Healthy Foods, Inc., sells 50-pound bags of grapes to the military for $10 a bag.
The fixed costs of this operation are $80,000, while the variable costs of the
grapes are $.10 per pound.
a. What is the break-even point in bags?
b. Calculate the profit or loss on 12,000 bags and on 25,000 bags.
c. What is the degree of operating leverage at 20,000 bags and at 25,000 bags?
Why does the degree of operating leverage change as the quantity sold
increases?
d. If Healthy Foods has an annual interest expense of $10,000, calculate the
degree of financial leverage at both 20,000 and 25,000 bags.
e. What is the degree of combined leverage at both sales levels?
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To answer these questions, we'll first need to calculate several values based on the given information:
a. Break-even point in bags:
Fixed costs = $80,000
Variable cost per bag = 50 pounds * $0.10 per pound = $5 per bag
Break-even point in bags = Fixed costs / Contribution margin per bag
Contribution margin per bag = Selling price per bag - Variable cost per bag
Contribution margin per bag = $10 per bag - $5 per bag = $5 per bag
Break-even point in bags = $80,000 / $5 per bag = 16,000 bags
b. Profit or loss on 12,000 bags:
Revenue = 12,000 bags * $10 per bag = $120,000
Variable costs = 12,000 bags * $5 per bag = $60,000
Fixed costs = $80,000
Profit or loss = Revenue - Variable costs - Fixed costs
Profit or loss = $120,000 - $60,000 - $80,000 = -$20,000 (loss)
Profit or loss on 25,000 bags:
Revenue = 25,000 bags * $10 per bag = $250,000
Variable costs = 25,000 bags * $5 per bag = $125,000
Fixed costs = $80,000
Profit or loss = Revenue - Variable costs - Fixed costs
Profit or loss = $250,000 - $125,000 - $80,000 = $45,000 (profit)
c. Degree of operating leverage:
Degree of operating leverage (DOL) = Contribution margin / Operating income
At 20,000 bags:
Revenue = 20,000 bags * $10 per bag = $200,000
Variable costs = 20,000 bags * $5 per bag = $100,000
Fixed costs = $80,000
Contribution margin = Revenue - Variable costs = $200,000 - $100,000 = $100,000
Operating income = Contribution margin - Fixed costs = $100,000 - $80,000 = $20,000
DOL at 20,000 bags = $100,000 / $20,000 = 5
At 25,000 bags:
Revenue = 25,000 bags * $10 per bag = $250,000
Variable costs = 25,000 bags * $5 per bag = $125,000
Fixed costs = $80,000
Contribution margin = Revenue - Variable costs = $250,000 - $125,000 = $125,000
Operating income = Contribution margin - Fixed costs = $125,000 - $80,000 = $45,000
DOL at 25,000 bags = $125,000 / $45,000 = 2.78
The degree of operating leverage changes as the quantity sold increases because the contribution margin increases, resulting in a higher proportion of fixed costs being covered by the incremental increase in revenue.
d. Degree of financial leverage:
Degree of financial leverage (DFL) = Operating income / (Operating income - Interest expense)
At 20,000 bags:
Operating income = $20,000
Interest expense = $10,000
DFL at 20,000 bags = $20,000 / ($20,000 - $10,000) = 2
At 25,000 bags:
Operating income = $45,000
Interest expense = $10,000
DFL at 25,000 bags = $45,000 / ($45,000 - $10,000) = 1.73
e. Degree of combined leverage:
Degree of combined leverage (DCL) = DOL * DFL
At 20,000 bags:
DOL = 5
DFL = 2
DCL at 20,000 bags = 5 * 2 = 10
At 25,000 bags:
DOL = 2.78
DFL = 1.73
DCL at 25,000 bags = 2.78 * 1.73 = 4.81
a. To calculate the break-even point in bags, we need to determine the total costs and the selling price per bag.
Total costs = Fixed costs + (Variable costs per unit * Quantity)
Fixed costs = $80,000
Variable costs per unit = $0.10 per pound * 50 pounds = $5
Quantity (bags) = ? (to be determined)
Selling price per bag = $10
To break even, the total revenue must equal the total costs:
Total revenue = Selling price per bag * Quantity
Setting the total revenue equation equal to the total costs equation and solving for Quantity, we get:
$10 * Quantity = $80,000 + ($5 * Quantity)
Simplifying the equation:
10Q = 80,000 + 5Q
5Q = 80,000
Q = 16,000
Therefore, the break-even point in bags is 16,000 bags.
b. To calculate the profit or loss on a specific number of bags, we need to subtract the total costs from the total revenue.
For 12,000 bags:
Total revenue = $10 * 12,000 = $120,000
Total costs = Fixed costs + (Variable costs per unit * Quantity)
= $80,000 + ($5 * 12,000) = $80,000 + $60,000 = $140,000
Profit/Loss = Total revenue - Total costs
= $120,000 - $140,000 = -$20,000
So, there is a loss of $20,000 on 12,000 bags.
For 25,000 bags:
Total revenue = $10 * 25,000 = $250,000
Total costs = Fixed costs + (Variable costs per unit * Quantity)
= $80,000 + ($5 * 25,000) = $80,000 + $125,000 = $205,000
Profit/Loss = Total revenue - Total costs
= $250,000 - $205,000 = $45,000
So, there is a profit of $45,000 on 25,000 bags.
c. The degree of operating leverage (DOL) is the measure of how sensitive a company's operating income is to changes in quantity sold.
DOL = Contribution Margin / Operating Income
Contribution Margin = Total revenue - Variable costs
Operating Income = Total revenue - Total costs
For 20,000 bags:
Contribution Margin = ($10 * 20,000) - ($5 * 20,000) = $200,000 - $100,000 = $100,000
Operating Income = ($10 * 20,000) - ($80,000 + $5 * 20,000) = $200,000 - $180,000 = $20,000
DOL = $100,000 / $20,000 = 5
For 25,000 bags:
Contribution Margin = ($10 * 25,000) - ($5 * 25,000) = $250,000 - $125,000 = $125,000
Operating Income = ($10 * 25,000) - ($80,000 + $5 * 25,000) = $250,000 - $205,000 = $45,000
DOL = $125,000 / $45,000 ≈ 2.78
The degree of operating leverage changes as the quantity sold increases because the fixed costs remain the same, but the contribution margin (revenue minus variable costs) increases, leading to a higher operating income and a lower DOL.
d. The degree of financial leverage (DFL) measures the sensitivity of a company's earnings per share (EPS) to changes in operating income.
DFL = Earnings Before Interest and Taxes (EBIT) / Earnings Before Taxes (EBT)
EBIT = Operating Income
EBT = EBIT - Interest Expense
For 20,000 bags:
EBIT = Operating Income = $20,000
EBT = $20,000 - $10,000 = $10,000
DFL = $20,000 / $10,000 = 2
For 25,000 bags:
EBIT = Operating Income = $45,000
EBT = $45,000 - $10,000 = $35,000
DFL = $45,000 / $35,000 ≈ 1.29
e. The degree of combined leverage (DCL) combines both operating leverage and financial leverage.
DCL = DOL * DFL
For 20,000 bags:
DCL = 5 * 2 = 10
For 25,000 bags:
DCL = 2.78 * 1.29 ≈ 3.58
The degree of combined leverage increases as the quantity sold increases because both the operating leverage and financial leverage contribute to the overall leverage.