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We are asked to find the fair price of a stock based on its future dividend payments, with a required rate of return of 9.7%. Here's how to calculate it step by step:

### Step-by-Step Approach:

1. **Identify Dividend Payments:**
   - Year 1: Dividend of $2.97
   - Year 2: Dividend of $2.38
   - From Year 3 onwards: Constant dividend of $1.95

2. **Use the Dividend Discount Model (DDM):**
   Since the dividends are different for the first two years and constant thereafter, this is a **multi-stage dividend discount model** (a combination of a discounted cash flow for the first two years and the Gordon Growth Model starting from year 3).

3. **Present Value of Dividends in the First Two Years:**
   We'll discount the first two dividend payments to the present using the formula for the present value of a future cash flow:
   \[
   PV = \frac{D}{(1+r)^t}
   \]
   Where:
   - $ D $ is the dividend,
   - $ r $ is the required rate of return (9.7% or 0.097),
   - $ t $ is the number of years until the dividend is received.

4. **Present Value of Dividends Starting Year 3 (Gordon Growth Model):**
   Since the dividend becomes constant from year 3 onwards, we use the Gordon Growth Model for a perpetuity:
   \[
   P_2 = \frac{D_3}{r}
   \]
   This gives us the value of the stock at the end of year 2 based on the perpetuity starting in year 3. Then, we'll discount this value back to the present.

### Calculation:

1. **Dividend in Year 1:**
   \[
   PV_1 = \frac{2.97}{(1 + 0.097)^1} = \frac{2.97}{1.097} \approx 2.71
   \]

2. **Dividend in Year 2:**
   \[
   PV_2 = \frac{2.38}{(1 + 0.097)^2} = \frac{2.38}{(1.097)^2} \approx \frac{2.38}{1.204} \approx 1.98
   \]

3. **Value of Dividends from Year 3 onwards (perpetuity):**
   Since the dividend becomes constant at $1.95 from year 3 onwards, we use the Gordon Growth Model to find the value at the end of Year 2:
   \[
   P_2 = \frac{1.95}{0.097} \approx 20.10
   \]
   Now, discount this to the present (Year 0):
   \[
   PV_{P_2} = \frac{20.10}{(1.097)^2} \approx \frac{20.10}{1.204} \approx 16.69
   \]

4. **Total Present Value (Fair Price of Stock):**
   \[
   P_0 = PV_1 + PV_2 + PV_{P_2} \approx 2.71 + 1.98 + 16.69 \approx 21.38
   \]

Thus, the fair price of the stock today is **$21.38**.

---

Would you like further details or have any questions on this approach?

Here are some related questions for further exploration:
1. How does the required rate of return affect the stock price?
2. What happens if the dividends grow at a constant rate instead of being fixed from year 3?
3. How would changing the first two dividends impact the overall stock price?
4. What if the required rate of return was 7% instead of 9.7%?
5. How does this model differ from a scenario where dividends are expected to decrease?

**Tip:** Always double-check your inputs, such as rates and dividend values, as small changes can significantly affect the final stock price calculation.

You expect a stock to pay annual dividends of $2.97 and $2.38 in each of the next two years, with the first dividend occurring one year from today. Starting three years from now, and continuing every year thereafter, the stock will pay an annual dividend of $1.95. If the stock's required rate of return is 9.7%, what is a fair price for the stock today? Round your answer to the nearest penny.

Learn how to calculate the fair price of a stock that pays varying dividends over time using the Dividend Discount Model and the time value of money. This example explores dividends in the first two years and perpetuity from year three onward with a required return of 9.7%.

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