Question $2$

Suppose that two companies, $x$ and $Y,$ generate cash flows, on a pretax basis, either positive $$20$ million or negative $$10$ million each year. The probability of making a loss in a certain year is $50\%$ for both firms, although their earnings are perfectly negatively correlated with each other. For example, when firm $x$ makes $$20$ million, firm $Y$ loses $$10$ million. Assume that the corporate tax rate is $40\%$ and that no loss will be carried back or forward.

a$)$ Determine the expected aftertax income for the two standalone firms.

b$)$ Suppose that the two firms are merged to form a single entity. Determine the aftertax income for the combined firm. How much will the tax savings be each year?