Chapter 10: Determining How Costs Behave

resource usage model

-can improve managerial control and decision making by encouraging mgers to pay more attn to controlling resource acquisition and usage -the model highlights the fact that reducing the quantity of an activity does not automatically lead to a reduction in costs -ex. a company may have 100 direct laborers that are being fully utilized to produce their products -by developing more efficient work methods, the company can now produce the same output of products w/ only 80 workers (ie a 20% reduction) -total labor costs will only go down to the extent thtat these 20 laborers are laid off or are redeployed into other areas needing add'l laborers -if they are retained in the same position, then the company will have excess or unused capacity w/ regard to labor

three criteria often used to evaluate cost drivers:

-economic plausibility: Is the cost driver and the cost related? Does it make sense that an increase in the independent variable will cause an increase in the costs? -goodness of fit: Are the differences b/w the actual costs and predicted costs small? In a LSR analysis, goodness of fit is measured by the R^2 state? Does it have a good/high R^2? -significance of independent variable: according to the text, if the regression line (or total cost line) has a steep slope, this indicates a strong relationship b/w the cost driver and the costs incurred --also, LSR software packages provide a statistical test statistic on the slope coefficient (ie testing whether it is is different from zero) --it is more imp. that the slope coefficient is statistically significant rather than steep

when are fixed costs unitized?

-for product-costing purposes, we unitize fixed costs -for decision-making purposes, per-unit fixed costs can be misleading b/c they differ at each level of output, so be careful when making decisions using per-unit fixed cost data

high-low limitations

-it relies on the two most extreme observations (w/ regard to the independent variable, but these may not be the most representative points -it ignores info in the other observations that may be useful in estimating the cost function -it can produce estimates that vary dramatically with the inclusion of a new high or low observation -it doesn't provide any insight on how well the estimated equation fits the data - there is no statistical measure of goodness of fit

what is our main objective?

-our main objective is to build models that provide accurate cost predictions for mgmt planning purposes -LSR is the tool you would probs use to do this -our discussion has not addressed the statistical issues surrounding LSR -these issues are imp., but they would be covered in an upper-division stats class

performance evaluation

-recall that a variance is computed by comparing actual performance w/ budgeted performance -if learning occurs, then the budgeted time allowed needs to be reduced to reflect this -mgers shouldn't allow 8 hrs for a process that will eventually take 6 t operform -b/c people will perform to the level needed to beat the budget it's likely that the workers won't work as efficiently as possible -moreover, rewarding a person for barely beating the eight-hour goal is meaningless when the person is capable of doing it in six hours -in the end, the company will have excess labor capacity and labor costs that are too high -application of learning curves

two takeaways from MT and AT learning curve models

-the incremental (marginal) time lies below the avg time - in fact, the incremental (marg) time is pulling the avg down -the rate of learning slows down as more experience is gained

coefficient of determination in regression analysis

-used to determine the proportion of the total variation in the dependent variable (y) explained by the independent variable (x) -sqaure of the coefficient of correlation -the higher the coefficient of determination, the greater the proportion of the total variation in y that is explained by the variation in x -the higher it is, the better is the fit of the regression line

solving learning curves w/o formulas

-you can solve doubling points without formulas (1, 2, 4, 8, 16, 32) -you need formula for nondoubling points

applications of learning curves

1. bidding on a large contract 2. performance evaluation

six steps when estimating a mixed-cost equation w/ historical data

1. choose the total cost that we wish to predict (ie choose y) 2. choose the activity measure (x) - there should be a cause-and-effect relationship b/w x and the resulting cost y (ie it should be a cost drive) 3. collect historical data on x and y - collect ordered pairs of observations 4. plot data on a scatterplot - this will help determine whether -there is a positive linear relationship bw x and y -there are outliers that can adversely affect the estimation of the cost function 5. estimate the cost function using one of the two methods (highlow or least squares) 6. evaluate the estimated cost function - you want a cost function that is -economically plausible (based on a cause-and effect economic relation) -fits the data well. this is measured by the coefficient of determination when least squares regression is used

two approaches to estimating mixed costs

1. high-low method 2. least squares regression

committed resources

acquired in advance of usage - a given quantity of a resource is acquired regardless of whether the resource will be fully used -b/c of this, there are situations when you have excess or unused capacity (ie quantity acquired > quantity used) -a characteristic of committed resources is that any unused capacity cannot be inventoried and used next period -generally fixed costs or step-fixed -committed fixed costs and discretionary fixed costs - which are defined by how long we are committed to these costs

