Cost Behavior

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CHAPTER 5 COST BEHAVIOR: ANALYSIS AND USE

Key Terms and Concepts to Know Cost Classifications for Predicting Cost Behavior

Costs may be classified by how they behave in total when the activity level changes:

In Total Per UnitVariable Cost Varies The sameFixed Cost The same Varies inversely Mixed Cost Varies Varies

(often inversely)

The relevant range is the range of activity levels throughout which the assumptions for cost behavior are valid. Outside the relevant range, total fixed costs may change and/or variable costs per unit may change.

The activity level or allocation base is a measure of the activity that causes total variable cost to change. Common activity bases are: direct labor hours, machine hours, units produced, and units sold.

Committed fixed costs relate to costs that the company will incur over the long-term. These costs, such as depreciation expense, property tax expense and insurance expense, cannot be changed during short periods of time and are only somewhat under the control of management.

Discretionary fixed costs usually arise from annual decisions by management and can be changed during short periods of time such as advertising, research and public relations.

Mixed costs contain both variable and fixed cost elements. For example, a company’s selling expenses may include fixed expenses, such as the advertising costs and the base salary of the sales manager; and variable costs, such as sales commissions paid to the regional salesmen.

Contribution Margin Income Statement

The traditional income statement separates expenses by function emphasizing the distinction between production, administration and selling expenses. Gross margin is the first key measure of profitability.

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The contribution margin income statement separates expenses by behavior, emphasizing the distinction those revenues and expenses that change when the level of activity changes and those that are unaffected by changes in the level of activity. Contribution margin is the first key measure of profitability.

Key Topics to Know

Separating Mixed Costs into Fixed and Variable Elements

In order to predict the profits of a company, it is necessary to separate all costs

into either fixed costs or variable costs. Many costs are clearly variable, such as direct labor, or, clearly fixed, such as rent.

Mixed costs must be separated into their fixed and variable elements using one of three methods and a regression line developed to predict total mixed costs at various levels of activity.

The equation of the regression line takes the form:

Total Cost = Fixed Cost + Variable CostY = a + b(X)

Least Squares Regression Method

A rigorous, mathematical approach in which a series of data points are used to develop a regression line to predict total costs.

Scattergraph Method

Plots a series of data points for the mixed costs and the activity which produced these costs. The Y axis is dollars of mixed cost and the X axis is the activity level.

A regression line is drawn by best guess through one of the data points and a point on the Y axis with an approximately the same number of data points above and below the line.

The point where the line crosses Y axis represents the fixed cost, the only cost incurred at zero activity. For any data point, the difference between the total mixed cost and the fixed cost is total variable cost and total variable cost divided by the activity level for the data point is variable cost per unit.

High-Low Method

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From a series of data points, uses only the high and low data points, based on

activity, to develop a regression line to predict total costs. Variable cost per unit (b) is calculated first:

High Point - Low Point = Change Cost $ $ $ $Activity activity activity activity

Change in Cost $ = Variable cost/unit Change in Activity

Using either the high point or low point, total fixed cost is calculated next:

Fixed Cost = Total Cost - Variable Cost a = Y - B(X)

Example # 1: Travis Inc. employed several maintenance engineers to keep the equipment running in peak condition. Over the past eight months, Travis incurred the following maintenance cost for these engineers. Plant activity is best measured by direct labor hours.

Month Direct Labor Hours Maintenance CostJanuary 1,700 $14,300February 1,900 $15,200March 1,800 $16,700April 1,600 $14,000May 1,500 $14,300June 1,300 $13,000July 1,100 $12,800August 1,400 $14,200

Required: Using the high-low method, determine the fixed and variable components of

the maintenance costs.

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Solution #1

High Point - Low Point = Change Cost $ $15,200 $12,800 $2,400Activity 1,900 1,100 800

Change in Cost $ = $2,400 = $3.00 variable cost/unit Change in Activity 800


Fixed Cost = Total Cost - Variable Cost $9,500 = $15,200 - $5,700 = $3.00 (1,900)

OR $9,500 = $12,800 - $3,300 = $3.00 (1,100)

Contribution Margin Income Statement

The contribution margin income statement separates expenses into fixed and variable categories.

