13. 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 s
To calculate the break-even point, we need to determine the quantity at which the total revenue equals the total costs.
a. Fixed Costs = $80,000
Variable Costs per bag = $0.10 per pound * 50 pounds = $5.00
Selling Price per bag = $10.00
Break-even point in bags = Fixed Costs / (Selling Price per bag - Variable Costs per bag)
Break-even point in bags = $80,000 / ($10.00 - $5.00)
Break-even point in bags = $80,000 / $5.00
Break-even point in bags = 16,000 bags
b. 12,000 bags:
Revenue = Selling Price per bag * Quantity = $10.00 * 12,000 = $120,000
Total Variable Costs = Variable Costs per bag * Quantity = $5.00 * 12,000 = $60,000
Total Costs = Fixed Costs + Total Variable Costs = $80,000 + $60,000 = $140,000
Profit or Loss = Revenue - Total Costs = $120,000 - $140,000 = -$20,000 (Loss)
25,000 bags:
Revenue = Selling Price per bag * Quantity = $10.00 * 25,000 = $250,000
Total Variable Costs = Variable Costs per bag * Quantity = $5.00 * 25,000 = $125,000
Total Costs = Fixed Costs + Total Variable Costs = $80,000 + $125,000 = $205,000
Profit or Loss = Revenue - Total Costs = $250,000 - $205,000 = $45,000 (Profit)
c. Degree of Operating Leverage (DOL) measures how sensitive the operating income is to changes in sales quantity. It can be calculated as follows:
DOL = Contribution Margin / Operating Income
At 20,000 bags:
Contribution Margin = Selling Price per bag - Variable Costs per bag = $10.00 - $5.00 = $5.00
Operating Income = Revenue - Total Costs = Selling Price per bag * Quantity - (Fixed Costs + Variable Costs per bag * Quantity)
Operating Income = $10.00 * 20,000 - ($80,000 + $5.00 * 20,000) = $100,000
DOL at 20,000 bags = $5.00 / $100,000 = 0.05
At 25,000 bags:
Contribution Margin = Selling Price per bag - Variable Costs per bag = $10.00 - $5.00 = $5.00
Operating Income = Revenue - Total Costs = Selling Price per bag * Quantity - (Fixed Costs + Variable Costs per bag * Quantity)
Operating Income = $10.00 * 25,000 - ($80,000 + $5.00 * 25,000) = $125,000
DOL at 25,000 bags = $5.00 / $125,000 = 0.04
The degree of operating leverage changes as the quantity sold increases because the fixed costs are spread over a larger number of units, resulting in a lower proportion of fixed costs in total costs. This decreases the impact of fixed costs on operating income, leading to a lower degree of operating leverage.
d. Degree of Financial Leverage (DFL) measures the sensitivity of earnings per share (EPS) to changes in operating income. It can be calculated as follows:
DFL = EBIT / (EBIT - Interest Expense)
At 20,000 bags:
EBIT = Operating Income
Interest Expense = $10,000
DFL at 20,000 bags = $100,000 / ($100,000 - $10,000) = 1.11
At 25,000 bags:
EBIT = Operating Income
Interest Expense = $10,000
DFL at 25,000 bags = $125,000 / ($125,000 - $10,000) = 1.18
e. Degree of Combined Leverage (DCL) is the combination of DOL and DFL. It can be calculated as follows:
DCL = DOL * DFL
DCL at 20,000 bags = 0.05 * 1.11 = 0.0555
DCL at 25,000 bags = 0.04 * 1.18 = 0.0472
To answer these questions, we need to use some basic formulas. Let's go step by step:
a. To find the break-even point in bags, we need to determine the total cost and the selling price per bag. The total cost consists of fixed costs and variable costs per bag.
Fixed Costs: $80,000
Variable Costs per Bag: $0.10 (given)
Selling Price per Bag: $10 (given)
The formula to find the break-even point is:
Break-even Point (in bags) = Fixed Costs / (Selling Price per Bag - Variable Costs per Bag)
Substituting the given values:
Break-even Point (in bags) = $80,000 / ($10 - $0.10)
Break-even Point (in bags) = $80,000 / $9.90
b. To calculate profit or loss, we need to subtract the total costs from the total revenue.
Total revenue for 12,000 bags = 12,000 bags * $10 = $120,000
Total costs for 12,000 bags = (Fixed Costs + Variable Costs per Bag * 12,000)
Profit/Loss for 12,000 bags = Total Revenue - Total Costs
Similarly, you can calculate the profit or loss for 25,000 bags using the same formula.
c. The degree of operating leverage is a measure of how sensitive the profit is to changes in sales. It can be calculated using the following formula:
Degree of Operating Leverage = Contribution Margin / Operating Income
Contribution Margin = (Selling Price per Bag - Variable Costs per Bag) / Selling Price per Bag
Operating Income = Total Revenue - Total Costs
So, substitute the values to calculate the degree of operating leverage at 20,000 bags and 25,000 bags using the formulas above.
The degree of operating leverage changes as the quantity sold increases because fixed costs remain the same, but the variable costs and revenue increase, impacting the profitability.
d. The degree of financial leverage measures the effect of financial leverage (borrowing money) on the company's profits. It can be calculated using the formula:
Degree of Financial Leverage = EBIT / EBIT - Interest Expense
EBIT (Earnings Before Interest and Taxes) = Operating Income - Interest Expense
Substitute the values (Operating Income = Total Revenue - Total Costs) to calculate the degree of financial leverage at 20,000 bags and 25,000 bags.
e. Finally, the degree of combined leverage combines both the operating leverage and the financial leverage. It can be calculated using the formula:
Degree of Combined Leverage = Degree of Operating Leverage * Degree of Financial Leverage
Substitute the previously calculated values of the degree of operating leverage and the degree of financial leverage to find the degree of combined leverage at both sales levels.