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Chapter 9

Inventory Costing and Capacity Analysis

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IntroductionThe reported income number captures the attention of managers in a way few other numbers do.This chapter examines two types of cost accounting choices in which the reported income number of manufacturing companies is affected by inventories.Variable costing and absorption costing

methods treat fixed manufacturing overhead differently:Under variable costing, fixed manufacturing overhead costs are excluded from inventoriable costs and are a cost of the period in which they are incurred.Under absorption costing, these costs are inventoriable and become expenses only when a sale occurs.

Under both methods all nonmanufacturing costs in the value chain (such as research and development and marketing), whether variable or fixed, are recorded as expenses when incurred.IAS 2,10-18 mandates absorption costing for inventory valuation.

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Direct Material Inventory

Payroll Work-in-Process InventoryVariablefactorylabor

Variable Overhead

Variable Costing

All variable manufacturing costs are assigned to production and they become part of the unit cost.Fixed costs are charged to the Income Summary

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Variable Costing

Payroll Work-in-Process InventoryFixed factorylabor

Income Summary Finished Goods

Cost of Goods Sold

Absorption costing

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Comparison of Variable and Absorption Costing

Inventory values are lower with variable costing because it capitalizes only variable cost as an asset.Inventory values using absorption costing have an additional fixed factory overhead per unitIncome in periods of increasing (decreasing) inventory are higher (lower) with absorption costing than with variable costingAbsorption costing operating income

– Variable costing operating income= Fixed manufacturing costs in ending inventory

under absorption costing– Fixed manufacturing costs in beginning

inventory under absorption costing

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Inventory Buildup

Absorption costing enables a manager to increase operating income in a specific period by increasing the production schedule, even if there is no customer demand for the additional production.While the utilized part of fixed costs is inventoried, production volume variance is not.

Reducing volume variance by producing to inventory evades disclosing a larger loss due to low demand

the loss is shifted to the future unless demand rises

fixed cost in inventory

Cost in inventory

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Undesirable incentive effects

Production of items that absorb minimal fixed manufacturing costs may be delayed, even if they have a higher contribution margin.A plant manager may accept a particular order to increase production even though another plant in the same company is better suited to handle that order.A plant manager may defer maintenance and use the idle time to produce to inventory

this reduces disclosed cost and increases inventory

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Revising Performance Evaluation

1 Budget carefully and use inventory planning.2 Discontinue the use of absorption costing for

internal reporting and instead use variable costing.3 Incorporate a carrying charge for inventory.4 Lengthen the time period used to evaluate

performance5 Include nonfinancial as well as financial variables in

the measures used to evaluate performance.Sales in units this period

÷ Ending inventory in units this periodEnding inventory in units this period

÷ Ending inventory in units last period

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Inventoriable costsabsorption costing

variable costing

Throughput costing

Throughput Costing...

treats all costs except those related to variable direct materials as period costs.Only direct materials costs are inventoriable costs.

Flexible cost budget

sales volume production volume

lossRevenue,both periods

Reported loss

absorption costingvariable costing

Throughput costing

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Comparison of Inventory Costing Methods

Actual Actual oror NormalNormal

oror StandardStandardCostingCosting

AbsorptionAbsorptionCostingCosting

ThroughputThroughputCostingCosting

VariableVariableCostingCosting

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Alternative Denominator-Level Concepts

The choice of the denominator used to allocate budgeted fixed manufacturing costs to products can greatly affect the numbers a normal or standard (absorption) costing system will report prior to the end of an accounting period.

Alternative Denominator-Level ConceptsTheoretical capacity xt (maximum or ideal capacity) • based on producing at full (peak) efficiency all the time.

Practical capacity xp• reduces theoretical capacity by unavoidable operating interruptions• The use of practical capacity is required by the IRS.

Normal capacityxn• based on the level of capacity utilization that satisfies average

customer demand over several periods• mandated in IAS 2,13• includes seasonal, cyclical, and trend factors.

Master-budget capacity xm• based on the expected level of capacity utilization for the next

budget period (typically one year).

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Budgeted Fixed Manufacturing Overhead Rate

Budgeted Fixed cost

Slope = fixed overhead rate

xxm m xxnn xxpp xxttxxaa

negative volume variance

volume variance forvolume variance fornormalnormal capacitycapacity

volume variance for xxpp

forfor xxtt

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Cost data from a normal or standard costing system are often used in pricing or product-emphasis decisions.Downward Demand Spiral

The use of normal capacity utilization or master-budgetcapacity utilization can result in capacity costs being spread over a small number of output units.Downward demand spiral: continuing reduction in demand that occurs when the prices of competitors are not met and demand drops.

