A company has an earning before interests and taxes of $$5,000,000$ per year, and a marginal tax rate of $30\%.$

The company is currently unlevered, and its market value of equity is $$15,000,000$ and its cash and cash equivalent is $$1,000,000.$

Its beta is currently $1\mathrm{.}3,$ with a risk free rate of $5\%$ and a equity market premium of $7\%.$

The company currently has a $0\%$ default probability, which allows it to issue debt at a rate of $10\%.$

Below is the probability of bankruptcy across various debt levels.

Debt amount Probability of bankruptcy

$2,000,0000\%$

$4,000,0005\%$

$6,000,00015\%$

$8,000,00025\%$

$10,000,00040\%$

$12,000,00053\%$

$14,000,00070\%$

$16,000,000100\%$

It is estimated that the loss in the company's value if it goes bankrupt is $$7,000,000.$

Fill in the blank:

a$)$ The company's current WACC is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_--$

b$)$ The optimal debt ratio is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$)$ The firm value at the optimal debt ratio is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

a$.$

a$)24\%$; b$)27\%$; c$)$ $$15\mathrm{.}75$ million

b$.$

a$)14\%$; b$)21\%$; c$)$ $$15\mathrm{.}85$ million

c$.$

a$)10\%$; b$)21\%$; c$)$ $$15\mathrm{.}95$ million

d$.$

a$)14\%$; b$)27\%$; c$)$ $$15\mathrm{.}6$ million