Chapter 16 The Behavior of Costs

Behavior of Costs Cost-volume relationships. Fixed and variable costs. Step-function costs.

Relation of costs to volume Higher volume causes higher costs. Variable costs = items of cost that vary, in total, directly and proportionately with volume. Fixed costs = non-variable costs = items of cost that, in total, do not vary at all with volume Semi-variable costs = semi-fixed costs = partly variable costs = mixed costs = costs that include a combination of variable cost and fixed cost items.

Variable Costs Items of cost that vary, in total, directly and proportionately with volume. Volume refers to activity level. Examples: Material costs varies with units sold. Electricity costs varies with production hours. Stationery and postage costs varies with number of letters written.

Fixed costs Non-variable costs = items of cost that, in total, do not vary at all with volume. Examples: Building rent, property taxes, management salaries. Fixed cost per unit of activity decreases as the level of activity increases. For fixed costs, cost per unit is an average cost. Fixed costs are fixed for a range of activity and a limited period of time. Fixed costs may change for reasons such as a deliberate management decision to change them.

Cost-volume (C-V) diagram Illustration 16-1. Y or vertical axis reflects total cost. X or horizontal axis reflects volume. y = mx + b. y is the cost at a volume of x; m is the rate of cost change per unit of volume change, or the slope (variable costs). b is the vertical intercept, which represents the fixed cost component.

TC = TFC +(UVC*X) TC = total cost; TFC = total fixed cost (per time period), UVC = Unit variable cost (per unit of volume), X = volume. Equations for: Variable cost line: TC = UVC*X Fixed cost line: TC = TFC Semivariable cost: TC = TFC + (UVC*X), same as above.

Cost Relations Average costs = total cost/volume. Average cost behaves differently than total cost. As volume goes up  Total fixed cost remains constant, total variable costs goes up, per unit variable costs stays the same, per unit fixed cost goes down, per unit total cost goes down. As volume increases without limit, unit cost approaches variable unit cost and fixed cost per unit approaches zero.

Limitations of C-V Relations A straight line approximates cost behavior only within a certain range of volume, the relevant range. When volume approaches zero, management takes steps to reduce fixed costs. When volume exceeds relevant range, fixed costs increase.

Limitations (continued) Amount of variable costs depends on the time period over which behavior is estimated (the relevant time period). If the time period is one day, few costs are variable. Over an extremely long time period, no costs are fixed. Environmental assumptions must be made. Wage rates, fringe benefits, material prices, technology changes.

“Sticky” Costs Generally considered variable but fall less with decreases of activity than they rise with increases. Managers tend to increase resources more quickly than they decrease. Examples: Sales commissions with minimum guarantees. Managers slower to fire employees than to hire.

Linear assumption C-V relationship is often not linear. Some cost functions are curved (curvilinear). Segments of the curve can be approximated by a straight line, each with its own relevant range. Step function costs = items of cost vary in steps.

Step-function costs Incurred when costs are added in discrete chunks, e.g., a supervisor for every 10. Adding the “chunk” of costs increases capacity. Height of a stair step (riser) indicates the cost of adding incremental capacity. Step width (tread) shows how much additional volume of that activity can be serviced by this additional increment of capacity.

Step function (continued) If treads” are narrow and “risers” are low (i.e., steps are small), then the steps can be approximated by a variable cost line. If is believed within the relevant time period that cost will remain within the relevant range for a single stair step (tread), then the cost is appropriately treated as a fixed cost for the time period. Step functions are often hidden in C-V diagrams as either variable or fixed costs.

Estimating C-V relationship First method: Judgment or account-by-account method. Each account in cost structure is estimated and divided between fixed and variable costs. Second: Scatter diagram Plot a number of observations (perhaps prior period results) of costs and volumes on a graph and visually draw a line of best fit.

Third method: High-Low method Estimate total costs for two volume levels, preferably one high level and one low level. To determine slope or variable cost per unit: Change in total cost between the two points divided by change in units of output. To determine fixed costs: Subtract from total costs at either one of the points the unit volume times the unit variable costs.

Fourth: Linear regression Use a statistical method of fitting a line to a number of observations of volume and cost (method of least squares or linear regression). Eliminate outliers, that is, unusual observations (e.g., period during which there was a strike). Assumes the future will be the same as the past (rarely a completely accurate assumption). Scattergrams covering long periods of time may reflect nothing more than price changes over the period (drift).

Measures of volume Have assumed a single-product. If multiple products, with different cost structures, unlikely that units would be a reliable measure of activity. Possible common denominators include: labor hours, labor dollars, machine hours, homogeneous quantities such as tons or barrels and sales value.

Questions to consider in selecting a volume measure Input (resources used) or output (goods or services produced)? Money or non-monetary quantities?

Input or output? Input measures: resources used: labor hours worked, labor cost, machine hours, kilowatt hours of electricity, pounds of material. Output measures: units or dollars. Manufacturing costs might use input measures such as labor or machine hours. Retail stores might use dollar sales.

Money or non-monetary quantities? A non-monetary measure is not affected by price changes and therefore may have some advantages. If price changes affect all costs equally, the use of labor costs as an activity measure implicitly allows for price changes. Best volume measure should be related to the activity that causes the cost. The more items of cost that are combined in the cost function the more difficult it is to relate the causality to a single measure.

Profit-graph Add revenue line to C-V diagram. Assumes constant selling price. UR = unit revenue TR = total revenue

Breakeven volume TR = UR*X TC = TFC + (UVC*X) Breakeven: TR = TC Substituting: UR*X = TFC + (UVC*X)  X = TFC/(UR - UVC)

Contribution Unit contribution = unit contribution margin = marginal income = unit selling price - variable cost per unit = UR - UVC. I = total income = (UR - UVC) * X - TFC. What is contribution: First it is the contribution to cover fixed costs. Then it is the contribution toward profit.

Break-even volume In units = Fixed costs/unit contribution In revenue dollars = Fixed costs / contribution percent Contribution percent = contribution margin percentage = contribution as a percent of revenues = (UR - UVC)/ UR

Target Profit Add to breakeven analysis to show units or dollar of sales to achieve a target (T) level of profit: UR*X = TFC + (UVC*X) + T X = (TFC+T)/(UR - UVC)

Cash versus accrual profit-graphs So far we have considered profit and costs on an accrual basis. To look at a profit-graph on a cash basis: Major difference is depreciation (a non-cash expense) Also to be meaningful sales volume should equal production volume.

Profit-graph shows to improve profit performance: Increase selling price. Decrease variable cost. Decrease fixed cost. Increase volume.

Margin of safety The amount or ratio by which the current volume exceeds breakeven volume.

C-V-P with Several products Relationships hold if each product has about the same contribution margin percentage. Profit-graph can be constructed by using sales revenue rather than units. Complicates C-V-P relationships: Particularly if different contribution margin percentages unless product mix remains constant. If product mix is constant can use a weighted average unit contribution.

Influences on Costs Changes in input prices. Rate at which volume changes. Rapid changes in volume make it more difficult to change personnel costs, therefore, the more likely costs depart from a straight line relationship. Direction of change in volume. Tends to be a lag in cost changes. Duration of change. Temporary changes affects costs less than a long term change.

Influences on Costs (cont.) Prior knowledge of change allows planning for change. As productivity changes costs change. Management discretion. Costs change because of management decisions. Learning curves. Productivity increases, i.e., unit production costs decrease, as the company gains experience producing the product.