Question

Companies U and L are identical in every respect except that U is unlevered while L has $10 million of 5% bonds outstanding. Both firms have an EBIT of $2 million. Assume that all of the MM assumptions are met.
a. Suppose that both firms are subject to a 40% federal-plus-state corporate tax rate, investors in both firms face a tax rate of Td = 28% on debt income and Ts = 20% (on average) on stock income, and the appropriate required pre-personal-tax rate rsU is 10%. What is the value of the unlevered firm, VU? What is the value of the levered firm, VL? What is the gain from leverage?
b. Now keep the other assumptions (D = $10 million, rd = 5%, EBIT = $2 million, and rsU = 10%) but set Tc = Ts = Td = 0. What is the value of the unlevered firm, VU? What is the value of the levered firm, VL? What is the gain from leverage?
c. Keep the other assumptions (D = $10 million, rd = 5%, EBIT = $2 million, and rsU = 10%), but now suppose Ts = Td = 0 and Tc = 40%. What is the value of the unlevered firm, VU? What is the value of the levered firm, VL? What is the gain from leverage?
d. Keep the other assumptions (D = $10 million, rd = 5%, EBIT = $2 million, and rsU = 10%), but now suppose that Td = 28%, Ts = 28%, and Tc = 40%. Now what is the value of the levered firm? What is the gain from leverage?

Answer 1

a. VU = EBIT(1 - TC)(1 - Ts) / rsU(1 - Ts) = $2(1 - 0.4)(1 - 0) / 0.10(1 - 0)

       = $12 million.

 

VL = VU + [1 - (1 - TC)(1 - Ts) / (1 - Td)] D

      = $12 + [1 - (1 - 0.4)(1 - 0.2) / (1 - 0.28)] $10

      = $12 + [1 - 0.67]$10 = $12 + 0.33($10)

      = $15.33 million.

Gain = VL − VU = $15.33 $12 = $3.33 million.

 

b. VU = EBIT(1 - TC)(1 - Ts) / rsU(1 - Ts) = $2(1 - 0)(1 - 0) / 0.10(1 - 0)

       = $20 million.

 

VL = VU + [1 - (1 - TC)(1 - Ts) / (1 - Td)] D

      = $20 + [1 - (1 - 0)(1 - 0) / (1 - 0)] $10

      = $20 + [1 − 1]$10

     = $15.33 million.

Gain = VL − VU = $20 − $20 = $0.

 

c. VU = EBIT(1 - TC)(1 - Ts) / rsU(1 - Ts) = $2(1 - 0.4)(1 - 0) / 0.10(1 - 0)

       = $12 million.

 

VL = VU + [1 - (1 - TC)(1 - Ts) / (1 - Td)] D

      = $20 + [1 - (1 - 0.4)(1 - 0) / (1 - 0)] $10

      = $20 + [1 − .6]$10

     = $16 million.

Gain = VL − VU = $16 − $12 = $4.

 

d. VU = EBIT(1 - TC)(1 - Ts) / rsU(1 - Ts) = $2(1 - 0.4)(1 - 0.28) / 0.10(1 - 0.28)

       = $12 million.

 

VL = VU + [1 - (1 - TC)(1 - Ts) / (1 - Td)] D

      = $20 + [1 - (1 - 0.4)(1 - 0.28) / (1 - 0.28)] $10

      = $20 + [1 − .6]$10

      = $16 million.

 

Gain = VL − VU = $16 − $12 = $4.