G PC Co. currently has an EPS of $.89 and the benchmark P/E ratio for its industry is expected to be 18. Its earnings are expected to grow at 5% per year. What is estimate of the stock price

$16.821.

Explanation:

Earnings per share (EPS) is a profitability ratio that helps to determine how much of earnings, income after paying all the expenses, interest, taxes, and preferred dividend, are generated by the company for each outstanding common share. A higher EPS indicates better profitability. It is calculated as follows:

Earnings per share (EPS) =

Net Income Available to Common Shareholders / No. of common outstanding shares

On the other hand, P/E ratio is a metric of relative valuation.  It tells us about the investors' behavior and the demand for shares of a company. This metric indicates that how much an investor is willing to pay for each earnings per share (EPS). The P/E ratio of a company is compared with that of industry to value the company, that's why is known as the metric of relative valuation. It is calculated as follows:

P/E ratio =  Price per share / Earnings per share

In the question given, we need to calculate the expected earnings per share that is the next year earnings, then simply re-arrange the equation of P/E ratio to calculate the estimated stock price.

⇒ Estimated Earnings per Share = .89 * (1 + 5%) = $.9345.

Now put this value along with expected P/E ratio of industry in the equation of P/E ratio, and re-arrange the equation;

⇒     18 = Price per share / .9345

OR   Price per share = 18 * 0.9345

⇒     Price per share = $16.821.