Cost-Volume-Profit Relationships

Cost-Volume-Profit Analysis is the examination of the relationships among selling prices,

sales and production volume, costs, expenses, and profits. Cost-volume-profit analysis is
useful for managerial decision making. Some of the ways cost-volume-profit analysis may
be used include:

1. Analyzing the effects of changes in selling prices on profits

2. Analyzing the effects of changes in costs on profits
3. Analyzing the effects of changes in volume on profits
4. Setting selling prices
5. Choosing among marketing strategies

Contribution Margin
Contribution Margin is the excess of sales over variable costs

Contribution Margin = Sales – Variable Costs

To illustrate, assume the following data for Lambert Inc.

Sales 50,000 units

Sales price per unit P20 per unit
Variable cost per unit P12 per unit
Fixed Costs P300,000

Income Statement for Lambert Inc. prepared in contribution margin format

Sales (50,000 units x P20) 1,000,000

Variable Costs (50,000 x P12) , 600,000
Contribution Margin (50,000 x P8) 400,000
Fixed Costs 300,000
Income from operations 100,000

Contribution Margin Ratio

The contribution Margin Ratio, sometimes called profit-volume ratio, indicates the percentage
of each sales peso available to cover fixed costs and to provide income from operations. The
contribution margin ratio is computed as follows:

The contribution margin ratio is 40% for Lambert Inc., computed as follows:
The contribution margin ratio is most useful when the increase or decrease in sales volume
is measured in sales peso. In this case, the change in sales peso multiplies by the CM ratio
equals the change in income from operations.

Change in Income from Operations = Change in Sales Peso x CM Ratio

To illustrate, if Lambert Inc. adds P80,000 in sales from the sale of an additional 4,000 units,
its income from operations will increase by P32,000

Change in Income from Operations = 80,000 x 40% = 32,000

Proof:
Sales (54,000 x P20) 1,080,000
Variable Cost (54,000 x P12) 648,000
Contribution Margin (54,000 x P8) 432,000
Fixed Costs 300,000
Income from operations 132,000

Unit Contribution Margin

The unit contribution margin is also useful for analyzing the profit potential of proposed
decisions. The unit contribution margin is computed as follows:

Unit Contribution Margin = Sales Price per unit – Variable Cost per unit

To illustrate, if Lambert Inc.’s unit selling price is P20 and its variable cost per unit is P12,
the unit contribution margin is P8

Unit Contribution Margin = P20 – P12 = P8

The unit contribution margin is most useful when the increase or decrease in sales volume is
measured in sales units (quantities). In this case, the change in sales volume multiplied by
the unit contribution margin equals the change in volume from operations.

Change in Income from Operations = Change in Sales Units x Unit CM

To illustrate, assume that Lambert Inc., sales could be increased by 15,000 units, from 50,000
units to 65,000 units. Lambert’s income from operations would increase by P120,000 (15,000
units x P8)

Change in Income from Operations = 15,000 units x P8 = P120,000

Proof:

Sales (65,000 units x P20) 1,300,000

Variable Costs (65,000 x P12) 780,000
Contribution Margin (65,000 units x P8) 520,000
Fixed Costs 300,000
Income from operations 220,000

Mathematical Approach to CVP Analysis

The mathematical approach to CVP Analysis uses equations to determine the
following:

1. Sales necessary to break even

2. Sales necessary to make a target or desired profit

BREAK-EVEN POINT

The break-even point is the level of operations at which a company’s revenues and expenses
are equal. At break-even, a company reports neither an income nor loss from operations.

Break-even point in Sales Unit

( )

To illustrate, assume the following data for Baker Corporation:

Fixed Costs 90,000

Unit Selling Price 25

Unit Variable cost 15
Unit Contribution Margin 10
The break-even point is 9,000 units

( )

Proof:

Sales (9,000 x P25) 225,000

Variable Costs (9,000 x P15) 135,000
Contribution margin 90,000
Fixed Costs 90,000
Income from operations 0

Break-even point in Sales Peso

( )

From the data of Baker Corporation

( )

 The break-even point is affected by changes in the Fixed Costs, Unit Variable Costs,
and the Unit Selling Price.

Effects of Changes in Fixed Costs

Changes in fixed costs affect the break-even point as follows:

1. Increases in fixed costs increase the break-even point.

2. Decreases in fixed costs decrease the break-even point

To illustrate, assume that Bishop Co. is evaluating a proposal to budget an additional

P100,000 for advertising. The data for Bishop Co. are as follows:

Current Proposed
Unit selling price P 90 P 90
Unit variable cost P 70 P 70
Unit contribution margin P 20 P 20
Fixed Costs 600,000 700,000
Break-even point before additional advertising expense

( )

Break-even point after additional advertising expense

( )

Effects of Changes in Unit Variable Costs

Changes in unit variable costs affect the break-even point as follows:

1. Increases in unit variable costs increase the break-even point.

2. Decreases in unit variable costs decrease the break-even point.

To illustrate, assume that Park Co. is evaluating a proposal to pay an additional 2%

commission on sales to its salespeople as an incentive to increase sales. The data for Park Co.
are as follows:

Current Proposed
Unit selling price P 250 P 90
Unit variable cost P 145 P 150*
Unit contribution margin P 105 P 100
Fixed Costs 840,000 840,000
*150 = 145 + (2% x 250 unit selling price)

