Alpha company is looking at two different capital structures, one an all-equity

Question

Alpha company is looking at two different capital structures, one an all-equity firm and the other a leverages firm with $2 million of debt financing at 8% interest. The all-equity firm will have a value of $4 million and 400,000 shares outstanding. The leveraged firm will have 200,000 shares outstanding.
a. Find the break even EBIT for Alpha company using EPS if there are no corporate taxes.
b.Find the break even EBIT for Alpha company using EPS if the corporate tax rate is 30%
c. What do you notice about these two break-even EBITs for Alpha company?

Explanation / Answer

a. with no corporate taxes we have the following EPS for each structure

(EBIT - $2,000,000 x 0.08) / 200,000 = EBIT / 400,000

(EBIT – $160,000) / 200,000 = EBIT / 400,000

400,000 EBIT – 400,000 x $160,000 = 200,000 EBIT

200,000 EBIT = 400,000 x $160,000

EBIT = 2 x $160,000 = $320,000

   b. with a tax rate of 30% we have the following EPS for each structure

[(EBIT - $2,000,000 x 0.08) x 0.70] / 200,000 = (EBIT x 0.70) / 400,000

[(EBIT – $160,000) x 0.70] / 200,000 = (EBIT x 0.70) / 400,000

2 [(EBIT –$160,000) x 0.70] = (EBIT x 0.70)

(EBIT - $160,000) x 1.40 = EBIT x 0.70

$160,000 x 1.40 = EBIT x (1.4 – 0.7)

224,000 = EBIT x 0.7

EBIT = $224,000 / 0.7= $320,000

c. The EBITs are the same because the tax rate does not impact the breakeven EBIT for an unlevered versus a levered company.

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