Cost-Volume-Profit Analysis

Transcription

1 ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER Cost-Volum-Profit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us cost-volum-profit (CVP) analysis to idntify th lvls of oprating activity ndd to avoid losss, achiv targtd profits, plan futur oprations, and monitor organizational prformanc. Managrs also analyz oprational risk as thy choos an appropriat cost structur. This Chaptr Addrsss th Following Qustions: Q Q Q3 Q4 Q5 Q6 What is cost-volum-profit (CVP) analysis, and how is it usd for dcision making? How ar CVP calculations prformd for a singl product? How ar CVP calculations prformd for multipl products? What is th brakvn point? What assumptions and limitations should managrs considr whn using CVP analysis? How ar margin of safty and oprating lvrag usd to assss oprational risk?

2 ch03.qxd 9/7/04 4:06 PM Pag 87 COLECO: FAULTY FORECASTS In th arly 980s, prsonal computrs wr still somwhat a novlty. At that tim, Colco manufacturd a small computr calld Adam. In addition, it sold Colcovision gams for hom computrs. Colco marktd Adam and its computr gams havily, hoping in 98 for a hot sllr during th Christmas and holiday gift sason. Howvr, Adam and Colcovision did not sll wll. Colco found itslf clos to bankruptcy. Thn in 983 Colco purchasd th licns to manufactur Cabbag Patch Dolls. It bgan production for Christmas 983. Colco widly publicizd th dolls arrival at toy stors, but managrs anticipatd gratr sals of Adam in thir production schduls. Thy did not mphasiz production of th Cabbag Patch Dolls. Ths dolls bcam hot sllrs that Christmas, and invntoris wr dpltd rapidly. Th scarcity gnratd so much intrst that customrs fought with ach othr for th dolls and vn wrckd som toy stors whil trying to purchas Cabbag Patch Dolls for th holidays. Bcaus of th shortag, advrtising for th dolls was cancld shortly aftr thir introduction. Colco s managrs continud to think that th company s rputation would b basd on computrs. Howvr, Cabbag Patch Dolls bcam thir most succssful product for th nxt svral yars. Aftr succss with Cabbag Patch Dolls and action figur toys calld Mastrs of th Univrs, Colco continud to aim for hot sllrs. This stratgy involvd a grat dal of uncrtainty, and by 988 th company was bankrupt. SOURCES: L. Brannon and A. McCab, Tim-Rstrictd Sals Appals, Cornll Hotl and Rstaurant Administration Quartrly, August/Sptmbr 00, pp ; and K. Fitzgrald, Toys Fac Scroog-Lik Christmas, Advrtising Ag, Sptmbr 9, 988, pp

3 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS DETERMINING A PROFITABLE MIX OF PRODUCTS Ky Dcision Factors for Colco What wnt wrong with Colco s dcision to mphasiz production of Adam instad of Cabbag Patch Dolls? Th problms bgan with uncrtaintis about which products would b popular at Christmas. Colco s managrs could not know which products would sll bst. Nvrthlss, it was ncssary for thm to mak dcisions about th typs and volums of products to manufactur. Thy forcast th numbr and typ of products that would sll and thn mad production dcisions accordingly. Th following discussion summarizs ky issus in Colco s dcision-making procss. Knowing. Knowldg about consumr markts, comptition, production procsss, and costs wr critical whn Colco s managrs dcidd which product to mphasiz. Colco ndd this knowldg for its potntial markts dolls, computrs, and gams. Givn th company s xprinc, its knowldg was probably gratr for producing Adam than for Cabbag Patch Dolls. Howvr, doll manufacturing was a rlativly simpl procss compard to producing computrs. Idntifying. Companis commonly fac major uncrtaintis in thir product markts, particularly in th toy industry whr comptition is oftn firc and consumr tasts chang rapidly. Howvr, Colco s uncrtaintis wr gratr than most bcaus of th rlativly nw and comptitiv computr markt. For xampl, th managrs did not know: How quickly consumrs would mbrac computrs What would prsuad consumrs to purchas a first computr How quickly computr tchnology and comptition would chang Exactly how much th computrs would cost to produc Exploring. Colco s managrs facd a difficult task in adquatly xploring thir dcision to mphasiz Adam ovr Cabbag Patch Dolls. Howvr, thorough analysis is crucial for this typ of dcision. For xampl, th managrs ndd to do th following: Anticipat which product would sll bst. Although markt rsarch hlps managrs stimat product dmand, thy would still hav considrabl uncrtainty about actual product sals. Avoid biasd forcasts and analyss. Managrs oftn hav motional attachmnts to sunk costs, such as th larg invstmnt alrady mad in Adam, that should not affct dcision making. Considr risks associatd with th cost structur for ach product. Compard to Adam, Cabbag Patch dolls probably had lowr fixd costs and a gratr proportion of variabl costs. Whn mor of a product s costs ar variabl, profit is lss risky bcaus th sals volums ndd to covr fixd costs ar rlativly lowr. Cabbag Patch may hav carrid lss oprating risk than Adam. Prioritizing. Givn limitd rsourcs and thir analyss of xpctd profit from th two products, Colco s managrs dcidd to prioritiz production of Adam ovr Cabbag Patch Dolls. This dcision might hav bn cloudd by managmnt biass, as alrady discussd. Envisioning. Dspit prvious poor sals of Adam, Colco s managrs continud promoting th product. In hindsight, it is asy to criticiz th company for this stratgy; howvr, it would hav bn difficult for Colco s managrs to adquatly stimat product sals. Latr, th managrs adoptd an ongoing stratgy of sking hot-slling toys. This stratgy ultimatly faild. Dcision Making Using Information about Rvnus and Costs Bcaus Colco s managrs ovrstimatd Adam sals and undrstimatd Cabbag Patch Doll sals, thy not only incurrd substantial losss on th Adam lin, but also lost th opportunity to gain mor profit by slling additional Cabbag Patch Dolls. In Chaptr, w focusd primarily on th stimation of costs. Howvr, managrs combin information about rvnus and costs to hlp thm dcid th mix and volums of goods or srvics to produc

