Considera firm whose eamings face a binomial distribution at the end of the period:

$6$ If the retailprice of the product is high, the firm will make $$210$ million EBT leamings before taxes with a probability of $0\mathrm{.}6$;

o I the retal price is low, the firm's EBT will be reduced to $$80$ million with a probability of $0\mathrm{.}4.$

The tax rate is a convex function of EBT $($earnings before taxes$)$:

$$ Tax rate is $10\%($of EBT when EBT is less than $$100$ million;

$$ Tax aleis $15\%$ when EBT is between $$100$ to $$150$ million $($not including $$150$ million$)$;

$$ Tax rate's $20\%$ when EBT is between $$150$ to $$200$ million $($not including $$200$ million$)$;

$$ Taxrateis $25\%$ when EBT is equal to or above $$200$ million.

Suppose that the fim decides to partially hedge its risk exposure, and after the hetigne the new distribution of the firm's EBT is $$180$ million with a probability of Oband $$125$ milion with a probablity of $0\mathrm{.}4.$ Please answer the following

questions:

Without hedging what are the expected earnings before taxes $($EBT$)$ of the firm?