Question

Change Corporation expects an EBIT of $55,000 every year forever. The company currently has no debt, and its cost of equity is 14 percent. The corporate tax rate is 22 percent.

  

a.	What is the current value of the company? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-1.	Suppose the company can borrow at 9 percent. What will the value of the firm be if the company takes on debt equal to 60 percent of its unlevered value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-2.	Suppose the company can borrow at 9 percent. What will the value of the firm be if the company takes on debt equal to 100 percent of its unlevered value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c-1.	What will the value of the firm be if the company takes on debt equal to 60 percent of its levered value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c-2.	What will the value of the firm be if the company takes on debt equal to 100 percent of its levered value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a. Perpetual EBIT = 55000, Since at present company does not have any debt, therefore cost of equity = unlevered cost of equity = 14% and current value of company = value of unleverd firm

In case of perpetual EBIT, Value of unlevered firm = [EBIT(1-tax rate)] / Unlevered cost of equity

Current value of company = Value of unlevered firm = [EBIT(1-tax rate)] / Unlevered cost of equity = [55000 (1-22%)] / 14% = [55000 x 78%] / 14% = 42900 / 14% = 306428.5714 = $306428.57 (rounded to two decimal places)

Current value of company = $306428.57

b-1 Value of debt = D = 60% of Value of unlevered firm = 60% x 306428.5714,

Tax rate = 22%

Since the company now has debt therefore value of company = Value of levered firm

Value of firm = Value of levered firm = Value of unlevered firm + tax rate x debt = 306428.5714 + 22% x 60% x 306428.5714 = 306428.5714 + 40448.5714 = 346877.1428 = 346877.14 (rounded to two decimal places)

Hence value of firm = 346877.14

b-2 Value of debt = D = 100% of Value of unlevered firm = 100% x 306428.5714

Since the company now has debt therefore value of company = Value of levered firm

Value of firm = Value of levered firm = Value of unlevered firm + tax rate x debt = 306428.5714 + 22% x 100% x 306428.5714 = 306428.5714 + 67414.2857 = 373842.8571 = 373842.86 (rounded to two decimal places)

Hence value of firm = 373842.86

c-1 Let V = Value of Levered firm, then debt = 60% of V

We know that ,

Value of firm = Value of levered firm = Value of unlevered firm + tax rate x debt

V = 306428.5714 + 22% x 60% x V

V = 306428.5714 + 0.1320V

V - 0.1320V = 306428.5714

0.8680V = 306428.5714

V = 306428.5714 / 0.8680 = 353028.3081 = 353028.31 (rounded to two decimal places)

Value of firm = 353028.31

c-2

Let V = Value of Levered firm, then debt = 100% of V

We know that ,

Value of firm = Value of levered firm = Value of unlevered firm + tax rate x debt

V = 306428.5714 + 22% x 100% x V

V = 306428.5714 + 0.22V

V - 0.22V = 306428.5714

0.78V = 306428.5714

V = 306428.5714 / 0.78 = 392857.1428 = 392857.14 (rounded to two decimal places)

Value of firm = 392857.14