4 ch03.qxd 9/7/04 4:06 PM Pag 89 COST-VOLUME-PROFIT ANALYSIS 89 and sll. Thy also us this information to monitor oprations and valuat profitability risk. In this chaptr, w combin rvnus and costs in our analyss. COST-VOLUME- PROFIT ANALYSIS Q Q What is cost-volumprofit (CVP) analysis, and how is it usd for dcision making? How ar CVP calculations prformd for a singl product? Cost-volum-profit (CVP) analysis is a tchniqu that xamins changs in profits in rspons to changs in sals volums, costs, and prics. Accountants oftn prform CVP analysis to plan futur lvls of oprating activity and provid information about: Which products or srvics to mphasiz Th volum of sals ndd to achiv a targtd lvl of profit Th amount of rvnu rquird to avoid losss Whthr to incras fixd costs How much to budgt for discrtionary xpnditurs Whthr fixd costs xpos th organization to an unaccptabl lvl of risk Profit Equation and Contribution Margin CVP analysis bgins with th basic profit quation. Profit Total rvnu Total costs Sparating costs into variabl and fixd catgoris, w xprss profit as: Profit Total rvnu Total variabl costs Total fixd costs CURRENT PRACTICE According to Jon Schumann, dirctor of th businss procss consulting firm Gunn Partnrs, succssful organizations nd a cultur that is attund to cost managmnt and that pays attntion to cost structurs. Th contribution margin is total rvnu minus total variabl costs. Similarly, th contribution margin pr unit is th slling pric pr unit minus th variabl cost pr unit. Both contribution margin and contribution margin pr unit ar valuabl tools whn considring th ffcts of volum on profit. Contribution margin pr unit tlls us how much rvnu from ach unit sold can b applid toward fixd costs. Onc nough units hav bn sold to covr all fixd costs, thn th contribution margin pr unit from all rmaining sals bcoms profit. If w assum that th slling pric and variabl cost pr unit ar constant, thn total rvnu is qual to pric tims quantity, and total variabl cost is variabl cost pr unit tims quantity. W thn rwrit th profit quation in trms of th contribution margin pr unit. whr Profit P Q V Q F (P V ) Q F P Slling pric pr unit V Variabl cost pr unit (P V ) Contribution margin pr unit Q Quantity of product sold (units of goods or srvics) F Total fixd costs W us th profit quation to plan for diffrnt volums of oprations. CVP analysis can b prformd using ithr: Units (quantity) of product sold Rvnus (in dollars) CVP Analysis in Units W bgin with th prcding profit quation. Assuming that fixd costs rmain constant, w solv for th xpctd quantity of goods or srvics that must b sold to achiv a targt lvl of profit. Profit quation: Profit (P V ) Q F F Profit Solving for Q: Q Quantity (units) rquird to obtain targt profit (P V ) Notic that th dnominator in this formula, (P V), is th contribution margin pr unit. Editorial, A Proactiv Approach to Cost Cutting, SmartPros, Jun 00,

5 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS Suppos that Magik Bicycls wants to produc a nw mountain bik calld Magikbik III and has forcast th following information. Pric pr bik $800 Variabl cost pr bik $300 Fixd costs rlatd to bik production $5,500,000 Targt profit $00,000 Estimatd sals,000 biks W dtrmin th quantity of biks ndd for th targt profit as follows: Quantity ($5,500,000 $00,000) ($800 $300),400 biks CVP Analysis in Rvnus Th contribution margin ratio (CMR) is th prcnt by which th slling pric (or rvnu) pr unit xcds th variabl cost pr unit, or contribution margin as a prcnt of rvnu. For a singl product, it is CMR To analyz CVP in trms of total rvnu instad of units, w substitut th contribution margin ratio for th contribution margin pr unit. W rwrit th quation to solv for th total dollar amount of rvnu w nd to covr fixd costs and achiv our targt profit as Rvnu P V P F Profit (P V )/P To solv for th Magikbik III rvnus ndd for a targt profit of $00,000, w first calculat th contribution margin ratio as follows: F Profit CMR CMR ($800 $300) $ A contribution margin ratio of 0.65 mans that 6.5% of th rvnu from ach bik sold contributs first to fixd costs and thn to profit aftr fixd costs ar covrd. Rvnu ($5,500,000 $00,000) 0.65 $9,0,000 HELPFUL HINT Computing th CVP using total rvnus and total variabl costs is usful in cass whr pr-unit variabl costs ar unknown. W chck to s that th two rsults ar idntical by multiplying th numbr of units (,400) tims pric ($800) to obtain th rvnu amount ($9,0,000). Th contribution margin ratio can also b writtn in trms of total rvnus (TR) and total variabl costs (TVC). That is, for a singl product, th CMR is th sam whthr w comput it using pr-unit slling pric and variabl cost or using total rvnus and total variabl costs. Thus, w can crat th following mathmatically quivalnt vrsion of th CVP formula. Rvnus For Magikbik III w could us th forcast information about volum (,000 biks) to dtrmin th contribution margin ratio. Total rvnu $800,000 biks $9,600,000 Total variabl cost $300,000 biks $3,600,000 Total contribution margin $9,600,000 $3,600,000 $6,000,000 Contribution margin ratio $6,000,000 $9,600, CVP for Multipl Products F Profit (TR TVC)/TR Many organizations sll a combination of diffrnt products or srvics. Th sals mix is th proportion of diffrnt products or srvics that an organization slls. For xampl, w larnd in th opning vigntt that Colco sold both Adam computrs and Cabbag Patch dolls. To us CVP in th cas of multipl products or srvics, w assum a constant sals mix in addition to th othr CVP assumptions. Assuming a constant sals mix allows CVP computations to b prformd using combind unit or rvnu data for an organization as a whol. Latr in th chaptr w will larn how to prform dtaild computations for th sals mix.

6 ch03.qxd 9/7/04 4:06 PM Pag 9 COST-VOLUME-PROFIT ANALYSIS 9 EXHIBIT 3. CVP Graph for Magik Bicycls Magikbik III. Brakvn point Total rvnu Total costs Dollars $9,0,000 $8,800,000 $5,500,000 Oprating loss ara Oprating incom ara Quantity of biks,000,400 Q4 What is th brakvn point? CURRENT PRACTICE Th U.S. Small Businss Administration Wb sit rcommnds th us of brakvn analysis and rfrs small businss ownrs to a brakvn analysis calculator and CVP graphing tool. Brakvn Point Managrs oftn want to know th lvl of activity rquird to brak vn. A CVP analysis can b usd to dtrmin th brakvn point, or lvl of oprating activity at which rvnus covr all fixd and variabl costs, rsulting in zro profit. W can calculat th brakvn point from any of th prcding CVP formulas, stting profit to zro. Dpnding on which formula w us, w calculat th brakvn point in ithr numbr of units or in total rvnus. For Magikbik III, brakvn points ar: Brakvn quantity ($5,500,000 $0) ($800 $300),000 biks Brakvn rvnu ($5,500,000 $0) 0.65 $8,800,000 Cost-Volum-Profit Graph A cost-volum-profit graph (or CVP graph) shows th rlationship btwn total rvnus and total costs; it illustrats how an organization s profits ar xpctd to chang undr diffrnt volums of activity. Exhibit 3. prsnts a CVP graph for Magikbiks III. Notic that whn no biks ar sold, fixd costs ar $5,500,000, rsulting in a loss of $5,500,000. As sals volum incrass, th loss dcrass by th contribution margin for ach bik sold. Th cost and rvnu lins intrsct at th brakvn point of,000, which mans zro loss and zro profit. Thn as sals incras byond this brakvn point, w s an incras in profit, growing by th $500 contribution margin for ach bik sold. Profits achiv th targt lvl of $00,000 whn sals volum rachs,400. GUIDE YOUR LEARNING 3. Ky Trms Stop to confirm that you undrstand th nw trms introducd in th last svral pags. Cost-volum-profit (CVP) analysis (p. 89) *Sals mix (p. 90) Contribution margin (p. 89) Brakvn point (p. 9) Contribution margin pr unit (p. 89) Cost-volum-profit graph (p. 9) Contribution margin ratio (CMR) (p. 90) For ach of ths trms, writ a dfinition in your own words. For th starrd trm, list at last on xampl that is diffrnt from th ons givn in this txtbook. Do a sarch for Brakvn Analysis at th U.S. Small Businss Administration Wb sit, availabl at