Decision Making

D1D2

φ1

φ2π x( )

φ x( )

x

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Chapter 10

Determining how costs behave

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Introduction

How do managers know what price to charge, whether to make or buy, or other questions related to costs.They need to have an understanding of how costs change in relation to various factors.This chapter will focus on how to determine cost behavior.

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Two Assumptions in Cost-Behavior Estimation

1. Changes in total costs can be explained by changes in the level of a single activity.

Variation in machine hours can explain variations in total costVariation in labor hours can explain variations in total cost.

2. Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range.

A linear cost function is a cost function in which the graph of total cost versus the level of a single activity is a straight line.

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Cost Function...

is a mathematical expression describing how costs change with changes in the level of an activity.Output producedDirect manufacturing labor hoursMachine hoursBatches of production

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Cost Function

La Bella Hotel offers Happy Airline three alternative cost structures to accommodate its crew overnight:$60 per night per room usage

Total room usage is the only factor whose change causes a change in total costs. The cost is variable.

$8,000 per monthThe total cost will be $8,000 per month regardless of room usage.The cost is fixed, not variable.

$3,000 per month plus $24 per roomThis is an example of a mixed cost.

What are the cost functions?

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Linear Cost Function

y = cost y

xx = activity level

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Constant Cost Function

y = cost y

$8,000

x x = activity level

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„Mixed“ Cost Function

y = cost y

$3,000

xx = activity level

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Cost Classification and Estimation

Choice of cost objectA cost item may be variable with respect to one cost object and fixed with respect to another.

Example: If the number of taxis owned by a taxi company is the cost object, annual taxi registration, and license costs would be a variable cost.If miles driven during a year on a particular taxi is the cost object, registration, and license costs for that taxi is a fixedcost.

Time spanWhether a cost is variable or fixed with respect to a particular activity depends on the time span.

More costs are variable with longer time spans.

Relevant range

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Relevant Range

Variable and fixed cost behavior patterns are valid for linear cost functions only within the given relevant range.

Costs may behave nonlinear outside the range.

pseudo-fixed cost

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Cost Estimation...

is the attempt to measure a past cost relationship between costs and the level of an activity.Managers are interested in estimating past cost-behavior functions primarily because these estimates can help them make more accurate cost predictions.The Cause-and-Effect Criterion In Choosing Cost Drivers

Physical relationship (materials costs)Contractual agreements (phone charges based on minutes)Implicitly established by logic (ordering costs driven by number of parts)

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Cost Estimation ApproachesIndustrial engineering method

also called the work-measurement method.estimates cost functions by analyzing the relationship between inputs and outputs in physical terms.

Conference methodestimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various sources.This method involves the pooling of expert knowledge.

Account analysis methodestimates cost functions by classifying cost accounts in the ledger as variable, fixed, or mixed with respect to the identified activity.Typically, managers use qualitative rather than quantitative analysis when making these cost-classification decisions.

Quantitative analysis methodsHigh-low-methodRegression analysis

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Account Analysis

Managers use judgment and experience to decompose different cost categories in differentaccountsExample: Quatisha & Co. sells software programs.

Total sales = $390,000The company sold 1,000 programs.Cost of goods sold = $130,000Manager’s salary = $60,000Secretary’s salary = $29,000Commissions = 12% of salesthe total fixed cost = $60,000 + $29,000 = $89,000

Classify these items according to fixed, proportional and mixed, and explain how todecompose mixed costs into fixed and variablecomponents

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Quantitative Analysis Methods

Quantitative analysis uses a formal mathematical method to fit linear cost functions to past data observations.Steps in Estimating a Cost Function

1 Choose the dependent variable.2 Identify the independent variable cost driver(s).3 Collect data on the dependent variable and the cost

driver(s).4 Plot the data.5 Estimate the cost function.6 Evaluate the estimated cost function.

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1 Choose the dependent variable.Choice of the dependent variable (the cost to be predicted) willdepend on the purpose for estimating a cost function.

2 Identify the independent variable cost driver(s).The independent variable (level of activity or cost driver) is the factor used to predict the dependent variable (costs).RequirementsA It should have an economically plausible

relationship with the dependent variable.B It should be accurately measurable.

3. Collect data on the dependent variable and the cost driver(s).

Cost analysts obtain data from company documents, from interviews with managers, and through special studies.– Time-series data– Cross-sectional data

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4 Plot the data.The general relationship between the cost driver and the dependent variable can readily be observed in a plot of the data.The plot highlights extreme observations that analysts should check.

