Math Problem Statement

Financial analysts forecast XYZ company's growth for the future to be a constant 8%. XYZ's recent dividend was $0.88. What is the value of XYZ stock when the required return is 12%?

Solution

To find the value of XYZ's stock using the Dividend Discount Model (DDM), specifically the Gordon Growth Model, we can apply the following formula:

P0=D0×(1+g)rgP_0 = \frac{D_0 \times (1 + g)}{r - g}

Where:

  • P0P_0 is the present value of the stock (what we're solving for).
  • D0D_0 is the most recent dividend paid, which is $0.88.
  • gg is the constant growth rate of dividends, which is 8% or 0.08.
  • rr is the required return, which is 12% or 0.12.

Step-by-Step Calculation:

  1. Calculate the next expected dividend, D1D_1: D1=D0×(1+g)=0.88×(1+0.08)=0.88×1.08=0.9504D_1 = D_0 \times (1 + g) = 0.88 \times (1 + 0.08) = 0.88 \times 1.08 = 0.9504

  2. Apply the Gordon Growth Model formula to find the stock price, P0P_0: P0=0.95040.120.08=0.95040.04=23.76P_0 = \frac{0.9504}{0.12 - 0.08} = \frac{0.9504}{0.04} = 23.76

Final Answer:

The value of XYZ's stock is $23.76.

Do you want more details on this calculation or have any questions?

Related Questions:

  1. How does the required rate of return affect stock valuation?
  2. What happens to the stock value if the dividend growth rate changes?
  3. How is the Dividend Discount Model different from other stock valuation methods?
  4. What assumptions are made in the Gordon Growth Model?
  5. How can analysts estimate the future growth rate of a company's dividends?
  6. How does inflation impact the required rate of return?
  7. Can the Dividend Discount Model be used for companies that don't pay dividends?
  8. What other models can be used to value a stock with irregular dividend growth?

Tip:

When using the Dividend Discount Model, remember that it's most accurate for companies with stable and predictable dividend growth.

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Math Problem Analysis

Mathematical Concepts

Finance
Dividend Discount Model
Gordon Growth Model

Formulas

Dividend Discount Model formula
Gordon Growth Model formula

Theorems

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Suitable Grade Level

Professional