3. Companies U and L are identical in every respect except that U is unlevered w

Question

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

EBIT = $4.2 million

Cost of equity =10%

Value of the unlevered firm

VU= Value of equity+ value of debt

VU= EBIT/ Cost of equity + Interest/ cost of debt

=($4.2 million/0.10 )+(0) ( Since there is no debt for unlevered firm)

VU = $42 million

For unlevered firm rsU =10%

Value of the levered firm:

If U and L are identical then they should have the same value. So VL= $42 million and EBIT= $4.2 million

VL=   Value of equity + value of debt

VU=   Value of equity + $15 million( Since there is $15 million debt for @ 8% interest levered firm)

$42 million= Value of equity+ $15 million

Value of equity = $42 million- $15 million= $27 million

Value of equity= (EBIT/ rsL )= $27 million

$4.2 million/ rsL= $27 million

rsL= 15.55%

VL= $42 million

When taxes are levied on income, debt financing is more advantageous as interest paid on debt is a tax-deductible item whereas retained earnings or dividend so paid on equity share are not tax deductible. Thus, if debt capital is used in the total capital structure, the total income which is available for equity shareholders and/or debt holders will be more. In other words, the levered firm will have a higher value than the unlevered firm.

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.

Value of the unlevered firm:

VU = (EBIT(1-t)) / Cost of equity (t is the corporate tax @34% )

= ($4.2 million(1-0.34)) / 0.10

= $2.772 million/ 0.10 =$ 27.72 million

VU=$ 27.72 million

Value of equity= (EBIT/ rsL )= $27.72 million

$4.2 million/ rsU= $27.72 million

rsU= 15.15%

Value of the levered firm:

VL = VU + tD (t is the corporate tax @34% and D is the value of the debt =$ 15 million )

VL =$ 27.72 million+ (0.34*$15 million)

VL = $32.82 million

Value of equity = $32.82 million - $15 million= $ 17.82 million

Value of equity= (EBIT/ rsL )= $17.82 million

$4.2 million/ rsL= $17.82 million

rsL= 23.57%

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