Question

Change Corporation expects an EBIT of $37,000 every year forever. The company currently has no debt, and its cost of equity is 13 percent. The corporate tax rate is 23 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 40 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 40 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). Value of the unlevered firm = EBIT(1 - tc) / R

= $37,000(1 - 0.23) / 0.13 = $28,490 / 0.13 = $219,153.85

b-1). V_L = V_U + t_cB

where,

• VL = Value of levered firm
• Vu = Value of unlevered firm
• tc = Corporate tax rate
• B = Value of debt

V_L = $219,153.85 + [0.23(0.40 * $219,153.85)] = $219,153.85 + $20,162.15 = $239,316.00

b-2). V_L = V_U + t_cB

= $219,153.85 + [0.23 * $219,153.85] = $219,153.85 + $50,405.38 = $269,559.23

c-1). V_L = V_U + t_cB

V_L = $219,153.85 + [0.23(0.40 * V_L)]

V_L = $219,153.85 + 0.092V_L

V_L - 0.092V_L = $219,153.85

0.908V_L = $219,153.85

V_L = $219,153.85 / 0.908 = $241,358.86

c-2). V_L = V_U + t_cB

V_L = $219,153.85 + [0.23 * V_L]

V_L = $219,153.85 + 0.23V_L

V_L - 0.23V_L = $219,153.85

0.77V_L = $219,153.85

V_L = $219,153.85 / 0.77 = $284,615.38