Math Problem Statement

A stock's current price is $25.70 and its next dividend of $3.79 will be paid exactly one year from now. You expect future dividends will grow at a constant rate of 2.2% per year thereafter. What is the stock's required rate of return? Enter your answer as a decimal and show four decimal places. For example, if your answer is 5.25%, enter .0525

Solution

To find the stock's required rate of return, we can use the Gordon Growth Model (Dividend Discount Model), which is given by:

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

where:

  • D1D_1 is the expected dividend one year from now,
  • P0P_0 is the current stock price,
  • gg is the growth rate of dividends.

Given values:

  • P0=25.70P_0 = 25.70
  • D1=3.79D_1 = 3.79
  • g=2.2%=0.022g = 2.2\% = 0.022

Calculation:

  1. Calculate the dividend yield (the ratio of D1D_1 to P0P_0): D1P0=3.7925.70=0.1475\frac{D_1}{P_0} = \frac{3.79}{25.70} = 0.1475

  2. Add the growth rate gg to the dividend yield to find rr: r=0.1475+0.022=0.1695r = 0.1475 + 0.022 = 0.1695

Answer:

The stock's required rate of return is 0.1695 (or 16.95%).

Would you like more details, or do you have any questions?


Here are five additional questions related to this topic:

  1. How does the dividend growth rate affect the stock’s required rate of return?
  2. What would the required rate of return be if the dividend growth rate was 3% instead of 2.2%?
  3. How does a decrease in the current stock price affect the required rate of return?
  4. What assumptions does the Gordon Growth Model rely on?
  5. How would a change in the next dividend amount impact the required rate of return?

Tip: When using the Gordon Growth Model, ensure that the growth rate is less than the required rate of return; otherwise, the model becomes invalid.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Dividend Discount Model
Stock Valuation

Formulas

r = (D1 / P0) + g

Theorems

Gordon Growth Model

Suitable Grade Level

Grades 10-12