Question

GTB, Inc. has a 21 percent tax rate and has $100 million in assets, currently financed entirely with equity. Equity is worth $7 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		0.45				0.55
Expected EBIT in state	$	5	million		$	19	million

The firm is considering switching to a 40-percent-debt capital structure, and has determined that it would have to pay a 12 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

Interest in all states = interest rate * [wd * Total Assets]

= 0.12 * [0.40 * $100,000,000] = $4,800,000

Shares outstanding in 40-debt capital structure = [wE * Total Assets] / Price per share

= [0.60 * $100,000,000] / $7 = $60,000,000 / 7 = 8,571,428.571

Shares outstanding in all equity capital structure = [wE * Total Assets] / Price per share

= [1 * $100,000,000] / $7 = $100,000,000 / 7 = 14,285,714.29

EPS(40% Debt) = EPS(All Equity)

[{EBIT - Interest} * (1 - t)] / Shares Outstanding = [EBIT * (1 - t)] / Shares Outstanding

[{EBIT - $4,800,000} * (1 - 0.21)] / 8,571,428.571 = [EBIT * (1 - 0.21)] / 14,285,714.29

[{0.79 * EBIT} - $3,792,000] / 8,571,428.571 = [0.79 * EBIT] / 14,285,714.29

14,285,714.29 * [{0.79 * EBIT} - $3,792,000] = 8,571,428.571 * [0.79 * EBIT]

[11,285,714.29 * EBIT] - $541,714,285,700,000 = [6,771,428.57 * EBIT]

[11,285,714.29 * EBIT] - [6,771,428.57 * EBIT] = $541,714,285,700,000

[4,514,285.71 * EBIT] = $541,714,285,700,000

EBIT = $541,714,285,700,000 / 4,514,285.71 = $12,000,000