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Harrison Clothiers' stock currently sells for \(\$ 20\) a share. It just paid a dividend of \(\$ 1.00\) a share (that is, \(D_{0}=\$ 1.00\) ). The dividend is expected to grow at a constant rate of 6 percent a year. What stock price is expected 1 year from now? What is the required rate of return?

Short Answer

Expert verified
The stock price is expected to be $20.68 one year from now, and the required rate of return is 11.3%.

Step by step solution

01

Calculate Expected Dividend for Next Year

To find the expected dividend next year, use the formula for the expected dividend based on growth rate: \( D_1 = D_0 \times (1 + g) \) where \( D_0 = \\(1.00 \) and \( g = 6\% = 0.06 \). Calculate \( D_1 = 1.00 \times 1.06 = \\)1.06 \).
02

Calculate Expected Stock Price Next Year

To calculate the expected stock price one year from now, use the Gordon Growth Model (Dividend Discount Model): \( P_1 = \frac{D_1}{r - g} \), but first, we need to figure out \( r \).
03

Find the Required Rate of Return

The formula for the current price of a stock is \( P_0 = \frac{D_1}{r - g} \). Rearrange this formula to find \( r \): \( r = \frac{D_1}{P_0} + g \). Substitute the values: \( D_1 = \\(1.06 \), \( P_0 = \\)20 \), and \( g = 0.06 \), so \( r = \frac{1.06}{20} + 0.06 = 0.113 \) or \( 11.3\% \).
04

Verify Stock Price Next Year using Required Rate of Return

To find the expected stock price one year from now, use the calculated \( r \) to find \( P_1 \): \( P_1 = \frac{D_1}{r - g} \). Since \( D_1 = \\(1.06 \), \( r = 11.3\% \), and \( g = 6\% \), then \( P_1 = \frac{1.06}{0.113 - 0.06} = \\)20.68 \).

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Key Concepts

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

Stock Price Prediction
Predicting the future stock price is a magic everyone wishes for. Using the dividend growth model, also known as the Gordon Growth Model, we get a scientific approach to this. It helps to calculate the future stock price based on the expected growth of dividends. In this model, the expected stock price one year from now (or more) hinges on dividends expected to be paid in that future period.

The model formula revolves around the dividend expected for next year \( D_1 \) and the required rate of return \( r \). Mathematically, it is expressed as:
  • \( P_1 = \frac{D_1}{r - g} \)
Here, \( P_1 \) is the expected stock price, \( r \) is the required rate of return, and \( g \) is the dividend growth rate. In our example, we calculated that in a year, the stock price will be approximately $20.68. This model gives investors a target price they can expect based on the current dividend payment, adjusted by a growth rate.
Required Rate of Return
Understanding the required rate of return is crucial for investors. It's the minimum return investors expect to earn from an investment, compensating for the risk taken. To arrive at this in a dividend growth model, first, calculate the expected future dividends, then use the formula for the stock's price.

The required rate of return \( r \) in relation to current stock price can be calculated as:
  • \( r = \frac{D_1}{P_0} + g \)
Where \( D_1 \) is the expected dividend next year, \( P_0 \) is the current stock price, and \( g \) is the growth rate. In simpler terms, you start with the ratio of future dividends to the current stock price and add the constant growth rate. For Harrison Clothiers, using the given data, the required rate of return was found to be 11.3%. This measurement aids investors in deciding if the stock aligns with their financial goals.
Financial Management Concepts
Financial management is about planning, organizing, and controlling financial resources so that a company can achieve its goals. Concepts like stock price prediction and required rate of return are fundamental parts of understanding financial health and performance.

Key principles in financial management include:
  • Understanding growth rates for dividends or returns.
  • Using models like the Gordon Growth Model for informed predictions.
  • Evaluating investments based on risks and expected returns.
Whether managing personal investments or corporate finances, having a strong grasp of these concepts ensures better decision-making and control over financial outcomes. In essence, knowledge of financial management concepts allows individuals and businesses to align their financial strategies with their long-term objectives.

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Most popular questions from this chapter

Taussig Technologies Corporation (TTC) has been growing at a rate of 20 percent per year in recent years. This same growth rate is expected to last for another 2 years, then to decline to \(g_{n}=6 \%\). a. If \(\mathrm{D}_{0}=\$ 1.60\) and \(\mathrm{r}_{\mathrm{s}}=10 \%\) what is TTC's stock worth today? What are its expected dividend and capital gains yields at this time, that is, during Year \(1 ?\) b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect the price, dividend yield, and capital gains yield? Answer in words only. c. What will TTC's dividend and capital gains yields be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy. d. Of what interest to investors is the changing relationship between dividend and capital gains yields over time?

