$1.$ Protos, Inc., has no debt outstanding and a total market value of $$300,000.$ Earnings before interest and taxes, EBIT, are projected to be $$25,000$ if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be $25$ percent higher. If there is a recession, then EBIT will be $50$ percent lower. Money is considering a $$100,000$ debt issue with an interest rate of $6$ percent. The proceeds will be used to repurchase shares of stock. There are currently $5,000$ shares outstanding. Ignore taxes for this problem.

a$)$ Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. Also calculate the

percentage changes in EPS when the economy expands or enters a recession.

b$)$ Repeat part $($a$)$ assuming that Protos goes through with recapitalization. What do you observe? $2.$Repeat parts $($a$)$ and $($b$)$ in Problem $1$ assuming Protos has a tax rate of $25$ percent.