increase the value of the firm (share price).

If the firm earns less on retained equity than the required rate of return, and the firm increases the retention rate and the growth rate, the firm decreases firm value, as reflected by share price. In this scenario, the shareholders would prefer that the firm pay out more of earnings in dividends, which the shareholders could invest at a greater rate of return than that earned by the firm (ROE).
If the required rate of return equals the ROE, investors are indifferent between the firm’s retaining earnings and paying out dividends. As a result, the retention rate and the growth rate in this scenario have no effect on firm value (stock price).

Question 4: Discuss the various forms of market efficiency. Include in your discussion the information sets involved in each form and the relationships across information sets and across forms of market efficiency. Also discuss the implications for the various forms of market efficiency for the various types of securities’ analysts. 


The weak form of the efficient markets hypothesis (EMH) states that stock prices immediately reflect any information contained market data. Market data refers to stock prices and trading volume. Technicians attempt to predict future stock prices based on historic stock price movements. Thus, if the weak form of the EMH holds, the work of the technician is of no value.

The semi-strong form of the EMH states that stock prices reflect all public information, which includes the information contained in market data and all other publicly available information, such as financial statements, and all information reported in the press relevant to the firm. Thus, market trading information is a subset of all public information. As a result, if the semi-strong form of the EMH holds, the weak form must hold also. If the semi-strong form holds, then the fundamentalist, who attempts to identify undervalued securities by analyzing public information, is unlikely to do so consistently over time. In fact, the work of the fundamentalist may make the markets even more efficient! (Grossman-Stiglitz Paradox)

The strong form of the EMH states that all information (public and private) is immediately reflected in stock prices. Public information is a subset of all information, thus if the strong form of the EMH holds, the semi-strong form must hold also. The strong form of EMH states that even with inside (legal or illegal) information, one cannot expect to outperform the market consistently over time.

Studies have shown the weak form to hold when transactions costs are considered. Studies have shown the semi-strong form to hold in general, although some anomalies have been observed. Studies have shown that some insiders (specialists, major shareholders, and major corporate officers) do outperform the market.

Question 5: The weather report says that a devastating and unexpected freeze is expected to hit Florida tonight, during the peak of the citrus harvest. In an efficient market one would expect the price of Florida Orange’s stock to

A. drop immediately.
B. remain unchanged.
C. increase immediately.
D. gradually decline for the next several weeks.
E. gradually increase for the next several weeks.


The correct answer is A.

In an efficient market the price of the stock should drop immediately when the bad news is announced. If later news changes the perceived impact to Florida Orange, the price may once again adjust quickly to the new information. A gradual change is a violation of the EMH.

Question 6: Matthews Corporation has a beta of 1.2. The annualized market return yesterday was 13%, and the risk-free rate is currently 5%. You observe that Matthews had an annualized return yesterday of 17%. Assuming that markets are efficient, this suggests that

A. bad news about Matthews was announced yesterday.
B. good news about Matthews was announced yesterday.
C. no news about Matthews was announced yesterday.
D. interest rates rose yesterday.
E. interest rates fell yesterday.


The correct answer is B.

AR = 17% – (5% + 1.2 (8%)) = +2.4%. A positive abnormal return suggests that there was firm-specific good news.

Question 7: If stock prices follow a random walk

A. it implies that investors are irrational.
B. it means that the market cannot be efficient.
C. price levels are not random.
D. price changes are random.
E. price movements are predictable.


The correct answer is D.

A random walk means that the changes in prices are random and independent.

Question 8: Proponents of the EMH typically advocate

A. buying individual stocks on margin and trading frequently.
B. investing in hedge funds.
C. a passive investment strategy.
D. buying individual stocks on margin and trading frequently and investing in hedge funds
E. investing in hedge funds and a passive investment strategy


The correct answer is C.

Believers of market efficiency advocate passive investment strategies, and an investment in an index fund is one of the most practical passive investment strategies, especially for small investors.