Cooperton Mining just announced it will cut its dividend from $4.16 to $2.56 per share and use the extra funds to expand. Prior to the​ announcement, Cooperton's dividends were expected to grow at a 3.1% ​rate, and its share price was $48.39. With the new​ expansion, Cooperton's dividends are expected to grow at a 5.1% rate. What share price would you expect after the​ announcement? (Assume​ Cooperton's risk is unchanged by the new​ expansion.)

What share price would you expect after the​ announcement?
A) The equity cost of capital is ____

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.

Cooperton Mining just announced it will cut its dividend from $4.16 to $2.56 per share and use the extra funds to expand. Prior to the announcement, Cooperton's dividends were expected to grow at a 3.1% rate, and its share price was $48.39. With the new expansion, Cooperton's dividends are expected to grow at a 5.1% rate. What share price would you expect after the announcement? (Assume Cooperton's risk is unchanged by the new expansion.) What share price would you expect after the announcement? A) The equity cost of capital is ____

Learn how to calculate Cooperton Mining's new share price after a dividend cut using the Dividend Discount Model (DDM). The problem involves calculating the equity cost of capital, growth rates, and expected future dividends. Suitable for finance students and professionals.

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