In the MM world there is only benefit to borrowing. A firm$$s debt capacity is limited by factors such as growth, asset structure, earning volatility, macro conditions, etc. According to financial theories these impediments result in financial distress and agency costs associated with debt usage. The tradeoff theory combines these factors together and suggests that managers should select an optimal capital structure that balances the tax benefit of debt against the financial distress and agency costs of debt.

The following problem is a quantitative, albeit simplistic, example of the tradeoff theory. Jon Jane, CFO of the Silly Pool Corp., is evaluating the firm$$s current capital structure.

Currently, the firm has $$2\mathrm{.}0$ million debt in market value. The corporate tax rate is $40$ percent. The following table provides pertinent information concerning the combined financial distress and agency costs associated with different levels of borrowing.

Amount of debt Costs as a percent of debt

$1\mathrm{.}0$ million $5\%$

$2\mathrm{.}0$ million $7\%$

$3\mathrm{.}0$ million $10\%$

$4\mathrm{.}0$ million $14\%$

$5\mathrm{.}0$ million $20\%$

Given the firm$$s current capital structure the combined financial distress and agency costs amount to $7\%$ of the current borrowing which is $2\mathrm{.}0$ million.

According to Jon$$s estimate the firm$$s $\backslash$beta $0$ is $1\mathrm{.}5$ and Vu should be about $$9\mathrm{.}0$ million. Expected return on the market portfolio, E$($rm$),$ is $14\%.$ Expected return on a risk$-$free portfolio, rf$,$ is $2\%.$

$1)$ Find Silly Pool$$s current firm value. $(20$ points$)$

$2)$ Is the firm$$s current capital structure optimal? If the current capital structure is not optimal, indicate which capital structure provided above results in the optimal financial position of the firm. Define your answer and provide quantitative evidence to support your answer. $\{$Requirement: You must define what you mean by an $$optimal$$ capital structure and then use that definition to determine the firms$$ optimal current capital structure.$\}(50$ points$)$