Problems and Solutions




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Chapter 12

Problems and Solutions


5. EBIT Breakeven (with and without taxes) – Alpha Company is looking at two different capital structures, one an all-equity firm the second leveraged firm with $2,000,000 of debt financing at 8% interest. The all-equity firm has $4,000,000 value and 400,000 shares outstanding. The leveraged firm will have 200,000 shares outstanding. Find the breakeven EBIT for Alpha company using EPS if

a. there are no corporate taxes

b. the corporate tax rate is 30%

c. what do you notice about these two breakeven EBITs for Alpha Company?

Solution:

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.




  1. M&M, World of Taxes – Air America in problem number 11 has lost it’s not for profit status and the corporate tax rate is now 35%. If the value of Air America was $5,000,000 as an all equity firm what is the value of Air America under a 50 – 50 debt equity ratio? Assume that the $5,000,000 is the after-tax value of the unlevered firm.

Solution:

VL = VU + D x Tc and D is 50% of the $5,000,000 or $2,500,000

VL = $5,000,000 + $2,500,000 x 0.35 = $5,875,000


  1. M&M, World of Taxes – Fox Broadcasting Incorporated in problem 12 was originally an all equity firm with a value of $25,000,000. Fox now pays taxes at 40% rate. What is the value of Fox under the 1 to 3 debt to equity capital structure? Under the 3 to 1 capital structure?

Solution:

The low-leveraged firm

VL = VU + D x Tc and D is 25% of the $25,000,000 or $6,250,000

VL = $25,000,000 + $6,250,000 x 0.40 = $27,500,000

The high-leverage firm

VL = VU + D x Tc and D is 75% of the $25,000,000 or $18,750,000



VL = $25,000,000 + $18,750,000 x 0.40 = $32,500,000





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