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?

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.

[tex]Value=\frac{\text{dividend at the end of the first year}}{r-g}[/tex]

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

[tex]Value=\frac{\text{dividend at the end of the first year}}{r-g}\\\\\$ 49.35=\frac{4.03}{r-3.4\%}[/tex]

[tex]r-0.034=4.03/49.35\\\\r=4.03/49.35+0.034=0.116[/tex]

Now use r = 0.116 for the new dividends.

New price

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

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.