The problem provides the dividends for years 1 to 4. The dividend for year 4, $D_0 = 3.1$, is assumed to grow at a constant rate, and the required rate of return is $r = 0.45$. The goal is to determine the growth rate $g$ and the price of the stock.

1. Problem Description

The problem provides the dividends for years 1 to

4. The dividend for year 4, $D_0 = 3.1$, is assumed to grow at a constant rate, and the required rate of return is $r = 0.45$. The goal is to determine the growth rate $g$ and the price of the stock.

2. Solution Steps

First, we need to determine the growth rate based on the previous dividends. We can calculate the growth rate between consecutive years and then average them.

Growth rate from year 1 to year 2: $g_{12} = \frac{2.5 - 1.7}{1.7} = \frac{0.8}{1.7} \approx 0.4706$

Growth rate from year 2 to year 3: $g_{23} = \frac{2.7 - 2.5}{2.5} = \frac{0.2}{2.5} = 0.08$

Growth rate from year 3 to year 4: $g_{34} = \frac{3.1 - 2.7}{2.7} = \frac{0.4}{2.7} \approx 0.1481$

Now, we can calculate the average growth rate:

$g = \frac{g_{12} + g_{23} + g_{34}}{3} = \frac{0.4706 + 0.08 + 0.1481}{3} = \frac{0.6987}{3} \approx 0.2329$

The price of the stock can be calculated using the Gordon Growth Model:

$P_0 = \frac{D_1}{r - g} = \frac{D_0(1 + g)}{r - g}$

Where:

$P_0$ is the current price of the stock

$D_0$ is the most recent dividend (year 4 dividend), which is $3.1

$D_1$ is the expected dividend next year

$r$ is the required rate of return, which is $0.45

$g$ is the constant growth rate

$P_0 = \frac{3.1(1 + 0.2329)}{0.45 - 0.2329} = \frac{3.1(1.2329)}{0.2171} = \frac{3.822}{0.2171} \approx 17.60$

So, the growth rate is approximately $0.2329$ and the price of the stock is approximately $17.60$.

3. Final Answer

Growth rate: 0.2329

Price of the stock: 17.60