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?
To calculate the break-even point in bags, we need to determine the total cost and the selling price per bag.
1. Calculate the total cost per bag:
Fixed costs = $80,000
Variable costs per bag = $0.10 * 50 pounds = $5
Total cost per bag = Fixed costs + Variable costs per bag
Total cost per bag = $80,000 + $5 = $80,005
2. Calculate the break-even point in bags:
Break-even point (in bags) = Fixed costs / (Selling price per bag - Variable costs per bag)
Break-even point = $80,000 / ($10 - $5)
Break-even point = $80,000 / $5
Break-even point = 16,000 bags
a. The break-even point in bags is 16,000 bags.
To calculate the profit or loss, we need to find the total revenue and deduct the total cost.
3. Calculate the total revenue:
Total revenue = Selling price per bag * Number of bags
For 12,000 bags:
Total revenue = $10 * 12,000 bags
Total revenue = $120,000
Profit or loss = Total revenue - Total cost
For 12,000 bags:
Profit or loss = $120,000 - ($80,005 * 12,000)
Profit or loss = $120,000 - $960,060
Profit or loss = -$840,060 (loss)
For 25,000 bags:
Total revenue = $10 * 25,000 bags
Total revenue = $250,000
Profit or loss = Total revenue - Total cost
For 25,000 bags:
Profit or loss = $250,000 - ($80,005 * 25,000)
Profit or loss = $250,000 - $2,000,125
Profit or loss = -$1,750,125 (loss)
b. The profit or loss on 12,000 bags is a loss of $840,060.
The profit or loss on 25,000 bags is a loss of $1,750,125.
To calculate the degree of operating leverage, we need to find the contribution margin and the operating income.
4. Calculate the contribution margin:
Contribution margin = Selling price per bag - Variable costs per bag
Contribution margin = $10 - $0.10
Contribution margin = $9.90
Operating income = Contribution margin * Number of bags - Fixed costs
For 20,000 bags:
Operating income = ($9.90 * 20,000) - $80,000
Operating income = $198,000 - $80,000
Operating income = $118,000
For 25,000 bags:
Operating income = ($9.90 * 25,000) - $80,000
Operating income = $247,500 - $80,000
Operating income = $167,500
c. The degree of operating leverage at 20,000 bags is Operating income / Profit
The degree of operating leverage at 25,000 bags is Operating income / Profit
At 20,000 bags:
Degree of operating leverage = $118,000 / $840,060
Degree of operating leverage = 0.14
At 25,000 bags:
Degree of operating leverage = $167,500 / $1,750,125
Degree of operating leverage = 0.10
The degree of operating leverage changes as the quantity sold increases because fixed costs remain constant, but the contribution margin per unit decreases.
To calculate the degree of financial leverage, we need to find the operating income and the interest expense.
Operating income and interest expense remain the same for both quantities sold.
Operating income = $118,000 (from above)
Interest expense = $10,000
d. The degree of financial leverage at 20,000 bags = Operating income / Interest expense
The degree of financial leverage at 25,000 bags = Operating income / Interest expense
At 20,000 bags:
Degree of financial leverage = $118,000 / $10,000
Degree of financial leverage = 11.8
At 25,000 bags:
Degree of financial leverage = $167,500 / $10,000
Degree of financial leverage = 16.8
To calculate the degree of combined leverage, we multiply the degree of operating leverage by the degree of financial leverage.
e. The degree of combined leverage at 20,000 bags = Degree of operating leverage * Degree of financial leverage
The degree of combined leverage at 25,000 bags = Degree of operating leverage * Degree of financial leverage
At 20,000 bags:
Degree of combined leverage = 0.14 * 11.8
Degree of combined leverage = 1.65
At 25,000 bags:
Degree of combined leverage = 0.10 * 16.8
Degree of combined leverage = 1.68
To answer these questions, we need to understand the concepts of fixed costs, variable costs, breakeven point, profit/loss, degree of operating leverage, degree of financial leverage, and degree of combined leverage.
a. The breakeven point is the point at which the company's revenue equals its total costs, resulting in neither profit nor loss. Let's calculate the breakeven point in bags:
Fixed costs = $80,000
Variable costs per bag = $0.10/lb * 50 lb/bag = $5
Breakeven point (in bags) = Fixed costs / Contribution margin per bag
Contribution margin per bag = Selling price per bag - Variable cost per bag = $10 - $5 = $5
Breakeven point (in bags) = $80,000 / $5 = 16,000 bags
Therefore, the breakeven point is 16,000 bags.
b. To calculate the profit or loss on a specific number of bags, we need to determine the total revenue and total costs.
Total revenue = Selling price per bag * Number of bags
Total costs = Fixed costs + Variable cost per bag * Number of bags
On 12,000 bags:
Total revenue = $10 * 12,000 = $120,000
Total costs = $80,000 + ($0.10 * 50 * 12,000) = $80,000 + $60,000 = $140,000
Profit/Loss = Total revenue - Total costs = $120,000 - $140,000 = -$20,000 (loss)
On 25,000 bags:
Total revenue = $10 * 25,000 = $250,000
Total costs = $80,000 + ($0.10 * 50 * 25,000) = $80,000 + $125,000 = $205,000
Profit/Loss = Total revenue - Total costs = $250,000 - $205,000 = $45,000 (profit)
c. The degree of operating leverage measures the change in operating income (profit) for a given change in sales quantity.
Degree of Operating Leverage = Contribution margin / Operating Income
At 20,000 bags:
Contribution margin per bag = Selling price per bag - Variable cost per bag = $10 - $5 = $5
Operating Income = Total revenue - Total costs = $10 * 20,000 - ($80,000 + $0.10 * 50 * 20,000) = $200,000 - $180,000 = $20,000
Degree of Operating Leverage = $5 / $20,000 = 0.00025
At 25,000 bags:
Contribution margin per bag = $5
Operating Income = $10 * 25,000 - ($80,000 + $0.10 * 50 * 25,000) = $250,000 - $205,000 = $45,000
Degree of Operating Leverage = $5 / $45,000 = 0.00011
The degree of operating leverage changes as the quantity sold increases because the fixed costs remain constant while the contribution margin per unit decreases. This means that the contribution margin is spread over a larger number of units, resulting in a smaller impact on the operating income.
d. The degree of financial leverage measures the sensitivity of net income to changes in operating income. It is calculated using the following formula:
Degree of Financial Leverage = Operating Income / (Operating Income - Interest Expense)
At 20,000 bags:
Operating Income = $20,000
Interest Expense = $10,000
Degree of Financial Leverage = $20,000 / ($20,000 - $10,000) = $20,000 / $10,000 = 2
At 25,000 bags:
Operating Income = $45,000
Interest Expense = $10,000
Degree of Financial Leverage = $45,000 / ($45,000 - $10,000) = $45,000 / $35,000 = 1.2857
e. The degree of combined leverage combines the effects of operating leverage and financial leverage. It is calculated by multiplying the degree of operating leverage by the degree of financial leverage.
At 20,000 bags:
Degree of Combined Leverage = Degree of Operating Leverage * Degree of Financial Leverage = 0.00025 * 2 = 0.0005
At 25,000 bags:
Degree of Combined Leverage = Degree of Operating Leverage * Degree of Financial Leverage = 0.00011 * 1.2857 = 0.0001417
The degree of combined leverage changes as the sales level changes because it reflects the combined impact of both the operating leverage and financial leverage. As the sales level increases, the contribution margin decreases (operating leverage decreases), which in turn lowers the degree of combined leverage.