Chapter 12

Necessary pretax income

*= Desired net income / (1-tax rate)*

BEP per unit

*= FC / CM per unit*

BEP per $

*= FC / CM ratio*

Aftertax profits

*= Pretax profits / (1-tax rate)*

MS (margin of safety) per $

*= actual sales in $ / break-even sales in $*

MS (margin of safety) per unit

*= actual units sold / break-even units*

DOL (degree of leverage)

*= total CM / pretax profit*

Profit

*= total revenues - total costs *P = R(x) - VC(x) - FC* -- Profits = 0 @ break-even point *P= CM(x) - FC*

Assumptions concerning BEP and CVP analysis

1.) The company is operating within its relevant range of activity 2.) All costs are categorized as either variable or fixed 3.) Both selling price and variable cost are constant per unit and, thus, will change in total in direct proportion to level of activity or volume. 4.) Contribution margin is constant per unit. Per unit contribution margin is the difference between the selling price per unit and the total variable cost per unit. Because both of these items are constant per unit, so is contribution margin. The contribution margin indicates the amount of revenues available to contribute to the coverage of fixed costs and to generate profits. (Total contribution margin is equal to total revenues minus total variable costs for all units sold.) 5.) Total fixed cost is constant per period and, thus, fixed cost per unit varies inversely with changes in volume.

Degree of operating leverage

A measure of the extent to which a percentage change in sales from the current level will affect profits (or losses); calculated as total contribution margin divided by pretax profit.

Incremental analysis

A method of finding solutions to problems by focusing only on the factors that change from one course of action to another.

Cost-volume-profit analysis

A model that expands the break-even model to include the profitability effects created by the relationships among selling prices, costs, and volumes.

Profit-volume graph

A visual depiction of the relationships among revenue, volume, fixed costs, and variable costs showing the profit or loss amounts at each volume level; the point at which the total cost line insects the volume axis is the break-even point.

Break-even graph

A visual depiction of the relationships among revenue, volume, fixed costs, and variable costs; the point at which the total revenue and total cost lines intersect is the break-even point.

Constant mix assumption

An assumption made in break-even or cost-volume profit analysis for a multi-product firm that products will be produced and sold in a stated proportional relationship to one another.

Contribution margin

The difference between the selling price per unit (or in total) and the total variable cost per unit (or in total). *CM = R - VC*

Margin of safety

The excess sales over break-even point; calculated in units as actual sales in units minus break-even sales in units or in dollars as actual sales dollars minus break-even sales dollars; can also be calculated as a percentage.

Break-even point

The level of sales at which no profits are generated and no losses are incurred.

Contribution margin ratio

The percentage of revenue that remains after variable costs are covered; calculated as unit contribution margin divided by unit selling price. *CM ratio = CM / R*

Variable cost ratio

The variable cost percentage of each revenue dollar; calculated as (100% - CM ratio), or total variable cost per unit divided by unit selling price.