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Quizzes > Business & Finance > Business & Industry

Equation Quiz: Test Your Cost Behavior & Contribution Margin Skills

Think You Can Organize Costs by Behavior? Dive In & Test Your Skills!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style illustration with calculator graphs charts and equations over teal background for equation skills quiz

Ready to level up your accounting skills? Our Equation Quiz: Master Contribution Margin & Cost Behavior shows how contribution margin income statements organize costs by behavior in an interactive, free quiz. You'll test income statement cost behavior understanding, practice calculating contribution margin, and explore variable versus fixed costs. Perfect for students and finance pros tackling managerial accounting, this cost behavior quiz offers instant feedback. Jump in now with our contribution margin income statements organize costs by behavior session and sharpen insights with the average vs marginal cost quiz .

What is the contribution margin?
Revenue minus variable costs
Net profit
Gross profit
Revenue minus fixed costs
Contribution margin is defined as sales revenue less all variable costs. It shows how much revenue contributes to fixed costs and profit after covering variable costs. Companies use it to analyze profitability at different volumes.
How do you calculate contribution margin per unit?
Fixed cost per unit plus variable cost per unit
Selling price per unit minus variable cost per unit
Selling price per unit plus variable cost per unit
Total sales minus total fixed cost
Contribution margin per unit is simply the selling price per unit minus the variable cost per unit. This measures how much each unit sold contributes toward covering fixed costs and profit. It's a cornerstone of cost - volume - profit analysis.
What formula gives the break-even point in units?
Fixed costs divided by contribution margin per unit
Sales divided by contribution margin ratio
Variable cost per unit
Fixed cost divided by total cost per unit
The break-even point in units is calculated by dividing total fixed costs by contribution margin per unit. This tells you how many units must be sold to cover all costs. Beyond this point, profits begin.
A company has sales of $500,000 and variable costs of $300,000. What is the total contribution margin?
$800,000
$500,000
$200,000
$300,000
Total contribution margin equals total sales minus total variable costs. In this case, $500,000 minus $300,000 equals $200,000. It shows how much is available to cover fixed costs and profit.
Which cost behavior category changes in direct proportion to activity level?
Fixed cost
Variable cost
Mixed cost
Step cost
Variable costs change directly with activity level, meaning as production or sales volume increases, total variable costs increase in direct proportion. They are constant on a per-unit basis.
Which cost remains constant in total regardless of changes in activity level?
Mixed cost
Fixed cost
Variable cost
Step cost
Fixed costs remain constant in total across the relevant range of activity, meaning they do not change with production volume. They are constant in total but vary per unit as volume changes.
A mixed cost is best described as:
Containing both variable and fixed components
Neither fixed nor variable
Only fixed
Only variable
A mixed cost has both fixed and variable elements. Part of the cost remains constant regardless of activity, while another part changes with volume. An example is a utility bill with a base charge plus usage fees.
Which formula represents total cost behavior?
Total Cost = Fixed Cost + (Variable Cost per unit × Units)
Total Cost = Variable Cost per unit × Units only
Total Cost = Fixed Cost × Units + Variable Cost
Total Cost = Fixed Cost + Variable Cost
Total cost consists of fixed costs plus variable costs that change with the number of units produced. This formula captures both components accurately.
If a product has a contribution margin ratio of 40%, what percentage of sales represents variable cost?
40%
20%
30%
60%
Variable cost percentage plus contribution margin ratio equals 100%. If the CM ratio is 40%, then variable costs represent the remaining 60%. This relationship helps in CVP analysis.
How is the contribution margin ratio calculated?
Contribution margin minus sales
Contribution margin divided by sales
Sales minus contribution margin
Sales divided by contribution margin
The contribution margin ratio equals contribution margin (sales minus variable costs) divided by sales. It shows the percentage of each sales dollar available to cover fixed costs and profit.
Selling price per unit is $20 and variable cost per unit is $12. What is the contribution margin ratio?
20%
80%
60%
40%
Contribution margin per unit is $20 - $12 = $8. The ratio is $8 divided by $20, which equals 0.40 or 40%. This indicates 40% of sales contributes to fixed costs and profit.
If fixed costs are $50,000, variable cost per unit is $10, and selling price is $25, what is the break-even point in units?
2,000 units
2,500 units
3,334 units
5,000 units
Break-even units = Fixed costs ÷ (Selling price - Variable cost). Here, $50,000 ÷ ($25 - $10) = 50,000 ÷ 15 ? 3,333.33, rounded up to 3,334 units.
Multi-product break-even analysis requires which key assumption?
Fixed costs vary with volume
Sales mix is irrelevant
A constant sales mix
Variable costs remain fixed
In multi-product break-even, sales mix must remain constant because differing mixes change the weighted average contribution margin. This ensures stability in break-even calculations.
Which data points does the high-low method use to estimate costs?
Highest and lowest costs
Median cost observations
Average activity level
Highest and lowest activity levels
The high-low method uses the cost and activity at the highest and lowest activity levels to estimate variable cost per unit and total fixed cost. It ignores intermediate data points.
Using the high-low method, if cost at 5,000 units is $20,000 and cost at 1,000 units is $12,000, what is the variable cost per unit?
$0.50
$0.20
$4.00
$2.00
Variable cost per unit = (Cost at high activity - Cost at low activity) ÷ (High units - Low units) = ($20,000 - $12,000) ÷ (5,000 - 1,000) = $8,000 ÷ 4,000 = $2.00.
After finding the variable cost per unit using high-low, how do you compute the fixed cost?
Multiply variable cost per unit by total units
Divide total cost by variable cost per unit
Subtract total variable cost at a point from its total cost
Add the variable cost to total cost
Fixed cost = Total cost at a chosen activity level - (Variable cost per unit × Number of units at that level). This isolates the fixed component.
What does the margin of safety represent?
Ratio of fixed costs to variable costs
Net operating income
Total contribution margin
Excess of actual sales over break-even sales
Margin of safety measures how much sales can drop before a company reaches break-even. It's calculated as actual (or budgeted) sales minus break-even sales. This indicates risk of losses.
How is the degree of operating leverage (DOL) calculated?
