Companies U and L are identical in every respect except that U is unlevered whil

Question

Companies U and L are identical in every respect except that U is unlevered while L has $15 million of 8 percent bonds outstanding. Assume (1) that all of the MM assumptions are met, (2) that there are no corporate or personal taxes, (3) that EBIT is $4.2 million, and (4) that the cost of equity to Company U is 10 percent.

a. Find VU, VL, rsL, and rsU.

b. Now assume that both firms are subject to a 34 percent federal-plus-state corporate tax rate and that rsU from part (a) holds. Find VU, VL, rsL, and rsU.

Explanation / Answer

(a)Value of unlevered firm(Vu) = EBIT/Cost of equity = 4,200,000/ 0.10 = $42,000,000

Value of levered firm(VL) = Value of unlevered firm = 42,000,000 (Since there are no taxes)

rsU = Cost of equity = 10% (No debt)

rsL = 15/42* 8% +27/42 * 10% = 9.285%

(b) With taxes of 34%.

Value of unlevered firm(Vu) = EBIT*(1-Tax rate)/Cost of equity = 4,200,000*(1-0.34)/ 0.10 = $27,720,000

Value of levered firm(VL) = Value of unlevered firm + Tax advantage of debt = 27,720,000 + 0.34 * 15,000,000 = 32,820,000

rsU = Cost of equity = 10% (No debt)

rsL = 15/32.82* 8% *(1-0.34) +17.82/32.82 * 10% = 7.8427%

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