Final answer:
To value a stock using the P/E ratio method, calculate the growth rate of dividends from the retention ratio and ROE, then find the expected dividend and use the formula P0 = D1 / (k - g). The final answer will not align with the unrelated example share price of $256,500.
Step-by-step explanation:
To calculate the value of a share of stock using the P/E ratio approach to valuation, we must consider various factors as presented in the question. We are given that an investor's required rate of return is 16 percent, the expected level of earnings at the end of this year (E1) is $4, the firm plans to retain 60 percent of its earnings, the return on equity (ROE) is 15 percent, and similar shares of stock sell at multiples of 5.715 times earnings per share.
The growth rate of dividends (g) can be calculated as the retention ratio (b) multiplied by the return on equity (ROE), which equates to 60% of 15%, or 9%. The expected dividend next year (D1) can then be calculated by multiplying (1 - b) by E1, which results in 40% of $4, or $1.60.
To find the intrinsic value of the stock based on the P/E ratio, we utilize the formula P0 = D1 / (k - g), where P0 is the intrinsic value of the stock, D1 is the expected dividend next year, k is the required rate of return, and g is the growth rate of dividends.
Please note that the information provided in the reference text about PDV and the share price of $256,500 per share does not relate to the specific P/E ratio calculation required for this question. Hence, the final value will not reflect the reference price per share.