Behavior of Costs
Behavior of Costs and BEP AnalysisSessions 4-6 Behavior of CostsCost-volume relationshipsFixed and variable costsStep-function costs
Relation of costs to volumeHigher volume causes higher costsVariable costs = items of cost that vary, in total, directly and proportionately with volumeFixed 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
TC = TFC +(UVC*X)TC = total cost; TFC = total fixed cost (per time period),UVC = Unit variable cost (per unit of volume),X = volumeEquations for:[Illustration 16-1]Variable cost line: TC = UVC*XFixed cost line: TC = TFCSemivariable cost: TC = TFC + (UVC*X)
Cost RelationsAverage costs = total cost/volumeAverage cost behaves differently than total costAs 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 downAs volume increases without limit, unit cost approaches variable unit cost and fixed cost per unit approaches zero
Limitations of C-V RelationsA straight line approximates cost behavior only within a certain range of volume, the relevant rangeWhen volume approaches zero, management takes steps to reduce fixed costsWhen volume exceeds relevant range, fixed costs increase
Limitations 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 variableOver an extremely long time period, no costs are fixedEnvironmental assumptions must be made.Wage rates, fringe benefits, material prices, technology changes
Problem 16-1Categories of CostsSolutionCost of raw materials used by students Variable Costs Graph BDepreciation of machinery and equipment used Fixed Costs Graph ACost of Blueprint and manuals Semi Variable Costs[Step Costs]-Graph DUtilities and Maintenance- Semi variable costs -Graph C
Sticky CostsGenerally considered variable but fall less with decreases of activity than they rise with increases [Illustration 16-5]Managers tend to increase resources more quickly than they decreaseExamples:Sales commissions with minimum guaranteesManagers slower to fire employees than to hireStep-function costsIncurred when costs are added in discrete chunks, e.g. a supervisor for every 10 workersAdding the chunk of costs increases capacityHeight of a stair step (riser) indicates cost of adding incremental capacityStep width (tread) shows how much additional volume of activity can be serviced by an additional increment of capacityStep function If treads are narrow and risers are low (i.e. steps are small), then steps can be approximated by a variable cost lineIf 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 periodStep functions are often hidden in C-V diagrams as either variable or fixed costs
Profit-graphAdd revenue line to C-V diagramAssumes constant selling priceUP = unit price= selling priceTR = total revenue
Breakeven volumeTR = UP*XTC = TFC + (UVC*X)Breakeven: TR = TCSubstituting: UP*X = TFC + (UVC*X) X = TFC/(UP - UVC)
- Page no.469: Illustration
ContributionUnit contribution = unit contribution margin = marginal income = unit selling price - variable cost per unit = UP - UVCI = total income = (UP - UVC) * X - TFCWhat is contribution: [ Illustration 16-11]First: contribution to cover fixed costsThen: contribution toward profit
Break-even volumeIn units = Fixed costs in Rs /unit contribution in RsIn revenue Rs = Fixed costs in Rs / contribution percentContribution percent = contribution margin percentage = contribution as a percent of revenues = (UP - UVC)/ UP
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)Cash versus accrual profit-graphsSo far we have considered profit and costs on an accrual basisTo 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 how to improve profit performance:[Illustration 16-3]Increase selling priceDecrease variable costDecrease fixed costIncrease volume
Margin of SafetyExcess of actual sales over BEP sales in units or in RsFor E-g: [200 less 160 units/ 200 units ]*100= 20%Several Products2 OptionsBEP Product wise computationWeighted Average Contribution based BEP
Refer Exhibit 3 of Case 16-3 : Bill FrenchMeasures of volume So far we have assumed a single-productIf multiple products, with different cost structures, unlikely that units would be a reliable measure of activityPossible common denominators include: labor hours, labor dollars, machine hours, homogeneous quantities such as tons or barrels and sales valueQuestions to consider in selecting a volume measureInput (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 materialOutput measures: units or dollarsManufacturing firms might use input measures such as labor or machine hoursRetail 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 advantagesIf price changes affect all costs equally, use of labor costs as an activity measure implicitly allows for price changesBest volume measure should be related to the activity that causes costThe more items of cost that are combined in the cost function the more difficult it is to relate causality to a single measure
Operating LeverageVolumeFixed CostVariable CostTotal CostRevenue Profit200400200*6=1,2001,600200*8.5=1,700100300400300*6=1,8002,200300*8.5=2,550350Change 50%[+]No change50% change[+]37.5% change [+]50% change[+]250 % change [+]Operating LeverageAs production volume increases, average per unit cost decreases because the average fixed cost decreases= Change in profit / change in volume= 250% / 50% = 5 times
Leverage works both the ways
Other Influences of CostsChanges in Input PricesRate of Volume ChangeDirection of Change in VolumeDuration of Change in VolumePrior Knowledge of the changeProductivityManagement Discretion- Learning Curve [Appendix]Case 16-1Hospital Supply, Inc Case 16-1[1] BEP in units and sales value?[2] Do you recommend a price cut from $4,350 to $3,850? What would be the impact on monthly sales, costs and income?[3] What impact would accepting the government contract have on March Income?[4] What is the minimum unit price it should consider for accepting the foreign market order of 1000 units?31Case 16-1[5] what is the minimum price that would be acceptable in selling 200 units of an obsolete model?[6] what in-house unit cost should be used to compare with the quotation received from the supplier? Should the proposal be accepted for a price [payment to the contractor] of $2,475 per unit?[7] What is the maximum purchase price per unit that Hospital Supply should be willing to pay the outside contractor? Should the proposal be accepted for a price of $ 2,475 per unit to the contractor?
