Firm A has $10,000 in assets entirely financed with equity. Firm B also has $10,000 in assets, 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 increase? To answer the question, determine the earnings after taxes and compute the percentage increase in these earnings from the answers you derived in part b.
d. Why are the percentage changes different?
Firm A has $10,000 in assets entirely financed with equity. Firm B also has $10,000 in assets, 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?
EBIT = 10000 * 2.5 – 10000 * 1 – 12000 = $3000
b. What are the earnings after interest?
Earnings after interest (Firm A) = $3000 - 0 = $3000
Earnings after interest (Firm B) = $3000 – 500 = $2500
c. If sales increase by 10 percent to 11,000 units, by what percentage will each firm’s earnings after interest increase? To answer the question, determine the earnings after taxes and compute the percentage increase in these earnings from the answers you derived in part b.
New EBIT (Both Firms) = 11000 * 2.5 – 11000 * 1 – 12000 = $4500
New Earnings after interest (Firm A) = $4500 – 0 = $4500
New Earnings after interest (Firm B) = $4500 – 500 = $4000
Increase in Firm A Earnings = (4500 – 3000)/3000 = 50%
Increase in Firm B Earnings = (4000 – 2500)/2500 = 60%
d. Why are the percentage changes different?
The percentage changes are different because of the different capital structure between the two firms.
a. To calculate the operating income (EBIT) for both firms, we need to subtract the variable costs from the total revenue and then subtract the fixed production costs.
For Firm A:
Total revenue = 10,000 units * $2.50 per unit = $25,000
Variable costs = 10,000 units * $1 per unit = $10,000
EBIT (Operating Income) = Total revenue - Variable costs - Fixed production costs
= $25,000 - $10,000 - $12,000
= $3,000
For Firm B:
Total revenue = 10,000 units * $2.50 per unit = $25,000
Variable costs = 10,000 units * $1 per unit = $10,000
EBIT (Operating Income) = Total revenue - Variable costs - Fixed production costs
= $25,000 - $10,000 - $12,000
= $3,000
So, the operating income (EBIT) for both firms 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:
Earnings after interest = EBIT - Interest expense
= $3,000 - $0 (since Firm A is entirely financed with equity)
= $3,000
For Firm B:
Interest expense = $5,000 (debt) * 10% (interest rate) = $500
Earnings after interest = EBIT - Interest expense
= $3,000 - $500
= $2,500
So, the earnings after interest for Firm A is $3,000, and for Firm B is $2,500.
c. To calculate the earnings after taxes and the percentage increase, we need to assume a tax rate. Since no information is given about the tax rate, we will assume it to be 0% (no income tax).
For both firms:
Earnings after taxes = Earnings after interest (since no income tax is applied)
For Firm A, earnings after taxes remain the same: $3,000.
For Firm B, earnings after taxes also remain the same: $2,500.
Now, let's calculate the percentage increase in earnings after taxes:
Percentage increase = ((New earnings - Old earnings) / Old earnings) * 100
For both firms, the percentage increase is 0% because the earnings after taxes remain the same.
d. The percentage changes in earnings after interest are different for Firm A and Firm B because Firm B has interest expenses due to the debt it carries. As a result, the interest expense reduces the earnings after interest, which in turn affects the increase in earnings after taxes. Meanwhile, Firm A, being entirely financed with equity, has no interest expense, resulting in a consistent and unchanged earnings after interest and taxes.
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 sales revenue.
For Firm A:
Operating Income (EBIT) = Total Sales Revenue - Total Variable Costs - Fixed Production Costs
= (Number of Units Sold * Price per Unit) - (Number of Units Sold * Variable Cost per Unit) - Fixed Production Costs
= (10,000 * $2.50) - (10,000 * $1) - $12,000
= $25,000 - $10,000 - $12,000
= $3,000
For Firm B:
Operating Income (EBIT) = Total Sales Revenue - Total Variable Costs - Fixed Production Costs
= (Number of Units Sold * Price per Unit) - (Number of Units Sold * Variable Cost per Unit) - Fixed Production Costs
= (10,000 * $2.50) - (10,000 * $1) - $12,000
= $25,000 - $10,000 - $12,000
= $3,000
So, the operating income (EBIT) for both firms A and 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, as there is no debt, the earnings after interest will be the same as the operating income (EBIT):
Earnings After Interest (Firm A) = Operating Income (EBIT)
= $3,000
For Firm B, we need to subtract the interest expense from the operating income (EBIT):
Earnings After Interest (Firm B) = Operating Income (EBIT) - Interest Expense
= $3,000 - ($5,000 * 10%)
= $3,000 - $500
= $2,500
So, the earnings after interest for Firm A is $3,000, and for Firm B is $2,500.
c. To calculate the percentage increase in earnings after interest for both firms when sales increase by 10 percent, we need to calculate the earnings after taxes first.
To calculate the earnings after taxes, we need to subtract the taxes from the earnings after interest.
For both firms, as there is no income tax mentioned, the earnings after taxes will be the same as the earnings after interest:
Earnings After Taxes (Firm A) = Earnings After Interest (Firm A) = $3,000
Earnings After Taxes (Firm B) = Earnings After Interest (Firm B) = $2,500
Now, we can calculate the percentage increase in earnings after interest (or earnings after taxes) for both firms:
Percentage Increase = [(New Earnings - Old Earnings) / Old Earnings] * 100
For Firm A: When sales increase to 11,000 units, the new earnings after interest (or earnings after taxes) will still be $3,000.
Percentage Increase (Firm A) = [(New Earnings - Old Earnings) / Old Earnings] * 100
= [(3,000 - 3,000) / 3,000] * 100
= 0%
For Firm B: When sales increase to 11,000 units, the new earnings after interest (or earnings after taxes) can be calculated as follows:
New Earnings After Taxes (Firm B) = Total Sales Revenue - Total Variable Costs - Fixed Production Costs - Interest Expense
= (Number of Units * Price per Unit) - (Number of Units * Variable Cost per Unit) - Fixed Production Costs - Interest Expense
= (11,000 * $2.50) - (11,000 * $1) - $12,000 - ($5,000 * 10%)
= $27,500 - $11,000 - $12,000 - $500
= $4,000
Percentage Increase (Firm B) = [(New Earnings - Old Earnings) / Old Earnings] * 100
= [(4,000 - 2,500) / 2,500] * 100
= 60%
d. The percentage changes in earnings after interest between the two firms are different because Firm B has debt in its capital structure. As a result, Firm B has to pay interest expense, which lowers its earnings after interest compared to Firm A. When sales increase, the increase in earnings after interest for Firm B is higher in percentage terms because the interest expense remains fixed, while the operating income increases with the increase in sales. This amplifies the percentage increase in earnings for Firm B compared to Firm A.