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Cost-Volume-Profit Analysis
I. Overview
- Predicts the relationships among revenues, variable costs, and fixed costs at various production levels.
- Determines the probable effect of changes in unit volume, sale price, revenue mix, and etc.
- Revenue as a function of the price per unit and quantity produced.
- Fixed costs.
- Variable cost per unit or as a percentage of revenues.
- Profit per unit or as a percentage of revenue.
Cost and revenues.
The volume of output.
- Cost and revenue are deemed to be predictable and linear over the relevant range of activity and specified time span.
- All costs are either fixed or variable relative to a given cost object, and the time value of money is ignored.
- Total variable costs change proportionally within the activity level, but unit variable costs and total costs are constant over the relevant range.
- Unit sales prices and market conditions are constant and the revenue mix does not change.
- The volume of output is the sole revenue driver and cost driver, and any change in inventory is immaterial.
- The breakeven point is the output at which total revenue equals total costs.
- The unit contribution margin (UCM) is the unit selling price minus unit variable cost.
Unit contribution margin.
Fixed cost, unit-based variable cost (unit sold x unit variable cost), batch-level costs (batch-level driver x cost per unit), and product-level costs (product-level driver x cost per driver).
II. Concepts
It is when the contribution margin equals the total fixed costs.
- CVP analysis studies the relationships among sales volume, sales price, fixed costs, and profit.
- Allows management to determine that unit contribution margin, that is the difference between the unit sales price and unit variable cost.
- Making decisions including choice of product lines, pricing of products, marketing strategy, and use of productive facilities.
Contribution margin per unit for each additional unit sold.
Fixed expenses are listed separately from variable expenses.
Variable costs, contribution margin, fixed costs, and operating income.
The margin of safety.
Desired income plus fixed costs by dividing the contribution margin ratio (CMR).
Fixed costs are divided by the unit contribution margin (UCM).
A sensitive analysis.
Statistical hypothesis testing.
The percentage change in earnings before interest and taxes associated with the percentage change in revenues.
The percentage change in net income or earnings before taxes is divided by the percentage change in operating income or earnings before interest and taxes.
The volume at which total revenues equal to total costs.
The percentage change in net income is divided by the percentage change in revenue.
III. Assumptions
- Sales volume equals production volume.
- Variable costs are constant per unit.
- A given revenue mix is maintained for all volume changes.
- Unit selling price and unit variable cost are constant within the relevant range.
- Unit contribution margin, marginal revenue, and marginal cost are constant.
- Cost and revenue factors used in the formula are linear and do not fluctuate with volume.
- Fixed costs are assumed to be fixed over the relevant range of volume.
IV. High-Low Calculations
- This is a simple approximation of the mixed cost formula.
- The cost of using more sophisticated methods sometimes outweighs the incremental accuracy achieved.
The least squares method.
Computer simulation.
V. Calculating the Effect of Changes in CVP variables
An increase in direct labor cost will increase the BEP and decrease the margin of safety.
The breakeven point is the level of revenue at which total revenue equals total cost.
The margin of safety is the excess of budget revenue over the breakeven revenue.
Decrease in selling price.
VI. Target Income
Target unit sales = (Fixed costs + Target Operating Income) / Unit contribution margin.
- Knowledge of the behavior of business cycles.
- Information on the seasonal variations in demand.
- Economic modeling.