We are tasked with finding the current dividend per share for a company's stock based on the given conditions. Let's break this down using the Dividend Discount Model (DDM) with constant growth, which can be expressed as:

$P_0 = \frac{D_0 (1 + g)}{r - g}$

Where:

• $P_0$ is the current stock price ($65.60).
• $D_0$ is the current dividend (what we need to find).
• $r$ is the required rate of return (10% or 0.10).
• $g$ is the growth rate of dividends.
• $D_1 = D_0 (1 + g)$ is the next dividend.

Step 1: Break down the total return

We know the total return (required return) is 10%, and it's evenly divided between capital gains yield and dividend yield. This means:

• Dividend yield = 5% or 0.05 (half of 10%)
• Capital gains yield (growth rate, $g$) = 5% or 0.05 (the other half of 10%)

Step 2: Dividend yield formula

Dividend yield is the ratio of the next dividend to the current stock price:

$\text{Dividend yield} = \frac{D_1}{P_0}$

We know: $\frac{D_1}{P_0} = 0.05$

Substitute the values: $\frac{D_0 (1 + g)}{65.60} = 0.05$

Since $g = 0.05$, we can substitute $g$ into the equation:

$\frac{D_0 (1 + 0.05)}{65.60} = 0.05$

$\frac{1.05 D_0}{65.60} = 0.05$

Step 3: Solve for $D_0$

Now solve for $D_0$:

$1.05 D_0 = 65.60 \times 0.05$

$1.05 D_0 = 3.28$

$D_0 = \frac{3.28}{1.05}$

$D_0 = 3.12$

Final Answer:

The current dividend per share is $3.12.

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Do you want more details or have any questions?

Here are 5 related questions to consider:

1. How would the current dividend change if the growth rate was higher?
2. What would happen to the stock price if the required return decreased?
3. How is the capital gains yield affected by changes in the stock's growth rate?
4. How could you estimate future stock prices using the Dividend Discount Model?
5. What are the limitations of the Dividend Discount Model in stock valuation?

Tip: In finance, the dividend yield is often a key factor in determining a stock's appeal to income-focused investors. Make sure to always check for sustainable dividend growth.