Math Problem Statement

Mannix Corporation stock currently sells for $105 per share. The market requires a return of 14 percent on the firm's stock.

If the company maintains a constant 8 percent growth rate in dividends, what was the most recent dividend per share paid on the stock?

Solution

We can solve this problem using the Dividend Discount Model (DDM), specifically the Gordon Growth Model. The formula for the price of a stock with constant dividend growth is:

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

Where:

  • P0P_0 is the current stock price.
  • D1D_1 is the dividend to be paid next year.
  • rr is the required return (14% or 0.14).
  • gg is the dividend growth rate (8% or 0.08).

We are looking for D0D_0, the most recent dividend paid, but the formula gives D1D_1, the next dividend. We can relate the two using:

D1=D0(1+g)D_1 = D_0(1 + g)

Step 1: Rearrange the formula to solve for D1D_1

D1=P0×(rg)D_1 = P_0 \times (r - g) D1=105×(0.140.08)D_1 = 105 \times (0.14 - 0.08) D1=105×0.06=6.30D_1 = 105 \times 0.06 = 6.30

Step 2: Solve for D0D_0

Since D1=D0(1+g)D_1 = D_0(1 + g), we can solve for D0D_0: D0=D11+gD_0 = \frac{D_1}{1 + g} D0=6.301+0.08=6.301.085.83D_0 = \frac{6.30}{1 + 0.08} = \frac{6.30}{1.08} \approx 5.83

Thus, the most recent dividend paid per share was approximately $5.83.


Would you like more details or have any questions?

Here are 5 related questions you might explore next:

  1. How does a change in the required return affect the stock price?
  2. What happens to the stock price if the dividend growth rate increases?
  3. How do companies decide on their dividend growth rate?
  4. Can the Dividend Discount Model be used for non-dividend paying stocks?
  5. What are other methods of valuing stocks?

Tip: The Gordon Growth Model assumes that dividends grow at a constant rate indefinitely, so it's best applied to mature companies with stable dividend growth.

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Math Problem Analysis

Mathematical Concepts

Finance
Dividend Discount Model
Algebra

Formulas

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

Theorems

Gordon Growth Model (Dividend Discount Model)

Suitable Grade Level

Undergraduate Finance or Business