Question

GTB, Inc. has a 20 percent tax rate and has $86,076,000 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		0.52				0.48
Expected EBIT in state	$	5.70	million		$	19.70	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

Answer 1

All financials are in $.

As is situation:

Assets = Equity = 86,076,000

Share Price = 6

Number of shares outstanding, N = Equity / Share price = 86,076,000 / 6 =  14,346,000

Hence, EPS = EBIT x (1 - T) / N = EBIT x (1 - T) / 14,346,000

Proposed situation:

Debt = 25% x Asset = 25% x 86,076,000 =  21,519,000

Interest, I = yield x debt = 9% x  21,519,000 =  1,936,710

Equity = (1-25%) x Asset = 75% x 86,076,000 = 64,557,000

Number of shares outstanding now, N₁ = 64,557,000 / 6 =  10,759,500

Hence, EPS = (EBIT - I) x (1 - T) / N₁ = (EBIT - 1,936,710) / 10,759,500

At break even EBIT, the EPS in two cases should be same.

Hence, EBIT x (1 - T) / 14,346,000 = (EBIT - 1,936,710) / 10,759,500

Or, 10,759,500 x EBIT = 14,346,000 x (EBIT - 1,936,710)

Break even EBIT = 14,346,000 x 1,936,710 / (14,346,000 - 10,759,500) = $  7,746,840