Question

GTB, Inc. has a 25 percent tax rate and has $85,536,000 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		0.42				0.58
Expected EBIT in state	$	4.70	million		$	18.70	million

The firm is considering switching to a 25-percent-debt capital structure, and has determined that it would have to pay a 9 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.)

Answer 1

Expected EBIT = 4.7*0.42+18.7*0.58 =	$                 12.82	million
Break even level of EBIT is that EBIT level for which EPS is the
same under both the alternatives capital structures.
EPS (under the exisitng CS):
Number of shares = 85536000/6 =	14256000	shares
EPS = E*(1-25%)/14256000 =
EPS (under the new capital structure):
Number of shares = 85536000*75%/6 =	10692000	shares
Borrowings = 85536000*25% =	$     2,13,84,000
Interest = 21384000*9% =	$        19,24,560
EPS = E*(1-25%)/10692000 =
Where E = Break even EBIT
Equating the two EPS equations, we have:
EPS = E*75%/14256000 = (E-1924560)*75%/10692000
Solving for E,
E*3 = (E-1924560)*4
E = 1924560*4 =	$        76,98,240
CHECK:
	Existing CS	Proposed CS
EBIT	$        76,98,240	$       76,98,240
Interest	0	$       19,24,560
EBT	$        76,98,240	$       57,73,680
Tax at 25%	$        19,24,560	$       14,43,420
NI	$        57,73,680	$       43,30,260
Number of shares	14256000	10692000
EPS	$                   0.41	$                  0.41