You expect a share of stock to pay dividends of $2.20, $2.55, and $2.70 in each of the next 3 years. You believe the stock will sell for $34.00 at the end of the third year.

What is the stock price if the discount rate for the stock is 20%?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

To calculate the stock price today based on the expected dividends and the future stock price, we can use the **Dividend Discount Model (DDM)**. Specifically, since we are given dividends over the next three years and a stock price at the end of the third year, we'll use the following formula:

\[
P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3 + P_3}{(1+r)^3}
\]

Where:
- $P_0$ = Price of the stock today
- $D_1, D_2, D_3$ = Dividends expected in years 1, 2, and 3
- $P_3$ = Stock price at the end of year 3
- $r$ = Discount rate (20% or 0.20)

### Given:
- $D_1 = 2.20$
- $D_2 = 2.55$
- $D_3 = 2.70$
- $P_3 = 34.00$
- $r = 0.20$

Now, let's calculate $P_0$:

\[
P_0 = \frac{2.20}{(1 + 0.20)^1} + \frac{2.55}{(1 + 0.20)^2} + \frac{2.70 + 34.00}{(1 + 0.20)^3}
\]

We'll calculate each term step by step.

### Step 1: Calculate each term

1. $\frac{2.20}{1.20^1}$
2. $\frac{2.55}{1.20^2}$
3. $\frac{2.70 + 34.00}{1.20^3}$

I'll compute these values now.The price of the stock today, based on the given dividends and discount rate, is approximately **$24.84**.

Would you like more details on any part of the calculation, or do you have any other questions?

Here are 5 related questions to explore further:
1. How would the stock price change if the discount rate was lower?
2. What happens to the stock price if the dividends increase in the second year?
3. How would a delayed dividend payment affect the stock price?
4. What if the stock price at the end of the third year was expected to be $40 instead of $34?
5. How does the present value of dividends change with higher discount rates?

**Tip:** The higher the discount rate, the lower the present value of future cash flows like dividends. This is why higher risk (represented by a higher discount rate) generally lowers stock prices.

You expect a share of stock to pay dividends of $2.20, $2.55, and $2.70 in each of the next 3 years. You believe the stock will sell for $34.00 at the end of the third year. What is the stock price if the discount rate for the stock is 20%? Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

Learn how to calculate the current stock price based on expected dividends of $2.20, $2.55, and $2.70 over 3 years, with a future stock price of $34 and a 20% discount rate. This example uses the Dividend Discount Model (DDM) to find the stock's value today.

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