Cooperton Mining just announced it will cut its dividend from $$4\mathrm{.}00$ to $$2\mathrm{.}50$ per share and use the extra funds to expand. Prior to the announcement, Cooperton's dividends were expected to grow at a $3\mathrm{.}0\%$ rate, and its share price was $$50\mathrm{.}00.$ With the planned expansion, Cooperton's dividends are expected to grow at a $5\mathrm{.}0\%$ 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 $$,.($Round to the nearest cent.$)$