Question

Cooperton Mining just announced it will cut its dividend from $ 4.03 to $ 2.69 per share and use the extra funds to expand. Prior to the​ announcement, Cooperton's dividends were expected to grow at a 3.4 % ​rate, and its share price was $ 49.35. With the planned​ expansion, Cooperton's dividends are expected to grow at a 4.6 % 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? The new price for​ Cooperton's stock will be ​$ nothing. ​(Round to the nearest​ cent.) Is the expansion a good​ investment?

Answer 1

• 1. The expansion is not a good investment because the price of the share will decrease.

• 2. The new price for Cooperton's stock will be $38.43 per share.

Step-by-step explanation:

To calculate the share price you would expect after the​ announcement, you must use the formula for the value of the stock when the dividends are expected to grow at a constant rate g and the expected rate of return is r.

`Value=\frac{\text{dividend at the end of the first year}}{r-g}`

After the announcement, Cooperton's dividends are $2.69 per share and are expected to grow at a 4.6 % rate.

You are only missing the rate of return, r.

Since you assume that the new expansion does not change​ Cooperton's risk, the rate of return is the same.

You can calculate the rate of return from the ifnormation priot to the announcement: dividends of $4.03 per share, expected to grow at a 3.4% ​rate, and share price was $49.35.

Thus, use the same formula quoted above to solve for r.

Rate of return

`Value=\frac{\text{dividend at the end of the first year}}{r-g}\\\\\$ 49.35=(4.03)/(r-3.4\%)`

`r-0.034=4.03/49.35\\\\r=4.03/49.35+0.034=0.116`

Now use r = 0.116 for the new dividends.

New price

`Value=\frac{\text{dividend at the end of the first year}}{r-g}\\\\Value=(\$ 2.69)/(0.116-4.6\%)\\\\Value=(\$ 2.69)/(0.116-0.046)\\ \\Value=\$ 38.43`

Therefore, the new price is expected to fall from $49.35 per share to $38.43 per share, so this is not a good investment.