7 ch03.qxd 9/7/04 4:06 PM Pag 9 9 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS ALTERNATIVE TERMS Som popl us th trms oprating incom (loss) or incom (loss) bfor incom taxs instad of prtax profit (loss). Similarly, som popl us nt incom (loss) instad of aftr-tax profit (loss). CVP with Incom Taxs Up to this point, our CVP calculations ignord incom taxs. An organization s aftr-tax profit is calculatd by subtracting incom tax from prtax profit. Th tax is usually calculatd as a prcntag of prtax profit. Aftr-tax profit Prtax profit Taxs Prtax profit (Tax rat Prtax profit) Prtax profit ( Tax rat) If w want to know th amount of prtax profit ndd to achiv a targt lvl of aftr-tax profit, w solv th prcding formula for prtax profit: Prtax profit Aftr-tax profit ( Tax rat) Suppos that Magik Bicycls plans for an aftr-tax profit of $0,000 and its tax rat is 30%. Thn, Prtax profit $0,000 ( 0.30) $8,57 Th company nds a prtax profit of $8,57 to arn an aftr-tax profit of $0,000. Th following illustration dvlops a cost function to calculat th volums ndd to brak vn and to achiv a targt aftr-tax profit whn multipl products ar involvd. DIE GEFLECKTE KUH EIS (THE SPOTTED COW CREAMERY) (PART ) CVP ANALYSIS WITH INCOME TAXES Di Gflckt Kuh Eis (Th Spottd Cow Cramry) is a popular ic cram mporium nar a univrsity in Munich, Grmany. Information for th most rcnt month (amounts in uros) appars hr. Rvnu 40,000 Cost of food and bvrags sold 0,000 Labor 5,000 Rnt, Prtax profit 4,000 Incom taxs (5%), Aftr-tax profit 3, Th stor ownr askd th managr, Holgr Sodrstrom, to stimat rsults for th nxt month. This particular outlt has not prformd as wll as th ownr s othr thr outlts. Holgr blivs that sals volums will incras to 48,000 nxt month bcaus it has bn an unusually hot and dry summr. Estimating th Cost Function To prform CVP analysis, Holgr first stimats th cost function. Using accounting rcords, h classifis ach cost as fixd or variabl and thn stimats nxt month s cost. Of th costs listd in th accounting rcords, labor ( 5,000) and rnt (,000) ar most likly fixd (assuming mploys work fixd schduls). Assuming that fixd costs do not chang from month to month, Holgr s bst stimat of nxt month s fixd costs is 6,000 ( 5,000,000). Th rmaining itm, cost of food and bvrags sold ( 0,000), is most likly a variabl cost. Bcaus Th Spottd Cow Cramry s focus is rtail sals of ic cram and othr food itms, Holgr can rasonably assum that sals volum drivs this variabl cost. Thus, h stimats xpctd variabl costs as a prcnt of rvnu: 0,000 40, , or 50% of rvnu Holgr combins his fixd and variabl cost stimats to crat th following cost function for nxt month: TC Estimating Aftr-Tax Profit 6,000 (50% Rvnus) If nxt month s rvnus ar 48,000, Holgr xpcts total variabl costs to b (50% 48,000) 4,000. Thrfor, his stimat of prtax profit is Prtax profit 48,000 6,000 4,000 8,000

8 ch03.qxd 9/7/04 4:06 PM Pag 93 COST-VOLUME-PROFIT ANALYSIS 93 Holgr stimats incom taxs and aftr-tax profit, assuming that incom taxs rmain at 5% of prtax profit: Aftr-tax profit 8,000( 0.5) 6,000 Calculating Rvnus to Achiv Targtd Aftr-Tax Profit Holgr prsnts th prcding information to th ownr. Howvr, th ownr still has concrns about this outlt bcaus th othr outlts hav achivd aftr-tax profits of about 8,000 ach during th last fw months. Th ownr thinks that sals volum might b th problm. To hlp analyz this possibility, Holgr dtrmins th sals volum ncssary to arn aftr-tax profits of 8,000 pr month. H bgins by calculating th targtd prtax profit: Prtax profit 8,000 ( 0.5) 0,667 Nxt, h uss th following CVP formula to solv for targtd rvnu: Substituting in th prcding information: Rvnus F Profit CMR Rvnus ( 6,000 0,667) ,334 Notic that Holgr uss th contribution margin ratio calculatd with th sals rvnu and variabl costs from his original analysis. Holgr summarizs his targt profit calculations for th ownr as follows: Rvnu 53,334 Cost of food and bvrags sold (50% of 53,334) 6,667 Labor (fixd) 5,000 Rnt (fixd), Prtax profit 0,667 Incom taxs (5%), Aftr-tax profit 8, For th outlt to achiv an aftr-tax profit of 8,000, rvnus nd to incras by 33% [( 53,334 40,000) 40,000] ovr last month. Holgr prsnts this information to th ownr and argus that sals will incras to 53,334 bcaus th wathr will b hottr nxt month. Howvr, th ownr thinks that Holgr may b worrid about bing rplacd, and so his rvnu stimats ar probably biasd upwards. Th ownr dcids to invstigat Holgr s stimats furthr by comparing his rvnus and costs to thos in th othr outlts. GUIDE YOUR LEARNING 3. Th Spottd Cow Cramry (Part ) Th Spottd Cow Cramry (Part ) illustrats a multipl-product CVP analysis with incom taxs. For this illustration: Idntify Problm Dfin It and Information Idntify Uncrtaintis Explor Assumptions Explor Biass Which dfinitions, analysis tchniqus, and computations wr usd? What dcisions wr bing addrssd? What information was rlvant to th dcisions? What typs of uncrtaintis wr thr? Considr uncrtaintis about: Rvnu and cost stimats Intrprting rsults Rlvant rang of oprations Fasibility of activity lvl Rrad th first part of this chaptr and idntify th assumptions usd in dvloping th CVP formulas. How rasonabl ar ths assumptions for Th Spottd Cow Cramry? Why and how might th managr s bias influnc th computations? Why would th ownr b uncrtain whthr th managr had cratd biasd rvnu or cost stimats?