Q-1:BEP in units and sales value?Total Fixed Costs = FC per unit times normal volume = {660+770}*3000 = $42,90,000-Contribution margin per unit = SP-VC= 4,350-2,070= $2,280Therefore BEP in units = $ 42,90,000/2,280 = 1,882 unitsBEP in sales = 42,90,000/ {2,280/4,350} = $81,85,461= or 1,882* $4,350=$81,86,700
2.Do you recommend a price cut from $4,350 to $3,850? What would be the impact on monthly sales, costs and income?ParticularsBefore Price Reduction [ in $]After PriceReduction [in $]Difference[in $]Selling Price4,3503,850 {500}Quantity3,000 units3,500 units 500Revenue1,30,50,0001,34,75,0004,25,000Variable Manufacturing Costs{53,85,000}{62,82,500}{8,97,500}Variable Marketing costs{8,25,000}{9,62,500}{1,37,500}Contribution margin68,40,00062,30,000{6,10,000}Fixed manufacturing costs{19,80,000}{19,80,000}-Fixed marketing costs{23,10,000}{23,10,000}-Income Before Tax 25,50,00019,40,000{6,10,000}Recommendations-Q-2The differential contribution margin and differential income are the sameLowering prices reduces income, hence the company should not reduce the priceQ-3: what impact would accepting the government contract have on March Income?Particulars{1} Without government contract [in$] {2}Regular[in $]{3}-3500 unitsGovernment[in $]{4}- 500 unitsTotal{5} ={3+4}Difference
{2-5}
Revenue1,74,00,0001,52,25,00014,20,0001,66,45,000{7,55,000}Less: Variable mfg,,Mktg costs71,80,00011,00,00062,82,500 9,62,5008,97,500------------------71,80,000 9,62,500----------------- 1,37,500Contribution margin91,20,00079,80,0005,22,50085,02,500{6,17,500}Less:Fixed mfg cost
,,Mktg costs19,80,000
23,10,00019,80,000
23,10,000-----------------
-----------------Income Before Tax 48,30,00042,12,500[6,17,500}RecommendationAccepting government order reduces the profit amount Q-4: what is the minimum unit price Hospital Supply should consider for accepting the foreign market order of 1000 units?Using the BEP formulaeX units= TFC / {UR-UVC}= 1000 units = 22,000 / {UR- 2,205}1000[UR-2,205} = 22,0001000 UR 22,05,000 = 22,0001000 UR = 22,27,000Therefore UR = 22,27,000/1000 = 2,227 $ Q-5:what is the minimum price that would be acceptable in selling 200 units of an obsolete model?-The manufacturing costs are sunkAny price in excess of the differential costs of selling the hoists will add to incomeHere the differential costs = $275 per unit variable marketing costs= the minimum priceUnder opportunity cost concept, the price should exceed the sum of {a] the differential marketing costs and {b} the potential scrap proceedsQ-6: what in-house unit cost should be used to compare with the quotation received from the supplier? Should the proposal be accepted for a price [payment to the contractor] of $2,475 per unit?ParticularsAll ProductionIn-house [ in $ ]-3,000 unitsUnits contracted and 2000 units in house production [in $]Total Revenue1,30,50,0001,30,50,000Less:Total variable manufacturing costs,, ,, Mktg costs53,85,000 8,25,00035,90,000 7,70,000Total Contribution Margin68,40,00086,90,000Less: Total fixed mfg costsTotal fixed mktg costs19,80,00023,10,00013,86,00023,10,000
Payment to contractor--------------------XIncome Before Tax 25,50,00049,94,000 - XQ-6 : Solution49,94,000 X = 25,50,000
Therefore X = 24,44,000 or
$ 2,444 per unit as the maximum purchase priceTherefore at $ 2,475 purchase price is not acceptable ; it would decrease income by $31,000 i.e{2,475-2,444} * 1000Q.7: What is the maximum purchase price per unit that Hospital Supply should be willing to pay the outside contractor? Should the proposal be accepted for a price of $ 2,475 per unit to the contractor?Particulars3000 regular hoists produced in-houseRegular[In][2000 units]Regular [out][1000 units]Modified[800 units]TotalRevenue1,30,50,00087,00,00043,50,00039,60,0001,70,10,000Less:v.mfg.costsv.mkt.costs53,85,000 8,25,00035,90,000 5,50,000---------2,20,00024,20,000 4,40,00060,10,00012,10,000Contribution margin68,40,00045,60,00041,30,00011,00,00097,90,000 F.mfg.costs F.mktg.costs19,80,00023,10,000
