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Cost Behavior

Chapter 6

Objective 1

Describe key characteristics and graphs of various cost behaviors

Cost Behavior

Cost behavior—how costs change as volume changes.

There are three common cost behaviors:

Variable costs

Fixed costs

Mixed costs

Key Characteristics of Variable Costs

Total variable costs change in direct proportion to changes in volume

Variable cost per unit remains constant

Slope

Total variable cost (y) =

Variable cost per unit of activity (v) x Volume of activity (x)

y=vx

Cost Graphs

Vertical (y-axis) always shows total costs

Horizontal axis (x-axis) shows volume of activity

Total

Costs

Total volume of activity

Note that the variable cost per customer remains constant in each of the graphs.

Total Variable Costs

Objective 2

Use cost equations to express and predict costs

Cost Equation

Is a mathematical equation for a straight line, to predict total cost

Total cost = total variable cost + total fixed cost or Y = vx + f

Where

Y = total mixed cost

v = variable cost per unit of activity

x = volume of activity

f = fixed cost over a given period of time

Key Characteristics of Fixed Costs

Total fixed costs stay constant over relevant range*

Fixed costs per unit of activity vary inversely with changes in volume

Total fixed cost (y) = Fixed amount over a period of time (f)

y = f

*Relevant range is the normal operating range of activity

Total Fixed Costs

Costs and Decisions

Committed fixed costs

Discretionary fixed costs

Key Characteristics of Mixed Costs

Total mixed costs increase as volume increases

Total mixed costs can be expressed as a combination of the variable and fixed cost equations:

Total mixed cost = total variable cost + total fixed cost or Y = vx + f

Where

Y = total mixed cost

v = variable cost per unit of activity

x = volume of activity

f = fixed cost over a given period of time

Mixed Costs

Variable

Fixed

Now turn to S6-1

S6-1 Identify Cost Behavior

Cost A
Cost B
Cost C

Variable Cost

Fixed Cost

Mixed Cost

Relevant Range

Band of volume where total fixed costs remain constant at a certain level

Variable costs per unit remain constant at a certain level

Other Cost Behaviors

Step Costs

Other Cost Behaviors

Curvilinear Costs

Now turn to E6-22A

E6-22A

	Garments
	4,500	6,000	7,500
Total Variable Costs		$5,100
Total Fixed Costs
Total Operating Costs

Variable Cost/garment
Fixed Cost/garment		$2.40
Average cost/garment

E6-22A (cont.)

	Garments
	4,500	6,000	7,500
Total Variable Costs		$5,100
Total Fixed Costs
Total Operating Costs

Variable Cost/garment	$0.85	$0.85	$0.85
Fixed Cost/garment		$2.40
Average cost/garment

E6-22A (cont.)

	Garments
	4,500	6,000	7,500
Total Variable Costs	$3,825	$5,100	$6,375
Total Fixed Costs
Total Operating Costs

Variable Cost/garment	$0.85	$0.85	$0.85
Fixed Cost/garment		$2.40
Average cost/garment

E6-22A (cont.)

	Garments
	4,500	6,000	7,500
Total Variable Costs	$3,825	$5,100	$6,375
Total Fixed Costs	$14,400	$14,400	$14,400
Total Operating Costs

Variable Cost/garment	$0.85	$0.85	$0.85
Fixed Cost/garment		$2.40
Average cost/garment

E6-22A (cont.)

	Garments
	4,500	6,000	7,500
Total Variable Costs	$3,825	$5,100	$6,375
Total Fixed Costs	$14,400	$14,400	$14,400
Total Operating Costs	$18,225	$19,500	$20,775

Variable Cost/garment	$0.85	$0.85	$0.85
Fixed Cost/garment		$2.40
Average cost/garment

E6-22A (cont.)

	Garments
	4,500	6,000	7,500
Total Variable Costs	$3,825	$5,100	$6,375
Total Fixed Costs	$14,400	$14,400	$14,400
Total Operating Costs	$18,225	$19,500	$20,775

Variable Cost/garment	$0.85	$0.85	$0.85
Fixed Cost/garment	$3.20	$2.40	$1.92
Average cost/garment

E6-22A (cont.)

	Garments
	4,500	6,000	7,500
Total Variable Costs	$3,825	$5,100	$6,375
Total Fixed Costs	$14,400	$14,400	$14,400
Total Operating Costs	$18,225	$19,500	$20,775

Variable Cost/garment	$0.85	$0.85	$0.85
Fixed Cost/garment	$3.20	$2.40	$1.92
Average cost/garment	$4.05	$3.25	$2.77

E6-22A (cont.)

The average cost per garment changes as volume changes, due to the fixed component of the dry cleaner’s costs. The fixed cost per unit decrease as volume increases, while the variable cost per unit remains constant.