9 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS PERFORMING CVP ANALYSES WITH A SPREADSHEET Spradshts ar oftn usd for CVP computations, particularly whn an organization has multipl products. Spradshts simplify th basic computations and can b dsignd to show how changs in volums, slling prics, costs, or sals mix altr th rsults. Q3 How ar CVP calculations prformd for multipl products? CVP Calculations for a Sals Mix Although Th Spottd Cow Cramry slls multipl products, th CVP analysis prformd by th stor managr did not provid computations for individual products. Instad, th analysis focusd on th total amount of rvnu ndd to achiv a targt profit. If th managr wants to us CVP rsults to plan futur oprations for individual products, th rquird rvnu for ach product nds to b dtrmind. Such computations ar prformd using th sals mix. Th sals mix should b statd as a proportion of units whn prforming CVP computations in units, and it should b statd as a proportion of rvnus whn prforming CVP computations in rvnus. Sals mix computations can bcom cumbrsom if prformd manually; it is asist to us a spradsht. To dmonstrat CVP computations using a spradsht, suppos that Magik Bicycls dvlopd thr diffrnt products, a small bik for childrn and youths, a road bik, and a mountain bik. Total fixd costs for th company ar $4,700,000. Forcastd sals volums ar as follows. Th sals mix in prcntags is calculatd from ths volums. Youth Road Mountain Total Forcastd volum (units) 0,000 8,000,000 40,000 Expctd sals mix in units 5% 45% 30% 00% Bcaus of incrasd comptition and an conomic downturn, th managrs of Magik Bicycls ar uncrtain about th company s ability to achiv th forcastd lvl of sals. Thy would lik to know th minimum amount of sals ndd for an aftr-tax profit of $00,000. Th company s incom tax rat is 30%. Th xpctd unit slling prics, variabl costs, and contribution margins for ach product ar as follows: CURRENT PRACTICE Spradsht skills ar important profssionally. Th Amrican Institut of Crtifid Public Accountants (AICPA) stats that an ntry-lvl accountant should b abl to appropriatly us lctronic spradshts and othr softwar to build modls and simulations. 3 Youth Road Mountain Pric pr unit $00 $700 $800 Variabl cost pr unit Contribution margin pr unit $ 5 $ $ Exhibit 3. shows a sampl CVP spradsht for Magik Bicycls. Notic that all of th input data is placd in an ara labld as Input sction in th spradsht. Th calculations ar prformd outsid of this ara (formulas for this spradsht ar shown in Appndix 3A). Spradshts dsignd this way allow usrs to altr th assumptions in th input sction without prforming any additional programming. Th spradsht in Exhibit 3. first uss th input data to comput xpctd rvnus, costs, and incom. Th rvnus and variabl costs for ach product ar computd by multiplying th xpctd sals volum tims th slling pric and variabl cost pr unit shown in th input ara. Th rvnus and variabl costs for th thr products ar thn combind to dtrmin total rvnus and total variabl costs for th company. Aftr subtracting xpctd fixd costs and incom taxs (30% of prtax incom), th xpctd aftr-tax incom is $455,000. Whn an organization producs and slls a numbr of diffrnt products or srvics, w us th wightd avrag contribution margin pr unit to dtrmin th brakvn point or targt profit in units. Similarly, w us th wightd avrag contribution margin ratio to dtrmin th brakvn point or targt profit in rvnus. Wightd avrag hr rfrs to th xpctd sals mix: 0,000 youth biks or $,000,000 in rvnus, 8,000 road biks or 3 This skill is an lmnt of th comptncy Lvrag Tchnology to Dvlop and Enhanc Functional Comptncis, AICPA Cor Comptncy Framwork, accssd through th Library at ca.aicpasrvics.org/.

10 ch03.qxd 9/7/04 4:06 PM Pag 95 PERFORMING CVP ANALYSES WITH A SPREADSHEET 95 EXHIBIT 3. Spradsht for Magik Bicycls CVP with Multipl Products Input sction Expctd sals volum-units Pric pr unit Variabl cost pr unit Fixd costs Dsird aftr-tax profit Incom tax rat Contribution Margin Units Rvnu Variabl costs Contribution margin Contrib. margin pr unit Contrib. margin ratio Expctd sals mix in units Expctd sals mix in rvnus Expctd Incom Contribution margin (abov) Fixd costs Prtax incom Incom taxs Aftr-tax incom Prliminary CVP Calculations Targt prtax profit for CVP analysis Fixd costs plus targt prtax profit A CVP analysis in units CVP calculation in units Rvnu Variabl costs Contribution margin Fixd costs Prtax incom Incom taxs Aftr-tax incom CVP analysis in rvnus CVP calculation in rvnus Variabl costs Contribution margin Fixd costs Prtax incom Incom taxs Aftr-tax incom B C D E Youth Biks 0,000 $00 $75 $4,700,000 $00,000 30% Youth Biks 0,000 $,000, ,000 $,50,000 $ % 5.00% 8.6% Youth Biks 9, $,933,93 75, $,08,70 Youth Biks $,933,93 75, $,08,70 Road Biks 8,000 $700 $50 (ntr zro for brakvn) Road Biks 8,000 $,600,000 4,500,000 $8,00,000 $ % 45.00% 5.07% Road Biks 7, $,83,73 4,35,36 $7,83,387 Road Biks $,83,73 4,35,36 $7,83,387 Mtn. Biks,000 $800 $300 Mtn. Biks,000 $9,600,000 3,600,000 $6,000,000 $ % 30.00% 39.67% Mtn. Biks, $9,8,89 3,48,06 $5,80,768 Mtn. Biks $9,8,89 3,48,06 $5,80,768 Total Biks 40,000 $4,00,000 8,850,000 $5,350,000 $ % 00.00% 00.00% $5,350,000 4,700, ,000 95,000 $455,000 $4,857 $4,84,857 Total Biks 38,678 $3,400,465 8,557,608 4,84,857 4,700,000 4,857 4,857 $00,000 Total Biks $3,400,465 8,557,608 4,84,857 4,700,000 4,857 4,857 $00,000 Not: Appndix 3A provids a vrsion of this spradsht showing th cll formulas. $,600,000 in rvnus, and,000 mountain biks or $9,600,000 in rvnus. Givn th sals mix, th wightd avrag contribution margin pr unit is calculatd as th combind contribution margin ($5,350,000) dividd by th total numbr of units xpctd to b sold (40,000), or $ pr unit as computd in Exhibit Th wightd avrag contribution margin ratio is th combind contribution margin ($5,350,000) dividd by combind rvnu ($4,00,000), or 63.43%. 5 4 Anothr way to comput th wightd avrag contribution margin pr unit is to sum th contribution margins for th thr products, wightd by numbr of units sold as follows: (0,000 40,000)($00 $75) (8,000 40,000)($700 $50) (,000 40,000)($800 $300) $ Anothr way to comput th wightd avrag contribution margin ratio is to sum th contribution margin ratios for th thr products, wightd by rvnus as follows: ($,000,000 $4,00,000)[($00 $75) $00] ($,600,000 $4,00,000)[($700 $50) $700] ($9,600,000 $4,00,000)[($800 $300) $800] 63.43%.

