Your client is a biochemist who has discovered a technique to create a new biofuel. He estimates it will take him $2$ years to make it economically feasible at a cost of $$2,000,000.$ He expects he has an $80\%$ chance at success; if so$,$ he expects to be able to sell the patents for $$10,000,000.$ Assume that all of the costs incurred were capitalized as costs of the patent, he has a combined federal and state tax rate of $30\%$ and he has an expected rate of return of $8\%.$ What is the present value of his expected payoff?