A firm is considering two different capital structures.The first option is an all-equity firm with 40,000 shares of stock.The second option is 28,000 shares of stock plus some debt.Ignoring taxes,the break-even level of earnings before interest and taxes between these two options is $52,000.How much money is the firm considering borrowing if the interest rate is 9 percent?
A)$175,000
B)$173,333
C)$208,333
D)$216,667
E)$225,000

Question

Quizplus · Accepted Answer

First, we need to calculate the earnings before interest and taxes (EBIT) for the two options using the all-equity option as a reference:

EBIT(all-equity) = 40,000 shares * EPS = 40,000 shares * (EBIT - 0) / 40,000 shares = EBIT

EBIT(28,000 shares + debt) = (28,000 shares * EPS) - (interest expense)

We know that the break-even level of EBIT is $52,000, so we can set up an equation:

EBIT(all-equity) = EBIT(28,000 shares + debt)

$52,000 = EBIT(28,000 shares + debt)

$52,000 = (28,000 shares * EPS) - (interest expense)

To solve for the amount of debt, we need to know the EPS. We don't have that information, but we can use some algebra to eliminate it:

EBIT(all-equity) = EBIT(28,000 shares + debt)

EBIT = (28,000 shares * (EBIT - interest expense) / (28,000 shares + debt))

Multiplicity by (28,000 shares + debt) on both sides, we have:

EBIT(28,000 shares + debt) = (28,000 shares * EBIT - 28,000 shares * interest expense) + debt * EBIT

$52,000 = (28,000 shares * EBIT - 28,000 shares * 0.09 * debt) + 0.09 * debt * EBIT

$52,000 = $28,000 * EBIT - $2,520 * debt + $0.09 * debt * EBIT

Simplifying:

$2,520 * debt = $0.09 * EBIT * debt

$2,520 = $0.09 * EBIT

EBIT = $28,000

Now we can solve for debt:

$52,000 = (28,000 shares * EPS) - (interest expense)

$52,000 = (28,000 shares * $2) - (0.09 * debt)

$52,000 = $56,000 - $0.09 * debt

$0.09 * debt = $4,000

debt = $44,444

Therefore, the firm is considering borrowing $44,444 at a 9% interest rate. The best choice depends on the goals and priorities of the firm, such as maximizing shareholder value or minimizing financial risk.

A Firm Is Considering Two Different Capital Structures