Part Three Cost Behavior Analysis
Cost Behavior • Cost behavior is the manner in which a cost changes as some related activity changes • An understanding of cost behavior is necessary to plan and control costs • A relevant range is the range over which we are interested in the cost’s behavior
COST BEHAVIOR ANALYSIS Ø Definition: The study of how specific costs respond to changes in the level of business activity Ø Some costs change; others remain the same Ø Helps management plan operations and make decisions Ø Applies to all types of businesses and entities
COST BEHAVIOR ANALYSIS Continued Ø Starting point is measuring key business activities Ø Activity levels may be expressed in terms of § Sales dollars (in a retail company) § Miles driven (in a trucking company) § Room occupancy (in a hotel) § Dance classes taught (by a dance studio)
COST BEHAVIOR ANALYSIS Continued Ø Many companies use more than one measurement base Ø For an activity level to be useful: Changes in the level or volume of activity should be correlated with changes in cost
COST BEHAVIOR ANALYSIS Continued Ø The activity level selected is called the activity (or volume) index § Identifies the activity that causes changes in the behavior of costs § Allows costs to be classified according to their response to changes in activity as: Variable Costs Fixed Costs Mixed Costs
COST BEHAVIOR ANALYSIS VARIABLE COSTS Ø Costs that vary in total directly and proportionately with changes in the activity level Ø If the activity level increases 10 percent, total variable costs increase 10 percent Ø If the activity level decreases by 25 percent, total variable costs will decrease by 25 percent
COST BEHAVIOR ANALYSIS VARIABLE COSTS ­ Continued Ø Variable costs also remain constant per unit at every level of activity Ø Examples of variable costs include § Direct material and direct labor for a manufacturer § Sales commissions for a merchandiser § Gasoline in airlines and trucking companies
COST BEHAVIOR ANALYSIS VARIABLE COSTS ­ Continued Example: Continued
Step­Variable Costs Cost Total cost remains Total cost remains constant within a constant within a narrow range of narrow range of activity.
activity. Activity Step­Variable Costs Cost Total cost increases to a Total cost increases to a new higher cost for the new higher cost for the next higher range of next higher range of activity.
activity. Activity COST BEHAVIOR ANALYSIS FIXED COSTS Ø Costs that remain the same in total regardless of changes in the activity level. Ø Per unit cost varies inversely with activity: As volume increases, unit cost decline, and vice versa Ø Examples include § Property taxes § Insurance § Rent § Depreciation on buildings and equipment
COST BEHAVIOR ANALYSIS FIXED COSTS ­ Continued Example: Continued
Types of Fixed Costs Committed Committed Discretionary Discretionary Long­term, cannot be Long­term, cannot be reduced in the short reduced in the short term.
term. May be altered in the May be altered in the short­term by current short­term by current managerial decisions managerial decisions Examples Examples Examples Examples Depreciation on Depreciation on Buildings and Buildings and Equipment Equipment Advertising and Advertising and Research and Research and Development Development COST BEHAVIOR ANALYSIS RELEVANT RANGE Ø Throughout the range of possible levels of activity, a straight­line relationship usually does not exist for either variable costs or fixed costs § The relationship between variable costs and changes in activity level is often curvilinear § For fixed costs, the relationship is nonlinear – some fixed costs will not change over the entire range of activities, others may
COST BEHAVIOR ANALYSIS RELEVANT RANGE ­ Continued
COST BEHAVIOR ANALYSIS RELEVANT RANGE ­ Continued Ø Defined as the range of activity over which a company expects to operate during a year Ø Within this range, a straight­line relationship usually exists for both variable and fixed costs
COST BEHAVIOR ANALYSIS MIXED COSTS Ø Costs that have both a variable cost element and a fixed cost element Ø Sometimes called semivariable cost Ø Change in total but not proportionately with changes in activity level
Mixed Costs A mixed cost has both fixed and variable A mixed cost has both fixed and variable components. Consider the example of utility cost. components. Consider the example of utility cost. Total Utility Cost Y T
