Final answer:
The price-earnings ratio of No-Growth Industries cannot be calculated directly without the stock price. However, the earning yield, which is reciprocal to the P/E ratio, is $2 divided by the discount rate of 10%, resulting in a value of $20, hence the P/E ratio is 20.
Step-by-step explanation:
To calculate the price-earnings ratio (P/E ratio) for No-Growth Industries, we first need the price of the stock (P) which isn't provided and the earnings per share (EPS). Since the company pays out all of its earnings as dividends, the EPS is equal to the dividend. The next $2 per share dividend is the EPS.
The P/E ratio is the stock price (P) divided by the earnings per share (EPS). However, without the stock price, we can only determine the reciprocal of the price-earnings ratio, also known as the earnings yield (E/P), which is EPS divided by the stock price. With an EPS of $2 and a discount rate (required return) of 10%, the E/P ratio can be calculated as EPS divided by the required return, resulting in an earning yield of $2/0.10 = $20. The reciprocate of this, 1/20, yields 0.05, which equates to a P/E ratio of 20.