give me solution as soon as possible ;

question :

A newly merged company, Zeus-Goliath Companies (ZG), is considering what debt

level, if any, is optimal for the new firm. The firm does not have any debt at this time and

has a total market value of $300 million (all common equity). ZG understands there will

be bankruptcy and agency costs that rise as they undertake additional debt. Investment

bankers have informed them that the interest rate will also rise and together have

calculated that the present value of bankruptcy costs and agency costs will be as follows:

Debt level

Present Value

$ 0

$ 0

100,000,000

6,000,000

200,000,000

12,000,000

300,000,000

20,000,000

400,000,000

30,000,000

500,000,000

50,000,000

600,000,000

95,000,000

The firm can only issue debt in increments of $100 million and believes that the present

value of tax-shield benefits is equal to 15% of the amount of the debt raised. (For ease of

analysis, assume that debt is perpetual.)

a)

What is the present value of the tax-shield benefits at each debt level?

b)

What is the total firm value at each potential debt level?

c)

What is the debt ratio for the firm at its optimal capital structure?