Firm A had $10,000 in assets entirely financed with equity. Firm B also has $10,000, but these assets are financed by $5,000 in debt (with a 10 percent rate of interest) and $5,000 in equity. Both firms sell 10,000 units of output at $2.50 per unit. The variable costs of production are $1, and fixed production costs are $12,000. (to ease the calculation, assume no income tax.)
A. What is the operating income (EBIT) for both firms?
B. What are the earnings after interest?
C. If sales increase by 10 percent to 11,000 units, by what percentage will each firm's earnings after interest income? To answer the question, determine the earnings after taxed and compute the percentage increase in these earnings from the answers you derived in part b.
D. Why are the percentage changes different?
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.
A. To calculate the operating income (EBIT) for both firms, we need to subtract the total variable costs and fixed production costs from the total revenue.
For Firm A:
Total revenue = Total units sold * Price per unit = 10,000 * $2.50 = $25,000
Total variable costs = Total units sold * Variable cost per unit = 10,000 * $1 = $10,000
Fixed production costs = $12,000
EBIT (Operating Income) = Total revenue - Total variable costs - Fixed production costs
EBIT (Firm A) = $25,000 - $10,000 - $12,000 = $3,000
For Firm B:
Total revenue = Total units sold * Price per unit = 10,000 * $2.50 = $25,000
Total variable costs = Total units sold * Variable cost per unit = 10,000 * $1 = $10,000
Fixed production costs = $12,000
EBIT (Operating Income) = Total revenue - Total variable costs - Fixed production costs
EBIT (Firm B) = $25,000 - $10,000 - $12,000 = $3,000
Therefore, the operating income for both firms (Firm A and Firm B) is $3,000.
B. To calculate the earnings after interest, we need to subtract the interest expense from the operating income (EBIT).
For Firm A:
Interest expense = 0 (as there is no debt)
Earnings after interest (Firm A) = EBIT (Firm A) - Interest expense = $3,000 - $0 = $3,000
For Firm B:
Interest expense = Debt * Interest rate = $5,000 * 10% = $500
Earnings after interest (Firm B) = EBIT (Firm B) - Interest expense = $3,000 - $500 = $2,500
Therefore, the earnings after interest for Firm A are $3,000, and for Firm B are $2,500.
C. To calculate the new earnings after interest if sales increase by 10%, we need to first calculate the new revenue and then subtract the interest expense.
For both firms:
New units sold = 10% increase in units sold = 10,000 + 10% of 10,000 = 10,000 + 1,000 = 11,000
New total revenue = New units sold * Price per unit = 11,000 * $2.50 = $27,500
New earnings after interest (Firm A) = New total revenue - Total variable costs - Fixed production costs = $27,500 - $10,000 - $12,000 = $5,500
New earnings after interest (Firm B) = New total revenue - Total variable costs - Fixed production costs - Interest expense = $27,500 - $10,000 - $12,000 - $500 = $5,000
To calculate the percentage increase in earnings after interest for each firm:
Percentage increase = [(New earnings - Old earnings) / Old earnings] * 100
Percentage increase (Firm A) = [(New earnings after interest - Old earnings after interest) / Old earnings after interest] * 100
Percentage increase (Firm A) = [(($5,500 - $3,000) / $3,000] * 100 = 83.33%
Percentage increase (Firm B) = [(New earnings after interest - Old earnings after interest) / Old earnings after interest] * 100
Percentage increase (Firm B) = [(($5,000 - $2,500) / $2,500] * 100 = 100%
Therefore, if sales increase by 10%, Firm A's earnings after interest would increase by approximately 83.33% and Firm B's earnings after interest would increase by 100%.
D. The percentage changes in earnings after interest are different for both firms due to the difference in their capital structure and interest expense.
Firm A has no debt and is entirely financed by equity, so it does not incur any interest expense. Therefore, when sales increase, Firm A's earnings increase directly with the increase in revenue.
Firm B has $5,000 in debt, which incurs an interest expense of $500. When sales increase, Firm B needs to pay the fixed interest expense before calculating the earnings after interest. As a result, the impact of the increase in revenue on earnings is reduced.
The differences in the percentage changes in earnings after interest reflect the impact of the interest expense on the overall earnings of Firm B.