Math Problem Statement

ou’ve collected the following information from your favorite financial website.

52-Week Price Stock (Dividend) Dividend Yield % PE Ratio Close Price Net Change Hi Lo 78.10 10.50 Acevedo .43 2.9 6 14.60 −.24 55.81 33.42 Georgette, Incorporated 1.54 3.8 10 40.43 −.01 130.93 69.50 YBM 2.00 2.2 10 88.97 3.07 50.24 13.95 Manta Energy .80 5.2 6 15.43 −.26 35.00 20.74 Winter Sports .32 1.5 28 ??question mark .18 According to analysts, the growth rate in dividends for Acevedo for the previous 10 years has been 4.25 percent. If investors feel this growth rate will continue, what is the required return for the company's stock?

Note: Do not ro

Solution

To calculate the required return for Acevedo's stock, we can use the Gordon Growth Model (also known as the Dividend Discount Model for stocks with constant growth). The formula is:

r=D1P0+gr = \frac{D_1}{P_0} + g

Where:

  • rr is the required return.
  • D1D_1 is the expected dividend for the next year.
  • P0P_0 is the current price of the stock.
  • gg is the growth rate of dividends.

Step 1: Identify the given values:

  • Current dividend D0=0.43D_0 = 0.43 (Acevedo's current dividend).
  • Dividend growth rate g=4.25%=0.0425g = 4.25\% = 0.0425.
  • Current price P0=14.60P_0 = 14.60.

Step 2: Calculate the expected dividend D1D_1:

Since dividends are expected to grow, the expected dividend D1D_1 for next year is: D1=D0×(1+g)D_1 = D_0 \times (1 + g) D1=0.43×(1+0.0425)=0.43×1.0425=0.4483D_1 = 0.43 \times (1 + 0.0425) = 0.43 \times 1.0425 = 0.4483

Step 3: Apply the formula:

Now we can calculate the required return: r=0.448314.60+0.0425r = \frac{0.4483}{14.60} + 0.0425 r=0.0307+0.0425=0.0732 or 7.32%r = 0.0307 + 0.0425 = 0.0732 \text{ or } 7.32\%

Conclusion:

The required return for Acevedo's stock is 7.32%.

Would you like more details or explanations on any part of the solution?

Here are 5 related questions you might consider:

  1. How does the Gordon Growth Model work for stocks with non-constant growth?
  2. What impact does a higher dividend growth rate have on the required return?
  3. Can the required return be negative under certain circumstances?
  4. What are the limitations of using the Dividend Discount Model for stock valuation?
  5. How does the dividend yield factor into stock price predictions?

Tip: Always ensure that the dividend growth rate is sustainable by looking at the company's long-term financial health.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Stock Valuation
Growth Rate
Dividend Discount Model (Gordon Growth Model)

Formulas

r = D1 / P0 + g
D1 = D0 × (1 + g)

Theorems

Gordon Growth Model

Suitable Grade Level

Undergraduate Finance or Economics