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Managerial Accounting Unit 4: Cost Behavior and Contribution Margin

Costs behave differently as activity changes. Knowing which costs are variable and which are fixed lets managers build the contribution format income statement and predict profit.

Covers: Variable, fixed and mixed costs, Relevant range and step costs, High-low method and regression, Contribution format income statement, Contribution margin per unit and ratio, Absorption vs. variable costing

Study guide

Cost behavior describes how a cost changes as activity changes. A variable cost changes in total in proportion to activity but stays constant per unit, like the flour in each loaf of bread. A fixed cost stays constant in total within the relevant range but falls per unit as volume rises, like monthly rent. The relevant range is the band of activity where these patterns hold; beyond it, a company may need a new building or extra supervisors. Some costs are step costs that stay flat and then jump at thresholds. A mixed cost has both a fixed part and a variable part, like a phone plan with a monthly fee plus per-minute charges.

To plan, managers split mixed costs into fixed and variable parts using a cost formula, Y = a + bX, where a is fixed cost, b is the variable cost per unit of activity and X is activity. The high-low method uses the highest and lowest activity levels: b = change in cost ÷ change in activity, and a = total cost - bX at either point. Always pick the points by activity, not by cost. High-low is quick but uses only two observations, which may be unusual. Least-squares regression fits a line through all the data and is more accurate. A scatter plot is a good first check for outliers before using either method.

The contribution format income statement organizes costs by behavior rather than by function. It starts with sales, subtracts all variable costs (manufacturing and selling) to get contribution margin, then subtracts all fixed costs to get net operating income. Contribution margin is the amount available to cover fixed costs and then provide profit. Per unit, CM = price - variable cost; as a ratio, CM ratio = CM ÷ sales. Because fixed costs do not change within the relevant range, the change in income equals the change in total contribution margin. That makes the CM ratio a quick tool: a $10,000 rise in sales with a 40% CM ratio adds $4,000 to income.

Absorption costing, required for external reporting, treats all manufacturing costs, including fixed manufacturing overhead, as product costs. Variable costing, used internally, treats fixed manufacturing overhead as a period cost and includes only variable manufacturing costs in inventory. When production exceeds sales, absorption costing defers part of fixed overhead in ending inventory, so its income is higher; when sales exceed production, it releases previously deferred overhead and its income is lower. The difference equals the change in inventory units times fixed overhead per unit. Variable costing removes the temptation to build inventory just to raise reported profit.

Key ideas

• Variable costs are constant per unit and change in total; fixed costs are constant in total and change per unit.
• Cost behavior assumptions are valid only within the relevant range.
• A mixed cost can be written as Y = a + bX and split using high-low or regression.
• Contribution margin = sales - all variable costs, and it covers fixed costs first, then profit.
• With fixed costs unchanged, change in income = CM ratio × change in sales.
• Absorption costing inventories fixed manufacturing overhead; variable costing expenses it.
• Income difference between methods = change in inventory units × fixed MOH per unit.

Formulas and rules

Common mistakes

• Saying fixed costs per unit are constant; it is the total that is constant.
• Choosing high-low points by highest and lowest cost instead of activity.
• Confusing contribution margin (sales - variable costs) with gross margin (sales - COGS).
• Leaving variable selling costs out of contribution margin, or putting them into product cost.
• Getting the direction of the absorption vs. variable income difference backward when inventory falls.

Before the test, make sure you can

• Explain how variable, fixed, mixed and step costs behave in total and per unit.
• Use the high-low method to estimate the variable rate and fixed cost.
• Predict a mixed cost at a new activity level using a cost formula.
• Prepare a contribution format income statement.
• Calculate contribution margin per unit, total and ratio, and use them to predict income changes.
• Compute unit product cost under absorption and variable costing.
• Explain and calculate the income difference between absorption and variable costing.

Words to know

Variable cost

A cost that changes in total in direct proportion to activity and is constant per unit.

Fixed cost

A cost that stays constant in total over the relevant range regardless of activity.

Mixed cost

A cost with both fixed and variable components, also called a semivariable cost.

Step cost

A cost that is fixed over a narrow range of activity and then jumps to a new level.

Relevant range

The range of activity within which cost behavior assumptions are valid.

Cost formula

Y = a + bX, where a is fixed cost and b is variable cost per unit of activity X.

High-low method

A cost estimation method using the highest and lowest activity points to split a mixed cost.

Least-squares regression

A statistical method that fits a cost line through all data points to estimate fixed and variable costs.

Contribution margin

Sales minus all variable costs; the amount that covers fixed costs and then provides profit.

CM ratio

Contribution margin divided by sales; the share of each sales dollar that contributes to fixed costs and profit.

Variable expense ratio

Variable costs divided by sales; equals 1 - CM ratio.

Contribution format income statement

An income statement that subtracts variable costs, then fixed costs, from sales.

Absorption costing

A costing method that includes all manufacturing costs, including fixed overhead, in product cost.

Variable costing

A costing method that includes only variable manufacturing costs in product cost and expenses fixed overhead.

Committed fixed cost

A long-term fixed cost, such as depreciation or a lease, that cannot be cut quickly.

Discretionary fixed cost

A fixed cost set by yearly management decisions, such as advertising or training.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.