Math Problem Statement

A firm recently paid an annual dividend of $6.90 per share. This divided increases at 4.1% per year. The stock currently sells for $36.09 per share. What is the rate of return?

Solution

To calculate the rate of return (also called the dividend yield or required rate of return) on the stock, we can use the Dividend Discount Model (DDM) or the Gordon Growth Model since the dividend is growing at a constant rate.

The formula for the rate of return rr is:

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

Where:

  • D1D_1 is the expected dividend next year.
  • P0P_0 is the current stock price.
  • gg is the growth rate of the dividend.

Step 1: Calculate the expected dividend next year D1D_1.

Since the most recent dividend D0D_0 was $6.90 and the dividend grows at 4.1%, the expected dividend next year is:

D1=D0×(1+g)=6.90×(1+0.041)=6.90×1.041=7.18D_1 = D_0 \times (1 + g) = 6.90 \times (1 + 0.041) = 6.90 \times 1.041 = 7.18

Step 2: Plug values into the formula.

Now, we can calculate the rate of return:

r=7.1836.09+0.041r = \frac{7.18}{36.09} + 0.041

r=0.199+0.041=0.240 or 24.0%r = 0.199 + 0.041 = 0.240 \text{ or } 24.0\%

Conclusion:

The rate of return for the stock is approximately 24.0%.


Would you like further details or have any questions? Here are some related topics you could explore:

  1. How does the Gordon Growth Model differ from other dividend valuation models?
  2. What factors affect the stock price in the long term?
  3. How can a firm adjust its dividend policy to increase its stock price?
  4. How does the rate of return impact investment decisions?
  5. What are the risks associated with relying on dividend growth models for stock valuation?

Tip: The rate of return is sensitive to the growth rate and the stock price. Even small changes in the growth rate can have a big impact on your expected return!

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Math Problem Analysis

Mathematical Concepts

Finance
Dividend Discount Model
Growth Rate
Rate of Return

Formulas

r = D1 / P0 + g

Theorems

Dividend Discount Model (Gordon Growth Model)

Suitable Grade Level

Grades 11-12