11 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS Th spradsht in Exhibit 3. prforms CVP computations using both units and rvnus. To achiv an aftr-tax targt profit of 00,000, th company must arn a prtax profit of $4,857 [$00,000 ( 0.30)]. To comput th total numbr of units (biks) that must b sold to achiv th targt profit, w divid th fixd costs plus th targt profit by th wightd avrag contribution margin pr unit: F Profit $4,700,000 $4,857 Units ndd for targt profit Q 38,678 units (P V ) $ pr unit Magik nds to sll 38,678 units to achiv an aftr-tax targt profit of $00,000. To dtrmin th numbr of units for ach product that must b sold, w multiply th total numbr of units (38,678) by ach product s xpctd sals mix in units. For xampl, th company must sll 38,678 units (0,000 units 40,000 units), or 9,670 youth biks. To calculat th amount of rvnu ndd to achiv th targt aftr-tax profit of $00,000, w divid th fixd costs plus th targt prtax profit by th wightd avrag contribution margin ratio: F Profit $4,700,000 $4,857 Rvnus $3,400,373 CMR 63.43% Th diffrnc btwn th spradsht and this hand-calculatd amount is du to rounding, as ar any diffrncs in th following amounts. To dtrmin th rvnus for ach product that must b sold, w multiply th total rvnus ($3,400,373) by ach product s xpctd sals mix in rvnus. For xampl, th company must achiv $3,400,373 ($,000,000 $4,00,000), or $,933,94 in rvnus from youth biks. Notic that th rquird rvnu for ach product is qual to th rquird numbr of units tims th xpctd slling pric. For youth biks, 9,670 units $00 pr unit $,934,000. Th rsults of calculations using units and rvnus ar always idntical. Bcaus information in th xampl was givn in units, it would hav bn asist to crat th spradsht using only th computations for CVP in units. Howvr, in som situations pr-unit information is not availabl. In thos cass, it is ncssary to prform CVP calculations using rvnus. Latr in th chaptr w rvisit th ic cram shop illustration to analyz th influnc of sals mix on th total contribution margin. Q5 What assumptions and limitations should managrs considr whn using CVP analysis? CVP Snsitivity Analysis On of th bnfits of crating a spradsht with a sparat input sction is that additional CVP analyss can asily b prformd by th changing input data. For xampl, suppos th managrs of Magik Bicycls want to know th numbr of biks thy must sll to brak vn. W can rturn to th spradsht in Exhibit 3. and chang th Dsird aftr-tax profit to zro. Th rsulting spradsht, showing only CVP calculations in units, is prsntd in Exhibit 3.3. Th managrs of Magik Bicycls could us th CVP spradsht to prform svral diffrnt typs of snsitivity analyss. Suppos sals of th mountain bik ar falling bhind EXHIBIT 3.3 Spradsht Rsults for Magik Bicycls Brakvn Analysis A Prliminary CVP Calculations Targt prtax profit for CVP analysis Fixd costs plus targt prtax profit CVP analysis in units CVP calculation in units Rvnu Variabl costs Contribution margin Fixd costs Prtax incom Incom taxs Aftr-tax incom B C D E Youth Biks 9, $,95,309 78,4 $,97,068 Road Biks 7, $,066,450 4,309,446 $7,757,003 Mtn. Biks, $9,93,485 3,447,557 $5,745,98 $0 $4,700,000 Total Biks 38,306 $3,75,44 8,475,44 4,700,000 4,700, $0

12 ch03.qxd 9/7/04 4:06 PM Pag 97 PERFORMING CVP ANALYSES WITH A SPREADSHEET 97 xpctations. Thy could dtrmin th ffcts of th chang in sals mix on rsults. Evry assumption in th data input box is asily changd to updat information. Snsitivity analysis hlps managrs xplor th potntial impact of variations in data thy considr to b particularly important or uncrtain. Q What is cost-volumprofit (CVP) analysis, and how is it usd for dcision making? CHAPTER REFERENCE Chaptr 4 uss CVP analysis for additional typs of dcisions. W also larn that dcisions ar oftn influncd by qualitativ information that is not valud in numrical trms. CHAPTER REFERENCE In Chaptr 0, CVP analysis is usd to crat flxibl budgts for masuring and monitoring prformanc at diffrnt lvls of activity. Discrtionary Expnditur Dcision CVP analysis also hlps managrs mak businss dcisions such as whthr to incras or dcras discrtionary xpnditurs. For xampl, suppos th managrs of Magik Bicycls want to advrtis on of thir products mor havily. A distributor pointd out that th road bik pric was lss than a comptitor s pric for a modl with fwr faturs. Th comptitor s brand nam is quit wll known, but th distributor thinks that h could sll at last 0% mor road biks if Magik launchd a rgional advrtising campaign. Th managrs of Magik stimat that an additional xpnditur of $00,000 in advrtising will incras road bik sals by 5%, to 8,900 biks. To stimat th ffcts of th proposd xpnditur, w rturn to th spradsht in Exhibit 3. and mak two changs. First, fixd costs would incras by $00,000 to $4,800,000. Scond, th xpctd volum of road biks sold would incras to 8,900. Th rsulting spradsht in Exhibit 3.4 indicats that aftr-tax profits ar xpctd to incras by $3,500 from $455,000 to $668,500. Notic on th spradsht that th chang in sals mix affcts th wightd avrag contribution margin; it changs from to $385.. W could prform th sam calculation without th spradsht by subtracting th $00,000 invstmnt in fixd costs from th additional contribution margin of $405,000 [900 biks ($700 $50)]. Th rsulting incrmntal aftr-tax profit is $3,500 [($405,000 $00,000)( 0.30)]. Bcaus profits ar xpctd to incras mor than costs for this advrtising campaign, th managrs would b likly to mak th additional invstmnt. Planning, Monitoring, and Motivating with CVP CVP analyss ar usful for planning and monitoring oprations and for motivating mploy prformanc. If th ownr of Th Spottd Cow Cramry obtains similar information for th othr outlts, rsults can b compard to idntify diffrncs in rvnu lvls and cost functions. For xampl, unusually high labor costs might suggst that th low-profit outlt is ovrstaffd or infficint. Onc th ownr analyzs th rasons for diffrncs in profitability, mphasis can b placd on incrasing rvnus, rducing costs, or both. Th ownr can also hold managrs mor accountabl for prformanc, which should motivat thir work fforts toward th ownr s goals. EXHIBIT 3.4 Spradsht for Magik Bicycls Advrtising Expnditur Dcision A Contribution Margin Units Rvnu Variabl costs Contribution margin Contrib. margin pr unit Contrib. margin ratio Expctd sals mix in units Expctd sals mix in rvnus Expctd Incom Contribution margin (abov) Fixd costs Prtax incom Incom taxs Aftr-tax incom B C D E Road Biks 8,900 $3,30,000 4,75,000 $8,505,000 Mtn. Biks,000 $9,600,000 3,600,000 $6,000,000 Youth Biks 0,000 $,000, ,000 $,50,000 $ % 4.45% 8.05% $ % 46.% 53.8% $ % 9.34% 38.66% Total Biks 40,900 $4,830,000 9,075,000 $5,755,000 $ % 00.00% 00.00% $5,755,000 4,800, ,000 86,500 $668,500