Net operating income divided by contribution margin
Contribution margin divided by net operating income
Sales divided by net operating income
Fixed costs divided by variable costs
DOL = Contribution margin ÷ Net operating income. It measures sensitivity of operating income to changes in sales. A higher DOL indicates greater risk and potential reward.
If the degree of operating leverage is 4, what is the expected percentage change in operating income for a 5% increase in sales?
20%
9%
80%
4%
Percent change in operating income = DOL × Percent change in sales. Here, 4 × 5% = 20%. This demonstrates leverage effect.
If the contribution margin ratio is 30% and sales increase by $50,000, by how much will operating profit increase?
$50,000
$30,000
$5,000
$15,000
Increase in operating profit = Increase in sales × Contribution margin ratio = $50,000 × 0.30 = $15,000. This applies CVP principles.
On a cost-volume-profit graph, what are the typical axes?
Time (x-axis) and dollars (y-axis)
Time (x-axis) and units (y-axis)
Units (x-axis) and dollars (y-axis)
Dollars (x-axis) and units (y-axis)
A CVP graph plots activity (units sold or produced) on the horizontal axis and costs/revenue in dollars on the vertical axis. This visualizes break-even and profit regions.
Which cost classification includes depreciation on a factory building?
Direct labor
Variable manufacturing overhead
Direct materials
Fixed manufacturing overhead
Depreciation on a factory building is a fixed manufacturing overhead cost because it does not change with production volume. It's part of product cost under absorption costing.
Product A has a contribution margin of $12 per unit (70% sales mix) and Product B has $8 per unit (30% sales mix). What is the weighted average contribution margin per unit?
$8.00
$11.20
$9.60
$10.80
Weighted average CM = ($12 × 0.70) + ($8 × 0.30) = $8.40 + $2.40 = $10.80. This ensures break-even for mixed-product companies.
What is the formula to compute the required units to achieve a target profit?
(Fixed costs - Target profit) ÷ Contribution margin ratio
Target profit ÷ Contribution margin ratio
(Fixed costs + Target profit) ÷ Contribution margin per unit
Fixed costs ÷ Contribution margin per unit
To find the units needed for a target profit: add fixed costs and desired profit, then divide by contribution margin per unit. This extends break-even analysis to profit planning.
If fixed costs increase, what happens to the degree of operating leverage (DOL) at the same sales level?
It remains unchanged
It becomes zero
It decreases
It increases
An increase in fixed costs (with no change in CM) lowers net operating income, which increases DOL (CM ÷ NOI). Higher fixed costs raise operating leverage, making profits more sensitive to sales changes.
Which income statement format classifies costs by behavior and highlights contribution margin?
Cash flow statement
Traditional income statement
Statement of retained earnings
Contribution margin income statement
The contribution margin income statement separates variable and fixed costs, showing sales, variable costs, contribution margin, fixed costs, and net operating income. This aids CVP analysis.
Under variable costing, how are fixed manufacturing overhead costs treated?
Allocated to selling expenses
Included in inventory cost
Expensed in the period incurred
Deferred to the next period
Variable costing treats fixed manufacturing overhead as a period expense rather than a product cost. It is fully expensed in the period incurred, improving view of cost behavior.
If inventory levels increase, how will net operating income compare under absorption costing versus variable costing?
The same under both methods
Higher under variable costing
Cannot be determined
Higher under absorption costing
When inventory increases, absorption costing defers some fixed manufacturing overhead into inventory, resulting in higher net operating income compared to variable costing, which expenses all fixed overhead.
What is the segment margin in a segmented contribution margin income statement?
Segment revenue minus variable costs and traceable fixed costs
Segment contribution margin minus common fixed costs
Total revenue minus all fixed costs
Total contribution margin minus traceable variable costs
Segment margin = Segment sales - Variable costs - Traceable fixed costs. It shows profitability of each segment before common costs.
Within the relevant range, what happens to fixed manufacturing overhead cost per unit as production increases?
It decreases
It increases
It remains constant
It fluctuates randomly
Total fixed manufacturing overhead remains constant, so when more units are produced within the relevant range, the fixed overhead cost per unit decreases. This improves per-unit costing.
How do you calculate break-even in sales dollars?
Fixed costs divided by contribution margin per unit
Variable costs divided by contribution margin ratio
Total costs divided by sales dollars
Fixed costs divided by contribution margin ratio
Break-even in sales dollars = Fixed costs ÷ Contribution margin ratio. This converts unit-based break-even into a dollar measure.
What statistical measure indicates the proportion of variance explained in regression cost estimation?
R-squared
P-value
Standard error
Beta coefficient
R-squared, or the coefficient of determination, measures how well regression variables explain the variation in costs. A higher R-squared indicates a better fit.
If the degree of operating leverage is 5 and sales decrease by 8%, by what percentage will net operating income change if initial income was $100,000?
Decrease by 40% to $60,000
Increase by 40% to $140,000
Increase by 20% to $120,000
Decrease by 20% to $80,000
Percent change in NOI = DOL × percent change in sales = 5 × (-8%) = -40%. Thus $100,000 × (1 - 0.40) = $60,000. This shows high leverage risk.
Three products have contribution margins of $20, $15, and $10 with sales mixes of 50%, 30%, and 20% respectively. What is the weighted average contribution margin per unit?
$15.00
$18.00
$12.50
$16.50
Weighted CM = ($20×0.50) + ($15×0.30) + ($10×0.20) = $10 + $4.50 + $2 = $16.50. This guides break-even and profit planning in multi-product settings.
A cost regression yields an intercept of $1,000 and a slope of $0.75 per unit. What do these represent?
Fixed cost of $0.75 and variable cost of $1,000 per unit
Total cost of $1,000 for 1,000 units
Variable cost of $1,000 plus fixed cost per unit
Fixed cost of $1,000 and variable cost of $0.75 per unit
In cost regression, the intercept represents total fixed cost ($1,000) and the slope represents variable cost per unit ($0.75). This equation predicts total cost by activity level.
Which limitation applies to the high-low method of cost estimation?
It uses only two data points for estimation
It employs full regression analysis
It provides the most accurate cost estimates
It accounts for outliers effectively
The high-low method only uses the highest and lowest activity points, ignoring all other data, which can lead to inaccurate cost estimates if those points are outliers.
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Study Outcomes

