Cooperton Mining just announced it will cut its dividend from $ $4\mathrm{.}15$ to $ $2\mathrm{.}44$ per share and use the extra funds to expand. Prior to the$$ announcement, Cooperton's dividends were expected to grow at a $3\mathrm{.}2\%$rate$,$ and its share price was $ $50\mathrm{.}03.$ With the planned$$ expansion, Cooperton's dividends are expected to grow at a $4\mathrm{.}6\%$ 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?

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Part $1$

The new price for$$ Cooperton's stock will be $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$