Question

A company has 2 million shares outstanding. It paid a dividend of \(\$ 2\) during the past year, and expects that dividends will grow at 6 percent annually in the future. Stockholders require a rate of return of 13 percent. What would you expect the price of each share to be today, and what is the value of the company's common stock?

Short answer

The expected price per share is \$30.29, and the value of the company's common stock is \$60,580,000.

Step-by-step solution

Use the Gordon Growth Model

To estimate the price of each share, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model is given by the formula: \( P_0 = \frac{D_0 (1 + g)}{r - g} \), where \( P_0 \) is the price of the stock today, \( D_0 \) is the dividend paid in the last period, \( g \) is the rate of dividend growth, and \( r \) is the required rate of return.

Calculate the Expected Price of Each Share

Substitute the given values into the Gordon Growth Model formula. \( P_0 = \frac{\$2 (1 + 0.06)}{0.13 - 0.06} = \frac{\$2 (1.06)}{0.07} = \frac{\$2.12}{0.07} = \$30.29 \).

Calculate the Total Value of the Company's Common Stock

Multiply the price per share by the total number of shares outstanding to get the company's total value: \( \$30.29 \times 2,000,000 = \$60,580,000 \).

Key concepts

Dividend Discount Model

The Dividend Discount Model (DDM) is a method of valuing a company's stock based on the hypothesis that its stock is worth the sum of all of its future dividend payments when discounted back to their present value. This approach takes into account the time value of money, presuming that receiving a dollar today is worth more than receiving one in the future because of the dollar's potential earning capacity. The DDM formula is expressed as:

\[ P_0 = \frac{D_0 (1 + g)}{r - g} \]
where:

• \(P_0\) is the present stock price,
• \(D_0\) is the dividend paid in the last period,
• \(g\) is the constant growth rate of dividends, and
• \(r\) is the required rate of return by investors.

The model operates under a set of assumptions, the most important of which are that dividends will continue to increase at a constant growth rate indefinitely and that the required rate of return does not change. It is primarily used for companies that pay dividends regularly and have a history of stable growth rates.

Stock Valuation

Stock valuation is the process of determining the intrinsic value of a share of a company's stock. It's a fundamental practice in financial management education and a cornerstone for investors who aim to identify undervalued stocks or assess if a stock aligns with their investment strategy. There are several methods to value stocks, such as dividend-based models, cash flow analysis, and the use of earnings multiples.

The Gordon Growth Model, as used in the exercise, is a part of the larger Dividend Discount Model category, which specifically accounts for companies with stable dividend growth.

Application of the Model

Investors may apply the model by plugging in the dividend payout, projected growth rate, and required rate of return into the formula to ascertain the theoretical fair value of the stock. This valuation technique can then be compared against the current market price to guide investment decisions. However, it is essential to recognize that this method has limitations and works best for firms with predictable dividend payments and growth rates, making it less applicable to companies with fluctuating dividends or those that do not pay dividends at all.

Financial Management Education

Financial management education encompasses a broad range of topics that equip individuals with the knowledge to make prudent financial decisions. This includes an understanding of concepts like the time value of money, risk and return, and portfolio management.

Stock valuation and concepts like the Dividend Discount Model are pivotal in this field of study. Students are taught not only how to calculate the value of an investment but also the underlying principles that influence these valuations.

Importance in the Curriculum

Students of finance must grasp these fundamental principles to evaluate potential investments critically. When utilizing models like the Gordon Growth Model employed in the example, it's imperative for students to understand both the mathematical calculations as well as the assumptions and limitations inherent in the models they use. Effective financial management education lays the foundation for making informed investment decisions, which is crucial for prospective financial analysts, portfolio managers, or any individual managing personal investment strategies.