  1. Understand Contribution Margin Income Statements -

    Identify the key elements and structure of contribution margin income statements to evaluate product profitability.

  2. Analyze Cost Behavior Patterns -

    Distinguish between fixed, variable, and mixed costs using income statement cost behavior concepts.

  3. Calculate Contribution Margin -

    Compute contribution margin per unit and ratio accurately for better decision-making.

  4. Organize Costs by Behavior -

    Apply techniques to organize costs by behavior, enhancing clarity in financial reporting.

  5. Apply Cost Behavior Equations -

    Use cost behavior quiz problems to practice setting up and solving real-world equations.

  6. Evaluate Profitability Impacts -

    Interpret how changes in costs and sales volume influence overall profitability.

Cheat Sheet

  1. Reading the Contribution Margin Income Statement -

    This handy format uses contribution margin income statements to organize costs by behavior, listing sales, variable costs, and fixed costs before arriving at operating income. For example, if sales are $100,000 and variable costs are $60,000, the contribution margin is $40,000, clearly showing how much revenue contributes to covering fixed costs and profit. (Source: University of Michigan Ross School of Business)

  2. Classifying Costs with the y = a + bx Model -

    Pro tip: use the equation y = a + bx to organize costs by behavior - where "a" is total fixed cost and "b" is variable cost per unit times activity level x. For instance, if fixed costs (a) are $500 and variable cost per unit (b) is $5 at 100 units, total cost y = 500 + 5×100 = $1,000. (Source: Harvard Business School Online)

  3. Calculating Contribution Margin & Ratio -

    Quick trick: contribution margin equals Sales minus Variable Costs, and the contribution margin ratio is Contribution Margin ÷ Sales. If your contribution margin is $40,000 on $100,000 in sales, the ratio is 40%, showing each sales dollar contributes $0.40 toward fixed costs and profit. (Source: Institute of Management Accountants)

  4. Break-even & Target Profit Analysis -

    Break-even in units = Fixed Costs ÷ Contribution Margin per Unit; break-even in dollars = Fixed Costs ÷ Contribution Margin Ratio. For example, with fixed costs of $20,000 and a $10 contribution margin per unit, you need 2,000 units to break even. To hit a target profit, simply add desired profit to fixed costs in the numerator. (Source: Chartered Institute of Management Accountants)

  5. Estimating Costs via the High-Low Method -

    This simple approach finds variable cost per unit by dividing the cost difference between high and low activity levels by the change in units. For example, if costs are $18,000 at 3,000 units and $12,000 at 1,000 units, variable cost = ($18,000 - $12,000)/(3,000 - 1,000) = $3 per unit. Then calculate fixed cost by subtracting total variable cost at either activity level from total cost. (Source: Journal of Cost Analysis & Management)

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