Cost Behavior Chapter 6

Identify key features of various cost behaviors Objective 1 Identify key features of various cost behaviors

Cost Behavior How costs change in response to changes in volume Variable costs Fixed costs Mixed costs

Variable Costs Change in total in direct proportion to changes in volume Total variable costs = variable cost per unit of activity x volume of activity

Total Variable Costs Assume we pay sales commissions of 5% on all sales. The cost of sales commissions increase proportionately with increases in sales.

Fixed Costs Do not change over wide ranges of volume

Total Fixed Costs Assume we pay our sales staff a salary of $2,000 per month. If a sales person makes sales of $500, she gets paid $2,000 salary. If she has sales of $100,000, she get paid $2,000 salary

Mixed Costs Contain both variable and fixed components

Mixed Costs A mixed cost has elements of both fixed and variable costs. Assume we pay our sales staff, $2,000 plus 5% commission on each sales dollar.

Mixed Costs Variable Fixed

S6-1 ____ b. Wood for speaker enclosures ____ a. Depreciation on equipment used to cut wood enclosures ____ b. Wood for speaker enclosures ____ c. Patents on crossover relays (internal components) ____ d. Crossover relays ____ e. Grill cloth ____ f. Glue ____ g. Quality inspector’s salary F V F V V V F

E6-15 a.

E6-15 b.

E6-15 c.

Forecast costs using cost equations Objective 2 Forecast costs using cost equations

Total variable costs + Total fixed costs Cost Equation Total costs = Total variable costs + Total fixed costs y = vx + f y = total cost v = variable cost per unit of activity (slope) x = volume of activity (x) f = fixed cost over a given period of time (vertical y intercept)

Relevant Range Band of volume where total fixed costs remain constant and variable cost per unit remains constant. Outside the relevant range, the cost either increases or decreases

Other Cost Behaviors Step costs – fixed over small range of activity, then jump to new fixed level

Other Cost Behaviors Curvilinear Costs

E6-17 1. Variable costs per unit: $2,625 / 3,500 garments = $0.75 Total fixed costs: $2 x 3,500 garments = $7,000

E6-17 1. Garments 2,000 3,500 5,000 Total Variable Costs $1,500 $2,625 $3,750 Total Fixed Costs 7,000 Total Operating Costs $8,500 $9,625 $10,750 Variable Cost/garment $0.75 Fixed Cost/garment 3.50 2.00 1.40 Average cost/garment $4.25 $2.75 $2.15 Garments 2,000 3,500 5,000 Total Variable Costs Total Fixed Costs Total Operating Costs Variable Cost/garment Fixed Cost/garment Average cost/garment $1,500 $2,625 $3,750 7,000 $8,500 $9,625 $10,750 2. The average cost per garment changes, as volume changes, due to the fixed component of the drycleaner’s costs. The fixed cost per unit decreases as volume increases, while the variable cost per unit remains constant.

E6-17 3. Actual costs at 2,000 garments $8,500 Total predicted costs: ($2.15 × 2,000 garments) (4,300 ) Underestimated costs $4,200 If Dan Perreth uses the average cost per unit at full capacity ($2.15) to predict total costs for a volume of 2,000 units, he will predict total costs as $4,300 ($2.15 × 2,000 garments). Since his actual costs at this volume will be $8,500, he will have underestimated costs by $4,200.

E6-18 a. 1,000 x $26.43 $26,430 b. Total costs $26,430 Less total fixed costs (18,000) Total variable costs $8,430 ÷ 1,000 Variable cost per mailbox $8.43

E6-18 c. y = $8.43x + $18,000 d. $26.43 x 1,200 mailboxes $31,716 e. y = ($8.43 • 1,200) + $18,000 = $28,116

E6-18 f. Using average at 1,000 $31,716 Using cost equation 28,116 $3,600 The plant manager’s forecast would be about $3,600 too high if he uses the average cost per unit to predict costs. The average cost per unit is based on a mixed cost that will change as volume changes. If the manager uses the average cost to predict costs, he is erroneously assuming that the average cost per unit does not change at different volumes. He’s basically assuming it is all a variable cost. The manager should use the cost equation to predict costs since it takes into account the variable and fixed components of producing mailboxes.

Objective 3 Determine cost behavior using account analysis, the high-low method, and regression analysis

High-Low Method Method to separate mixed costs into variable and fixed components Select the highest level and the lowest level of activity over a period of time

High-Low Method – E6-21 Step 1: Find slope of the mixed cost line (variable cost/unit) = Δ in cost (y) / Δ in volume (x) ($5,748-$5,020) ÷ (17,300-14,500) $728 ÷ 2,800 = $0.26 The highest volume month is February and the lowest volume month is July. The high-low method uses only these two months to determine the cost equation.

