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For the past six years, the stock price of Slippery Rock Mining has been increasing at a rate of 8.4 percent per year. Currently, the stock is selling for \( \$ 83 \) per share and has a required return of 10.1 percent. What is the dividend yield? a. \( 1.7 \% \) ob. \( 9.2 \% \) c. \( 3.6 \% \) (d. \( 5.2 \% \) e. \( 8.4 \% \)

Ask by Romero Dawson. in the United States
Mar 12,2025

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Tutor-Verified Answer

Answer

The dividend yield is 1.7%.

Solution

1. The stock price can be modeled using the Gordon Growth Model: \[ P = \frac{D_1}{r - g} \] where: - \( P \) is the current stock price, - \( D_1 \) is the expected dividend next period, - \( r \) is the required return, - \( g \) is the dividend growth rate (which in this case equals the rate at which the stock has been increasing). 2. Rearranging the formula to solve for the dividend yield \( \frac{D_1}{P} \), we have: \[ \frac{D_1}{P} = r - g \] 3. Given: \[ r = 10.1\% = 0.101 \quad \text{and} \quad g = 8.4\% = 0.084 \] 4. Substitute the values: \[ \frac{D_1}{P} = 0.101 - 0.084 = 0.017 \] 5. Converting \( 0.017 \) to a percentage gives: \[ 0.017 \times 100\% = 1.7\% \] Thus, the dividend yield is \(1.7\%\).

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To find the dividend yield, we can use the formula: Dividend Yield = Required Return - Growth Rate. In this case, the required return is 10.1% and the growth rate is 8.4%. So, we have: Dividend Yield = 10.1% - 8.4% = 1.7%. Thus, the correct answer is (a) \( 1.7 \% \). Understanding the difference between dividend yield and growth rate is key for investors. The dividend yield focuses on the income generated from investments, while the growth rate reflects the potential appreciation of stock value over time. Keeping these terms straight can help make informed investment decisions! An excellent way to comprehend dividend yield is to watch various companies and their practices over the years. Dividend Aristocrats, for example, are companies that have consistently increased their dividends for decades. They serve as a remarkable study for balancing growth and income in a portfolio, providing insights into the long-term reliability of dividend yields!

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