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To solve this problem, we need to use the **Dividend Discount Model (DDM)** with constant growth, specifically starting from a future dividend.

Here’s the breakdown:

- The first dividend $ D_1 = 3.75 $ will be paid exactly 3 years from now.
- The dividends will grow at a constant rate $ g = 4.1\% $ thereafter.
- The required rate of return $ r = 10.5\% $.
  
### Step 1: Calculate the value of the stock at year 3 (just before the first dividend).
Since the dividend grows at a constant rate after year 3, the stock price at year 3 can be calculated using the **Gordon Growth Model**:

\[
P_3 = \frac{D_4}{r - g}
\]

Where:
- $ D_4 $ is the dividend in year 4.
- $ P_3 $ is the stock price at the end of year 3.
  
Since the first dividend in year 3 is $ D_3 = 3.75 $, the dividend in year 4 is:

\[
D_4 = D_3 \times (1 + g) = 3.75 \times (1 + 0.041) = 3.75 \times 1.041 = 3.905375
\]

Now, the price at the end of year 3 is:

\[
P_3 = \frac{D_4}{r - g} = \frac{3.905375}{0.105 - 0.041} = \frac{3.905375}{0.064} = 61.02
\]

### Step 2: Calculate the present value of the stock today.
Since $ P_3 = 61.02 $ is the value of the stock at the end of year 3, we need to discount this value back to the present (year 0):

\[
P_0 = \frac{P_3}{(1 + r)^3} = \frac{61.02}{(1 + 0.105)^3} = \frac{61.02}{1.349858625} \approx 45.21
\]

Thus, the fair price for the stock today is approximately **$45.21**.

Would you like further clarification on any of the steps?

Here are 5 related questions to explore:
1. How does the dividend growth rate affect the stock price?
2. What happens if the required rate of return changes?
3. Can the DDM model apply if dividends don’t grow at a constant rate?
4. How would the stock price change if the first dividend were delayed further?
5. How do you adjust the model for non-dividend-paying companies?

**Tip**: When using the DDM model, ensure the growth rate is always less than the required rate of return to avoid unrealistic results.

A stock currently pays no dividends. However, you believe it will pay its first dividend of $3.75 exactly 3 years from now. Future dividends will grow at a constant 4.1% every year thereafter. If the stock's required rate of return is 10.5%, what is a fair price for the stock today? Round your answer to the nearest penny.

Calculate the fair price of a stock with no current dividends but expected future growth. Using the Dividend Discount Model, learn how to apply discounting techniques to determine the present value of the stock based on projected dividends, growth rates, and required returns.

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