Problem 84 - Elementary Algebra

Question

If the market value per share of Apple, Inc. stock is \(\$ 138.91\) and the earnings per share is \(\$ 3.16\), find the \(\mathrm{P} / \mathrm{E}\) ratio. Round to the nearest hundredth.

Step-by-Step Solution

Answer

The P/E ratio is approximately 43.96.

Step 1 - Understand P/E Ratio

The Price-to-Earnings (P/E) ratio is calculated by dividing the market value per share by the earnings per share (EPS). The formula is: \ \ \ \ \ \ \[ \mathrm{P} / \mathrm{E} = \frac{\text{Market Value per Share}}{\text{Earnings per Share}} \]

Step 2 - Insert Given Values

Substitute the given values into the formula: \ \ \[ \mathrm{P} / \mathrm{E} = \frac{138.91}{3.16} \]

Step 3 - Perform the Division

Divide the market value per share by the earnings per share: \ \ \[ \mathrm{P} / \mathrm{E} = \frac{138.91}{3.16} \approx 43.96 \]

Step 4 - Round to the Nearest Hundredth

Round the result to the nearest hundredth. The P/E ratio is approximately 43.96.

Key Concepts

Price-to-Earnings ratio

The Price-to-Earnings (P/E) ratio is a critical financial metric used to evaluate a company's stock price relative to its earnings. This ratio helps investors understand if a stock is overvalued or undervalued. The P/E ratio can be calculated using the formula:
ewline ewline \[ \mathrm{P} / \mathrm{E} = \frac{\text{Market Value per Share}}{\text{Earnings per Share}} \]
In simpler terms, it tells us how many dollars investors are willing to pay for each dollar of earnings. For instance, a P/E ratio of 20 means investors are willing to pay \(20 for every \)1 the company earns.
Understanding this ratio is essential for making informed investment decisions. It offers insight into market expectations and helps compare companies within the same industry.

Market value per share

Market value per share refers to the current price at which a particular stock is trading on the market. This value fluctuates based on supply and demand, company performance, and broader economic factors.
To find the market value per share, you simply look at the stock's current trading price in the stock market. For example, in our exercise, the market value per share for Apple, Inc. is \( \$ 138.91 \).
Market value per share is used in various financial metrics, including the P/E ratio, to provide investors with insights into a stock’s valuation.

Earnings per share

Earnings per share (EPS) is a measure of a company's profitability, calculated by dividing the company's net earnings by the total number of outstanding shares. The formula is:
ewline ewline \[ \text{EPS} = \frac{\text{Net Earnings}}{\text{Outstanding Shares}} \]
For example, if a company has \(1 million in net earnings and 1 million shares outstanding, the EPS would be \)1.
In our exercise, Apple's EPS is \( \$ 3.16 \).
EPS is a crucial component for calculating the P/E ratio, providing insight into how much money a company makes per share, which aids in investment analysis.

Rounding numbers

Rounding numbers is a mathematical technique used to simplify figures for ease of interpretation. In financial calculations, rounding is often performed to the nearest hundredth (two decimal points).
For instance, after calculating the P/E ratio, we arrived at 43.95949. By rounding this to the nearest hundredth, we get 43.96.
Rounding helps in presenting data more clearly without compromising the accuracy significantly. It's essential to round consistently within financial reports to maintain uniformity and clarity.