Aspen Company is financed with $50 million of 8% debt and $75 million of common

Question

Aspen Company is financed with $50 million of 8% debt and $75 million of common equity. The firm has 1 million shares of common stock outstanding. Aspen needs to raise $20 million and is undecided between two possible plans for raising this capital:

Plan A: Equity Financing. Under this plan, common stock will be sold at $100 per share.

Plan B: Levered Financing. Under this plan, half of the capital will be raised with equity at $100 per share and half will be raised by selling 12% coupon bonds.

At what level of operating income (EBIT) will the firm be indifferent between the two plans? Assume a 34% marginal tax rate.

A.) $18.4 million B.) $62.4 million C.) $11.2 million D.) $32 million E.) $12.8 million

Explanation / Answer

Indifferent point/level is that EBIT level at which the Earnings Per Share (EPS) is the same for two alternative financial plans. In this case, the point of indifference can be calculated using the following formula: equating EPS under the two alternatives {(X - fixed interest costs) ( 1 - Tax rate)} / no of equity shares   (under option 1)= {(X - fixed interest costs) ( 1 - Tax rate)} / no of equity shares (under option 2) where X = EBIT indifference level The 2 options available are: Raising the entire amount by equity shares ($ 20,000,000) and Raising $10,000,000 by equity and $ 10,000,000 by debt to maintain a debt-equity ratio of 1:1. Option 1: Interest = $0 (as no debt) Number of equity shares = $20,000,000 /$100 par ? 200,000 shares. Option 2: Interest = $ 10,000,000 x 12% ? $ 1,200,000 Number of equity shares = $10,000,000/$100 par ? 100,000 shares. Calculation of Indifference point: {(X - 0) ( 1 - 0.34)} / 200,000   (under option 1)= {(X - 1200000) ( 1 - 0.34)} / 100000 shares (under option 2) 0.66 X (100000) = 200000 (0.66 X - 792000) Solving for X , we get X , $ 2400,000 Verification: EPS (under option 1 )   @ indifference level of $ 2,400,000   (0.66 * 2400000 ) / 200000 = $ 7.92 EPS (under option 2 )   @ indifference level of $ 2,400,000   Earnings = (2400000 - 1200000 ) = 1200000 - tax 408000 = 792000 EPS = 792000 /100000 = $ 7.92 Keeping the existing capital structure ( 50 mn debt; 75 mn equity) indifference point (EBIT) is calculated as follows: Option 1: Raising Full equity Existing - 8% Debt $ 50000000   - Interest expense $ 4,000,000 Equity     $ 75000000 at $100/share       750000 shares New Equity 20000000 shares @ $ 100/share         200000 shares Total equity shares outstanding           950000 shares Option 2: Raising half equity and half 12% debt Existing - 8% Debt $ 50000000 - interest expense           $ 4,000,000 New - 12% Debt $ 10000000 - Interest expense               $ 1,200,000 Total interest                                                                                 $ 5,200,000 Existing Equity $ 75000000 @ $ 100/share                          750,000 shares New Equity $ 10000000 @ $ 100/share                                100,000 shares Total equity shares outstanding                                             850,000 shares Calculation of Indifference point: Equating EPS, {(x-4000000)*0.66}/950000 [under option 1]   = {(x-5200000)*0.66}/850000 [under option 2]     Solving for x , we get x= $ 15400000 Verification Option 1 Option 2 EBIT 15400000 15400000 Less: Debt int. 4000000 5200000 EBT 11400000 10200000 Tax @ 34% 3876000 3468000 EAT 7524000 6732000 No.of eq.shares o/s 950000 850000 EPS (EAT/sh.o/s) 7.92 7.92

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