Question

The current P/E ratio (price-to-earnings ratio) of a stock is defined as $$R=\frac{P}{E}$$ where $P$ is the current market price per share of the stock and $E$ is the earnings per share for the most recent 12 -month period. a. What is the domain of the function $R$ b. The earnings per share of IBM Corporation for 2011 were $\$ 13.09$, and its price per share on March 19,2012 was $\$ 205.56 .$ What was the $\mathrm{P} / \mathrm{E}$ ratio of IBM at that time?

Name: Problem 33, Chapter 8: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-17T15:35:11-08:00
Duration: 1 min 2 s
Channel: Tyler Moulton

    The current P/E ratio (price-to-earnings ratio) of a stock is defined as
$$R=\frac{P}{E}$$
where $P$ is the current market price per share of the stock and $E$ is the earnings per share for the most recent 12 -month period.
a. What is the domain of the function $R$
b. The earnings per share of IBM Corporation for 2011 were $\$ 13.09$, and its price per share on March 19,2012 was $\$ 205.56 .$ What was the $\mathrm{P} / \mathrm{E}$ ratio of IBM at that time?

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 8, Problem 33

Instant Answer

Solved by Expert Tyler Moulton

05/17/2021

Step 1

Step 1: Understand the P/E Ratio Formula The P/E ratio, denoted as $ R $, is calculated using the formula: \[ R = \frac{P}{E} \] where $ P $ is the price per share and $ E $ is the earnings per share. Show more…

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The current P/E ratio (price-to-earnings ratio) of a stock is defined as $$R=\frac{P}{E}$$ where $P$ is the current market price per share of the stock and $E$ is the earnings per share for the most recent 12 -month period. a. What is the domain of the function $R$ b. The earnings per share of IBM Corporation for 2011 were $\$ 13.09$, and its price per share on March 19,2012 was $\$ 205.56 .$ What was the $\mathrm{P} / \mathrm{E}$ ratio of IBM at that time?

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Key Concepts

Domain of a Function

The domain of a function consists of all possible input values for which the function produces a valid output. In the context of the P/E ratio, this means that the earnings per share, represented by E, must not be zero because division by zero is undefined. Thus, the domain is all real numbers excluding zero, ensuring that the function remains mathematically valid.

Price-to-Earnings (P/E) Ratio

The P/E ratio is a financial metric used to evaluate the relative value of a company's share price compared to its earnings per share (EPS). It is calculated by dividing the current market price of one share by the earnings per share. This ratio is widely used in investment analysis as it reflects how much investors are willing to pay per dollar of earnings, enabling comparisons between companies and industries, as well as insights into market expectations.

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