Question

GTB, Inc., has a 20 percent tax rate and has $85,776,000 in assets, currently financed entirely with equity. Equity is worth $6 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 below: State Pessimistic Optimistic Probability of state 0.47 0.53 Expected EBIT in state $ 5.20 million $ 19.20 million The firm is considering switching to a 25-percent-debt capital structure, and has determined that it would have to pay a 10 percent yield on perpetual debt in either event. What will be the break-even level of EBIT? (Enter your answer in dollars, not in millions. Do not round intermediate calculations and round your final answer to the nearest whole dollar amount.) EBIT $

Answer 1

Let Breakeven EBIT be $x

Current Capital Structure:

Value of Assets = $85,776,000
Price per share = $6

Number of shares outstanding = Value of Assets / Price per share
Number of shares outstanding = $85,776,000 / $6
Number of shares outstanding = 14,296,000

EPS = (EBIT - Interest Expense) * (1 - tax) / Number of shares outstanding
EPS = ($x - $0) * (1 - 0.20) / 14,296,000
EPS = $x * 0.80 / 14,296,000

Proposed Capital Structure:

Value of Assets = $85,776,000
Price per share = $6

Value of Debt = 25% * Value of Assets
Value of Debt = 25% * $85,776,000
Value of Debt = $21,444,000

Interest Expense = 10% * Value of Debt
Interest Expense = 10% * $21,444,000
Interest Expense = $2,144,400

Value of Equity = 75% * Value of Assets
Value of Equity = 75% * $85,776,000
Value of Equity = $64,332,000

Number of shares outstanding = Value of Equity / Price per share
Number of shares outstanding = $64,332,000 / $6
Number of shares outstanding = 10,722,000

EPS = (EBIT - Interest Expense) * (1 - tax) / Number of shares outstanding
EPS = ($x - $2,144,400) * (1 - 0.20) / 10,722,000
EPS = ($x - $2,144,400) * 0.80 / 10,722,000

EPS under Current Capital Structure = EPS under Proposed Capital Structure
$x * 0.80 / 14,296,000 = ($x - $2,144,400) * 0.80 / 10,722,000
$x / 7,148 = ($x - $2,144,400) / 5,361
5,361 * $x = 7,148 * $x - $15,328,171,200
$15,328,171,200 = 1,787 * $x
$x = $8,577,600

So, Breakeven EBIT is $8,577,600