Question

Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company's return on equity (ROE) is 16%. Assuming the plowback ratio and the ROE are expected to remain constant forever:

Suppose that you are confident that 10% is the required rate of return on the stock. What does the market price of $50.00 per share imply about the market’s estimate of the company’s expected return on equity? (please give a number)

Answer 1

Growth rate (g) = Retention ratio*ROE

It is given that the  company plows back 50% of its earnings.

It means it retains 50% of the earning and distrubute 50% of the earning as dividend.

Retention ratio= 50%

Dividemd payout ratio = 50%

Growth rate (g)= 50% * 16% = 8%

Current Price(P0)=

D1 = Next expected dividend per share

D1 = Next EPS * Dividend payout ratio= $5.00 * 50% = $2.50

K= required rate of return on stock

g = growth rate

As per your Expectation the Required rate of return = 10%

Hence Current rice(P0)as per your Required rate of return =

There fore as per your expectation the price shold be $125.

But the Current price is Actually $50

Let the market’s estimate of the company’s expected return on equity = K

Hence,

=> K = 0.13 or 13%

Hence the market’s estimate of the company’s expected return on equity = 13%