Foundations of Finance
Solutions to Homework 3
Prof. Eduardo D´vila a Topic 6: Equity Valuation
1. Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be E1 = $5.00 per share. Suppose that the company tends to plow back 50% of its earnings and pay the rest as dividends. If the Chief Financial Officer (CFO) estimates that the company’s growth rate will be 8% from now onwards, answer the following questions. (a) If your estimate of the company’s required rate of return on its stock is 10%, what is the equilibrium price of the stock?
The equilibrium price of a stock can be determined using Gordon’s growth formula as follows: E1 (1 − b)
P0 =
R−g
where b = .5 the plow back ratio, R = .10 the required rate of return, and g = .08 is the growth rate. Thus, the price should be:
P0 =

$5(1 − .5)
= $125
.10 − .08

(b) Suppose you observe that the stock is selling for $50.00 per share, and that this is the best estimate of its equilibrium price. What would you conclude about either (i) your estimate of the stock’s required rate of return; or (ii) the CFO’s estimate of the company’s future growth rate?
Recall from the formula above, that a higher required rate of return implies a lower equilibrium price of the stock. On the other hand, a higher growth rate implies a higher stock price. Thus, a lower equilibrium stock price ($50 < $125) could indicate that either: (1) the required rate of return is higher than originally expected, and/or (2) the growth rate is less than originally estimated.
1

(c) Suppose your own 10% estimate of the stock’s required rate of return is shared by the rest of the market. What does the market price of $50.00 per share imply about the market’s estimate of the company’s growth rate?
To solve for the expected growth rate, use Gordon’s growth model:
$50