To answer these questions, we need to calculate the financial metrics for both Firm A and Firm B. Let's go step by step:
A. Operating Income (EBIT):
Operating Income (EBIT) is calculated by subtracting the total variable costs and fixed production costs from the total revenue.
For both firms:
Total Revenue = Units Sold * Price per Unit = 10,000 units * $2.50 per unit = $25,000
Total Variable Costs = Variable Cost per Unit * Units Sold = $1 per unit * 10,000 units = $10,000
Operating Income (EBIT) = Total Revenue - Total Variable Costs - Fixed Production Costs
Operating Income (EBIT) = $25,000 - $10,000 - $12,000 = $3,000
So, the operating income (EBIT) for both Firm A and Firm B is $3,000.
B. Earnings After Interest:
Earnings After Interest is calculated by subtracting the interest expense from the operating income (EBIT).
For Firm A, as there is no debt financing:
Earnings After Interest = Operating Income (EBIT)
For Firm B, with $5,000 debt at a 10% interest rate:
Interest Expense = Debt * Interest Rate = $5,000 * 0.10 = $500
Earnings After Interest = Operating Income (EBIT) - Interest Expense
Earnings After Interest = $3,000 - $500 = $2,500
So, the earnings after interest for Firm A is $3,000 and for Firm B is $2,500.
C. Increase in Earnings After Interest:
To calculate the percentage increase in earnings after interest, we need to first determine the earnings after tax.
Assuming no income tax, the earnings after tax will be the same as earnings after interest for both firms.
For Firm A: Earnings After Tax = Earnings After Interest = $3,000
For Firm B: Earnings After Tax = Earnings After Interest = $2,500
Then, we can calculate the percentage increase in earnings after tax for both firms as sales increase by 10%.
For both firms:
New Units Sold = 10,000 units * 1.10 = 11,000 units
New Total Revenue = New Units Sold * Price per Unit = 11,000 units * $2.50 per unit = $27,500
New Operating Income (EBIT) = New Total Revenue - Total Variable Costs - Fixed Production Costs
New Operating Income (EBIT) = $27,500 - $10,000 - $12,000 = $5,500
Again, assuming no income tax, the new earnings after tax will be:
New Earnings After Tax = New Earnings After Interest = New Operating Income (EBIT)
New Earnings After Tax = $5,500
Now, let's calculate the percentage increase in earnings after tax for both firms:
Percentage Increase = (New Earnings After Tax - Old Earnings After Tax) / Old Earnings After Tax * 100%
For Firm A:
Percentage Increase = ($5,500 - $3,000) / $3,000 * 100%
Percentage Increase = $2,500 / $3,000 * 100% ≈ 83.33%
For Firm B:
Percentage Increase = ($5,500 - $2,500) / $2,500 * 100%
Percentage Increase = $3,000 / $2,500 * 100% = 120.00%
D. Different Percentage Changes:
The percentage changes in earnings after tax are different for Firm A and Firm B because the capital structure (debt vs. equity financing) affects the interest expense and ultimately the earnings after interest.
Firm B has debt financing, which requires payment of interest, reducing earnings after interest. As sales increase, both firms experience an increase in operating income (EBIT), but the interest expense negatively impacts Firm B's earnings after interest to a greater extent, resulting in a higher percentage increase in earnings after tax for Firm B compared to Firm A.