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Stock Values White Wedding Corporation will pay a \(\$ 3.05\) per share dividend next year. The company pledges to increase its dividend by 5.25 percent per year, indefinitely. If you require an 11 percent return on your investment, how much will you pay for the company's stock today?

Short Answer

Expert verified
Using the Dividend Growth Model, we find the stock price today by the formula \(P_0 = \frac{D_1}{r - g}\), where \(D_1 = \$3.05\), \(r = 0.11\), and \(g = 0.0525\). Plugging these values in, we have \(P_0 = \frac{\$3.05}{0.11 - 0.0525} = \frac{\$3.05}{0.0575} = \$53.04\). Therefore, an investor would be willing to pay \(\$53.04\) per share for the company's stock today.

Step by step solution

01

Write down the given values

We are given the following information: - The dividend for next year (\(D_1\)) will be \(\$3.05\) per share - The growth rate of the dividend (g) is 5.25% per year, or 0.0525 as a decimal - The required return on investment (r) is 11%, or 0.11 as a decimal
02

Apply the Dividend Growth Model

Now we can use the Dividend Growth Model to calculate the stock price today: \(P_0 = \frac{D_1}{r - g}\) Plugging in the given values: \(P_0 = \frac{\$3.05}{0.11 - 0.0525}\)
03

Calculate the stock price

Now we simplify the expression and calculate the stock price today: \(P_0 = \frac{\$3.05}{0.0575}\) \(P_0 = \$53.04\) So, based on the given information, an investor would be willing to pay \(\$53.04\) per share for the company's stock today.

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Key Concepts

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

Dividend Growth Rate
The Dividend Growth Rate represents the annualized percentage growth of a company's dividend per share. It is a crucial component of the Dividend Discount Model (DDM), used for valuing a stock. In practice, this rate helps investors understand how much they can expect their dividend payments to grow over time, providing insight into a company’s potential for investment income.

Here's why the dividend growth rate is important:
  • Predictive Power: A steady growth rate indicates strong company performance and management's confidence in future earnings.
  • Investment Planning: Knowing this rate helps investors plan for long-term investments by estimating future returns.
In calculations, like the one in our example, the growth rate (\(g\)) of 5.25% is expressed as a decimal (\(0.0525\)) when applying formulas.

The dividend growth rate is often estimated using historical data, but can be influenced by various factors such as company earnings, market conditions, or changes in business strategy.
Stock Valuation
Stock Valuation is the process of determining the intrinsic value of a company's stock. The Dividend Discount Model is a popular method used by investors to evaluate if a stock is appropriately priced based on its future dividend payments. The formula used is:\[ P_0 = \frac{D_1}{r - g} \]Here, \(P_0\) is the present value of the stock, \(D_1\) is the expected dividend in the next period, \(r\) is the required rate of return, and \(g\) is the growth rate of the dividend.

Let's break down each component:
  • Expected Dividend (\(D_1\)): This is the dividend expected next year, which in our example is \(\$3.05\).
  • Required Rate of Return (\(r\)): This reflects the investor's minimum acceptable return rate. For the given exercise, it's 11%.
  • Growth Rate (\(g\)): The rate at which dividends are expected to grow, which is given as 5.25%.
By plugging these values into the formula, you can derive the stock's intrinsic value, which helps investors decide if the current market price is a good deal. If the intrinsic value is higher than the market price, the stock might be undervalued, representing a potential buying opportunity.
Required Rate of Return
The Required Rate of Return (RRR) is the minimum rate of return an investor expects from an investment. It reflects the investor's opportunity cost of capital, accounting for the risks associated with the investment. In our example, the RRR is 11%.

Investors use this rate to determine whether a stock is worth buying; it essentially acts as a benchmark that potential investments must meet or exceed. This rate is influenced by several factors, including:
  • Risk Level: Higher risk investments typically require a higher RRR to be attractive.
  • Market Conditions: Economic conditions can influence expectations and thus affect the RRR.
  • Investment Horizon: Longer-term investments may accept lower rates due to time for compounding returns.
The RRR is integral to financial models like the Dividend Discount Model, where it helps determine the present value of expected dividends. If dividends grow at a slower rate than the RRR, the calculated stock value will be lower, indicating less projected return compared to the risk.

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Most popular questions from this chapter

Price-Earnings Ratio Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported earnings of \(\$ 750,000\). Without new projects, both firms will continue to generate earnings of \(\$ 750,000\) in perpetuity. Assume that all earnings are paid as dividends and that both firms require a 14 percent rate of return. 1\. What is the current PE ratio for each company? 2\. Pacific Energy Company has a new project that will generate additional earnings of \(\$ \mathbf{1 0 0 , 0 0 0}\) each year in perpetuity. Calculate the new PE ratio of the company. 3\. U.S. Bluechips has a new project that will increase earnings by \(\$ 200,000\) in perpetuity. Calculate the new PE ratio of the firm.

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