Earnings Multiplier Model and P/E Ratios | CFA Level 1 Exam Analysis

Comparison of P/E Ratios for Stocks A and B

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Question

Tim Jan, CFA, relies on the earnings multiplier model in performing his fundamental analysis. His model is based on the constant-growth DDM. Jan is evaluating two stocks, A and B, that have the same 10% required rate of return and the same expected growth rate in dividends. Stock A has a higher retention rate than stock B. Which stock should have the higher P/E ratio?

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A. B. C.

Explanation

In this scenario, Tim Jan, CFA, is using the earnings multiplier model, which is based on the constant-growth Dividend Discount Model (DDM), to perform fundamental analysis on two stocks, A and B. Both stocks have the same required rate of return of 10% and the same expected growth rate in dividends. However, stock A has a higher retention rate than stock B. The question asks which stock should have the higher price-to-earnings (P/E) ratio.

The P/E ratio is calculated by dividing the price per share of a stock by its earnings per share (EPS). It represents the market's valuation of a company's earnings and is a commonly used metric to assess the relative value of a stock.

In the context of the constant-growth DDM, the P/E ratio can be derived using the Gordon Growth Model, which is a simplified version of the DDM. The Gordon Growth Model is as follows:

P0 = D1 / (r - g)

Where: P0 = Current stock price D1 = Dividend expected to be paid in the next period r = Required rate of return g = Expected constant growth rate in dividends

Since both stocks have the same required rate of return and expected growth rate in dividends, these variables can be assumed to be equal for stocks A and B.

Now, let's consider the impact of the higher retention rate of stock A on its P/E ratio. The retention rate is the proportion of earnings that a company retains for reinvestment purposes rather than distributing them as dividends. A higher retention rate implies that stock A pays out a smaller portion of its earnings as dividends compared to stock B.

In the Gordon Growth Model, the expected dividend in the next period (D1) is derived by multiplying the current dividend (D0) by the expected growth rate (g). Since both stocks have the same expected growth rate, D1 for stock A and stock B would be equal.

However, since stock A has a higher retention rate, it retains a larger portion of its earnings for reinvestment. This implies that stock A has a smaller dividend payout ratio (dividends divided by earnings) compared to stock B.

As the P/E ratio is calculated by dividing the stock price by earnings per share, a smaller dividend payout ratio for stock A implies that its earnings per share will be higher compared to stock B, assuming all other factors remain constant.

Therefore, stock A, with its higher retention rate, should have the higher P/E ratio. Hence, the correct answer is option A: Stock A.