Nova Corporation just had its IPO. It does not plan to pay any dividends on its stock for the next $12$ years. At year $13,$ the stock expects to pay a $$7\mathrm{.}50$ dividend. Its dividends are expected to grow at an annual rate of $18\%$ until year $32.$ After year $32,$ the growth rate drops to $2\mathrm{.}5\%$ and will stay at this rate forever. What is the present value of the stock using a $15\%$ discount rate?