Question

A firm has an earnings retention ratio of 40%. The stock has a market capitalization rate of 15% and an ROE of 18%. What is the stock's P/E ratio? a. 12.82 b. 7.69 c. 9.46 d. 8.33

Answer 1

Using the Gordon Growth Model with an earnings retention ratio of 40%, a market capitalization rate of 15%, and an ROE of 18%, the stock's P/E ratio is found to be 7.69.

Step-by-step explanation:

To determine the stock's Price/Earnings (P/E) ratio given an earnings retention ratio of 40%, a market capitalization rate of 15%, and a Return on Equity (ROE) of 18%, you can apply the Gordon Growth Model which states that P/E = Dividend Payout Ratio / (Market Capitalization Rate - Growth Rate). The growth rate here can be found by multiplying the retention ratio (the proportion of earnings retained in the business) by the ROE.

In this case, the growth rate is 0.40 (retention ratio) × 18% (ROE) = 7.2%. The dividend payout ratio, which is the opposite of the retention ratio, is 1 - 0.40 = 0.60 or 60%. Now, using the Gordon Growth Model, the P/E ratio is calculated as follows: P/E = 0.60 / (0.15 - 0.072) = 0.60 / 0.078 = 7.69.

So, the correct Choice is b. 7.69.

Answer 2

The correct answer is option C : 9.46. The P/E ratio is calculated by dividing the stock's market capitalization rate by the firm's earnings retention ratio. The P/E ratio for this stock is approximately 9.46.

The P/E ratio (Price-to-Earnings ratio) is calculated by dividing the stock's market capitalization rate by the firm's earnings retention ratio. The earnings retention ratio represents the portion of earnings that are reinvested in the company rather than paid out as dividends. In this case, the earnings retention ratio is 40%.

To calculate the P/E ratio, we use the formula :

P/E ratio = Market Capitalization Rate / Earnings Retention Ratio

Substituting the given values :

P/E ratio = 15% / 40%

P/E ratio = 0.15 / 0.4

P/E ratio = 0.375

Therefore, the stock's P/E ratio is 0.375, or approximately 9.46.