The net income of Duke Corporation, which has $10,000$ outstanding shares and a $100\%$ payout policy, is $$32,000$ today. The expected value of the firm one year hence is $$1,545,600.$ The appropriate discount rate for Duke is $12\%.$

$1.$ What is the current value of the firm? Show calculations

$2.$ What is the ex$-$ dividend price of Duke$$s stock if the board follows its current dividend policy? Show calculations

$3.$ Provide an explanation for the change in Duke$$s stock price using your calculations to support your explanation