Actual costs at 4,500 garments

$12,465 Total predicted costs ($2.77 × 4,500 garments)

(18,225) Actual costs at 4,500 garments

$5,760 Difference (underestimated)

Now turn to E6-25A

E6-25A

Data: Freedom Mailbox produces decorative mailboxes. The company’s average cost per unit is $24.43 when it produces 1,300 mailboxes.

1. 1,300 x $24.43	$31,759

2. Total costs	$31,759
Less total fixed costs	(21,359)
Total variable costs	$10,400
	÷ 1,300
Variable cost per mailbox	$8.00

E6-25A

3. y = $8.00x + $21,359

4. $24.43 x 1,700 mailboxes = $41,531

5. y = ($8.00 x 1,700) + $21,359 = $34,959

E6-25A

6. Using average at 1,700 $41,531

Using cost equation $34,959

$6,572

Sustainability and Cost Behavior

Sustainable companies and changes in cost behavior

E-banking and e-billing drive down variable costs

Greener lifestlyes

Environmental Impact

Objective 3

Use account analysis and scatter plots to analyze cost behavior

Cost Behavior Analysis

Four methods to analyze cost behavior

Account Analysis

Scatter Plots

High-Low Method

Regression Analysis

Account Analysis

Use of judgment to classify each general ledger account as variable, fixed, or mixed

Subjective

Scatter Plots

Use historical data to determine a cost’s behavior

Scatter plot is the graph of historical cost data on the y-axis and volume data on the x-axis

Helps managers visually determine how strong the relationship is between the cost and the volume of the chosen activity base

Scatter Plot Example

Miles Driven

Total Cost

Objective 4

Use the high-low method to analyze cost behavior

High-Low Method

Step 1: Find variable cost per unit (slope) of cost line

Step 2: Find the fixed costs (vertical intercept)

Step 3: Create the cost equation

Advantage: Easy to use

Disadvantage: Only uses 2 data points

Turn to E6-28A

High-Low Method: E6-28A

Step 1: Find slope of the mixed cost line

(variable cost/unit) = Δ in cost (y) / Δ in volume (x)

The slope represents the variable cost per unit of activity

($5,730 -$5,040) ÷ (18,500-15,500)

$690 ÷ 3,000 = $0.23

High-Low Method: E6-28A (cont.)

Step 2: Find the vertical intercept

Fixed costs = Total mixed cost – Total variable cost

$5,730 – ($0.23 • 18,500) = $1,475

$5,040 – ($0.23 • 15,500) = $1,475

High-Low Method: E6-28A (cont.)

Step 3: Create and use an equation to show the behavior of a mixed cost

Y = $0.23 per mile + $1,475

Predicted operating costs at 16,000 miles:

($0.23 x 16,000) + $1,475 = $5,155

Objective 5

Use regression analysis to analyze cost behavior

Regression Analysis – Exhibit 6-15

Statistical procedure to find the line that best fits data (cost equation)

Uses all data points

R-square, Intercept, X Variable 1

Regression Analysis – Exhibit 6-15

Intercept = Fixed cost

X Variable 1 = Variable cost per activity unit

R Square = goodness of fit

Regression Analysis – Exhibit 6-15

Utilities monthly cost equation =

y = $7.85x + $14,538

where y = total monthly utilities cost

x = number of guests

R-Square Value

“Goodness of fit”

How well does the line fit the data points?

Ranges from 0 to 1

Predicting Costs & Data Concerns

Data Concerns

Only valid within relevant range

Seasonal variations

Inflation

Outliers – abnormal data points

Objective 6

Describe variable costing and prepare a contribution margin income statement

Absorption Costing

Required by GAAP for external reporting

Assign all manufacturing costs to products (DM, DL, Variable MOH, and Fixed MOH)

Traditional (conventional) income statement

Traditional (Conventional) Income Statement

Sales

- Cost of Goods Sold

Gross Margin

- Selling, general, and administrative costs

Operating Income

Variable Costing

Assigns only variable manufacturing costs to products (DM, DL, and Variable MOH)

Fixed manufacturing overhead = period cost

For internal management decisions

Contribution Margin income statement

Contribution Margin Income Statement

Sales

- Variable Costs

Contribution Margin

- Fixed Costs

Operating Income

Reconciling Operating Income Between the Two Costing Systems

Difference in Operating Income = (Change in inventory level, in units) x (Fixed MOH per unit)

Now turn to E6-44A

E6-44A

Conventional (Absorption Costing) Income Statement

E6-44A

Conventional (Absorption Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000

E6-44A

Conventional (Absorption Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Less: Cost of Goods Sold (205,000 x $26)		( 5,330,000)

Fixed mfg per unit = $2,475,000 fixed MOH / 225,000 units produced = $11 per unit

Variable MOH per unit $15 (given)

Total manufacturing cost per unit = $11 + $15 = $26

E6-44A

Conventional (Absorption Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Less: Cost of Goods Sold (205,000 x $26)		( 5,330,000)
Gross Profit		3,690,000

Fixed mfg per unit = $2,475,000 fixed MOH / 225,000 units produced = $11 per unit

