Question 5

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 you observe that the stock is selling for $50.00 per share, what would you conclude about either your belief of the stock’s required rate of return or the CFO’s estimate of the company’s return on equity? (select all that apply)

1 the ROE on funds plowed back is less than originally estimated

the ROE on funds plowed back is more than originally estimated
2

3 the required rate of return is lower than originally expected

4
the required rate of return is higher than originally expected

1 answer

To analyze the situation, we'll need to calculate the expected growth and then compare the stock price with its implied value based on the Gordon Growth Model (or the Dividend Discount Model for a firm with constant growth).

The expected earnings next year per share are $5.00. The company plows back 50% of its earnings, which means:

Earnings retained (plowed back) = 50% of $5.00 = $2.50
Earnings paid out as dividends = 50% of $5.00 = $2.50

The expected growth rate (g) of the earnings and dividends can be calculated by using the return on equity (ROE):

\[ g = \text{Plowback ratio} \times \text{ROE} \]

Here:

Plowback ratio = 50% = 0.50
ROE = 16% = 0.16

Thus:

\[ g = 0.50 \times 0.16 = 0.08 \text{ or } 8% \]

According to the Gordon Growth Model, the price of the stock (P) can be calculated as follows:

\[ P = \frac{D_1}{r - g} \]

Where:

$ D_1 $ = expected dividend next year = $2.50
$ r $ = required rate of return
$ g $ = growth rate = 0.08 (or 8%)

Rearranging for $ r $:

\[ r = \frac{D_1}{P} + g \]

Substituting the observed stock price ($50.00):

\[ r = \frac{2.50}{50} + 0.08 \] \[ r = 0.05 + 0.08 = 0.13 \text{ or } 13% \]

This means the required rate of return is estimated to be 13%.

Now, we can conclude:

Since the CFO estimated a ROE of 16%, and with the calculated growth rate of 8% consistent with a plowback ratio of 50%, if the stock is selling for $50, this suggests that market participants may be expecting a higher required rate of return than 13% to justify that price.

Thus, we can conclude:

The ROE on funds plowed back is less than originally estimated - This can be a plausible conclusion since the implied required returns from the stock price indicate that the market might believe the growth expectations or sustainability of ROE are lower.
The required rate of return is higher than originally expected - This also fits because the market price suggests that a higher rate of return is necessary for the justification of the given stock price.

So, the correct selections would be:

1: The ROE on funds plowed back is less than originally estimated
4: The required rate of return is higher than originally expected