Microtech Corporation is expanding rapidly and currently needs to retain all of its earnings, hence it does not pay dividends. However, investors expect Microtech to begin paying dividends, beginning with a dividend of \(\$ 1.00\) coming 3 years from today. The dividend should grow rapidly-at a rate of 50 percent per year-during Years 4 and \(5,\) but after Year 5 growth should be a constant 8 percent per year. If the required return on Microtech is 15 percent, what is the value of the stock today?

Robert Balik and Carol Kiefer are senior vice presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company's pension fund management division, with Balik having responsibility for fixed income securities (primarily bonds) and Kiefer being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities, and Balik and Kiefer, who will make the actual presentation, have asked you to help them. To illustrate the common stock valuation process, Balik and Kiefer have asked you to analyze the Bon Temps Company, an employment agency that supplies word-processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions: a. Describe briefly the legal rights and privileges of common stockholders. b. (1) Write out a formula that can be used to value any stock, regardless of its dividend pattern. (2) What is a constant growth stock? How are constant growth stocks valued? (3) What are the implications if a company forecasts a constant \(g\) that exceeds its \(r_{s} ?\) Will many stocks have expected \(g > r_{s}\) in the short run (that is, for the next few years)? In the long run (that is, forever)? c. Assume that Bon Temps has a beta coefficient of \(1.2,\) that the risk-free rate (the yield on T-bonds) is 7 percent, and that the required rate of return on the market is 12 percent. What is Bon Temps' required rate of return? d. Assume that Bon Temps is a constant growth company whose last dividend (D), which was paid yesterday) was \(\$ 2.00\) and whose dividend is expected to grow indefinitely at a 6 percent rate. (1) What is the firm's expected dividend stream over the next 3 years? (2) What is its current stock price? (3) What is the stock's expected value 1 year from now? (4) What are the expected dividend yield, capital gains yield, and total return during the first year? e. Now assume that the stock is currently selling at \(\$ 30.29\). What is its expected rate of return? f. What would the stock price be if its dividends were expected to have zero growth? g. Now assume that Bon Temps is expected to experience nonconstant growth of 30 percent for the next 3 years, then to return to its long-run constant growth rate of 6 percent. What is the stock's value under these conditions? What are its expected dividend and capital gains yields in Year 1? Year 4? h. Suppose Bon Temps is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 6 percent in the fourth year. What would its value be then? What would its expected dividend and capital gains yields be in Year \(1 ?\) In Year \(4 ?\) i. Finally, assume that Bon Temps' earnings and dividends are expected to decline at a constant rate of 6 percent per year, that is, \(g=-6 \%\). Why would anyone be willing to buy such a stock, and at what price should it sell? What would be its dividend and capital gains yields in each year? j. Suppose Bon Temps embarked on an aggressive expansion that requires additional capital. Management decided to finance the expansion by borrowing \(\$ 40\) million and by halting dividend payments to increase retained earnings. Its WACC is now 10 percent, and the projected free cash flows for the next 3 years are \(-\$ 5\) million, \(\$ 10\) million, and \(\$ 20\) million. After Year \(3,\) free cash flow is projected to grow at a constant 6 percent. What is Bon Temps' total value? If it has 10 million shares of stock and \(\$ 40\) million of total debt, what is the price per share? k. For Bon Temps' stock to be in equilibrium, what relationship must exist between its estimated intrinsic value and its current stock price and between its expected and required rates of return? Are the equilibrium intrinsic value and expected rate of return the values that management estimates or values as estimated by some other entity? Explain. l. If equilibrium does not exist, how will it be established? m. Suppose Bon Temps decided to issue preferred stock that would pay an annual dividend of \(\$ 5,\) and the issue price was \(\$ 50\) per share. What would the expected return be on this stock? Would the expected rate of return be the same if the preferred was a perpetual issue or if it had a 20 -year maturity?

Smith Technologies is expected to generate \(\$ 150\) million in free cash flow next year, and \(\mathrm{FCF}\) is expected to grow at a constant rate of 5 percent per year indefinitely. Smith has no debt or preferred stock, and its WACC is 10 percent. If Smith has 50 million shares of stock outstanding, what is the stock's value per share?

Martell Mining Company's ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of 5 percent per year. If \(\mathrm{D}_{0}=\$ 5\) and \(\mathrm{r}_{\mathrm{s}}=15 \%\), what is the value of Martell Mining's stock?

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