Module 7: Cost Behavior & Cost-Volume-Profit Analysis

ACG 2071Created by: M. Mari

Fall 2007-1

Cost-Volume-Profit Analysis (CVP)

Which helps them predict how changes in costs and sales levels affect income

CVP analysis involves computing the sales level at which a company neither earns an income nor incurs a loss – break even point

Cost Behavior

refers to the manner in which a cost changes as a related activity changes.

Activity bases – activities that are thought to cause the cost to be incurred.

Relevant range – range of activity over which the changes in the cost that are of interest.

Cost Classifications

Three types Variable Cost Fixed Cost Mixed Cost

Variable costs

costs that vary in proportion to changes in the level of activity.

Direct materials Direct labor

Units Produced Direct Materials per unit

Total Direct Material Costs

5,000 units $10 $ 50,000

10,000 units $10 100,000

15,000 units $10 150,000

Fixed Costs

costs that remain the same in total dollar amounts as the level of activity changes.

Number of Bottles Total Salary for Supervisor

Salary per bottle produced

50,000 $75,000 $1.50

100,000 $75,000 $0.75

150,000 75,000 $0.50

Mixed Costs

has characteristics of both a variable and a fixed cost. Could behave as a fixed costs for part of the

relevant range and then variable cost

Contribution Margin Concept

Contribution margin = Sales – Variable costs

Contribution margin ratio =

Sales – Variable costs Sales

Is most useful when the increase or decrease in

sales volume is measured in sales dollars Unit contribution margin

= Sales price per unit – Variable cost per unit

Example The Company has sales of $1,000,000, variable costs of $800,000.

The company sold 50,000 units. Compute the contribution margin and the contribution margin ratio.

Contribution margin = Sales – Variable cost = $1,000,000 - $800,000 = $200,000

Contribution margin ratio = (Sales – VC)/Sales = (1,000,000 – 800,000)/1,000,000 = 20%

Unit Contribution margin = Contribution margin Units sold = $200,000 50,000 = $4

Break-even Analysis

to determine the units of sales necessary to achieve the break even pint in operations

to determine the units of sales necessary to achieve a target or desired profit

Break-Even Point

Is the level of operations at which a business’s revenues and expired costs are exactly equal?

A business will have neither an income nor a loss from operations.

Break Even Point

Revenues Expenses

Break even formula

BEP = Fixed Costs__________

Unit contribution margin

Example Suppose that selling price is $25, variable cost $15 and fixed costs

are $90,000. What is break even point?

BEP = Fixed costs / Unit Contribution Margin = $90,000/ (25 – 15) = $90,000/$10 = 9,000 units

At sales level of 9,000 units will result in no gain or loss to the company.

Proof: Sales: ($25 X 9,000) $225,000 Variable cost: ($15 x 9,000) 135.000 Contribution margin 90,000 Fixed costs 90,000 Operating income -0-

Changes in fixed costs

Example: Suppose that selling price is $25, variable cost $15 and fixed costs are $90,000. What is break even point if fixed costs increase to $100,000?

BEP = Fixed costs/ Unit Contribution margin = $100,000/ (25-15) = 10,000 units

Due to an increase in fixed costs from $90,000 to $100,000, break even point increased

Changes in variable costs

Example: Suppose that selling price is $25, variable cost $15 and fixed costs are $90,000. What is break even point if variable costs decrease to $10?

BEP = Fixed costs/ Unit Contribution margin = $90,000/ (25-10) = 6,000 units

Due to a decrease in variable costs from $15 to $10, break even point decreased to 6,000 units from 9,000 units or a decrease of 3,000 units

Changes in selling price

Example: Suppose that selling price is $25, variable cost $15 and fixed costs are $90,000. What is break even point if selling price increase to $30?

BEP = Fixed costs/ Unit Contribution margin = $90,000/ (30-15) = 6,000 units

Due to an increase in sales price from $25 to $30, break even point decreased to 6,000 units from 9,000 units or a decrease of 3,000 units.

Desired or Target Profit BEP = Fixed costs + Desired Profit Unit contribution margin

Example: Suppose that selling price is $45, variable cost $30, and fixed costs are $60,000. The company wants a desired profit of $45,000. What is break even point?

