Final answer:
Based on the Gordon Growth Model, if the stock price is $50 and dividends grow at 8% (half of the 16% ROE being plowed back), the required rate of return would be 18%. Thus, if the actual stock price is $50, either the market's required rate of return is lower than 18%, or the CFO's estimate of the company's ROE may not be accurate.
Step-by-step explanation:
The scenario presented involves a company whose earnings per share are projected to be $5.00, with a plowback ratio of 50% and a return on equity (ROE) of 16%. Since half of the earnings are retained, the expected growth rate of dividends, given by the plowback ratio times the ROE, is 8% (0.50 * 16%). To value the stock, we can use the Gordon Growth Model, which assumes a constant growth in dividends:
Price = Dividend per share / (Required rate of return - Growth rate)
Given the stock price of $50, we can set up the equation as follows, with D1 representing the dividend next year:
$50 = ($5.00 * (1 - 0.50)) / (Required rate of return - 0.08)
Rearranging to solve for the Required rate of return, we find it to be 18%:
Required rate of return = ($2.50 / $50) + 0.08 = 0.18 or 18%
If the stock is selling for $50 and we assume the CFO's ROE estimation is accurate, this implies that the market's required rate of return might be lower than our calculated 18%. Conversely, if we believe the market's required rate of return is around 18%, we might question the accuracy of the ROE estimate provided by the CFO.