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Variable Cost per KW X Activity (Kilowatt Hours) Fixed Monthly Utility Charge Mixed Costs The total mixed cost line can be expressed The total mixed cost line can be expressed as an equation: as an equation: Y = a + bX Y = a + bX Where: Where: Total Utility Cost Y T
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Y Y = = the total mixed cost the total mixed cost a a = = the total fixed cost (the the total fixed cost (the vertical intercept of the line) vertical intercept of the line) b b = = the variable cost per unit of the variable cost per unit of activity (the slope of the line) activity (the slope of the line) X X = = the level of activity the level of activity Variable Cost per KW X Activity (Kilowatt Hours) Fixed Monthly Utility Charge The Analysis of Mixed Costs ØMixed costs must be classified into their fixed and variable elements ØThe methods to analysis of mixed costs includes:
The Analysis of Mixed Costs Account Analysis Engineering Approach Scattergraph Plot
High­Low Method Least­Square Regression Method Account Analysis & Engineering Estimates Each account is classified as either Each account is classified as either variable or fixed based on the analyst’s variable or fixed based on the analyst’s knowledge of how the account behaves. knowledge of how the account behaves. Cost estimates are based on an Cost estimates are based on an evaluation of production methods, evaluation of production methods, and material, labor and overhead and material, labor and overhead requirements.
requirements. The Scattergraph Method
Total Cost in 1,000’s of Dollars Y 20 10 Plot the data points on a Plot the data points on a graph (total cost vs. activity). graph (total cost vs. activity). * * * * * * * * * * 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced Quick­and­Dirty Method Draw a line through the data points with about an Draw a line through the data points with about an equal numbers of points above and below the line.
equal numbers of points above and below the line. Total Cost in 1,000’s of Dollars Y 20 10 * * * * * * * * * * Intercept is the estimated Intercept is the estimated fixed cost = $10,000 fixed cost = $10,000 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced Quick­and­Dirty Method The slope is the estimated variable cost per unit. The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Slope = Change in cost ÷ Change in units Total Cost in 1,000’s of Dollars Y 20 10 * * * * * * * * * * Horizontal Horizontal distance is distance is the change in the change in activity.
activity. Vertical distance is Vertical distance is the change in cost. the change in cost. 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced High­Low Method – Compares the points of highest and lowest activities, and their related costs, and calculates the formula for a straight line connecting the two points – Dividing the incremental cost by the incremental units of activity gives the variable cost per unit of activity – The variable cost per unit is substituted into the cost formula to determine the fixed cost • Total cost = fixed cost + variable cost per unit * number of units of activity
High­Low Method Cost High point $ 18,000 Low point 12,000 Difference $ 6,000 Units of activity 10,000 6,000 4,000 $6,000 / 4,000 = $1.50 per unit At the low point: $12,000 = Fixed cost + $1.50 per unit * 6,000 units $3,000 = Fixed cost Total cost = $3,000 + $1.50 per unit * number of units
Applications of Cost Behavior Concepts • Contribution margin – Excess of sales over variable costs – Contribution is the incremental amount of each sale that is available to cover fixed costs and provide a profit – Knowing the contribution margin allows us to predict changes in net income that will result from a change in sales volume
Applications of Cost Behavior Concepts Total Percentage Per unit* Sales $ 1,000,000 100% $ 1,000 Variable costs 600,000 60% 600 Contribution margin $ 400,000 40% $ 400 Fixed costs 300,000 Net income $ 100,000 * ­ assume 1,000 units are sold
Applications of Cost Behavior Concepts • Contribution margin percentage – Proportion of each sales dollar that is available to cover fixed costs and provide a profit • If sales increase by $100,000, profit will increase by $40,000 ($100,000 * 40%) • Contribution margin per unit – Dollar amount that each unit contributes toward covering fixed costs and providing a profit • If 50 more units are sold, profit will increase by $20,000 (50 units * $400)
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