CostCost ofofactivityactivity

Level ofLevel of activityactivity

Estimated cost functionEstimated cost function

Fixed cost Fixed cost

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5 Estimate the cost function C(x) = a + bx.– High-low method

Choose the highest and lowest value of the cost driver and their respective costs.Determine a and b

pseudo-fixed

cost aa

l h bb ==

aa == C(h) – bh == C(l) – bl

C(h ) – C(l )h – l

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High-Low Method

High capacity December:55,000 machine hoursCost of electricity: $80,450

Low capacity September: 30,000 machine hoursCost of electricity: $64,200

What is the variable rate?($80,450 – $64,200) ÷ (55,000 – 30,000) = $0.65

What is the fixed cost?$80,450 = Fixed cost + 55,000 x $0.65Fixed cost = $80,450 – $35,750 = $44,700$64,200 = Fixed cost + 30,000 x $0.65Fixed cost = $64,200 – $19,500 = $44,700

Cost = $44,700 + ($0.65 × Machine-hours)

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Regression Analysis...

is used to measure the average amount of change in a dependent variable, such as electricity, that is associated with unit increases in the amounts of one or more independent variables, such as machine hours.Regression analysis uses all available data to estimate the cost function.

Simple regression analysis estimates the relationship between the dependent variable and one independent variable.Multiple regression analysis estimates the relationship between the dependent variable and multiple independent variables.

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Regression Analysis

The regression equation and regression line are derived using the least-squares technique.The objective of least-squares is to develop estimates of the parameters a and b.The vertical difference (residual term) measures the distance between the actual cost and the estimated cost for each observation.The regression method is more accurate than the high-low method.

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6. Evaluate the estimated cost function.

A key aspect of estimating a cost function is choosing the appropriate cost driver.Criteria to Evaluate and Choose Cost Drivers

1 Economic plausibility2 Goodness of fit

The coefficient of determination (r²) expresses the extent to which the changes in (x) explain the variation in (y).An (r²) of 0.80 indicates that more than 80 percent of the change in the dependent variable can be explained by the change in the independent variable.

3 Slope of the regression lineA relatively steep slope indicates a strong relationship between the cost driver and costs.A relatively flat regression line indicates a weak relationship between the cost driver and costs.

( )( )∑

∑−

−= 2

22 ˆ

yyyy

rkk

kk

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Nonlinearity and Cost FunctionsA nonlinear cost function is a cost function in which the graph of total costs versus the level of a single activity is not a straight line within the relevant range.Economies of scale

Economies of scale in advertising may enable an advertising agency to double the number of advertisements for less than double the cost.

Quantity discountsQuantity discounts on direct materials purchases produce a lower cost per unit purchased with larger orders.

Learning Curves / Experience Curvea function that shows how labor-hours per unit decline as units of output increase.a function that shows how the costs per unit in various value chain areas decline as units produced and sold increase.

Step cost functionscost is constant over various ranges of the level of activity, but the cost increases by discrete amounts as the level of activity changes from one range to the next.

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Learning Models

Cumulative Average Time Learning Model:Cumulative average time per unit is reduced by a constant percentage each time the cumulative quantity of units produced is doubled.

Cumulative average time per unit =

Y/X= aXb

Incremental unit-time Learning Model: The time needed to produce the last unit is reduced by a constant percentage each time the cumulative quantity of units produced is doubled.

Total time for cumulative output (Y)Cumulative output (X)

dYdX

= αX β

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a = 100, learning rate = 80%, X = 1,2,3,4

Cumulative Average-Time Learning Model

Incremental Unit-Time Learning Model

Number of units Cumulative average labor hours per unit

Cumulative total labor hours

Individual time for Xth unit

1 100 100 100 2 80 160 60 3 70.21 210.63 50.63 4 64 256 45.37

Number of units Individual time for Xth unit

Cumulative total labor hours

Cumulative average labor hours per unit

1 100 100 100 2 80 180 90 3 70.21 250.21 83.40 4 64 314.21 78.55

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Data Collection and Adjustment IssuesThe ideal database for cost estimation has two characteristics:

1 It contains numerous reliably measured observations of the cost driver(s) and the cost that is the dependent variable.

2 It considers many values for the cost driver that span a wide range.Pitfalls:

Time periods do not match.Fixed costs are allocated as if they were variable.Data are either not available or not reliable.Inflation may play a role. Extreme values of observations occur from errors in recording costs.• Analysts should adjust or eliminate unusual observations before

estimating a cost relationship.There is no homogeneous relationship.The relationship between the cost driver and the cost is not stationary

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Multivariate Regression: Tests

F-Test: Can the null hypothesis be rejected that all the estimated coefficients are zero?t-Test: Is a single cost driver „significant“?

means: is the estimated b-value for the cost driver greater than its standard error (the expected random effects on the estimate, according to the assumed normal error distribution) ?

