2. Unlevered Corporation (Firm U) has a total market value of $5,000,000, a tax

Question

2. Unlevered Corporation (Firm U) has a total market value of $5,000,000, a tax rate of 40 percent, and earnings before interest and taxes (EBIT) of $1,000,000. Levered Corporation (Firm L) is identical in all respects to Firm U, but Firm L has $3,000,000 market (and book) value of debt outstanding. Firm L pays total annual interest of $270,000 on this debt. Both firms satisfy the MM assumptions.

      a. What is the value of Firm L according to MM’s Proposition I with corporate taxes?

      b. What is Firm U’s cost of equity?

      c. What is Firm L’s cost of equity?

      d. What is Firm L’s weighted average cost of capital?

Explanation / Answer

Revised working

Details Amt $ Unlevered Value of Firm U =          5,000,000 Tax Rate =40% Interest on Debt of Firm L=              270,000 Tax Benefit on Debt interest =270000*0.40              108,000 a Value of Firm L =Value of Firm U+ Tax benefit on interest=5000000+108000=          5,108,000 b Value of firm U =          5,000,000 EBIT =1000000 Tax @40%=-400,000 EBT =600,000 Assume cost of Equity =k So 600,000/k=5,000,000 k=12% So cost of Equity of Firm U =12% c Firm Value of L =          5,108,000 Less Market Value of Debt =          3,000,000 Market Value of Equity of Firm L=          2,108,000 Cost of Equity ungeared =kUG=12% Interest of firm L =270000 Cost of Debt =kD=9% t=Tax Rate =40% Assume cost of Geared Equity =kG kG=kUG+[(1-t)*D/E*(kUG-kD) =0.12+0.6*(3000000/2108000)*(0.12-0.09) =14.56% So Cost of Equity of L =14.56% Post Tax cost of Debt =9%*(1-0.40)=5.4% d WACC of L =kUG*E/(D+E) +kD(1-t)*D/(D+E) =0.1456*(2108000/5108000)+0.054*(3000000/5108000)                                               = 9.18% So WACC of Firm L =9.18%

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