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.

(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?

(d) Under the probabilities in (c) the expected growth rate of the firm is 8%. How come the valuation in part (c) is different from the valuation in part (a)?

Answer 1

Ans. b: Given:

                Value of Stock (P)= $ 50

                E1 = $5

                Plow Back = 60%

                Dividend Payout Ratio = 100 -60 = 40%

                D1 = $ 5 * (60/100) = $3

                Growth Rate (g)               = 8%

Value of Stock = D1/ (r-g)

50 = 3/ (r-.08)

r-.08 = 3/50 = .06

r = .06 + .08

r = .14 = 14%

Required rate of return = 14%

Since Growth Rate = Return on Equity×(1−Dividend Payout Ratio)

8 = ROE * (1-0.40)

ROE = 8/ (1-0.40)

Therefore, ROE = 13.33%

So, the CFO’s estimate of the company’s future growth rate is based on ROE of 13.33%.

Ans. C):

Market values of the firm assuming growth rate of 6%

= D1/ (r-g) = 3 / (0.14 – 0.06) = 3 / 0.08 = $37.5

Market values of the firm assuming growth rate of 10%

= D1/ (r-g) = 3 / (0.14 – 0.10) = 3 / 0.04 = $75

Market values of the firm assuming growth rates of 6% and 10% have equal probability:

Growth rate = (6% *0.50) + (10%*0.50) = 8%

Market values of the firm =

D1/ (r-g) = 3 / (0.14 – 0.08) = 3 / 0.06 = $50

Ans. d):

Since there is no part (a) given in the question, the valuation in part (c) can not be compared with the valuation in part (a).