a$.$ According to the trade$-$off theory on capital structure, what should firms do to maximize the firm value in the real world? $(2$ pts$)$

b$.$ What is the key difference between pecking order theory and trade$-$off theory?$(1$ pts$)$

c$.$ Executive Chalk is currently financed with $$100$ millions of debt and has a total market value of $$250$ millions. You are asked to evaluate the firm value if it issues $$50$ million of debt and uses the proceeds to buy back common stock. After doing some research, you gather some additional information:

The cost of current and newly issued debt is $8$ percent

The unlevered cost of capital is $12$ percent

Tax rate: $30\%$

c$1.$ Assume there is do backruptcy cost; what happens to the firm Dew cost of equiry if it issues $$50$ million of debt and uses the proceeds to buy back common stock? $(2$ pts$)$

c$2.$ Now, managers are worried about that issuing additional debt will increase the likelibood of bankruptcy. If managers estimate the present value of expested bankruptcy costs to be $$5$ million. What should the firm value be after the debt is issued. $(1pts)$