Defenestration Industries plans to pay a $$4\mathrm{.}00$ dividend this year and you expect that

the firm's earnings are on track to grow at $6\%$ per year for the foreseeable future.

Defenestration's equity cost of capital is $14\%.$

a$.$ Assuming that Defenestration's dividend payout rate and expected growth rate remain constant, and Defenestration does not issue or repurchase shares, then what is Defenestration's stock price?

b$.$ Suppose that Defenestration decides to pay a dividend of only $$2$ per share this year and use the remaining $$2$ per share to repurchase stock. If Defenestration's payout rate remains constant, then what is Defenestration's stock price?

c$.$ Suppose that Defenestration decides to pay a dividend of only $$2$ per share this year and use the remaining $$2$ per share to repurchase stock. If Defenestration maintains this dividend and total payout rate, then what is the rate at which Defenestration's dividends and earnings per share are expected to grow?