Question

Suppose that the consensus forecast of security analysts of NoWork Inc. is that earnings next year will be E1 = $5.00 per share. The company tends to plow back 60% of its earnings and pay the rest as dividends. The CFO estimates that the company’s growth rate will be 8% from now on.

(a) If your estimate of the company’s required rate of return is 12%, what is the equilibrium price of the stock?

(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?

(c) Suppose there is uncertainty about the growth rate. With 50% probability the growth rate will be 6%, with 50% probability the growth rate will be 10%. What are the respective market values under the two growth rates? What must be the price of the stock, given that both growth rates have equal probability?

Answer 1

(a) Price of the stock = Dividend next year / ( required rate of return - growth rate )

DIvidend next year = 5 * 0.4 = 2

Price of the stock = 2 / ( 0.12 - 0.08) = 50

b)

The stock is trading @ $50 and intrinsic value is $50 the estimates regarding the required rate of return and growth rate are correct.

c)

value of share at g= 6% = 2 / ( 0.12 - 0.06) = 33.33

value of share at g= 10% = 2 / ( 0.12 - 0.1) = 100

value of share at g = 8% = 2 / ( 0.12 0.08) = 50

( expecetd growth rate = (10+6)2 = 8)