Consider a single period model in a MM world: Executive Cheese currently has senior debt with a market value of $$100$m and has outstanding $15$m shares with a market price of $$10$ per share. The cash flow of the company at the end of the period is either $$150$m in bad state or $$350$m in good state. Assume each state has equal probability of occurring. The company now announces that it intends to issue a junior debt with face value of $$100$m and use the proceeds to buy back common stock.

a$.$ What is the market value of the firm $($in millions$)$ after the change in capital structure?