--------------------------19,80,00023,10,000Payment to contractor------X---XIncome Before Tax25,50,00055,00,000- xQ-7: Maximum payment55,00,000 -X= 25,50,000X = $ 29,50,000 OR $ 2,950 per unit = maximum price
Now the proposal should be accepted at a price of $2,475Prestige Telephone CompanyCase 16-2 Questions..Which expenses are variable with respect to revenue hours? Which expenses are fixed with respect to revenue hours?For each expense that is not variable with respect to revenue hours calculate the cost per revenue hourCreate a contribution margin income statement for Prestige Data Services. Assume that intra-company usage is 205 hours. Assume commercial usage is at the March levelQuestions..4. Assuming the intra-company demand for service will average 205 hours per month, what level of commercial revenue hours of computer use would be necessary to break even each month5. Estimate the effect on income of each of the options as followsIncreasing the price to commercial customers to $1,000 per hour would reduce demand by 30%Reducing the price to commercial customers to $600 per hour would increase demand by 30%Increased promotion would increase revenue hours by up to 30%. Bradley is unsure how much promotion this would take. [ How much could be spent and still leave Prestige Data Services with no reported loss each month if commercial hours were increased 30%]16 hours operations on weekdays and 8 hours on Saturdays result in 20% of commercial revenue hours
Questions6. Based on your analysis above, is Prestige Data Services really a problem to Prestige Telephone Company? What should Rowe do about Prestige Data Services?
SolutionQ-1:Which expenses are variable with respect to revenue hours? ExpenseAmount [ in $]Variable Expenses
Materials [Jan = 27.44; Feb= 27.63 & March = 28.58]28.58 Power cost per hour [ based on segregation into fixed and variable using high-low method ] 4.70Operations wages[ based on segregation into fixed and variable using high-low method ]
24 Total Variable Expenses per hour57.28Q-1: Which expenses are fixed with respect to revenue hours?ExpenseAmount [ in $]Non variable Expenses SpaceCustodialComputer LeaseComputer MaintenanceDepreciation on computer equipment and office equipment and fixturesPower cost [High-low method] 8,000 1,24095,000 5,400 26,180106 Wages& Salaries [ Non-Variable Expenses] Operations [ High-low method] Systems development Administration Sales 21,60012,000 9,000 11,200Sales Promotion [ assumed as programmed cost] 8,000Corporate Services 15,400Total Non-variable Expenses2,13,126Q-2: Cost per revenue hourExpenseAmount [ in $]Cost per revenue hour [ March]-361Non variable Expenses SpaceCustodialComputer LeaseComputer MaintenanceDepreciation on computer equipment and office equipment and fixturesPower Cost[ High Low Method] 8,000 1,24095,000 5,400 26,18010622.16 3.43263.1614.96
72.520.29 Wages& Salaries [ Non-Variable Expenses] Operations Systems development Administration Sales 21,60012,000 9,000 11,20059.8333.2424.9331.03Sales Promotion [ assumed as programmed cost] 8,00022.17Corporate Services 15,40042.66Total Non-variable Expenses2,13,126590.38Q-2: cost per revenue hourCategoryCost per revenue hour[Based on March= 361 hours] Total Variable cost per revenue hour 57.28Total Non-variable expenses per revenue hour590.38Total expenses per revenue hour647.66Q-3: Contribution Margin Income Statement [illustration]ParticularsAmount [in INR]Amount [in INR]Revenues*****Less: Variable Costs Variable mfg. costs Variable non-mfg costs*********Contribution Margin***Less: Fixed CostsFixed mfg costsFixed non-mfg costs*********Operating Income before tax***Contribution Income Statement of Prestige Telephone Company[March Com.usage]ParticularsAmount [in $]Amount [in $]Revenues[at 205 intra company and 138 commercial usage]205*400 = 82,000
