Healthy food, sell 50-pound bags of grapes to the military for $10.00 a bag. The fixed cost of this operation are $80,000, while the variable cost of the grapes are $.10 per pound. what is the degree of operating leverage at 20,000 and 25,000 bags?
To calculate the degree of operating leverage (DOL), we need to use the following formula:
DOL = (Sales - Variable Cost) / (Sales - Variable Cost - Fixed Cost)
First, let's calculate the total sales at 20,000 bags:
Total sales = Selling price per bag * Number of bags
Total sales = $10.00 * 20,000 bags
Total sales = $200,000
Next, we need to calculate the total variable cost:
Variable cost per pound = $0.10
Total variable cost = Variable cost per pound * Number of pounds
Total variable cost = $0.10 * 50 pounds * 20,000 bags
Total variable cost = $100,000
Now, we can calculate the DOL at 20,000 bags using the formula:
DOL = ($200,000 - $100,000) / ($200,000 - $100,000 - $80,000)
DOL = $100,000 / $20,000
DOL = 5
The degree of operating leverage at 20,000 bags is 5.
Now, let's calculate the DOL at 25,000 bags:
Total sales = $10.00 * 25,000 bags
Total sales = $250,000
Total variable cost = $0.10 * 50 pounds * 25,000 bags
Total variable cost = $125,000
DOL = ($250,000 - $125,000) / ($250,000 - $125,000 - $80,000)
DOL = $125,000 / $45,000
DOL = 2.78 (rounded to two decimal places)
The degree of operating leverage at 25,000 bags is approximately 2.78.
To calculate the degree of operating leverage (DOL), we need two pieces of information: the contribution margin and the operating income.
To find the contribution margin, we subtract the variable cost per unit from the selling price per unit. In this case, the selling price per bag is $10 and the variable cost per pound is $0.10. Since there are 50 pounds per bag, the variable cost per bag is $0.10 x 50 = $5. Therefore, the contribution margin per bag is $10 - $5 = $5.
Now let's calculate the operating income. The operating income is the difference between the total revenue and the total cost. The total revenue can be calculated by multiplying the selling price per bag by the number of bags sold. Since each bag is being sold for $10 and we want to calculate the DOL at two different levels of bag sales, we can use the following calculations:
At 20,000 bags:
Total Revenue = $10 x 20,000 = $200,000
Total Cost = Fixed Cost + (Variable Cost per Bag x Number of Bags)
Total Cost = $80,000 + ($0.10 x 50 x 20,000) = $80,000 + $100,000 = $180,000
Operating Income = Total Revenue - Total Cost
Operating Income = $200,000 - $180,000 = $20,000
At 25,000 bags:
Total Revenue = $10 x 25,000 = $250,000
Total Cost = $80,000 + ($0.10 x 50 x 25,000) = $80,000 + $125,000 = $205,000
Operating Income = $250,000 - $205,000 = $45,000
Now, we can calculate the degree of operating leverage (DOL) using the formula:
DOL = % Change in Operating Income / % Change in Sales
For the first scenario (20,000 bags):
% Change in Operating Income = [(Operating Income at 20,000 bags - Operating Income at 0 bags) / Operating Income at 0 bags] x 100
% Change in Operating Income = [($20,000 - $0) / $0] x 100 = 100%
% Change in Sales = [(Sales at 20,000 bags - Sales at 0 bags) / Sales at 0 bags] x 100
% Change in Sales = [(20,000 - 0) / 0] x 100 = Infinity or undefined
Since the % Change in Sales is undefined, the DOL at 20,000 bags is also undefined.
For the second scenario (25,000 bags):
% Change in Operating Income = [($45,000 - $0) / $0] x 100 = Infinity or undefined
% Change in Sales = [(25,000 - 0) / 0] x 100 = Infinity or undefined
Similarly, since both the % Change in Operating Income and % Change in Sales are undefined, the DOL at 25,000 bags is also undefined.
In conclusion, the DOL is undefined at both 20,000 and 25,000 bags sold.