Solutions to Homework 3,
FINC-UB.0002.02

Xuyang Ma
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. Sup-

pose that the company tends to plow back 50% of its earnings and pay the rest as dividends. If the Chief Financial Ocer (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:

P0 = where E1 (1 − b) R−g

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
1

(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 required rate of return; or pany'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. a lower equilibrium stock price ($50 either: Thus,

(i) your estimate of the stock's

(ii) the CFO's estimate of the com-

<

$125) could indicate that

(1) the required rate of return is higher than originally

expected, and/or (2) the growth rate is less than originally estimated. (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 =