138*800 = 1,10,4001,92,400Less: Variable CostsPower cost Operations wages Material Total Variable costs4.70* 343= 1,61224*343= 8,23228.58*343 = 9,8031,6128,2329,80319,647Contribution Margin1,72,753 [ per hour = 503.65]Less: Fixed Costs2,13,126Operating Income[loss][40,373]Q-4 : Assuming the intra-company demand for service will average 205 hours per month, what level of commercial revenue hours of computer use would be necessary to break even each monthBEP in hours for Commercial demand= {TFC-allowed costs after VC of Intra company operations }/ Contribution per hour=2,13,126 - [82,000 {205 hours*57.28=11,743} ] / {800- 57.28}= [2,13,126 70,257]/ 742.72= 1,42,869/742.72 = 192.36 or 193 hoursQ-5: Analyzing options[a] increase in price to commercial customers to $1,000 per hour- expected to reduce demand by 30% from 138 hours in March 2004 to 97 hours [ 138*.70 = 96.6 hours]Contribution = 97 hours *[1,000- 57.28] = $91,444Present Contribution= 138 hours * {800- 57.28} = $1,02,496Therefore income will be higher if the firm retains the selling price at the present level Q-5: Analyzing options[b] Reducing the price to commercial customers to $600 per hour- expected to increase demand by 30% to 179 hours [ 138* 1.30 = 179.4 hours] Present contribution = $1,02,496Expected contribution from the proposal= 179 hours * [$600-$ 57.28] = $ 97,147Therefore price reduction decreases profit by $ 5,349 per monthQ-5: Analyzing Options[c] How much could be spent and still leave Prestige Data Services with no loss when commercial hours are increased by 30%?30% increase in commercial hours lead to 179 hours per monthTotal contribution = 179 hours * [$800-$ 57.28]=$1,32,947 and the present contribution is at $ 1,02,496 therefore $ 30,451 could be spent without reducing incomeQ5 [d] Reducing operations to 16 hrs on weekdays and 8 hrs on saturdays with a 20% decrease in comm.hrsPresent Contribution: $1,02,496Revised Commercial Hours : 138 *0.8 = 110.4 = 111 hoursContribution Per Hour at the existing rate = 800- 57.28 $ = $ 742.72Revised Contribution = 111* $742.72= $ 82,442 . Lower than the present contributionQ-6: Based on your analysis above, is Prestige Data Services really a problem to Prestige Telephone Company? What should Rowe do about Prestige Data Services?
Prestige Data Services is not a problem to Prestige Telephone Company becauseCommercial revenue hours appear to be increasing[ w/o increase in expenses ]Additional sales promotion and acceptance of the service increased utilization-increased revenue- profits not lossesThe promise behind the set up of Prestige Data Services is being realized by Prestige Telephone company- evident from the available data excess hours/ capacity need to be converted into Commercial revenue hours- increased profitability of the subsidiary and the parent Consideration of alternatives to reduce costs heads such as Rent, Custodial Services, Depreciation on machinery vs leasing
Bill FrenchCase 16-3Case 16-3 Bill FrenchQuestionsAssumptions implicit in Bills CalculationsBEP on various situationsShould the company alter the product mix in favour of product C? Does BEP help in this regard?BEP of individual products? Why the sum of individual BEP differ from the aggregate?What are the uses of BEP analysis?
