A firm that has an ROE of $12\%$ is considering cutting its dividend payout. The stockholders of the firm desire a dividend yield of $4\%$ and a capital gain yield of $9\%.$ Given this information, which of the following statements is $($are$)$ definitely correct?

All else equal, the firm's growth rate will accelerate after the payout change.

All else equal, the firm's stock price will go up after the payout change.

All else equal, the firm's P$/$E ratio will increase after the payout change.

Multiple Choice

$1$ and $2$ only

$1$ only

$1,2$ and $3$

$2$ and $3$ only