Break-even point before additional 2% commission

( )

Break-even point after additional 2% commission

( )

Effects of Changes in Unit Selling Price

Changes in unit selling price affect the break-even point as follows:

1. Increases in the unit selling price decrease the break-even point.

 2. Decreases in the unit selling price increase the break-even point.

To illustrate, assume that Graham Co. is evaluating a proposal to increase the unit selling
price of its product from P50 to P60. The data of Graham Co. are as follows:

Current Proposed
Unit selling price P 50 P 60
Unit variable cost P 30 P 30
Unit contribution margin P 20 P 30
Fixed Costs 600,000 600,000

Break-even point before the price increase

( )

Break-even point after the price increase

( )

Target Profit

( )

To illustrate, assume the following data for Waltham Co.:

Fixed Costs 200,000

Target Profit 100,000

Unit Selling Price 75

Unit Variable Cost 45
Unit CM 30

The sales necessary to earn the target profit of P100,000 would be 10,000 units computed as
follows:

( )

Proof:

Sales (10,000 units x P75) 750,000

Variable Cost (10,000 x P45) 450,000
CM 300,000
Fixed Costs 200,000
Income from Operations 100,000
 ( )

Graphic Approach to CVP Analysis

1. Cost-Volume-Profit (Break-even) Chart

A CVP chart, sometimes called a break-even chart, graphically shows sales, costs,
and the related profit or loss for various levels of units sold. It assists in
understanding the relationship among sales, costs, and operating profit or loss.

Based on the following data:

Total Fixed Cost 100,000

Unit selling price 50

Unit variable cost 30
Unit CM 20

2. Profit-Volume Chart

The profit-volume chart plots only the difference between total sales and total costs
(or profits). It allows managers to determine the operating profit (loss) for various
levels of units sold.
Assumptions of CVP Analysis

CVP Analysis depends on several assumptions. The primary assumptions are as follows:

1. Total sales and total costs can be represented by straight lines.

2. Within the relevant range of operating activity, the efficiency of operations does not
change.
3. Costs can be divided into fixed and variable components.
4. The sales mix is constant.
5. There is no change in the inventory quantities during the period.

Special CVP Relationships

Sales Mix Considerations

The sales mix is the relative distribution of sales among the products sold by a company.

To illustrate, assume that Cascade Company sold Products A and B during the past year, as
follows:

Total Fixed Costs 200,000

Product A Product B
Unit Selling Price 90 140
Unit Variable Cost 70 95
Unit CM 20 45

Unit Sold 8,000 2,000

Sales Mix 80% 20%
For break-even analysis, it is useful to think of Products A and B as components of one
overall enterprise called E.

Product E Product A Product B

Unit Selling Price of E P100 (90 x .80) + (140 x .20)
Unit Variable Cost of E P 75 (70 x .80) + (95 x .20)
Unit CM of E P 25 (20 x .80) + (45 x .20)

( )

Since the sales mix for Products A and B is 80% and 20% respectively, the break-even
quantity of A is 6,400 units and B is 1,600 units.

Product A Product B Total

Sales
6,400 x 90 576,000 576,000
1,600 x 140 224,000 224,000
Total Sales 576,000 224,000 800,000
Variable Costs
6,400 x 70 448,000 448,000
1,600 x 95 152,000 152,000
Total Variable Costs 448,000 152,000 600,000
Contribution Margin 128,000 72,000 200,000
Fixed Costs 200,000
Income From Operations 0

Operating Leverage

The relationship between a company’s CM and income from operations is measured by

operating leverage.

Companies with high fixed costs will normally have high operating leverage.

To illustrate, assume the following data from Jones Inc. and Wilson Inc.

Jones Inc. Wilson Inc.

Sales 400,000 400,000
Variable Costs 300,000 300,000
CM 100,000 100,000
Fixed Costs 80,000 50,000
Income from Operations 20,000 50,000
Jones Inc.

Wilson Inc.

Operating leverage can be used to measure the impact of changes in sales on income from
operations. Using operating leverage, the effect of changes in sales on income from
operations is computed as follows:

Percent Change in Income from Operations = Percent Change in Sales x Operating Leverage

To illustrate, assume that sales increased by 10% or 40,000 for Jones and Wilson.

Jones Inc.

Percent Change in Income from Operations = 10% x 5 = 50%

Wilson Inc.

Percent Change in Income from Operations = 10% x 2 = 20%

Jones Inc. Wilson Inc.

Sales 440,000 440,000
Variable Costs 330,000 330,000
CM 110,000 110,000
Fixed Costs 80,000 50,000
Income from Operations 30,000 60,000

The impact of change in sales on income from operations for companies with high and low
operating leverage can be summarized as follows:

Operating Leverage Percentage Impact on Income from

Operations from a Change in Sales
High Large
Low Small
Margin of Safety

The margin of safety indicated the possible decrease in sales that may occur before an
operating loss results. Thus, if margin of safety is low, even a small decline in sales may
result in an operating loss.

The margin of safety may be expressed in the following ways:

1. Peso sales
2. Unit sales
3. Percent of current sales

To illustrate, assume the following data:

Sales 250,000
Sales at break-even 200,000
Unit Selling Price 25

Margin of Safety (Peso Sales) = 250,000 – 200,000 = 50,000

Margin of Safety (Unit Sales) = 50,000/25 = 2,000