Contribution margin income statement takes the form: Sales - Variable costs = Contribution margin - Fixed costs = Operating income

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Example #2: Strummer Inc. manufactures and sells guitars for beginning students. Their income statement for April, 2010 was as follows:

Sales $600,000Cost of Goods Sold 400,000Gross Margin 200,000Selling and Administrative Expenses: Selling expense 60,000Administrative expense 90,000 150,000Operating Income $50,000

The product sells for $300 each. Variable selling expenses are $20 per unit sold with the remaining selling expenses being fixed. The administrative expenses are 40% fixed. The company’s manufacturing costs are 75% variable. Required: Prepare an income statement using the contribution margin approach. Solution #2:

Units sold $600,000/$300 2,000 Sales $600,000Variable Expenses: Cost of goods sold $400,000*75% 300,000Selling expenses $20*2,000 40,000Administrative expenses $90,000-36,000 54,000 394,000Contribution Margin $206,000Fixed Expenses: Cost of goods sold $400,000-300,000 100,000Selling expenses $60,000-40,000 20,000Administrative expenses $90,000*40% 36,000 156,000Operating Income $50,000

Variable and Absorption Costing

Absorption costing includes variable and fixed manufacturing costs in unit product costs and inventory.

The fixed manufacturing overhead included in inventory is the predetermined fixed overhead rate * units in inventory.

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The fixed manufacturing overhead included in inventory is deferred or not recognized as an expense until the units are sold in a subsequent period.

Variable costing includes only variable manufacturing costs in unit product costs and inventory.

Variable costing treats fixed manufacturing costs as period costs. Compared to absorption costing, variable costing has a lower product costs per

unit and higher period costs. The effect on operating income of treating fixed manufacturing overhead as a

product cost (absorption costing) versus a period cost (variable costing) may be summarized as follows:

Beginning Finished Goods Inventory= ending Finished Goods Inventory

Income is the same under both methods

Finished Goods Inventory increases (beginning Finished Goods Inventory < ending Finished Goods Inventory)

Absorption costing has higher income than variable costing because manufacturing fixed costs are deferred for the units added to Inventory

Finished Goods Inventory decreases (beginning Finished Goods Inventory > ending Finished Goods Inventory)

Absorption costing has lower income than variable costing because manufacturing fixed costs are included in the units sold from Inventory

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Practice Problems Practice Problem #1: Active Company accumulated the following data for a delivery truck.

Miles Driven Total Cost Miles Driven Total Cost

January 10,000 $15,000 March 9,000 $12,500February 8,000 $14,500 April 7,500 $13,000

Required:

a) Determine the equation to predict total costs for the delivery truck. b) What should total costs be if 12,187 miles were driven?

Practice Problem #2: The Lawn Mower Shop is a retailer that sells lawn mowers. The income statement for the month of June showed a gross margin of $60,000 and operating income of $20,000. Selling and administrative expenses were 50% fixed. Two hundred mowers were sold at an average price of $750 per unit. All mowers are purchased from Toro and John Deere. Required:

a) Prepare an income statement for the month using the contribution approach.

b) What is the contribution margin per unit? Practice Problem #3: When the Tom-Tom Company’s controller was asked to budget the cost of manufacturing supplies for the next year, she plotted supplies cost and units produced by month for the year. She then drew a regression line through the point she plotted for November when the supplies cost was $21,000 and 5,000 drum sets were produced. Required: If the regression line intersected the Y axis at $6,000, determine the equation of the

regression line.

