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Chapter 3

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Chapter Overview

Cost–volume-profit (CVP) analysis helps managers

•understand the interrelationships among cost, volume, and profit by focusing their attention

on the interactions among the process of products, volume of activity, per unit variable

costs, total fixed costs, and mix of products sold.

•choose the most favourable combination of variable costs, fixed costs, selling price, sales

volume, and mix of products sold.

Various concepts will be covered such as the unit contribution margin, the break-even point,

the CM ratio, margin of safety, operating leverage, and the sales mix.

A.The Basics of Cost-Volume-Profit (CVP) Analysis. Cost-volume-profit (CVP)

analysis is a key step in many decisions. CVP analysis involves specifying a model of the

relations among the prices of products, the volume or level of activity, the unit variable costs, the

total fixed costs, and the mix of products sold. This model is used to predict the impact on profits

of changes in those parameters.

1. Contribution Margin. Contribution margin is the amount remaining from sales revenue

after variable expenses have been deducted. It contributes towards covering fixed costs and

then towards profit.

2. Unit Contribution Margin. When there is a single product, the unit contribution margin

can be used to predict changes in the contribution margin and in profits (assuming there is

no change in fixed costs) as a result of changes in unit sales. To do this, the unit

contribution margin is simply multiplied by the change in unit sales.

3.Contribution Margin Ratio. The contribution margin (CM) ratio is the ratio of the

contribution margin to total sales. It shows how the contribution margin is affected by a

given dollar change in total sales. Managers often find the contribution margin ratio

easier to work with than the unit contribution margin, particularly when a company has

multiple products. This is because the contribution margin ratio is denominated in sales

dollars, which is a convenient way to express activity in multi-product firms.

B. Some Applications of CVP Concepts. CVP analysis is typically used to estimate the

impact on profits of changes in selling price, variable cost per unit, sales volume, and total fixed

costs. CVP analysis can be used to estimate the effect on profits of a change in any one (or any

combination) of these parameters. A variety of examples of applications of CVP are provided in

the text.

C.CVP Relationships in Graphic Form. Graphs of CVP relationships can be used to

gain insight into the behaviour of expenses and profits. The basic CVP graph is drawn with

dollars on the vertical axis and volume in units on the horizontal axis. Total fixed expense is

drawn first, then variable expense is added to the fixed expense in order to draw the total

expense line. Finally, the total revenue line is drawn. The total profit (or loss) is the vertical

difference between the total revenue and total expense lines.

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total

revenue

total

expenses

D.Break-Even Analysis and Target Profit Analysis. Target profit analysis is concerned

with estimating the level of sales required to attain a specified target profit. Break-even analysis

is a special case of target profit analysis in which the target profit is zero.

1. Basic CVP equations. Both the equation and contribution (formula) methods of break-

even and target profit analysis are based on the contribution approach to the income

statement. The format of this statement can be expressed in equation form as:

Profits = Sales − Variable expenses − Fixed expenses

In CVP analysis this equation is commonly rearranged and expressed as:

Sales = Variable expenses + Fixed expenses + Profits

a.The above equation can be expressed in terms of unit sales:

Price × Unit sales = Unit variable cost × Unit sales + Fixed expenses + Profits

⇓

Unit contribution margin × Unit sales = Fixed expenses + Profits

⇓

Unit sales =

marginon contributiUnit

Profits+ expenses Fixed

b. The basic equation can also be expressed in terms of sales dollars using the variable

expense ratio:

Sales = Variable expense ratio × Sales + Fixed expenses + Profits

⇓

(1 − Variable expense ratio) × Sales = Fixed expenses + Profits

⇓

Contribution margin ratio* × Sales = Fixed expenses + Profits

⇓

Sales =

ratiomargin on Contributi

Profits+ expenses Fixed

* 1 − Variable expense ratio= 1−

Sales

expenses Variable

=

Sales

expenses Variable-Sales

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