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You are given the following information: Stockholders' equity = \(\$ 3.75\) billion, price/earnings ratio \(=3.5,\) common shares outstanding \(=50\) million, and market/book ratio \(=1.9 .\) Calculate the price of a share of the company's common stock.

Short Answer

Expert verified
The price of a share is $142.5.

Step by step solution

01

Understand the Relationship

The market/book ratio is given by the formula \(\text{Market/Book Ratio} = \frac{\text{Market Price Per Share}}{\text{Book Value Per Share}}\). We will use this formula, alongside the given values, to find the price per share of the company's common stock.
02

Calculate Book Value Per Share

First, calculate the Book Value Per Share using the formula: \(\text{Book Value Per Share} = \frac{\text{Stockholders' Equity}}{\text{Common Shares Outstanding}}\). Plug in the values: \(\text{Book Value Per Share} = \frac{3.75 \text{ billion}}{50 \text{ million}} = 75 \text{ dollars per share}\).
03

Calculate Market Price Per Share

Now, use the market/book ratio to calculate the Market Price Per Share: \(\text{Market Price Per Share} = \text{Market/Book Ratio} \times \text{Book Value Per Share}\). Substitute the known values to find: \(\text{Market Price Per Share} = 1.9 \times 75 = 142.5 \text{ dollars per share}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Market/Book Ratio
The Market/Book Ratio provides insight into how investors value a company compared to its book value. It's calculated by dividing the market price per share by the book value per share.

To compute this ratio, you start by determining the book value per share. This is done by taking the total stockholders' equity and dividing it by the number of outstanding shares. For example, if stockholders' equity is $3.75 billion and there are 50 million shares outstanding, the book value per share would be $75.

Once you have the book value, you use the market/book ratio to find the market price per share. The market price per share reveals how much investors are willing to pay over the company's current book value per share. In our example, a market/book ratio of 1.9 combined with a book value per share of $75 results in a market price per share of $142.5.
Stockholders' Equity
Stockholders' equity represents the ownership amount that shareholders hold in a company. Think of it as the net assets available to shareholders after all liabilities are accounted for. It's often referred to as the book value of the company.

The stockholders' equity is calculated by subtracting total liabilities from total assets. In some cases, it can also be referred to as the company's net worth. This figure is crucial because it gives insights into the company's financial health.

For example, with a stockholders' equity of $3.75 billion and 50 million shares outstanding, the book value per share is calculated as $75. This figure, when used in other financial ratios, can provide further insights into the company's performance and its valuation by the market.
Price/Earnings Ratio
The Price/Earnings (P/E) Ratio is a key financial metric used by investors to evaluate if a stock is over or undervalued. It represents how much investors are willing to pay per dollar of earnings.

The P/E Ratio is determined by dividing the current market price of a stock by its earnings per share (EPS). For instance, if a company's stock is trading at $142.5 and the company has a P/E ratio of 3.5, it helps investors understand how the market values the company's earnings.

A low P/E ratio might indicate that the stock is undervalued or that the company's earnings are not expected to grow significantly. Conversely, a high P/E ratio may suggest expectations of future growth in earnings. Understanding this ratio can provide investors with valuable insights into how a company is performing and its future potential.

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Most popular questions from this chapter

Midwest Packaging's ROE last year was only \(3 \%\); but its management has developed a new operating plan that calls for a total debt ratio of \(60 \%\), which will result in annual interest charges of \(\$ 300,000 .\) Management projects an EBIT of \(\$ 1,000,000\) on sales of \(\$ 10,000,000,\) and it expects to have a total assets turnover ratio of \(2.0 .\) Under these conditions, the tax rate will be \(34 \%\). If the changes are made, what will be the company's return on equity?

Bartley Barstools has an equity multiplier of \(2.4,\) and its assets are financed with some combination of long-term debt and common equity. What is its debt ratio?

Central City Construction (CCC) needs \(\$ 1\) million of assets to get started, and it expects to have a basic earning power ratio of \(20 \% .\) CCC will own no securities, so all of its income will be operating income. If it so chooses, CCC can finance up to \(50 \%\) of its assets with debt, which will have an \(8 \%\) interest rate. Assuming a \(40 \%\) tax rate on all taxable income, what is the difference between CCC's expected ROE if it finances with \(50 \%\) debt versus its expected \(\mathrm{ROE}\) if it finances entirely with common stock?

Graser Trucking has \(\$ 12\) billion in assets, and its tax rate is \(40 \%\). Its basic earning power (BEP) ratio is \(15 \%\), and its return on assets (ROA) is \(5 \%\). What is its times-interest-earned (TIE) ratio?

A firm has a profit margin of \(2 \%\) and an equity multiplier of \(2.0 .\) Its sales are \(\$ 100\) million, and it has total assets of \(\$ 50\) million. What is its ROE?

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