Ski and Board are two identical firms of identical size operating in identical m

Question

Ski and Board are two identical firms of identical size operating in identical markets. Ski is unlevered with assets valued at $12000 and has 600 shares of stock outstanding. Board also has $12000 in assets and has $5000 in debt financed at an interest rate of 9.50% and has 350 shares of stock outstanding. Assume perfect capital markets.

Calculate the level of EBIT that would make earnings per share the same for Ski and Board. $ Place your answer to the nearest dollar. If applicable, your answer should NOT include a comma

Can someone please explain how to solve this question step by step?

Explanation / Answer

Earning per share (EPS) = Net Income (NI) / Number of shares outstanding

Let required EBIT be Z, for both firms.

For Ski, NI = EBIT - Interest - Tax = Z - 0 - 0 = Z

(**Since interest expense is zero, and in absence mention of a of tax rate, we assume tax is zero).

For Board, Interest expense = Debt x Interest rate = $5,000 x 9.5% = $475

NI = EBIT - Interest expense - Tax = Z - 475 - 0 = Z - 475

EPS for Ski = Z / 600

EPS for Board = (Z - 475) / 350

By question,

Z / 600 = (Z - 475) / 350

Z / 12 = (Z - 475) / 7 [Multiplying each side by 50]

7Z = 12Z - 5,700

5Z = 5,700

Z = 5,700 / 5 = 1,140

Required EBIT = $1140

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