Marcus Corporation currently sells 150,000 units a year at a price of $4.00 a unit. Its variable costs are approximately 30 percent of sales, and its fixed costs amount to 50 percent of revenues at its current output level. Although fixed costs are based on revenues at the current output level, the cost level is fixed. What is
Marcus's degree of operating leverage in sales dollars?
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A. B. C. D. E.B
Use the information provided and the formula for DOL in sales dollars: DOL(s) = [($150,000 x $4.00)-180,000]/[($150,000 x $4.00)-180,000-300,000] = 3.5
To calculate Marcus Corporation's degree of operating leverage (DOL) in sales dollars, we need to understand the components involved in the calculation.
Degree of Operating Leverage (DOL) is a financial metric that measures the sensitivity of a company's operating income (or operating profit) to changes in sales revenue. It helps to understand the impact of changes in sales on a company's profitability.
The formula to calculate DOL is:
DOL = (% Change in Operating Income) / (% Change in Sales)
In this case, we need to calculate DOL in sales dollars, which means we'll find the ratio of the change in operating income to the change in sales in dollar terms.
Let's break down the information given in the question:
Marcus Corporation sells 150,000 units a year at a price of $4.00 per unit. So, the total annual sales revenue is calculated as: Total Sales Revenue = Units Sold * Price per Unit Total Sales Revenue = 150,000 units * $4.00/unit Total Sales Revenue = $600,000
Variable costs are approximately 30 percent of sales. This means that the variable cost per unit is 30% of the selling price. Calculating the variable cost per unit: Variable Cost per Unit = 30% * Price per Unit Variable Cost per Unit = 0.30 * $4.00 Variable Cost per Unit = $1.20
Since fixed costs are based on revenues at the current output level, we can calculate the fixed costs as: Fixed Costs = 50% * Total Sales Revenue Fixed Costs = 0.50 * $600,000 Fixed Costs = $300,000
Now, we need to calculate the operating income at the current output level. Operating income can be calculated as the difference between total sales revenue and total costs (fixed costs + variable costs): Operating Income = Total Sales Revenue - (Fixed Costs + Variable Costs) Operating Income = $600,000 - ($300,000 + (Variable Cost per Unit * Units Sold)) Operating Income = $600,000 - ($300,000 + ($1.20 * 150,000)) Operating Income = $600,000 - ($300,000 + $180,000) Operating Income = $600,000 - $480,000 Operating Income = $120,000
Now, we need to calculate the operating income at the new output level. Let's assume that the new sales volume increases by 10%. This means the new sales volume would be 150,000 units * 1.10 = 165,000 units.
Using the same calculations as before, the new operating income would be: New Operating Income = Total Sales Revenue - (Fixed Costs + Variable Costs) New Operating Income = (Price per Unit * New Units Sold) - (Fixed Costs + (Variable Cost per Unit * New Units Sold)) New Operating Income = ($4.00 * 165,000) - ($300,000 + ($1.20 * 165,000)) New Operating Income = ($660,000) - ($300,000 + $198,000) New Operating Income = $660,000 - $498,000 New Operating Income = $162,000
Now, we can calculate the percentage change in operating income: % Change in Operating Income = (New Operating Income - Operating Income) / Operating Income * 100 % Change in Operating Income = ($162,000 - $120,000) / $120,000 * 100 % Change in Operating Income = $42,000 / $120,000 * 100 % Change