The problem provides dividend data for a company, SHELL, over the last four years: Year 1: $2.3$, Year 2: $2.6$, Year 3: $2.8$, Year 4: $3.1$. We are told that the Year 4 dividend ($3.1$) is the current dividend $D_0$ and that the dividends will grow at a constant rate. The required rate of return is given as $0.5$. We need to calculate the growth rate and the price of the stock.

1. Problem Description

The problem provides dividend data for a company, SHELL, over the last four years: Year 1: $2.3$, Year 2: $2.6$, Year 3: $2.8$, Year 4: $3.1$. We are told that the Year 4 dividend ($3.1$) is the current dividend $D_0$ and that the dividends will grow at a constant rate. The required rate of return is given as $0.5$. We need to calculate the growth rate and the price of the stock.

2. Solution Steps

First, we need to find the constant growth rate $g$. We can do this by calculating the growth rates between each consecutive year and then averaging them.

* Growth rate between Year 1 and Year 2: $g_{12} = \frac{2.6 - 2.3}{2.3} = \frac{0.3}{2.3} \approx 0.1304$

* Growth rate between Year 2 and Year 3: $g_{23} = \frac{2.8 - 2.6}{2.6} = \frac{0.2}{2.6} \approx 0.0769$

* Growth rate between Year 3 and Year 4: $g_{34} = \frac{3.1 - 2.8}{2.8} = \frac{0.3}{2.8} \approx 0.1071$

Average growth rate: $g = \frac{0.1304 + 0.0769 + 0.1071}{3} \approx 0.1048$

Since the dividends are assumed to grow at a constant rate like in the previous period, the best estimate for the growth rate is to consider the trend. However, given the question, we can also compute the growth by taking the beginning dividend and the ending dividend for the four periods.

$3.1 = 2.3*(1+g)^3$, so $(1+g)^3 = 3.1/2.3 = 1.3478$. So $1+g = (1.3478)^{1/3} = 1.1043$, so $g=0.1043$.

The dividend growth model states the price of a stock is:

$P_0 = \frac{D_1}{r - g}$

where $P_0$ is the current stock price, $D_1$ is the expected dividend next year, $r$ is the required rate of return, and $g$ is the constant growth rate.

We are given $D_0 = 3.1$, so $D_1 = D_0 * (1 + g) = 3.1 * (1 + 0.1043) = 3.1 * 1.1043 \approx 3.4233$.

Also, $r = 0.5$. Then, $P_0 = \frac{3.4233}{0.5 - 0.1043} = \frac{3.4233}{0.3957} \approx 8.6492 \approx 8.65$

2. Final Answer

Growth rate: 0.1043

Stock price: 8.65