Problem 16-17 Firm Value [LO2] Change Corporation expects an EBIT of $25,000 every year forever. The company currently has no debt, and its cost of equity is 12 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 6 percent. What will the value of the firm be if the company takes on debt equal to 50 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 6 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 50 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 and Explanation:

The computation is shown below:

a. The current value of the company is

As it is mentioned that the company has no debt that means it is unlevered firm that is equivalent to unlevered value of the company  

Unlevered value of the firm =  Vu  

Vu = EBIT ×  (1 - tax rate ) ÷ unlevered Cost of Equity

= EBIT × (1 - tax rate ) ÷ R0  

= $25,000  ×  (1 -  0.22 ) ÷ 12%  

= $162,500  

b-1.

The computation of the value of the firm in the case when the value of the firm is equivalent to 50% of unlevered value

VL = Vu + Borrowing × tax rate  

where,  

Debt = borrowing = 50% × unlevered value of company  

Debt = borrowing = 50% x Vu  

So,

VL = Vu + Borrowing x tax rate  

VL = $162,500 + ($162,500 × 50%) × 22%  

= $162,500 + $17,875  

= $180,375  

b-2.

The computation of the value of the firm in the case when the value of the firm is equivalent to 100% of unlevered value

Levered value of the firm VL  

VL = Vu + Borrowing × tax rate  

Debt = borrowing = 100% × unlevered value of company  

Debt = borrowing = 100% × Vu

So,    

VL = Vu + Borrowing x tax rate  

= $162,500 + ($162,500 × 100%) × 22%  

= $162,500 + 35,750  

= $198,250  

C.1.

The computation of the value of the firm in the case when the value of the firm is equivalent to 50% of the levered value

VL = Vu + Borrowing × tax rate  

= Vu + (VL × 50%) × tax rate  

VL = Vu + (VL × 50%) × 22%  

VL = Vu + 0.11 VL  

VL - 0.11 VL = 162,500  

0.89 VL = 162,500  

VL= 182,584.27  

C.2.

The computation of the value of the firm in the case when the value of the firm is equivalent to 100% of the levered value  

Levered value of the firm VL  

VL = Vu + Borrowing x tax rate  

VL = Vu + (VL × 100%) × tax rate  

= Vu + (VL × 100%) × 22%  

= Vu + 0.22 VL  

VL - 0.22 VL = 162,500  

0.78 VL = 162,500  

VL= $208,333.33

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