cost behavior and cost-volume-profit analysis

11-119-1

19

Cost Behavior and Cost-Volume-Profit

Analysis

Student Version

11-219-2

1

Classify costs as variable costs, fixed costs, or mixed costs.

19-2

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Variable Costs

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

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11-419-4

Jason Sound Inc. produces stereo systems. The parts for the stereo system are purchased from suppliers for $10 per unit (a variable cost) and assembled by Jason Sound Inc.

Jason Sound Inc.

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11-519-5

For Model JS-12, the direct materials for the relevant range of 5,000 to 30,000 units of production are shown below.

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11-619-6

Fixed Costs

Fixed costs are costs that remain the same in total dollar amount as the activity base changes.

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11-719-7

Minton Inc. manufactures, bottles, and distributes perfume. The production supervisor is Jane Sovissi. She is paid $75,000 per year. The plant produces from 50,000 to 300,000 bottles of La Fleur Perfume.

Minton Inc.

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Number ofBottles of Perfume

ProducedTotal Salary for

Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375

250,000 75,000 0.300300,000 75,000 0.250

Salary per Bottle of Perfume Produced

Fixed Versus Variable Cost of Jane Sovissi’s Salary per

Bottle of Perfume

1

11-919-9

Mixed Costs

Mixed costs (sometimes called semivariable or semifixed costs) have characteristics of both a variable and a fixed cost. Over one range of activity, the total mixed cost may remain the same. Over another range of activity, the mixed cost may change in proportion to changes in level of activity.

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11-1019-10

Simpson Inc. manufactures sails, using rented equipment. The rental charges are $15,000 per year, plus $1 for each machine hour used over 10,000 hours.

Simpson Inc.

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11-1119-11

The high-low method is a cost estimation method that may be used for separating mixed costs into their fixed and variable components.

High-Low Method

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11-1219-12

Production Total(Units) Cost

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

Fill in the formula for difference in cost.

$61,500 41,250$20,250

Variable Cost per Unit =Difference in ProductionDifference in Total cost$20,250

1

Estimating Variable Cost Using High-Low

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Difference in total cost

2,100 750

1,350

Then, fill in the formula for difference in production.



Variable Cost per Unit =Difference in Production

$20,250

1,350

1


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= $15

Variable cost per unit is $15



Variable Cost per Unit =$20,250

1,350

1


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The first step in determining fixed cost is to insert the variable cost of $15 into the following formula:

Total Cost = ($15 × Units of Production) + Fixed Cost

Estimating Fixed Cost Using High-Low

Total Cost = (Variable Cost per Unit × Units of Production) + Fixed Cost

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11-1619-16

Using the highest level of production, we insert the total cost and units produced in the formula.

Total cost = ($15 × Units of Production) + Fixed Cost$61,500 2,100 units)



Total Cost = (Variable Cost per Unit × Units of Production) + Fixed Cost

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11-1719-17

$61,500 = ($15 × 2,100 units) + Fixed cost$61,500 = $31,500 + Fixed cost

$61,500 – $31,500 = Fixed cost

$30,000 = Fixed cost

If the lowest level had been chosen, the results of the formula would provide the same fixed cost of $30,000.

1

11-1819-18

With fixed costs and variable costs estimated at $30,000 and $15 per unit, a formula is in place to estimate production at any level. If the company is expected to produce 950 units in November, the estimated total overhead would be calculated as follows:

Total Cost = (Variable Cost per Unit × Units of Production) + Fixed cost

Total Cost = $15 (950) + $30,000

Total Cost = $44,250

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11-1919-19

2

Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.

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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.

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The contribution margin is the excess of sales revenues over variable costs. It is especially useful because it provides insight into the profit potential of a company.

Contribution Margin

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Contribution Margin Ratio (in dollars)

The contribution margin ratio is most useful when the increase or decrease in sales volume is measured in sales dollars. In this case, the following formula is used to determine change in income from operations.

Change in Income from Operations

Change in Sales Dollars ×

Contribution Margin Ratio

=

2

11-2319-23


100% 60%

Contribution Margin Ratio =40%

Contribution Margin Ratio =

Sales – Variable CostsSales

$1,000,000 – $600,000$1,000,000


40% 30%10%

2

11-2419-24

Using Contribution Margin per Unit as a Shortcut

Lambert Inc.’s sales could be increased by 15,000 units from 50,000 to 65,000 units. Lambert’s income from operations would increase by $120,000 (15,000 × $8) as shown below.

Change in Income from Operations

Changes in Sales Units × Unit Contribution Margin

=

Change in Income from Operations 15,000 ×

$8=

Change in Income from Operations $120,000=

2

11-2519-25

3

Determine the break-even point and sales necessary to achieve a target profit.

19-25

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Baker Corporation’s fixed costs are estimated to be $90,000. The unit contribution margin is calculated as follows:

Unit selling price $25Unit variable cost 15Unit contribution margin $10

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11-2719-27

The break-even point (in units) is calculated using the following equation:

Break-Even Sales (units) =

Fixed CostsUnit Contribution

Margin

Break-Even Sales (units) =$90,000

$10

Break-Even Sales (units) = 9,000 units

3

11-2819-28

The break-even point (in dollars) is calculated using the following equation:

Break-Even Sales (dollars) =Fixed Costs


Break-Even Sales (dollars) = $225,000

$90,000.40

Break-Even Sales (dollars) =Unit

Contribution Margin

Unit Selling Price

$10

$25

3

11-2919-29

Park Co. is evaluating a proposal to pay an additional 2% commission on sales to its salespeople (a variable cost) as an incentive to increase sales. Fixed costs are estimated at $840,000. The unit contribution margin before the additional 2% commission is determined below.