13 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS DIE GEFLECKTE KUH EIS (THE SPOTTED COW CREAMERY) (PART ) THE INFLUENCE OF SALES MIX ON PROFITABILITY Th ownr of Th Spottd Cow Cramry has svral profitabl stors. H askd th stor managrs to provid information about thir sals mix, spcifically th amount of bvrag vrsus ic cram products sold. Bvrags provid a much largr contribution margin than ic cram. Aftr analyzing th data, h found that about half of th rvnus in th most profitabl stors wr for th sal of bvrags. In addition, ths stors hav mor stabl sals throughout th wintr bcaus thy sll spcialty coff bvrags as wll as soft drinks. Th ownr shard this information with Holgr, th managr of a lss profitabl stor. Holgr invstigats th contribution margins from bvrags and ic cram at his stor. H sts up a spradsht to xamin th influnc of th sals mix on profitability, shown in Exhibit 3.5(a). H finds that bvrags ar about 5% of total rvnu ( 6,000 40,000). Th contribution margin ratio for bvrags is 93% ( 5,600 6,000), whras th contribution margin for ic cram is 4% ( 4,400 34,000). Whn h changs th dsird sals mix in th spradsht from 5% to 50% bvrags to match th sals mix of mor profitabl stors, th aftr-tax incom incrass by a sizabl amount from 3,000 to 8,353 as indicatd in Exhibit 3.5(b). Holgr ralizs that svral stratgis would incras th prcntag of bvrags in his currnt sals mix. First, h could rquir th sals clrks to suggst a bvrag with ach sal. In addition, h could mphasiz bvrags in his advrtising. H could also analyz his comptitors bvrag prics to b crtain that his prics ar comptitiv. A small drop in th pric of bvrags might incras th volum of bvrags sold mor than nough to offst th dclin in contribution margin ratio. H uss th spradsht to prform snsitivity analysis around ths factors. EXHIBIT 3.5 Spradsht for Th Spottd Cow Cramry Input sction A Rvnu Variabl cost Currnt sals mix in rvnus Fixd costs Tax rat Dsird sals mix in rvnus Contribution margin ratio Incom statmnt Rvnu Variabl cost Contribution margin Fixd costs Prtax incom Taxs Aftr tax incom B C D Bvrag 6, % 5% 93% 6, ,600 Ic Cram 34,000 9,600 85% 85% 4% 34,000 9,600 4,400 Total 40,000 0,000 00% 6,000 5% 00% Wightd Avrag 50% 40,000 0,000 0,000 6,000 4,000,000 3, Input sction A Rvnu Variabl cost Currnt sals mix in rvnus Fixd costs Tax rat Dsird sals mix in rvnus Contribution margin ratio Incom statmnt Rvnu Variabl cost Contribution margin Fixd costs Prtax incom Taxs Aftr tax incom B C D Bvrag 6, % 50% 93% 0,000,333 8,667 Ic Cram 34,000 9,600 85% 50% 4% 0,000,59 8,47 Total 40,000 0,000 00% 6,000 5% 00% Wightd Avrag 68% 40,000,863 7,37 6,000,37,784 8,353 (a) Currnt Sals Mix (b) Dsird Sals Mix GUIDE YOUR LEARNING 3.3 Th Spottd Cow Cramry (Part ) Th Spottd Cow Cramry (Part ) illustrats th influnc of sals mix on profitability. For this illustration: Comput It Idntify Uncrtaintis Explor Uss For Exhibit 3.5, manually rcalculat: Sals mix in units Sals mix in rvnus Wightd avrag contribution margin ratio At th nd of th illustration, th stor managr was considring svral stratgis for changing his stor s sals mix. What uncrtaintis dos th managr fac? How was CVP information usd by th ownr? How was it usd by th managr?

14 ch03.qxd 9/7/04 4:06 PM Pag 99 ASSUMPTIONS AND LIMITATIONS OF COST-VOLUME-PROFIT ANALYSIS 99 ASSUMPTIONS AND LIMITATIONS OF COST-VOLUME- PROFIT ANALYSIS Q5 What assumptions and limitations should managrs considr whn using CVP analysis? CHAPTER REFERENCE Chaptr xplains th importanc of th rlvant rang in masuring th cost function. Exhibit 3.6 summarizs th input data, assumptions, and uss of CVP analysis. CVP analysis rlis on svral assumptions. In Chaptr w assumd for th linar cost function (F V Q) that production volums ar within a rlvant rang of oprations whr fixd costs rmain fixd and variabl costs rmain constant. In addition, for CVP analysis, w assum that slling prics rmain constant and that th sals mix is constant. Snsitivity analysis can b prformd to dtrmin th snsitivity of profits to ths assumptions. Uncrtaintis and Quality of Input Data As indicatd in Exhibit 3.6, CVP analysis rlis on forcasts of xpctd rvnus and costs. CVP assumptions rul out fluctuations in rvnus or costs that might b causd by common businss factors such as supplir volum discounts, larning curvs, changs in production fficincy, or spcial customr discounts. In addition, many uncrtaintis may aris about whthr CVP assumptions will b violatd, such as th following: Can volum of oprating activity b achivd? Will slling prics incras or dcras? Will sals mix rmain constant? Will fixd or variabl costs chang as oprations mov into a nw rlvant rang? Will costs chang du to unforsn causs? Ar rvnu and cost stimats biasd? EXHIBIT 3.6 Input Data, Assumptions, and Uss of CVP Analysis Input Data for CVP Analysis Expctd Rvnus (volum and slling pric) Expctd Costs (cost function) Sals Mix (for multipl products) CVP Analysis and Assumptions Calculat numbr of units or rvnus ndd for: Brakvn Targt profit Assumptions: Oprations within a rlvant rang Linar cost function Fixd costs rmain constant Variabl cost pr unit rmains constant Linar rvnu function Sals mix rmains constant Prics rmain constant Us Rsults to: Dscrib volum, rvnus, costs, and profits: Valus at brakvn or targt profit.: Units sold Rvnus Variabl, fixd, and total costs Snsitivity of rsults to changs in: Lvls of activity Slling pric Cost function Sals mix Indiffrnc point btwn altrnativs Fasibility of plannd oprations Assist with plans and dcisions such as: Budgts Product mphasis Slling pric Production or activity lvls Employ work schduls Raw matrial purchass Discrtionary xpnditurs such as advrtising Proportions of fixd vrsus variabl costs Monitor oprations by comparing xpctd and actual: Volums, rvnus, costs, and profits Profitability risk

