Kellogg pays $$2\mathrm{.}00$ in annual per share dividends to its common stockholders, and its recent stock price was $$82\mathrm{.}50.$ Assume that Kellogg$$s cost of equity capital is $5\mathrm{.}0\%.$

a$.$ Estimate Kellogg$$s stock price using the dividend discount model with constant perpetuity.