BEP = Fixed costs + Desired profit/ Unit Contribution margin = ($60,000)/ (45-30) = 4,000 units

BEP = Fixed costs + Desired profit/ Unit Contribution margin = ($60,000 + $45,000)/ (45-30) = 7,000 units

To create $45,000 of profit, must sell 7,000 units or 3,000 more than break even point

Charts

Costs

Units

Fixed costs

Variable

Total cost

Graphical – Break even point

$

Units0

Total costs

Sales

Break even pointSales = TC

Profit

Loss

Sales Mix Consideration

More than one product is sold at varying selling prices

Products often have different unit variable costs

Products have different contribution margin

Sales volume necessary must a mix of both products

Example 6:

Cascade Co produces two products Yuk and Gunk. Yuk has a selling price of $90 per unit and variable cost of $70. Gunk has a selling price of $140 and variable cost of $95. Fixed costs are $200,000. Gunk’s sales are approximately 80% of total sales for the company. What is the break even point for the sales mix?

Example 6:

Product Selling Price

Variable Cost

Contribution Margin

Sales

%

Sales mix Contribution

Margin

Yuk $90 $70 $20 80% $16

Gunk $140 $95 $45 20% $9

Sales mix

$25$25

Example 6:

BEP = Fixed Costs Sales mix CM

= $200,000 $25

BEP = 8,000 units

Of what products:

YUK: 8,000 units * 80% = 6,400 unitsGUK: 8,000 units * 20% = 1,600 units

Example 7:

ABC Company has two products Y and X. Y has a selling price of $100 and variable costs of $60. It is 70% of total sales. X has a selling price of $50 and variable cost of $25. Fixed costs are $248,500. What is BEP?

Margin of Safety

Indicates possible decrease in sales that may occur before an operating loss occurs.

Margin of Safety =

Sales – Sales at BEP

Sales

Margin of Safety

If sales are $400,000 and sales at break even are $300,000 what is margin of safety?

Ms = Sales – Sales BEP = $400 - $300

Sales $400

= 25%

High-Low Method

Cost estimation techniques

Steps1. Find the highest and

lowest level of production

2. Find the difference in total cost from highest to lowest level of production

3. Find the difference in total units from highest to lowest level of production

4. Variable cost per unit Difference in Total cost

Difference in Total units

5. Find fixed cost by solving this equation

Total cost = Fixed cost plus Variable cost

Example 1

Month Production Total Cost

June 1,000 $45,550

July 1,500 $52,000

Aug 2,100 $61,500

Sept 1,800 $57,500

Oct 750 $41,250

Example

Step 1: Find highest and lowest level of production.

Month Units Total Cost

High August 2,100 $61,500

Low October 750 $41,250

Step 2: Get the difference

Difference 1,350 $20,250

Example continued

Step 3: Compute Variable cost per unit Variable cost = Difference in Total Cost Difference in Units

=$20,250 1,350

= $15 per unit Total cost = FC + VC $61,500 = FC + ($15 *2,100 units) $61,500 = FC + 31,500 FC = $30,000

Example Cont’d

Step 4: Compute Fixed costs Total cost = Fixed Costs + Variable Cost using the data at 2,100 units of

production, we solve for fixed costs

$61,500 = FC + ($15 *2,100 units)

$61,500 = FC + 31,500

FC = $30,000

Example Continued

Given the information in the prior slide, what is the total cost at 2,000 units of output?

Total cost = Fixed costs + Variable costs

Total cost = $30,000 + ($15 X 2,000)

Total cost = $60,000

Example 2

Month Production Total Cost

June 2,500 $45,000

July 2,000 $40,000

Aug 1,500 $35.000

Sept 3,000 $50,000

Oct 1,800 $38,000What is the variable cost per unit and fixed cost?

Operating Leverage

o The relative mix of a business’s variable costs and fixed costs is measured by the operating leverage

Since the difference between contribution margin and income from operations is fixed costs, companies with large amounts of fixed costs will generally have a high operating leverage. Indicates that a small increase in sales will yield a

large percentage increase in income from operations. Low operating leverage

Indicates that a large increase in sales is necessary to significantly increase income from operations

Operating Leverage

Operating Leverage

= Contribution Margin

Income from operations