Firm A has $20,000 in assets entirely financed with equity.

Firm B also has $20,000 in assets, financed by $10,000 in debt (with a 10 percent rate of interest) and $10,000 in equity.

Both firms sell 30,000 units at a sale price of $4.00 per unit.
The variable costs of production are $3 per unit.
Fixed production costs are $25,000.
(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 33,000 units, by what percentage
will each firm’s earnings after interest increase? To answer the question,
determine the earnings after interest and compute the percentage
increase in these earnings from the answers you derived in part b.
d. Why are the percentage changes different?

a. To calculate the operating income (EBIT) for both firms, we need to subtract the variable costs and the fixed costs from the total sales revenue.

For Firm A:
Total Sales Revenue = Number of Units Sold * Sale Price per Unit
= 30,000 * $4.00
= $120,000

Total Variable Costs = Number of Units Sold * Variable Cost per Unit
= 30,000 * $3.00
= $90,000

Operating Income (EBIT) = Total Sales Revenue - Total Variable Costs - Fixed Costs
= $120,000 - $90,000 - $25,000
= $5,000

For Firm B:
Total Sales Revenue = 30,000 * $4.00 = $120,000
Total Variable Costs = 30,000 * $3.00 = $90,000
Operating Income (EBIT) = $120,000 - $90,000 - $25,000 = $5,000

b. To calculate the earnings after interest for both firms, we need to deduct the interest expense from the operating income.

For Firm A:
Earnings After Interest = Operating Income (EBIT) - Interest Expense
= $5,000 - $0
= $5,000

For Firm B:
Interest Expense = Debt * Interest Rate
= $10,000 * 10% = $1,000

Earnings After Interest = Operating Income (EBIT) - Interest Expense
= $5,000 - $1,000
= $4,000

c. To calculate the percentage increase in earnings after interest if sales increase by 10%, we need to determine the earnings after interest for the increased sales.

For Firm A (with no debt):
Earnings After Interest = Operating Income (EBIT) = $5,000

For Firm B (with debt):
Increased Sales Revenue = 33,000 * $4.00 = $132,000
Increased Variable Costs = 33,000 * $3.00 = $99,000

Increased Operating Income (EBIT) = Increased Sales Revenue - Increased Variable Costs - Fixed Costs
= $132,000 - $99,000 - $25,000
= $8,000

Earnings After Interest (increased sales) = $8,000 - $1,000 (interest expense) = $7,000

Percentage Increase = ((New Value - Old Value) / Old Value) * 100
= (($7,000 - $4,000) / $4,000) * 100
= 75%

d. The percentage changes in earnings after interest are different because Firm B has debt and incurs interest expenses. When sales increase, the interest expense remains the same for Firm B, and as a result, the increased sales contribute more to the earnings after interest. However, Firm A does not have any interest expenses, so the entire increase in sales contributes to the earnings after interest.