The Behavior of Costs1-*

1-*Behavior of CostsCost-volume relationships.Fixed and variable costs.Step-function costs.

1-*Relation of costs to volumeHigher 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 with volumeSemivariable costs = semifixed costs = partly variable costs = mixed costs = costs that include a combination of variable and fixed cost items.

1-*Variable CostsItems 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.

1-*Fixed costsNon-variable costs = items of cost that, in total, do not vary with volume.Examples: Building rent, property taxes, management salaries.Fixed cost per unit of activity decreases as the level of activity increases.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.

1-*Cost-volume (C-V) diagramY 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.

1-*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*XFixed cost line: TC = TFCSemivariable cost: TC = TFC + (UVC*X).

1-*Cost RelationsAverage 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.

1-*Limitations of C-V RelationsA 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.

1-*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.

1-*Sticky CostsGenerally 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.

1-*Step-function costsSome items of costs may vary in steps 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 cost of adding incremental capacity.Step width (tread) shows how much additional volume of activity can be serviced by an additional increment of capacity.

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

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

1-*Third method: High-Low methodEstimate 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 unit volume times unit variable costs.

1-*Measures of volumeHave 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.

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

1-*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.

1-*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, use of labor costs as an activity measure implicitly allows for price changes.Best volume measure should be related to the activity that causes cost.

1-*Profit-graphAdd revenue line to C-V diagram.Assumes constant selling price.UP = unit price= selling priceTR = total revenue

Contribution Analysis1-*

1-*Breakeven volumeTR = UP*XTC = TFC + (UVC*X)Breakeven: TR = TCSubstituting: UP*X = TFC + (UVC*X) X = TFC/(UP - UVC)

1-*Target ProfitAdd to breakeven analysis to show units or dollar of sales to achieve a target (T) level of profit:

UP*X = TFC + (UVC*X) + T

X = (TFC+T)/(UP - UVC)

1-*Break-even volumeIn units = Fixed costs/unit contributionIn revenue dollars = Fixed costs / contribution percentContribution percent = contribution margin percentage = contribution as a percent of revenues = (UP - UVC)/ UP

1-*Cash versus accrual profit-graphsSo 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.

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

1-*C-V-P with Several productsRelationships hold if each product has a similar 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.

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

Contribution (Contd..)Contribution Margin per Unit equals unit selling price less variable cost per unit CMu = SP VCuContribution Margin also equals contribution margin per unit multiplied by the number of units sold (Q)CM = CMu x QContribution Margin Ratio (percentage) equals contribution margin per unit divided by Selling PriceCMR = CMu SPInterpretation: how many $/Rs. out of every sales $/Rs are represented by Contribution Margin.

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1-*Margin of safetyThe amount or ratio by which current volume exceeds breakeven volume.One indicator of risk, the Margin of Safety (MOS) measures the distance between budgeted sales and breakeven sales:MOS = Budgeted Sales BE SalesThe MOS Ratio removes the firms size from the output, and expresses itself in the form of a percentage:MOS Ratio = MOS Budgeted Sales

Thank You1-*