Suppose the company ABC is currently all equity financed. The company will be worth either $250$M or $90$M depending on whether the economy is strong or weak in one year. The current risk free rate is $6\%$ and the cost of capital of the company is $25\%.$

a$)$ Suppose that the corporate tax rate is $40\%.$

What is the after tax cost of debt if ABC recapitalizes and borrows $$80$M at time t$=0?$ Explain

b$)$Now suppose that the corporate tax rate is $40\%.$ On the grided paper below draw graphs of rA $,$ rWACC, rE$,$ and the after tax cost of debt. Make your graph neat and detailed. Indicate the important values.