Variable MOH per unit $15 (given)

Total manufacturing cost per unit = $11 + $15 = $26

E6-44A

Conventional (Absorption Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Less: Cost of Goods Sold (205,000 x $26)		( 5,330,000)
Gross Profit		3,690,000
Operating Expenses [(205,000 x $6) + $250,000]		(1,480,000)

Fixed mfg per unit = $2,475,000 fixed MOH / 225,000 units produced = $11 per unit

Variable MOH per unit $15 (given)

Total manufacturing cost per unit = $11 + $15 = $26

E6-44A

Conventional (Absorption Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Less: Cost of Goods Sold (205,000 x $26)		( 5,330,000)
Gross Profit		3,690,000
Operating Expenses [(205,000 x $6) + $250,000]		(1,480,000)
Operating Income		$2,210,000

Fixed mfg per unit = $2,475,000 fixed MOH / 225,000 units produced = $11 per unit

Variable MOH per unit $15 (given)

Total manufacturing cost per unit = $11 + $15 = $26

E6-44A (cont.)

Now we turn to the Contribution Margin Income Statement (VARIABLE COSTING STMT)

First need to calculate:

Variable cost of goods sold

E6-44A (cont.)

Variable cost of goods sold:

Beginning finished goods inventory $ 0

Variable cost of goods manufactured ($15 x 225,000) 3,375,000

Variable cost of goods available for sale 3,375,000

Ending fin. goods inv. ($15 x 20,000) (300,000)

Variable cost of goods sold* $3,075,000

*Also can calculate as 205,000 units x $15 = $3,075,000

E6-44A (cont.)

Contribution Margin (Variable Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000

E6-44A (cont.)

Contribution Margin (Variable Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Variable expenses:
Variable COGS (from prior calculation)	$3,075,000*

E6-44A (cont.)

Contribution Margin (Variable Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Variable expenses:
Variable COGS (from prior calculation)	$3,075,000*
Sales comm expense ($6x205,000)	1,230,000	(4,305,000)

E6-44A (cont.)

Contribution Margin (Variable Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Variable expenses:
Variable COGS (from prior calculation)	$3,075,000*
Sales comm expense ($6x205,000)	1,230,000	(4,305,000)
Contribution margin		$4,715,000

E6-44A (cont.)

Contribution Margin (Variable Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Variable expenses:
Variable COGS (from prior calculation)	$3,075,000*
Sales comm expense ($6x205,000)	1,230,000	(4,305,000)
Contribution margin		$4,715,000
Fixed expenses:
MOH (given in exercise)	$2,475,000
Operating expenses (given)	250,000	(2,725,000)

E6-44A (cont.)

Contribution Margin (Variable Costing) Income Statement
Sales revenue (205,000  $44)		$9,020,000
Variable expenses:
Variable COGS (from prior calculation)	$3,075,000*
Sales comm expense ($6x205,000)	1,230,000	(4,305,000)
Contribution margin		$4,715,000
Fixed expenses:
MOH	$2,475,000
Operating expenses	250,000	(2,725,000)
Operating income		$1,990,000

E6-44A (cont.)

Req. 2

Difference between the two methods:

Change in inventory x Fixed MOH per unit =

(20,000 x $11*) = $220,000

*$11 is the fixed MOH per unit ($2,475,000 / 225,000)

Traditional method produces the higher operating income because of the fixed MOH still remaining in inventory.

Proof:

Traditional operating income $2,210,000

Contribution margin operating income 1,990,000

Difference $ 220,000

E6-44A (cont.)

Req. 3

Incremental analysis:

Increase in contribution margin $460,000

[($44-$21)*20,000 goggles]

Increase in fixed costs (145,000)

Increase in operating income $315,000

Now turn to S6-16

Patricia’s Quilt Shoppe
Traditional Income Statement
Month Ended February 28
Sales revenue (75 × $380)	$28,500
Less: Cost of goods sold (75 × $230)	(17,250)
Gross profit	11,250
Less: Operating expenses:
Sales commissions (10% × $28,500)	(2,850)
Payroll costs	(1,200)
Lease	(800)
Operating income	$ 6,400

S6-16

S6-16 (cont.)

Patricia’s Quilt Shoppe
Contribution Margin Income Statement
Month Ended February 28
Sales revenue (75 × $380)	$28,500
Less: Variable costs:
Cost of goods sold (75 × $320)	(17,250)
Sales commissions (10% × $28,500)	(2,850)
Contribution margin	8,400
Less: Fixed costs:
Payroll costs	(1,200)
Lease	(800)
Operating income	$ 6,400

Absorption Costing and Manager Incentives

When inventories increase, absorption costing income is higher than variable costing income.

When inventories decrease, absorption costing income is lower than variable costing income.

Therefore…managers may increase production to build up inventory to maximize income and, therefore, their own bonus.

End of Chapter 6

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Total Sales Compensation	$2,000	$2,500	$3,000	$3,500	$4,000

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