$(12$ points$)$ Shek Kip Mei Corporation is considering undertaking a new project, which in$-$volves developing a new product. One year from now, depending on the demand for thenew product, the present value of all future cash flows from the project will be either $$20,000,000($if the demand for the new product will be high$)$ or $$10,000,000($if the demand for the new product will be low$).$ The value of the project today, right before starting it$,$ is $$14,000,000.$ The firm can lend and borrow for one year at the $($annualized$,$ annually$-$com$-$pounded$)$ risk$-$free interest rate of $5\%.$ An insurance company is willing to provide insurance to Shek Kip Mei Corporation, according to which if in one year the demand for the new

product turns out to be low, Shek Kip Mei Corporation can sell the project to the insurance company for $$12,000,000.$ What is the highest price which Shek Kip Mei Corporation should pay to the insurance company now for this insurance, based on the binomial model?