GTB has a 20% tax rate and has $71,230,000 in assets, currently financed entirel
ID: 2752347 • Letter: G
Question
GTB has a 20% tax rate and has $71,230,000 in assets, currently financed entirely with equity. Equity is worth $5 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown: Probability of state 0.41 (pessimistic) 0.59 (optimistic) Expected EBIT in state $4,600,000 (pessimistic) $18,600,000 (optimistic). The firm is considering switching to a 30% debt capital structure, and has determined that it would have to pay a 10% yield on perpetual debt in either event. What will be the break-even level of EBIT? Please show work.
Explanation / Answer
All assets are completely financed out of equity.
Hence total value of equity = $71,230,000
Market Value = Book Value = 5$ per share
Hence number of Equity shares = 71,230,000/5 = 14,246,000
Break Even Level of EBIT = EBIT Level where EPS in both capital structures are the same
EPS with no Debt = EBIT / Number of Shares = EBIT / 14,246,000 – Equation 1
Proposed Capital Structure = 30% Debt
Amount of Debt Raised = 30% of Total Assets = 30% x 71,230,000 = 21,369,000
New number of shares in debt scenario = 14,246,000 – 21,369,000/5 = 9,972,200
EPS with Debt = EBIT – Interest / Number of Shares
Interest Rate = 10%
EPS with Debt = EBIT – 10% x 21,369,000 / Number of shares
= EBIT – 2,136,900 / 9,972,200 – Equation 2
Equating Equations 1 & 2 we get the breakeven level of EBIT
EBIT / 14,246,000 = ( EBIT – 2,136,900) / 9,972,200
9,972,200 x EBIT = 14,246,000 x EBIT – 2,136,900 x 14,246,000
2,136,900 x 14,246,000 = EBIT x (14,246,000 – 9,972,200)
EBIT = 14,246,000 x 2,136,900 / (14,246,000 – 9,972,200) = 7,123,000
Hence Break even level of EBIT = $7,123,000
To cross validate EPS in no debt scenario = EBIT / Number of Shares = 7,123,000 / 14,246,000 = 0.50
EPS in Debt Scenario = EBIT – Debt / Number of Shares = 7,123,000 – 2,136,900 / 9,972,200 = 4,986,100/9,972,200 = 0.50
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