15 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS EXHIBIT 3.7 Exampls of Businss Uncrtaintis Ashanti Goldfilds Company Ltd. Bank of Montral Coca-Cola FEMSA, S.A. d C.V. Bay, Inc. Nokia Corporation Sony Corporation Ghana Canada Mxico Unitd Stats Finland Japan Gold mining and xploration Crdit and noncrdit banking srvics Production and distribution of Coca-Cola products Wb-basd marktplac and paymnt srvics Mobil communications Elctronic quipmnt dsign and manufacturing Gold prics Anticipatd lif of mins Powr supply Labor rlations Changs in global capital markts Intrst rats Rgulatory changs Tchnological changs Dtrioration in rlationships with th Coca-Cola Company Govrnmntal pric controls Mor stringnt nvironmntal rgulations High inflation Rtaining activ usr bas Consumr confidnc in Wb sit scurity Managmnt of fraud loss Rtaining ky mploys Global ntwork rlianc on larg multiyar contracts Failur of product quality Systm or ntwork disruptions Elctromagntic fild-rlatd litigation Lvls of consumr spnding Spd and natur of tchnology chang Chang in consumr prfrncs Ability to rduc workforc Exampls adaptd from Forward-Looking Information in Form 0-F (fild with th SEC). Exampls adaptd from Caution Rgarding Forward-Looking Statmnts undr Invstor Rlations at www4.bmo.com. Exampls adaptd from Cautionary Statmnts in prsntation to J.P. Morgan, July 003 Exampls adaptd from Risk Factors That May Affct Rsults of Oprations and Financial Condition in 00 annual rport. Exampls adaptd from Risk Factors in 00 annual rport. Exampls adaptd from Cautionary Statmnt undr Invstor Rlations at indx.html. CHAPTER REFERENCE W addrss th quality of xpctd rvnu and cost information furthr in Chaptr 0 (budgting). All organizations ar subjct to uncrtaintis, lading to risk that thy will fail to mt xpctations. Exhibit 3.7 summarizs major businss uncrtaintis for six companis in a varity of industris around th world. Evn though ach organization is subjct to uniqu businss risks, all fac uncrtaintis rlatd to th conomic nvironmnt. Som organizations ar subjct to mor uncrtainty than othrs. For xampl, uncrtaintis ar gratr in industris xprincing rapid tchnological and markt chang or intns comptition. Quality of CVP Tchniqu To hlp managrs mak bttr dcisions, accountants valuat th quality of th tchniqus thy us, givn th organizational stting and dcisions to b mad. This valuation hlps dtrmin whn tchniqus such as CVP analysis ar likly to b an appropriat tool and how much rlianc to plac on th rsults. Th quality of information gnratd from an analysis tchniqu is highr if th conomic stting is consistnt with th tchniqu s undrlying assumptions. Strict CVP assumptions ar violatd in many businss sttings. Th typs of uncrtaintis alrady discussd can lad to nonlinar bhavior in rvnus and costs. In addition, it may b difficult to dtrmin th point of oprating activity whr oprations mov into a nw rlvant rang. Nvrthlss, in many businss sttings CVP analysis provids usful information. Accountants and managrs us thir knowldg of th organization s oprations and thir judgmnt to valuat whthr th CVP assumptions ar rasonabl for thir stting. Thy can rly mor on CVP rsults whn th assumptions ar lss likly to b violatd. Also, th data usd in CVP calculations must b updatd continually to b usful. CVP for Nonprofit Organizations Th basic CVP formulas in this chaptr ar writtn for typical for-profit businsss such as manufacturrs, rtailrs, or srvic providrs. Nonprofit organizations oftn rciv grants and donations. Ths rvnu sourcs complicat CVP calculations bcaus thy could b affctd by quantity of goods or srvics sold. Grants and donations that ar unrlatd to th

16 ch03.qxd 9/7/04 4:06 PM Pag 0 ASSUMPTIONS AND LIMITATIONS OF COST-VOLUME-PROFIT ANALYSIS 0 quantity of goods or srvics sold ar offst against fixd costs in th CVP formulas. Howvr, whn grants and donations vary with a not-for-profit organization s oprating activitis, thy might b includd in rvnus or subtractd from variabl costs. Th tratmnt dpnds on th natur of th grant or donation. Th following illustration continus th story of Small Animal Clinic from Chaptr. Rcall that Small Animal Clinic is a not-for-profit organization that trats small animals. It rcivd a foundation grant that matchs incoming rvnus. For xampl, if a pt ownr pays $30 in fs, th foundation matchs with an additional $30 to th clinic. In this cas, th grant is includd in rvnus for CVP calculations. SMALL ANIMAL CLINIC NOT-FOR-PROFIT ORGANIZATION CVP ANALYSIS WITH TWO RELEVANT RANGES Lticia Brown, Small Animal Clinic managr, and th accountant, Josh Hardy, ar complting th oprating budgt for 006. Lticia stimatd that th clinic will xprinc 3,800 animal visits, and Josh stimatd th cost function as follows: 6 TC $9,009 $6.40Q whr Q is th numbr of animal visits. Lticia and Josh budgtd rvnu pr animal visit at $60 ($30 in fs plus $30 in matching grant). Thus, thy stimatd that th clinic should achiv a surplus of $46,67[($60)(3,800) $9,009 ($6.40)(3,800)]. Th clinic is a not-for-profit organization and pays no incom taxs on its surplus. To complt th planning procss for nxt yar, Lticia asks Josh to comput th clinic s brakvn point. As managr of a not-for-profit organization, sh is particularly snsitiv to financial risk and wants to know how much th clinic s activity lvls could drop bfor a loss would occur. Brakvn Compard to Budgt Josh prforms th following calculations. With rvnu pr visit of $60, th contribution margin pr animal visit is P V $60.00 $6.40 $43.60 Josh solvs for Q with profit qual to $0 to find th brakvn point in numbr of animal visits: F Profit ($9,009 $0) Q,730 visits (P V ) $43.60 Lticia is plasd to s that th budgtd numbr of animal visits (3,800) is significantly highr than th brakvn numbr. This rsult givs hr considrabl assuranc that th clinic is not likly to incur a loss, vn if rvnus fail to achiv targtd lvls or if costs xcd stimatd amounts. Potntial Invstmnt in Nw Equipmnt During th first two months of 006, Lticia larns that th numbr of animal visits at Small Animal Clinic is running approximatly 0% highr than th budgt, and costs sm to b undr control. Lticia thinks that th clinic might b on track for a high surplus this yar. For th past two yars, Lticia has bn intrstd in purchasing quipmnt costing $00,000 to provid low-cost nutring srvics. This yar PAWS, a local charity, offrd to pay for half of th quipmnt cost, but only aftr th clinic raiss th othr half of th funds. Currntly th clinic has no xcss cash bcaus surpluss from prior yars wr invstd in othr projcts. Thus, th (continud) 6 In th Chaptr illustration Small Animal Clinic (Part ), th cost function was calculatd as: TC $9,009 ($5.0)(Numbr of animal visits) (0.04)(F rvnu). If avrag f rvnu is $30 pr animal visit, thn th last trm in th cost function can b rwrittn as (0.04)($30)(Numbr of animal visits), which can b simplifid as ($.0)(Numbr of animal visits). This substitution allows th cost function to b rwrittn as: TC $9,009 ($6.40)(Numbr of animal visits). This vrsion of th cost function is appropriat for stimating total costs for th clinic, but it would not b appropriat for stimating total costs for a singl animal visit, whr th fs vary dpnding on th srvics prformd.

