Cooperton Mining just announced it will cut its dividend from $\backslash (\backslash$$ $3\mathrm{.}79\backslash )$ to $\backslash (\backslash$$ $2\mathrm{.}55\backslash )$ per share and use the extra funds to expand. Prior to the announcement, Cooperton's dividends were expected to grow at a $\backslash (3\mathrm{.}5\backslash \%\backslash )$ rate, and its share price was $\backslash (\backslash$$ $51\mathrm{.}02\backslash ).$ With the planned expansion, Cooperton's dividends are expected to grow at a $\backslash (4\mathrm{.}6\backslash \%\backslash )$ 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 $\backslash (\backslash$$ $\backslash )$

$($Round to the nearest cent.$)$