High-Low Method – E6-21 Step 2: Find the vertical intercept (fixed costs) = Total mixed cost – Total variable cost $5,748 – ($0.26 • 17,300) = $1,250 or $5,020 – ($0.26 • 14,500) = $1,250

High-Low Method – E6-21 Step 3: Create and use an equation to show the behavior of a mixed cost Y = $0.26 per mile + $1,250 Predicted operating costs at 15,000 miles: ($0.26 • 15,000) + $1,250 = $5,150

Regression Analysis Statistical procedure to find the line that best fits data Uses all data points Results in equation of line and an R-square value

R-Square Value “Goodness of fit” How well does the line fit the data points? Ranges from 0 to 1 “0” – no relationship between costs and volume – activity is not a cost driver “1” – perfect relationship – activity is a cost driver

Data Concerns Seasonal variations Inflation Outliers – abnormal data points

E6-22

E6-22 4. The R-square is .901 (rounded). The r-square indicates that the cost equation explains 90.1% of the variability in the data. In other words, it fits the data quite well. Flower Power should feel confident using this cost equation to predict total costs at other volumes within the same relevant range.

E6-22 5. y = 0.29x + 802.39 y = ($0.29 • 15,000) + $802.39 y = $5,152.39 6. Even though the regression analysis is better because it uses all data points to estimate the cost equation, it’s prediction for total van operating costs at 15,000 miles is remarkably similar to that found using the high-low method ($5,150).

Objective 4 Prepare contribution margin income statements for service firms and merchandising firms

Traditional Income Statement Sales - Cost of Goods Sold Gross Margin - Selling,general & administrative costs Operating Income

Contribution Margin Income Statement Sales - Variable Costs Contribution Margin - Fixed Costs Operating Income

Contribution Margin Income Statement Predict how changes in volume will affect operating income

E6-25 Rachel’s Rock Shop Income Statement For the year ending 20XX Revenue: Sales Revenue (27,000 + 7,000) $34,000 Rental Revenue 22,000 Lesson Revenue 40,000 Total Revenue $96,000 Less: Cost of Goods Sold (7,500 + 2,000) (9,500) Gross Margin $86,500 Less Operating Costs: Depreciation $ 4,000 Employee Salary expenses 30,000 Musician wages 25,000 Lease 12,000 Total operating costs 71,000 Operating Income $15,500 E6-25

Contribution Margin Income Statement Rachel’s Rock Shop Contribution Margin Income Statement For the year ending 20XX Revenue: Sales Revenue (27,000 + 7,000) $34,000 Rental Revenue 22,000 Lesson Revenue 40,000 Total Revenue $96,000 Less: Variable Costs Cost of Goods Sold (7,500 + 2,000) $ 9,500 Musician wages 25,000 Total Variable costs (34,500) Contribution Margin $61,500 Less Fixed Costs: Depreciation $ 4,000 Employee Salary expenses 30,000 Lease 12,000 Total fixed costs (46,000) Operating Income $15,500 E6-25 The contribution margin income statement is a better management tool than the traditional income statement. If Rachel’s volume remains in the same relevant range, she can easily see that her fixed expenses will be $46,000. She also knows that her revenue and variable costs will increase in direct proportion to changes in volume. The traditional income statement does not provide any information on cost behavior.

Objective 5 Use variable costing to prepare contribution margin income statements for manufacturers (Appendix)

Variable Costing Assigns only variable manufacturing costs to products Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead = period cost Contribution margin income statements For internal management decisions

Absorption Costing Required by GAAP for external reporting Assign all manufacturing costs to product Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead Traditional income statement

Conventional (Absorption Costing) Income Statement Rays Conventional (Absorption Costing) Income Statement Year Ended December 31, 2008 Sales revenue (185,000  $35) $6,475,000 Less: Cost of Goods Sold: Beginning finished goods inventory $ 0 Cost of goods manufactured 5,000,000 Cost of goods available for sale Ending finished goods inventory (375,000) Cost of goods sold 4,625,000 Gross profit 1,850,000 Operating expenses 1,175,000 Operating income $ 675,000 E6-26

Contribution Margin (Variable Costing) Income Statement Rays Contribution Margin (Variable Costing) Income Statement Year Ended December 31, 2008 Sales revenue $6,475,000 Variable expenses: Variable cost of goods sold $2,775,000* Sales commission expense 925,000 3,700,000 Contribution margin $2,775,000 Fixed expenses: Manufacturing overhead $2,000,000 Operating expenses 250,000 2,250,000 Operating income $ 525,000 E6-26 Req. 2 Absorption costing operating income is higher than variable costing operating income. This is because absorption costing defers 15,000 goggles  $10 fixed manufacturing overhead per goggle = $150,000 of year 20X8 fixed manufacturing overhead as an asset in ending inventory. In contrast, variable costing expenses all the year 20X8 fixed manufacturing overhead during 20X8. Variable costing expenses $150,000 more costs during 20X8, so variable costing operating income is $150,000 less than absorption costing income in 2008 ($675,000 – $525,000). * computation of variable cost of goods sold

E6-26 Incremental analysis: Increase in contribution margin (($35-20) x 15,000 goggles) $225,000 Increase in fixed costs (150,000) Increase in operating income $75,000 Rays should go ahead with the promotion.

End of Chapter 6