Durbin-Watson Test: independence of residuals, autocorrelationLinearity: look at the plotGoldfeldt-Quandt Test: Heteroscedasticity would lead to erroneous estimated standard errorsMulticollinearity: cost drivers in a multivariate regression are correlated: standard errors are over estimated; t-Test disturbed.

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Quiz

1. A mixed cost function has a constant component of $20,000. If the total cost is $60,000 and the independent variable has the value 200, what is the value of the slope coefficient?a. $200 b. $400 c. $600 d. $40,000

2. Of the following methods, the one that would not be appropriate for analyzing how a specific cost behaves is

a. the scattergraph method.b. the industrial engineering approach.c. linear programming.d. statistical regression analysis.

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Quiz

3. When the high-low method is used to estimate a cost function, the variable cost per unit is found bya. performing regression analysis on the associated cost and cost driver database.b. subtracting the fixed cost per unit from the total cost per unit based on either the highest or lowest observation of the cost driver.c. dividing the difference between the highest and lowest observations of the cost driver by the difference between costs associated with the highest and lowest observations of the cost driver.d. dividing the difference between costs associated with the highest and lowest observations of the cost driver by the difference between the highest and lowest observations of the cost driver.

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Quiz

4. Tory Company derived the following cost relationship from a regression analysis of its monthly manufacturing overhead cost.

y = $80,000 + $12Xwhere:

y = monthly manufacturing overhead costX = machine-hours

The standard error of estimate of the regression is $6,000.

The standard time required to manufacture one six-unit case of Tory’s single product is four machine-hours. Tory applies manufacturing overhead to production on the basis of machine-hours, and its normal annual production is 50,000 cases.

Tory’s estimated variable manufacturing overhead cost for a month in which scheduled production is 10,000 cases would bea. $80,000. b. $480,000. c. $160,000. d. $320,000.

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Quiz

5. Tory Company derived the following cost relationship from a regression analysis of its monthly manufacturing overhead cost.

y = $80,000 + $12Xwhere:

y = monthly manufacturing overhead costX = machine-hours

The standard error of estimate of the regression is $6,000.

The standard time required to manufacture one six-unit case of Tory’s single product is four machine-hours. Tory applies manufacturing overhead to production on the basis of machine-hours, and its normal annual production is 50,000 cases.

1. Tory’s predetermined fixed manufacturing overhead rate would bea. $4.80/MH. b. $4.00/MH. c. $3.20/MH. d. $1.60/MH.

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Quiz

6. Three criteria to use in identifying cost drivers from the potentially large set of independent variables that can be included in a regression model are

a. goodness of fit, size of the intercept term, and specification analysis.

b. independence between independent variables, economic plausibility, and specification analysis.

c. economic plausibility, goodness of fit, and significance of independent variable.

d. spurious correlation, expense of gathering data, andmulticollinearity.

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Quiz

7. Companies that take advantage of quantity discounts in purchasing their materials have

a. decreasing cost functions.b. linear cost functions.c. nonlinear cost functions.d. stationary cost functions.

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Quiz

8. Stone Isle Manufacturing recently completed and sold an order of 50 units having the following costs:Direct materials $ 1,500Direct labor (1,000 hours @ $8.50) 8,500Variable overhead (1,000 hours @ $4.00)¹ 4,000Fixed overhead² 1,400

$15,400¹Allocated on the basis of direct labor-hours.²Allocated at the rate of 10% of variable cost.

The company has now been requested to prepare a bid for 150 units of the same product.

If an 80% learning curve is applicable, Stone Isle’s total cost on this order would be estimated ata. $26,400. b. $31,790. c. $37,950. d. $38,500.

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Quiz9. Stone Isle Manufacturing recently completed and sold an order of 50 units having the following costs:Direct materials $ 1,500Direct labor (1,000 hours @ $8.50) 8,500Variable overhead (1,000 hours @ $4.00)¹ 4,000Fixed overhead² 1,400

$15,400¹Allocated on the basis of direct labor-hours.²Allocated at the rate of 10% of variable cost.

The company has now been requested to prepare a bid for 150 units of the same product.

If Stone Isle had experienced a 70% learning curve, the bid for the 150 units would

a. show a 30% reduction in the total direct labor-hours required with no learning curve.

b. include 6.40 direct labor-hours per unit at $8.50 per hour.c. include 1,404 total direct labor-hours at $8.50 per hour.

d. be 10% lower than the total bid at an 80% learning curve.

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Quiz

10. Which of the following is not a common problem encountered in collecting data for cost estimation?

a. Lack of observing extreme valuesb. Missing datac. Changes in technologyd. Distortions resulting from inflation