We are dealing with a dividend discount model (DDM) problem, where the price of a stock is determined by the present value of its future dividends. This formula is typically used to value stocks that pay dividends and grow at a constant rate:

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

Where:

• $P_0$ is the current share price.
• $D_1$ is the dividend expected in the next period.
• $r$ is the equity cost of capital (required rate of return).
• $g$ is the dividend growth rate.

Step 1: Calculate the Equity Cost of Capital

We first need to find the equity cost of capital before the dividend cut, using the data before the announcement:

• Current price $P_0 = 48.39$
• Dividend expected next year $D_1 = 4.16 \times (1 + 0.031) = 4.29$
• Growth rate before announcement $g = 3.1\% = 0.031$

Using the formula:

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

Rearranging to solve for $r$:

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

Substitute the values:

$r = \frac{4.29}{48.39} + 0.031 = 0.08867 + 0.031 = 0.11967 \quad \text{or} \quad 11.97\%$

So, the equity cost of capital $r = 11.97\%$.

Step 2: Calculate the New Share Price After the Announcement

With the new dividend and growth rate, we can find the new share price using the same formula:

• New dividend $D_1 = 2.56 \times (1 + 0.051) = 2.56 \times 1.051 = 2.69$
• New growth rate $g = 5.1\% = 0.051$
• The equity cost of capital remains the same $r = 11.97\% = 0.1197$

Now, apply the formula for the new share price:

$P_0 = \frac{D_1}{r - g} = \frac{2.69}{0.1197 - 0.051} = \frac{2.69}{0.0687} = 39.15$

Final Answer

After the announcement, the expected new share price is approximately $39.15.

Summary:

• Equity cost of capital = 11.97%
• New share price after the announcement = $39.15

Would you like more details on this process, or do you have any specific questions?

Here are 5 related questions to deepen your understanding:

1. How would the stock price change if the growth rate was 6% instead of 5.1%?
2. How does changing the risk profile affect the cost of capital in the dividend discount model?
3. What is the impact of dividend cuts on investor sentiment and stock prices in general?
4. How would Cooperton’s decision to reinvest rather than pay dividends affect long-term growth?
5. How does the dividend discount model differ for companies with fluctuating dividends?

Tip: When using the DDM, remember that small changes in the growth rate ($g$) can have a significant impact on the stock price, as they affect the denominator in the valuation formula.