We are given the dividends paid by SHELL Company for the last four years. We are told that the Year 4 dividend (3.5) is $D_0$ and will grow at a constant rate like in the previous period. We need to find the price of the stock if the required rate of return is 0.29 percent.

1. Problem Description

We are given the dividends paid by SHELL Company for the last four years. We are told that the Year 4 dividend (3.5) is $D_0$ and will grow at a constant rate like in the previous period. We need to find the price of the stock if the required rate of return is 0.29 percent.

2. Solution Steps

First, we need to calculate the growth rate of the dividend between year 3 and year

4.

$g = \frac{D_4 - D_3}{D_3} = \frac{3.5 - 2.7}{2.7} = \frac{0.8}{2.7} \approx 0.2963$

So the growth rate $g$ is approximately $29.63\%$.

The required rate of return $r$ is given as $0.29\%$, which is $0.0029$ in decimal form.

We can calculate the price of the stock using the Gordon Growth Model (Dividend Discount Model):

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

where $P_0$ is the current price of the stock, $D_1$ is the expected dividend next year ($D_0 * (1+g)$), $r$ is the required rate of return, and $g$ is the growth rate.

Since we are given $D_0 = 3.5$, we first calculate $D_1$:

$D_1 = D_0 * (1 + g) = 3.5 * (1 + 0.2963) = 3.5 * 1.2963 \approx 4.53705$

Now, we can calculate the price of the stock:

$P_0 = \frac{4.53705}{0.0029 - 0.2963} = \frac{4.53705}{-0.2934} \approx -15.46$

However, the problem states "at a constant rate like in the previous period" which means we should calculate growth as the average growth over the past 3 periods.

$g_{12} = \frac{2.6-1.4}{1.4} = \frac{1.2}{1.4} \approx 0.8571$

$g_{23} = \frac{2.7-2.6}{2.6} = \frac{0.1}{2.6} \approx 0.0385$

$g_{34} = \frac{3.5-2.7}{2.7} = \frac{0.8}{2.7} \approx 0.2963$

This approach does not give a constant rate.

We should assume that the growth is like the *previous* period's growth, which we calculated as $g_{34}$.

We are given that $r = 0.0029$.

Then, the price of the stock is:

$P_0 = \frac{D_1}{r - g} = \frac{D_0(1+g)}{r-g} = \frac{3.5(1+0.2963)}{0.0029-0.2963} = \frac{3.5(1.2963)}{-0.2934} = \frac{4.53705}{-0.2934} \approx -15.46$

Since the growth rate $g$ is greater than the required rate of return $r$, the stock price is negative, which does not make sense. There may be an error in the stated required rate of return, as it is unusually low.

3. Final Answer

The calculated stock price is approximately -15.

4

6. Note: the negative result may indicate an issue with the parameters given, specifically that the growth rate exceeds the required rate of return. In the context of the Gordon Growth Model, this usually indicates an unsustainable situation or that the model itself is not appropriate to the problem.