Hema Corp. is an all$-$equity firm with a current market value of $$1,220$ million $($i$.$e$.,$ $$1\mathrm{.}22$ billion$),$ and will be worth $$1,098$ million or $$1,708$ million in one year. The risk$-$free interest rate is $5\%$ Suppose Hema Corp. issues zero$-$coupon, one$-$year debt with a face value of $$1,281$ million, and uses the proceeds to pay a special dividend to shareholders. Suppose that in the event Hema Corp. defaults, $$90$ million of its value will be lost to bankruptcy costs. Assume there are no other market imperfections.

a$.$ What is the present value of these bankruptcy costs, and what is their delta with respect to the firm's assets?

b$.$ In this case, what is the value and yield of Hema's debt?

c$.$ In this case, what is the value of Hema's equity before the dividend is paid? What is the value of equity just after the dividend is paid?