Math Problem Statement

inancial analysts forecast Apex Technologies Inc. (ATX) growth for the future to be 9.5 percent. ATX’s most recent dividend was $1.25.

What is the fair present value of Apex Technologies Inc.’s stock if the required rate of return is 12.0 percent?

Solution

To determine the fair present value of Apex Technologies Inc.'s stock using the Dividend Discount Model (DDM) with constant growth, we can use the following formula:

P0=D1rgP_0 = \frac{D_1}{r - g}

Where:

  • P0P_0 is the fair present value of the stock.
  • D1D_1 is the expected dividend in the next year.
  • rr is the required rate of return.
  • gg is the dividend growth rate.

Step 1: Calculate the expected dividend for next year

The most recent dividend is D0=1.25D_0 = 1.25, and the growth rate is g=9.5%g = 9.5\% or 0.095. So, the expected dividend next year D1D_1 is:

D1=D0×(1+g)D_1 = D_0 \times (1 + g)

D1=1.25×(1+0.095)=1.25×1.095=1.36875D_1 = 1.25 \times (1 + 0.095) = 1.25 \times 1.095 = 1.36875

Step 2: Apply the DDM formula

Now, using r=12.0%r = 12.0\% or 0.12 and g=9.5%g = 9.5\% or 0.095:

P0=1.368750.120.095P_0 = \frac{1.36875}{0.12 - 0.095}

P0=1.368750.025=54.75P_0 = \frac{1.36875}{0.025} = 54.75

Conclusion:

The fair present value of Apex Technologies Inc.'s stock is $54.75.

Would you like further details or clarification?


Here are some related questions for further exploration:

  1. How does the Dividend Discount Model handle non-constant growth rates?
  2. What factors could affect the required rate of return for a company?
  3. How would an increase in the growth rate affect the stock's value?
  4. What are the limitations of the Dividend Discount Model?
  5. How does this valuation method compare with Price-to-Earnings (P/E) ratio analysis?

Tip: The Dividend Discount Model assumes that dividends will grow at a constant rate forever, so it's ideal for companies with stable growth.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Finance
Dividend Discount Model (DDM)
Growth Rate

Formulas

P_0 = D_1 / (r - g)
D_1 = D_0 * (1 + g)

Theorems

Dividend Discount Model

Suitable Grade Level

Undergraduate Finance/Business Courses