Math Problem Statement

You’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 77.40 10.43 Acevedo .36 2.6 6 13.90 −.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 50.42 14.13 Manta Energy .98 6.3 6 15.61 −.26 35.00 20.74 Winter Sports .32 1.5 28 ??question mark .18 According to your research, the growth rate in dividends for Manta Energy for the previous 10 years has been negative 13 percent. If investors feel this growth rate will continue, what is the required return for the stock?

Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

Solution

To determine the required return for Manta Energy's stock, we can use the Dividend Discount Model (DDM), specifically the Gordon Growth Model. The formula is:

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

where:

  • rr = required return
  • D1D_1 = expected dividend next year
  • P0P_0 = current stock price
  • gg = growth rate of dividends

Step 1: Identify the values

  • Current dividend (D0D_0) for Manta Energy: $0.98
  • Current stock price (P0P_0): $15.61
  • Dividend growth rate (gg): -13% or -0.13

Step 2: Calculate the expected dividend (D1D_1)

D1=D0×(1+g)D_1 = D_0 \times (1 + g)

D1=0.98×(10.13)D_1 = 0.98 \times (1 - 0.13)

D1=0.98×0.87=0.8526D_1 = 0.98 \times 0.87 = 0.8526

Step 3: Use the Gordon Growth Model

r=0.852615.610.13r = \frac{0.8526}{15.61} - 0.13

r=0.054630.13r = 0.05463 - 0.13

r=0.07537 or 7.54%r = -0.07537 \text{ or } -7.54\%

Conclusion

The required return for Manta Energy's stock, given the continued negative dividend growth rate, is:

7.54%\boxed{-7.54\%}

Would you like more details or have any questions about this process?

Related Questions

  1. How does a negative dividend growth rate affect the stock's required return?
  2. What other models can be used to determine the required return if dividends are not consistent?
  3. Can a stock still be considered a good investment if the required return is negative?
  4. How do changes in the dividend yield impact the required return?
  5. What assumptions does the Gordon Growth Model rely on, and how can they limit its application?

Tip

The Gordon Growth Model is most effective for companies with stable dividend growth rates. For firms with irregular dividends, consider other valuation models.

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Math Problem Analysis

Mathematical Concepts

Finance
Dividend Discount Model
Gordon Growth Model
Negative Growth Rate

Formulas

r = D1 / P0 + g
D1 = D0 * (1 + g)

Theorems

Gordon Growth Model

Suitable Grade Level

Undergraduate Level (Finance or Economics)