Assumptions Implicit in Bills calculationsVariability of the VC is constantFC is fixed only in the relevant rangeReasonable constant relationship between production and sales patternConstant Sales MixConstant Selling PriceVarious BEPsSituation 1: Allowing for 10% increase in VC ,increase in SP of C & $60,000 per month increase in FC, change in product mix but not holding any dividend or retention requirements against operationsSituation 2 : No allowance for 10% increase in VC, no dividend requirement, no earnings retention goal but change in product mix, increased FC and change in selling price of product CSituation 3: Change in both VC & FC , Change in volume & selling price and coverage for dividend and RESituation 1ParticularsProdALast yearProdANext yearProdBLast yearProdBNext yearProdCLast yearProdCNext yearUnit capacityUnit achieved6,00,0004,00,0004,00,0004,00,0005,00,0009,50,000Selling price per unit[in$]1010992.404.80Sales revenue60,00,00040,00,00036,00,00036,00,00012,00,00045,60,000VC per unit[in $]7.508.253.754.1251.501.65FC[in $]9,60,0009,60,00015,60,00015,60,0004,50,00011,70,000PBT[in $]5,40,000(2,60,000)5,40,0003,90,000018,22,500[-]IT @50%2,70,000(1,30,000)2,70,0001,95,00009,11,250[-]DividendRESituation 1ParticularsTotalLast yearTotalNext yearUnit capacity[units]20,00,00020,00,000Unit achieved15,00,00017,50,000Selling price per unit[in$]-Wgt.avg7.206.95Sales revenue1,08,00,0001,21,60,000VC per unit[in $]-wgt.avg4.503.72FC[in $]29,70,00036,90,000PBT[in $]10,80,00019,52,500[-]IT @50%5,40,0009,76,250[-]Dividend3,00,0004,50,000RE2,40,0005,26,250Situation 1-BEPFC= $ 36,90,000Contribution per unit = $3.23BEP [in units] = $36,90,000/3.23 = 11,42,000 unitsCMP = 3.23/ 6.95 = 0.4647BEP in Revenue $= $36,90,000/0.4647= $ 79,40,000 Situation 2ParticularsTotalPdt APdt BPdt CSelling price per unit [in $]6.951094.80Variable Cost per unit [in $]3.397.53.751.5Contribution per unit [in $]3.562.55.253.3Units to be sold next year17,50,0004,00,0004,00,0009,50,000Total Contribution [in $]62,35,00010,00,00021,00,00031,35,000Situation 2-BEPFC= $ 36,90,000Contribution per unit = $3.56BEP [in units] = $36,90,000/3.56 = 10,36,500 unitsCMP = 3.56/ 6.95 = 0.5122BEP in Revenue $= $36,90,000/0.5122= $ 72,04,000
Situation 3 -BEPChange in both VC & FC, Change in Volume & Selling Price per unitCoverage required: Fc of $ 36,90,000, pre tax dividend of $ 6,00,000 and Pre tax RE of $3,00,000= Total of $ 45,90,000Unit Contribution = $ 3.23BEP in units = 14,21,000CMP = 0.4647BEP in Revenue $ = $ 98,77,000Summary of optionsParticularsFC [in $]Contribution per unit [in $]BEP[units]CMPBE [in revenue $]Situation 136,90,0003.2311,42,0000.464779,40,000Situation 236,90,0003.5610,36,5000.512272,04,000Situation 345,90,0003.2314,21,0000.464798,77,000Pay Extra dividend, no union increase, increased FC & RE of $1,50,00048,90,0003.5613,74,0000.512295,47,000Allow union increase, pay no extra dividend, increased FC & RE of $1,50,00045,90,0003.2314,21,0000.464798,77,000Pay extra dividend and union increase, increase FC & RE of $1,50,000048,90,0003.2315,14,0000.46471,05,23,000Q3: Should the company alter the existing product emphasisCMP of Product A is 18% while that of Product C is 66%The per unit contribution [in $] for Product A is $1.75 versus $ 3.15 for product CHence, the company should alter the existing product emphasis as it results in increased PBTQ 3: Amount to be invested for additional C capacityProduct A contributes 56% of Product C Contribution = 1.75/3.15=56%Means that company can afford to gain in C units only 44% of the number of A units that it gives upAmount of contribution available to pay for the added capacity and to return a reasonable profit i.e ROIHere for instance for an addition of 1,00,000 units of Product C must not give an additional FC of more than $ 3,15,000Q 4 : BEP of individual products[ using exhibit 3]ParticularsTotalPdt APdt BPdt CSelling price per unit [in $]7.201092.4(-) VC per unit [in $]4.57.53.751.5Contribution per unit [in $]2.72.55.250.9Sales units15,00,0006,00,0004,00,0005,00,000Total Contribution [in $]40,50,00015,00,00021,00,0004,50,000(-) FC [in $]29,70,0009,60,00015,60,0004,50,000PBT10,80,0005,40,0005,40,0000BEP in units11,00,0003,84,0002,97,1435,00,000BEP in $79,20,00038,40,00026,74,28712,00,000Q 4 : BEP of individual products[ using exhibit 3]Sum of Individual BEP units = 11,81,143 unitsBEP units [total] = 11,00,000Why there is a difference between the two numbers?Both will be equal only when the unit contribution is same for all three productsIn such situation, product mix is irrelevantQ5: Uses of BEP analysisWhat kind of decisions?What kind of insights?
Short run alternatives choices vs Long Run Alternative Choices?