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Practice Problem #4: The Cords Company manufactures and sells basketball nets in custom colors. The income statement for the month of December showed a gross margin of $60,000 and operating income of $20,000. Selling and administrative expenses were 50% fixed. Two thousand nets in Miami Heat team colors were sold at an average price of $75.00 per unit. During the month, 400 nets in Chicago Bulls colors were manufactured but not sold. Cost of goods sold was 20% fixed and 80% variable (direct material, direct labor and variable manufacturing overhead). Variable manufacturing costs are the same for all nets. Required:

a) Prepare an income statement for the month using variable costing. b) Prepare an income statement for the month using absorption costing. c) Reconcile the operating income under variable costing with the operating

income under absorption costing.

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Sample True / False Questions

1. The relevant range is the range in which costs remain variable. True False

2. A variable cost increases in total as the volume increases. True False

3. A fixed cost will stay constant on a per unit basis as the volume increases. True False

4. The equation for a mixed cost is total fixed costs + variable cost per unit units of activity. True False

5. Contribution margin is defined as sales revenue less variable costs. True False

6. Contribution margin plus variable cost per unit equals total sales revenue. True False

7. The unit contribution margin tells how much each additional unit sold will contribute to covering variable costs. True False

8. If volume increases, all costs will increase True False

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Sample Multiple Choice Questions

1. A cost that changes in total in direct proportion to changes in activity is a(n) a) absorption cost. b) contribution margin. c) fixed cost. d) variable cost.

2. If sales revenue doubles, variable costs will

a) decrease in total. b) increase in total. c) decrease on a per unit basis. d) increase on a per unit basis.

3. A cost that remains the same, in total, regardless of changes in activity level is a

a) variable cost. b) fixed cost. c) mixed cost. d) step-variable cost.

4. If sales revenue doubles, fixed costs will

a) decrease in total. b) increase in total. c) decrease on a per unit basis. d) increase on a per unit basis.

5. A mixed cost

a) is fixed over a wider range of activity than a step cost. b) is a fixed cost over the relevant range and a variable cost everywhere else. c) contains both fixed and variable components. d) always increases on a per unit basis.

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6. The per-unit amount of three different production costs for Jones, Inc., are as follows:

Production Cost A Cost B Cost C20,000 $12.00 $15.00 $20.0080,000 $12.00 $11.25 $5.00

What type of cost is each of these three costs? a) Cost A is fixed, Cost B is mixed, Cost C is variable. b) Cost A is fixed, Cost B is variable, Cost C is mixed. c) Cost A is variable, Cost B is mixed, Cost C is fixed. d) Cost A is variable, Cost B is fixed, Cost C is mixed.

7. A graph of the relationship between total cost and activity level is called a

a) relevant range. b) scattergraph. c) contribution margin graph. d) dependent variable.

8. Bud uses the high-low method of estimating costs. Bud had total costs of

$50,000 at its lowest level of activity, when 5,000 units were sold. When, at its highest level of activity, sales equaled 12,000 units, total costs were $78,000. Bud would estimate variable cost per unit as a) $10.00 b) $6.50 c) $4.00 d) $7.53

9. Smith, which uses the high-low method, had average costs per unit of $10 at its

lowest level of activity when sales equaled 10,000 units and average costs per unit of $6.50 at its highest level of activity when sales equaled 24,000 units. Smith would estimate fixed costs as a) $60,000 b) $16.50 c) $8.25 d) $100,000.

10. Arnold Corp has a selling price of $20, variable costs of $15 per unit, and fixed

costs of $25,000. Arnold expects profit of $300,000 at its anticipated level of production. What is Arnold's unit contribution margin? a) $5.00 b) $10.00 c) $27.50 d) $20.00.

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11. Cost behavior is a) the way in which costs change when the activity level changes. b) the difference between sales revenue and fixed costs. c) the same as absorption costing. d) the amount of sales necessary to achieve a specific profit.

12. When Stella, Inc. sells 40,000 units, its total variable cost is $96,000. What is its

total variable cost when it sells 45,000 units? a) $84,000 b) $96,000 c) $108,000 d) It cannot be determined from the information given.

