The problem provides the dividends paid by SHELL Company for the last four years: $1.7, $2.5, $2.7, $3.2$. It also states that the Year 4 dividend ($D_0$) is $3.2$ and will grow at a constant rate like in the previous period. The required rate of return is $0.47$. We need to find the growth rate of the dividends and the price of the stock.

1. Problem Description

The problem provides the dividends paid by SHELL Company for the last four years: $1.7,$2.5, $2.7,$3.2$. It also states that the Year 4 dividend ($D_0$) is$3.2$and will grow at a constant rate like in the previous period. The required rate of return is$0.47$. We need to find the growth rate of the dividends and the price of the stock.

2. Solution Steps

First, we need to find the growth rate $g$ of the dividends. Since the problem states that the dividends will grow at the same rate as in the previous period, we need to calculate the growth rate between each year.

Year 1 to Year 2: Growth rate = $(2.5 - 1.7) / 1.7 = 0.8 / 1.7 \approx 0.4706$

Year 2 to Year 3: Growth rate = $(2.7 - 2.5) / 2.5 = 0.2 / 2.5 = 0.08$

Year 3 to Year 4: Growth rate = $(3.2 - 2.7) / 2.7 = 0.5 / 2.7 \approx 0.1852$

Since the problem states that the dividend will grow at a constant rate "like in the previous period", we should use the growth from year 3 to year

4. So $g = 0.1852$.

Next, we use the Gordon Growth Model (also known as the Dividend Discount Model) to calculate the price of the stock. The formula for the stock price $P_0$ is:

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

where $D_1$ is the expected dividend next year, $r$ is the required rate of return, and $g$ is the growth rate.

We are given $D_0 = 3.2$, $r = 0.47$, and $g = 0.1852$. We can find $D_1$ by multiplying $D_0$ by $(1 + g)$:

$D_1 = D_0 * (1 + g) = 3.2 * (1 + 0.1852) = 3.2 * 1.1852 = 3.79264$

Now we can plug the values into the formula:

$P_0 = \frac{3.79264}{0.47 - 0.1852} = \frac{3.79264}{0.2848} \approx 13.316$

3. Final Answer

Growth rate: 0.1852

Price of the stock: 13.316