Atlantic Seafood has determined that $17,000 is the break-even level of earnings before interest and taxes for the two capital structures it is considering. The one structure consists of all equity with 12,000 shares of stock. The second structure consists of 9,000 shares of stock and $50,000 of debt. What is the interest rate on the debt?
To find the interest rate on the debt, we can use the break-even earnings before interest and taxes (EBIT) and the two capital structures.
Let's calculate the break-even earnings per share (EPS) for each capital structure:
For the first structure with all equity:
Break-even EPS = Break-even EBIT / Number of shares
= $17,000 / 12,000 shares
= $1.42 per share
For the second structure with both equity and debt:
Break-even EPS = Break-even EBIT / (Number of shares + Debt)
Now, let's substitute the known values:
$1.42 per share = $17,000 / (9,000 shares + $50,000 debt)
To solve for the interest rate, we need to rearrange the equation:
$1.42 * (9,000 shares + $50,000 debt) = $17,000
Expanding the equation:
$12,780 + $71,000 * interest rate = $17,000
Rearranging the terms:
$71,000 * interest rate = $17,000 - $12,780
$71,000 * interest rate = $4,220
Now, let's solve for the interest rate:
interest rate = $4,220 / $71,000
interest rate ≈ 0.0595
Therefore, the interest rate on the debt is approximately 5.95%.
To find the interest rate on the debt, we need to use the break-even level of earnings before interest and taxes.
For the all-equity capital structure, the break-even level of earnings before interest and taxes is $17,000.
For the structure with debt, we need to subtract the interest expense from the break-even level of earnings before interest and taxes to find the earnings available to equity holders.
Let's calculate the earnings available to equity holders for both structures:
For the all-equity capital structure:
Earnings available to equity holders = Break-even level of EBIT = $17,000
For the structure with debt:
Earnings before interest and taxes (EBIT) = Break-even level of EBIT + Interest expense
Earnings before interest and taxes (EBIT) = $17,000 + Interest expense
To find the interest expense, we need to know the interest rate on the debt. Let's assume the interest rate on the debt is 'x':
Interest expense = Debt * Interest rate
Interest expense = $50,000 * x
Substituting the values into the equation for the structure with debt:
$17,000 + ($50,000 * x) = Earnings available to equity holders
Now we can solve for 'x' to find the interest rate:
$17,000 + ($50,000 * x) = $17,000
($50,000 * x) = 0
x = 0
The interest rate on the debt is 0%.