$(10$ points$)$ The two firms, BSM and LAC, are identical except for their capital structure. Both

will earn $$120$ million in a boom and $$90$ million in a slump. Each state has a probability of

$50$ percent. BSM is entirely equity$-$financed, and its shares are valued at $$500$ million. LAC

has $$250$ million of risk$-$free debt on its balance sheet which pays an annual interest of $12$

percent on the face value. There are no taxes or other market imperfections. Investors can

borrow and lend at the risk$-$free rate of interest.

a$.$ What is the value of LAC's stock?

b$.$ Suppose that you invest $$20$ million in BSM$\text{'}$s stock. Is there an alternative investment in

LAC that would give identical payoffs in boom and slump? What is the expected payoff

from such a strategy?

c$.$ Now suppose that you invest $$20$ million in LAC's stock. Design an alternative strategy

using BSM$\text{'}$s stock with identical payoffs.