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MM with Corporate Taxes Companies U and L are identical in every respect except that U is unlevered while L has $16 million of 5% bonds outstanding

Finance Oct 26, 2020

MM with Corporate Taxes

Companies U and L are identical in every respect except that U is unlevered while L has $16 million of 5% bonds outstanding. Assume that: (1) All of the MM assumptions are met. (2) Both firms are subject to a 35% federal-plus-state corporate tax rate. (3) EBIT is $3 million. (4) The unlevered cost of equity is 12%.

  1. What value would MM now estimate for each firm? (Hint: Use Proposition I.) Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Round your answers to two decimal places.
  2. Company U: $    million
  3. Company L: $    million
  4.  
  5. What is rs for Firm U? Round your answer to one decimal place.
  6.   %
  7.  
  8. What is rs for Firm L? Do not round intermediate calculations. Round your answer to one decimal place.
  9.   %
  10.  
  11. Find SL, and then show that SL + D = VL results in the same value as obtained in Part a. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answers to two decimal places.
  12. SL = $    million
  13. SL + D = $    million
  14.  
  15. What is the WACC for Firm U? Do not round intermediate calculations. Round your answer to two decimal places.
  16.   %
  17. What is the WACC for Firm L? Do not round intermediate calculations. Round your answer to two decimal places.
  18.   %

Expert Solution

a. Value of Firm U, Vu = EBIT * (1 - Tax rate) / Unlevered Cost of Equity

= $3 million * (1 - 35%) / 12%

Value of Firm U, V= $16.25 millions

 

Value of Firm L, Vl = Vu + Tax rate * Debt

= $16.25 million + 35% * $16 million

= $16.25 million +$5.6 million

Value of Firm L, Vl = $21.85 million

 

b. rs for Firm U, rsu = Unlevered cost of equity = 12%

 

rs for Firm L, rsl = rsu + (rsu - rd) * (1 - Tax rate) * (Debt / Stock)

= 12% + (12% - 5%) * (1 - 35%) * ($16 million / ($21.85 million - $16 million)

= 12% + 4.55%*($16 million/$5.85 million)

= 12% + 12.44%

rs for Firm L, rsl = 24.44%

 

c. Value of Stock L, Sl = (EBIT - rd * Debt) * (1 - Tax rate) / rsl

= ($3 million - 5% * $16 million) * (1 - 35%) / 24.44%

= ($3 million - $0.80 million)*65%/24.44%

Value of Stock L, Sl = $5.85 million

 

Value of Firm L, Vl = Sl + Debt

= $5.85 million + $16 million

Value of Firm L, V= $21.85 million

 

d. WACCu = 12.00%

 

WACCl = (Debt / Vl) * rd * (1 - Tax rate) + (Sl / Vl) * rsl

= ($16 million / $21.85 million) * 5% * (1 - 35%) + ($5.6 million / $21.85 million) * 24.44%

= 2.38% + 6.26%

WACCl = 8.64%

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