5.2: Cost Volume Profit Analysis (CVP)

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Cost volume profit (CVP) analysis is a managerial accounting technique used to determine how changes in sales volume, variable costs, fixed costs, and/or selling price per unit affect a business’s operating income. The focus may be on a single product or on a sales mix of two or more different products.

The results of these analyses help managers make informed decisions about products or services they sell, such as setting selling prices, selecting combinations of different products to sell, projecting profitability, and determining the feasibility of offering a product or service for sale.

The elements of CVP analysis are defined as follows:

Selling price - the amount a customer pays to acquire a product or service
Cost - the variable and fixed expenses involved in producing or selling a product or service
Volume - the number of units or the amount of service sold
Profit - the difference between the selling price of a product (or service) minus the costs to produce (or provide) it

The following assumptions are made when performing a CVP analysis.

All costs are categorized as either fixed or variable.
Sales price per unit, variable cost per unit and total fixed cost are constant.
The only factors that affect costs are changes in activity.
All units produced are sold.

5.2.1 Contribution Margin

Managers must monitor a company’s sales volume to track whether it is sufficient to cover, and hopefully exceed, fixed costs for a period, such as a month. Contribution margin is useful in determining how much of the dollar sales amount is available to apply toward paying fixed costs during the period. Contribution margin is calculated at two different levels.

Unit contribution margin = selling price of one unit – variable cost of one unit
Total contribution margin = total sales – total variable costs

The following information relates to Jonick Company for the month of June:

Sales	1,000 units
Selling price per unit	$25
Variable cost per unit	$10
Fixed costs	$8,000

Unit contribution margin = selling price of one unit – variable cost of one unit $15 = $25 - $10
The unit contribution margin is $15, which is the $25 sales price per unit minus the $10 variable cost per unit. With each sale, $15 is left after the variable cost is paid to go toward paying down the fixed costs.

Total contribution margin = total sales – total variable costs

$15 x 1,000 units	=	$25 x 1,000 units	-	$10 x 10,000 units
$15,000	=	$25,000	-	10,000

Sales	$25,000
Variable costs	10,000
Contribution margin	$15,000
Fixed costs	8,000
Operating income	$7,000

Contribution margin may also be expressed as a ratio, showing the percentage of sales that is available to pay fixed costs. The calculation is simply the contribution margin divided by sales. The same percentage results regardless of whether total or per unit amounts are used.

Unit contribution margin ratio = $\ \frac{\text{selling price of one unit – variable cost of one unit}}{\text{selling price of one unit}}=\frac{$25 - $10}{$25}=\bf{60}$%
Total contribution margin = $\ \frac{\text{total sales – total variable costs}}{\text{total sales}}=\frac{$25,000 - $10,000}{$25,000}=\bf{60}$%

The higher the percentage, the more of each sales dollar that is available to pay fixed costs. To determine if the percentage is satisfactory, management would compare the result to previous periods, forecasted performance, contribution margin ratios of similar companies, or industry standards. If the company’s contribution margin ratio is higher than the basis for comparison, the result is favorable.

The following three independent examples show the effects of increases in sale volume, selling price per unit, and variable cost per unit, respectively.

Example

Change in sales volume: effect on contribution margin ratio

As the number of units sold increases, so does operating income when fixed costs are within their relevant range and remain the same. This is shown in the following two income statements with sales of 1,200 and 1,400 units, respectively.

1,200 units sold x $25 selling price 1,200 units sold x $10 variable cost		1,400 units sold x $25 selling price 1,400 units sold x $10 variable cost
Sales	$30,000	Sales	$35,000
Variable costs	12,000	Variable costs	14,000
Contribution margin	$18,000	Contribution margin	$21,000
Fixed costs	8,000	Fixed costs	8,000
Operating income	$10,000	Operating income	$13,000
(30,000 - 12,000) / 30,000 = 60% contribution margin		(35,000 - 14,000) / 35,000 = 60% contribution margin

Contribution margin remains at 60% regardless of the sales volume. As sales increase, variable costs increase proportionately.

Example

Change in selling price per unit: effect on contribution margin ratio

Alternatively, if the selling price per unit increases from $25 to $30 per unit, both operating income and the contribution margin ratio increase as well. Variable cost per unit remains at $10 and fixed costs are still $8,000.

Original: $25 x 1,000 = $25,000 in sales		Revised: $30 x 1,000 = $30,000 in sales
Sales	$25,000	Sales	$30,000
Variable costs	10,000	Variable costs	10,000
Contribution margin	$15,000	Contribution margin	$20,000
Fixed costs	8,000	Fixed costs	8,000
Operating income	$7,000	Operating income	$12,000
(25,000 - 10,000) / 25,000 = 60% contribution margin		(30,000 - 10,000) / 30,000 = 67% contribution margin

The contribution margin ratio with the selling price increase is 67%. The additional $5 per unit in unit selling price adds 7% to the contribution margin ratio.

Example

Change in variable cost per unit: effect on contribution margin ratio

Finally, if the selling price per unit remains at $25 and fixed costs remain the same, but unit variable cost increases from $10 to $15, total variable cost increases. As a result, the contribution margin and operating income amounts decrease.

Original: $10 x 1,000 = $10,000 in variable cost		Revised: $15 x 1,000 = $15,000 in variable cost
Sales	$25,000	Sales	$25,000
Variable costs	10,000	Variable costs	15,000
Contribution margin	$15,000	Contribution margin	$10,000
Fixed costs	8,000	Fixed costs	8,000
Operating income	$7,000	Operating income	$2,000
(25,000 - 10,000) / 25,000 = 60% contribution margin		(25,000 - 15,000) / 25,000 = 40% contribution margin

The contribution margin ratio with the unit variable cost increase is 40%. The additional $5 per unit in the variable cost lowers the contribution margin ratio 20%. Each of these three examples could be illustrated with a change in the opposite direction. A decrease in sales quantity would not impact the contribution margin ratio. A decrease in unit selling price would also decrease this ratio, and a decrease in unit variable cost would increase it. Any change in fixed costs, although not illustrated in the examples, would not affect the contribution margin ratio.