Cooperton Mining just announced it will cut its dividend from $ 3.96$3.96 to $ 2.58$2.58 per share and use the extra funds to expand. Prior to the​ announcement, Cooperton's dividends were expected to grow at a 3.3 %3.3% ​rate, and its share price was $ 48.78$48.78. With the planned​ expansion, Cooperton's dividends are expected to grow at a 4.9 %4.9% rate. What share price would you expect after the​ announcement? (Assume that the new expansion does not change​ Cooperton's risk.) Is the expansion a good​ investment?
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Part 1
The new price for​ Cooperton's stock will be ​$41.64

To determine whether Cooperton Mining's expansion is a good investment, we need to calculate the expected share price after the announcement using the **Dividend Discount Model (DDM)**. The model is expressed as:

\[
P = \frac{D}{r - g}
\]

Where:
- $ P $ is the price of the stock
- $ D $ is the expected dividend per share next year
- $ r $ is the required rate of return (or discount rate)
- $ g $ is the expected growth rate of dividends

### Step 1: Pre-announcement situation
Before the announcement, the stock price was \$48.78, the dividend was \$3.96, and the growth rate of dividends was 3.3%.

Using the DDM formula:

\[
48.78 = \frac{3.96}{r - 0.033}
\]

We solve for $ r $, the required rate of return:

\[
r - 0.033 = \frac{3.96}{48.78}
\]
\[
r - 0.033 = 0.0812
\]
\[
r = 0.0812 + 0.033 = 0.1142 \, \text{or} \, 11.42\%
\]

### Step 2: Post-announcement situation
After the announcement, the dividend is reduced to \$2.58 and the growth rate is expected to increase to 4.9%.

Now, we use the new dividend and growth rate in the DDM:

\[
P = \frac{2.58}{0.1142 - 0.049}
\]

\[
P = \frac{2.58}{0.0652}
\]

\[
P \approx 39.57
\]

Thus, the new price of Cooperton Mining's stock after the announcement would be approximately **\$39.57**.

### Step 3: Is the expansion a good investment?
The stock price has dropped from \$48.78 to \$39.57. Whether this is a good investment depends on whether the future growth potential from the expansion justifies the lower dividend and the current price drop. Investors are expecting higher future dividends due to the expansion, but in the short term, the stock price is likely to decline due to the reduced dividend.

### Conclusion
Given that the price of the stock is expected to fall from \$48.78 to \$39.57, the expansion may initially seem less attractive. However, the increased growth rate (from 3.3% to 4.9%) suggests that over time, investors may benefit from higher future dividends, which could justify the investment in the long run.

Would you like further details or have any questions?

Here are 5 questions related to this concept:
1. How would a higher required rate of return affect the stock price?
2. What are the key assumptions in the Dividend Discount Model?
3. How does a company's dividend policy impact its stock price?
4. What are the risks of relying solely on the Dividend Discount Model for stock valuation?
5. How does the growth rate of dividends influence investors' decisions?

**Tip**: Always consider both short-term and long-term effects when evaluating investments.

Cooperton Mining just announced it will cut its dividend from $3.96 to $2.58 per share and use the extra funds to expand. Prior to the announcement, Cooperton's dividends were expected to grow at a 3.3% rate, and its share price was $48.78. With the planned expansion, Cooperton's dividends are expected to grow at a 4.9% rate. What share price would you expect after the announcement? (Assume that the new expansion does not change Cooperton's risk.) Is the expansion a good investment?

Learn how to determine Cooperton Mining's stock price after a dividend cut and expansion using the Dividend Discount Model. This problem involves calculating stock valuation based on changes in dividend growth rates and understanding investment implications. Suitable for college-level finance students.

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