flexible resources

acquired when needed -acquired from outside sources w/ no long-term commitments -ex. electricity to run the factory equipment -the quantity of resources acquired = resource quantity used -no escess capacity -the cost of the resource increases as resource usage increases, so we view the cost as variable costs

if the level of volume falls from a point w/in the relevant range to a point below the lower boundary of the relevant range

both variable costs per unit and fixed costs in total could change

relevant range and mixed-cost equations

cost relationships are only valid w/in the relevant range, so don't use the estimated equations to predict costs outside the relevant range -the equation is based on observations w/in the relevant range, so it should only be used to make prediction w/in the relevant range

mixed cost

cost that has both a variable and a fixed component -producing a product in a factory will use both variable and fixed cost (ie cost is a mixed cost)

variable cost

cost that varies in direct proportion changes in an acitivity measure such as DL hours or machine hours -the activity measure can also be called the cost driver of the variable cost

step costs functions

costs are defined for ranges of activity rather than specific values -functions have the property of displaying a cost cost over a range of activity and then "jumping" to a different cost level as a new range of activity is encountered -step-variable costs -step-fixed costs

committed fixed costs

costs associated w/ resources acquired thru explicit long-term contracts and provide long-term capacity (ex. 5 yr lease on a building) -cannot be easily changed in the short run -LR

discretionary fixed costs

costs associated w/ resources acquired thru implicit contracts and provide short-term capacity (ex. most employment arrangements) -these costs can be changed in the short-run, if needed -SR

unit-level drivers

costs change as the number of units produced change -ie cost is a variable cost -ex. # of product produced, direct labor hours, machine hours, pounds of direct material, and kilowatt hrs used to run production machinery

fixed costs

costs that don't change in total as the activity measure changes -thus, the activity measure is not a cost driver for the fixed cost

step-variable costs

costs that remain constant over a relatively narrow range of activity -ex. if machines need to be lubricated after producing 100 units then lubrication costs would jump every 100 units -generally if the width of the step is narrow, we will usually approximate a step-variable cost as a strictly variable cost -if the cost of lube is $25, we would treat is as a variable cost of $0.25 ($25/100 units)

step-fixed costs

costs that remain constant over a wide range of activity -ex. if each machine can produce 10k units a week, then a new machine would need to be acquired at each 10k increment -many costs are step-fixed in nature - ex. equipment, people

how is it determined whether a cost is fixed or variable?

depends on how the cost changes in total with changes in the activity measure

resources

economic inputs consumed in performing activities -acquiring resources gives you the capacity to perform activities (ex. renting a machine or hiring a salesperson) -some resources are acquired when needed while others are acquired in advance of usage -commited/flexivle resources

learning curve

function that shows how labor time per unit decreases as output increases -two models: incremental (marginal) unit-time learning model and cumulative average-time learning model -mgers decide b/w models on a case by case basis

what additional statistical information can be used to assess how reliable the estimated cost function is using LSR

goodness of fit statistic - called the coefficient of determination (Or R^2) -it measures how well the independent variable explains variation in the dependent variable -it is interpreted as the percentage of variability in the dependent variable (ex. cost) that is explained by the independent variable (ex. activity measure), so it's value is b/w 0 and 1 (ie b/w 0 and 100%) --given the types of cost functions we are estimating, we should obtain high R^2s (above 70%)

in short run relevant range

in short run, for a given plant size, variable costs will be approximately linear w/in the relevant range -economists often suggest that below the relevant range variable costs would increase at a decreasing rate (reflecting increasing returns to the variable input) and above the relevant range they would increase at an increasing rate (reflecting decreasing returns to the variable input

learning curve formula

incremental or average time = pX^q or aX^b where p- the time reqd to produce the first unit x- the cumulative number of units produced q = the index of learning (where q is calculated as q= ln(% learning /ln2) -note that the formula is the same, but interpretation differs depending on which model you're using

learning

instead of assuming that variable costs change in direct proportion to changes in the cost driver (linear), we assume that workers get faster as they get more experience performing repetitive tasks (learn) -ex. direct labor time per unit decreases as production increases which will decrease DL cost per unit

