NHL Inc.$\text{'}$s current return on equity $($ROE$)$ is $20\%,$ its current book equity per share is $$50,$ and it pays out half of its earnings as dividends. Both the ROE and payout ratio will stay constant for the next two years. After year $2,$ competition will force ROE down to $8\%,$ and NHL will increase its payout ratio to $75\%.$ The market capitalization rate or expected return for NHL$\text{'}$s stock is $10\%.$ What is NHL$\text{'}$s stock price today?