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11-3019-30

Without additional 2% commission:

$250 – [$145 + ($250 × 2%)] = $100

Break-Even in Sales (units) =$840,000

$105=

8,000 units

With additional 2% commission:

Break-Even in Sales (units) =$840,000

$100=

8,400 units

Break-Even in Sales (units) =Fixed Costs

Unit Contribution Margin

3

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Target Profit

The sales volume required to earn a target profit is determined by modifying the break-even equation.

Sales (units) = Fixed Costs + Target ProfitUnit Contribution Margin

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Units Required for Target Profit

Fixed costs are estimated at $200,000, and the desired profit is $100,000. Unit contribution margin is $30.


Sales (units) =

Fixed Costs + Target ProfitUnit Contribution Margin$30

Sales (units) = 10,000 units

$200,000 $100,000

3

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Unit Contribution MarginUnit Selling Price


$30 $75

from Slide 32


40%

Sales (dollars) =Fixed Costs + Target ProfitContribution Margin Ratio

Sales (dollars) =$200,000 + $100,000

40%=

$750,000

3

Target Profit

Necessary sales to have a $100,000 target profit

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4

Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit.

19-34

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Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

The cost-volume-profit chart in Slides 36 to 48 is based on Exhibit 5. Exhibit 5 was constructed using the following data:

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Sal

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(in

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0Units of Sales (in thousands)

$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50

Dollar amounts are indicated along the vertical axis.

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(continued)Volume is shown on the horizontal axis.

Cost-Volume-Profit Chart

4

Exhibit 5

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Using maximum sales of $500,000 and knowing that each unit sells for $50, we can find the values of the two axis. Where the horizontal sales and costs line intersects the vertical 10,000 unit of sales line is Point A in Slide 38.

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Point APoint A

Cost-Volume-Profit Chart (continued)

4

Exhibit 5

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Sal

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0

$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50

Units of Sales (in thousands)

Point A could have been plotted at any sales level because linearity is assumed.

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Point APoint A

Cost-Volume-Profit Chart (continued)

4

Exhibit 5

Sal

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0

$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50

1 2 3 4 5 6 7 8 9 10Units of Sales (in thousands)

Beginning at zero on the left corner of the graph, connect a straight line to the dot (Point A).

11-4019-40Fixed cost of $100,000 is a horizontal line.

4

Cost-Volume-Profit Chart (continued)Exhibit 5

Sal

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$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50

0 1 2 3 4 5 6 7 8 9 10Units of Sales (in thousands)

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A point on the chart is needed to establish the revenue line. An arbitrary sales amount is picked of 10,000 units. At this sales level, the cost should be $400,000, calculated as follows: [(10,000 × $30) + $100,000] = $400,000.

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11-4219-42A line is drawn between fixed cost ($100,000) and the point.

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$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50


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The line would be the same if another point had been picked. For example, assume that 8,000 units had been chosen. At this sales level, the cost should be $400,000 [(8,000 × $30) + $100,000 = $340,000].

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4

Break-Even Point


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$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50


11-4519-45Break-even is sales of 5,000 units or $250,000.

Break-Even Point

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$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50


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Operating Loss Area

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$500

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$ 50


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Operating Profit Area

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$500

$450

$400

$350

$300

$250

$200

$150

$100

$ 50


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Cost-Volume-Profit Chart (concluded)

4

Exhibit 5

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Revised Cost-Volume-Profit Chart

Break-even in sales would be reduced from $250,000 to $200,000 (5,000 to 4,000 in units).

4

Exhibit 6

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Sales (10,000 units × $50) $500,000 Variable costs (10,000 units × $30) 300,000 Contribution margin (10,000 units × $20) $200,000 Fixed costs 100,000 Operating profit $100,000

The maximum operating loss is equal to the fixed costs of $100,000. Assuming that the maximum unit sales within the relevant range is 10,000 units, the maximum operating profit is $100,000, computed as follows:

Maximum Profit

4

11-5119-51

5

Compute the break-even point for a company selling more than one product, the operating leverage, and the margin of safety.

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Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows:

Unit Unit Unit SalesSelling Variable Contribution Mix

Product Price Cost Margin %

A $ 90 $70 $20 80%B 140 95 45 20%

Cascade Company Example

5

11-5319-53

It is useful to think of the individual products as components of one overall enterprise product. For Cascade Company, the overall enterprise product is called E.

Unit selling price of E: ($90 × 0.8) + ($140 × 0.2) = $100

Unit variable cost of E: ($70 × 0.8) + ($95 × 0.2) = 75

Unit contribution margin of E: $ 25

5

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Fixed CostsUnit Contribution

Margin


$200,000$25

Break-Even Sales (units) = 8,000 units

Break-Even Point of 8,000 Units of E

5

11-5519-55

Both companies have the same contribution margin.

Jones Inc. Wilson Inc.

Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000

Operating leverage ? ?

Operating Leverage Example

5

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Contribution Margin

Income from Operations

$100,000

$20,000= 5 Jones Inc.:





5

5

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5 2

Contribution Margin

Income from Operations

$100,000

$50,000= 2 Wilson Inc.:

5

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Margin of Safety

The margin of safety indicates the possible decrease in sales that may occur before an operating loss results.

5

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cost behavior and cost-volume-profit analysis

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