An all$-$equity business has $120$ million shares outstanding selling for $$20$ a share. Management believes that interest rates are unreasonably low and decides to execute a leveraged recapitalization $($a recap$).$ It will raise $$1$ billion in debt and repurchase $50$ million shares.a$.$ What is the market value of the firm prior to the recap? What is the market value of equity?Note: Enter your answers in billions rounded to $2$ decimal places.b$.$ Assuming$$the Irrelevance Proposition holds, what is the market value of the firm after the recap? What is the market value of equity?Note: Enter your answers in billions rounded to $2$ decimal places.d$.$ Assume now that the recap increases total firm cash flows, which adds $$140$ million to the value of the firm. Now what is the market value of the firm? What is the market value of equity?Note: Enter your answers in billions rounded to $2$ decimal places.$$