13. Which of the following is a variable cost?

a) A cost that is $20,000 when production is 50,000, and $20,000 when production is 70,000.

b) A cost that is $20,000 when production is 50,000, and $28,000 when production is 70,000.

c) A cost that is $20,000 when production is 50,000, and $40,000 when production is 70,000.

d) A cost that is $40,000 when production is 50,000, and $40,000 when production is 70,000.

14. Which of the following is a mixed cost?

a) A cost that is $20.00 per unit when production is 50,000, and $20.00 per unit when production is 80,000.

b) A cost that is $20.00 per unit when production is 50,000, and $12.50 per unit when production is 80,000.

c) A cost that is $20.00 per unit when production is 50,000, and $16.25 per unit when production is 80,000.

d) A cost that is $40.00 per unit when production is 50,000, and $40.00 per unit when production is 80,000.

15. The slope of the cost line on a scattergraph represents

a) fixed cost per unit. b) total fixed cost. c) variable cost per unit. d) sales price per unit.

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Solutions to Practice Problems Practice Problem #1

a) High Point - Low Point = Change

Cost $ $15,000 $13,000 $2,000Activity 10,000 7,500 2,500

Change in Cost $ = $2,000 = $.80 variable cost/unit Change in Activity 2,400


Fixed Cost = Total Cost - Variable Cost $7,000 = $15,000 - $8,000 = $.80 (10,000)

OR $7,000 = $13,000 - $6,000 = $.80 (7,500)

b)

Total Cost = Fixed Cost + Variable Cost Y = a + B(X)

$16,750 = $7,000 + $9,750 = $.80 (12,187)

Practice Problem #2

a) Per Unit TotalUnits sold 1 200 Sales $750.00 $150,000Variable expenses:

Cost of goods sold $150,000 – 60,000 450.00 90,000S & A expenses $60,000-20,000 x 50% 100.00 20,000

Contribution margin 200.00 $40,000Fixed expenses:

Cost of goods sold All variable for a retailer 0S & A expenses $60,000-20,000 x 50% 20,000

Operating income $20,000

b) $200.00

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Practice Problem #3: Since the Y intercept is known, use the “quick-and-dirty” method to solve for the variable cost per unit:

Variable Cost = Total Cost - Fixed Costb (X) = Y - a

b (X) = $15,000 = $21,000 - $6,000b = $3.00 = $15,000

5,000 Practice Problem #4:

a) Absorption costing income statement

Total Units produced 2,400 Units sold 2,000 Sales $75.00 x 2,000 $150,000 Variable expenses:

Cost of goods sold ($150,000 – 60,000)x80% 72,000 S & A expenses $60,000-20,000 x 50% 20,000

Contribution margin $58,000 Fixed expenses:



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b) Variable costing income statement Fixed overhead in cost of goods sold: Sales $150,000- Gross margin 60,000= Cost of goods sold 90,000X Fixed % 20%= Fixed overhead in cost of goods sold 18,000/ Units sold 2,000= Fixed overhead rate per unit $9.00X Units produced 2,400= Total fixed overhead $21,600

Total Units produced 2,400 Units sold 2,000 Sales $75.00 x 2,000 $150,000 Variable expenses:


Contribution margin $58,000 Fixed expenses:

Cost of goods sold See schedule 21,600 S & A expenses $60,000-20,000 x 50% 20,000


c) Variable costing operating income $16,400Less: fixed overhead deferred in inventory

$9.00 x 400 nets manufactured and not sold 3,600

Absorption costing operating income $20,000

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Solutions to True / False Problems

1. False because not only do total variable costs remain variable, but both variable costs per unit and total fixed costs remain constant.

2. True 3. False because fixed costs remain constant in total and decrease per unit as

volume increases. 4. True 5. True 6. False because both revenue and contribution margin are stated in total

whereas variable cost is stated per unit. The statement would be true if all three were stated per unit or in total.

7. False because contribution margin contributes to covering fixed costs. 8. False because if volume increases, only variable costs will increase.

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Solutions to Multiple Choice Questions

1. D 2. B 3. B 4. C 5. C 6. C 7. B 8. C 9. A 10. A 11. A 12. C 13. B 14. C 15. C

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