be careful to not say it cost 13.33/unit b/c

it's only true at that unit level of production (ex. 300 units)

bidding on a large contract

it's unlikely that the company will receive the contract (ie their bid will be too high) if learning isn't taken into consideration -if workers will become more efficient, then this needs to be taken into consideration -application of learning curves

mixed costs

many costs encountered by firms are mixed (they have both fixed and variable elements) -predicting these costs underlies many of the topics in mgmt accounting: --planning (ex. cost-volume-profit analysis and budgeting) --controlling (ex. comparing actual and budgeted costs) --decision making (ex. pricing and nonroutine decisions)

high low method

merely fitting a straight line through two points -always choose the points associated w/ the hgih and low activity levels (high and low x values), regardless of the associated y values (note that the high and low x values may not correspond to the high and low y values -basically find line

do fixed costs change with changes in activity measure?

no, they don't, but if unitized (put on a per-unit basis), the constant total fixed cost implies that per-unit fixed costs are inversely related to the cost driver (when X goes up, AFC goes down)

nonunit-level drivers

not a pure variable cost w/ respect to production output -examples include: equipment setups, inspection hours, and material moves -often step-fixed costs

cost behavior

refers to the way in which costs react to changes in an actibity measure -variable, fixed, mixed costs

high-low method advantage

simple and objective

cumulative avg-time learning model

states that the cumulative avg time per unit is reduced by a constant percentage each time the quantity of units produced is doubled -ex. 80 % LC, when quantity is doubled, x to 2x, the average time per unit for 2x is 80% of the time for x -formula gives you AT, then multiply by units to get TT, then subtract times (TTn-TTn-1) to get MT

incremental (marginal) unit-time learning model

states that the incremental unit time (the time needed to produce the last unit) is reduced by a constant percentage each time that the cumulative quantity of units produced is doubled -learning curve model -ex. 80% LC - when quantity of untis produced is doubled from x to 2x the time needed to produce the unit corresponding to 2x is 80% of the time needed to produce the Xth unit -formula gives you MT, then add these to give you TT, then divide by total units to get AT

relevant range

the range of the cost driver over which cost relationships are valid -the range over which fixed costs remain constant and variable costs vary in direct proportion with the cost driver -can be viewed as the firm's normal operating range and is a short-run concept, but in LR firm's relevant range can change --fixed costs would (increase) decrease if you were going to (increase) decrease activity outside the relevant range --ex. increasing output beyond the upper limit of the relevant range would reguire the acquisition of add'l equipment that would in turn increase depr charges -an imp. concept with cost behavior

are marginal variable cost and average (per-unit) variable cost equal?

they are numerically the same regardless of output level b/c total variable costs change in direct proportion to changes in the activity measure (or cost driver), but they are conceptually different MCn = TCn-TCn-1 = TVCn-TVCn-1

objective of high-low and least squares

to estimate a linear cost function in following form: y=a+bx -where a is estimated component of total costs that w/in the relevant range, doesn't vary w/ changes in the level of x (the cost driver), also called the y-intercept, is an estimate of total fixed costs w/in the relevant range, but does NOT represent an estimate of total fixed costs at zero activity b/c that is out of relevant range -b is an estimate of the variable cost per unit of x the cost driver, also called the slope coefficient -x is the level of the activity measure (cost driver) and is also called the independent variable -y is the estimated total cost (at a given level of x) and also called dependent variable also equal to TC = TFC + TVC where TC is the total cost estimate (y), TFC is the total fixed cost estimate (a), and TVC is the total variable cost estimate (bx)

least squares regression

to overcome weaknesses in high-low method, you would generally use least squares regression (LSR) -minimizes sum of residuals (squared distance from point to line) -simple and multiple regression equations can be calculated using Excel as well as more sophisticated statistical software packages -conceptually the LSR equation is the best line in the sense that it minimizes the sum of the squared deviations from the line

simple regression

uses one independent variable to predict costs whereas multiple regression uses more than one independent variable -multiple regression may be the preferable method given that many costs in reality have multiple cost drivers, but we only use simple in class

does experience matter?

yes, in addition to the cost estimating techniques discussed in this chapter, mgers often use their own judgment and experience when separating mixed costs into fixed and variable components