17 ch03.qxd 9/7/04 4:06 PM Pag 0 0 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS clinic nds to rais $00,000 to rciv th PAWS grant. Lticia asks Josh to calculat th numbr of animal visits ndd to achiv a surplus of $00,000. Calculating and Analyzing Targtd Activity Lvl Josh calculats th xpctd quantity ndd to achiv $00,000 surplus as follows: F Profit $9,009 $00,000 $9,009 Q 5,04 animal visits P V $60.00 $6.40 $43.60 H thn calculats th total dollar amount of rvnu ndd: F Profit $9,009 $00,000 Rvnus $30,389 (P V )/P $43.60/$60.00 Josh tlls Lticia that th clinic will nd to arn $30,389 in rvnus or 5,04 visits to achiv a surplus of $00,000. Th budgtd lvl of activity (3,800 animal visits) is substantially highr than th lvl of activity ndd to brak vn (,730 animal visits). If animal visits continu to xcd this yar s budgt by 0%, Josh stimats that animal visits will rach 4,80 (3,800.0) by yar-nd. Howvr, h thinks that it would b vry difficult to achiv a targtd surplus of $00,000 (5,04 animal visits). CVP Adjustd for Chang in Rlvant Rang As Josh works on his rport, h ralizs that th clinic s cost function might chang if th numbr of animal visits gts vry high. Lticia told him that sh will probably hir anothr tchnician and nd to rnt mor spac and purchas additional quipmnt if animal visits xcd 4,000 this yar. Thrfor, Josh s cost function for 5,04 visits is wrong. H dvlops a nw cost function assuming that an additional tchnician, spac, and quipmnt will incras fixd costs by about $60,000 pr yar. TC ($9,009 $60,000) $6.40Q $79,009 $6.40Q, for Q 4,000 Thus, Josh s arlir CVP analysis was incorrct whn animal visits xcd 4,000. Th lvl of activity ndd for a targtd surplus of $00,000 nds to b rcalculatd: ($79,009 $00,000) $ ,400 for Q 4,000 Josh notics that an activity lvl of 6,400 animal visits is noticably highr than th 5,04 visits h first calculatd. H ralizs how important it is to adjust for th rlvant rang whn prforming CVP analyss. Whn Josh shows Lticia th nw rsults, thy agr that th clinic cannot rais th funds for nw quipmnt by incrasing th numbr of visits to 6,400. Lticia may nd to cut costs or sk othr ways to pay for th nutring quipmnt. Th additional fixd cost would also rquir th clinic to hav a much highr volum of oprations to avoid a loss. GUIDE YOUR LEARNING 3.4 Small Animal Clinic Small Animal Clinic illustrats a CVP analysis with targt profit and two rlvant rangs for a not-for-profit organization. For this illustration: Idntify Problm Dfin It and Information Idntify Uncrtaintis Explor Assumptions Dscrib how th CVP computations chang whn mor than on rlvant rang is involvd. What dcisions wr bing addrssd? Why was CVP information usful for th dcisions? What wr th uncrtaintis? Considr uncrtaintis about: Rvnu and cost stimats Intrprting rsults Rlvant rang of oprations Fasibility of activity lvl How rasonabl ar th CVP assumptions for Small Animal Clinic?

18 ch03.qxd 9/7/04 4:06 PM Pag 03 MARGIN OF SAFETY AND DEGREE OF OPERATING LEVERAGE 03 MARGIN OF SAFETY AND DEGREE OF OPERATING LEVERAGE In Small Animal Clinic, th managr usd CVP information to hlp hr larn how much th volum of businss could dclin bfor th clinic would incur a loss. Th managr of Spottd Cow Cramry was abl to idntify th spcific products to mphasiz for incrasd profitability. Managrs ar oftn intrstd in ths typs of qustions. In addition, information from CVP analysis can b usd to hlp manag oprational risk. Q6 How ar margin of safty and oprating lvrag usd to assss oprational risk? Margin of Safty Th margin of safty is th xcss of an organization s xpctd futur sals (in ithr rvnu or units) abov th brakvn point. Th margin of safty indicats th amount by which sals could drop bfor profits rach th brakvn point: Margin of safty in units Actual or stimatd units of activity Units at brakvn point Margin of safty in rvnus Actual or stimatd rvnu Rvnu at brakvn point Th margin of safty is computd using actual or stimatd sals valus, dpnding on th purpos. To valuat futur risk whn planning, us stimatd sals. To valuat actual risk whn monitoring oprations, us actual sals. If th margin of safty is small, managrs may put mor mphasis on rducing costs and incrasing sals to avoid potntial losss. A largr margin of safty givs managrs gratr confidnc in making plans such as incurring additional fixd costs. Th margin of safty prcntag is th margin of safty dividd by actual or stimatd sals, in ithr units or rvnus. This prcntag indicats th xtnt to which sals can dclin bfor profits bcom zro. Margin of safty prcntag in units Margin of safty prcntag in rvnus Margin of safty in units Actual or stimatd units Margin of safty in rvnu Actual or stimatd rvnu Whn th original budgt was cratd for Small Animal Clinic, th brakvn point was calculatd as,730 animal visits, or $63,800 in rvnus. Howvr, Lticia and Josh xpctd 3,800 animal visits, for $8,000 in rvnu. Thir margin of safty in units of animal visits was,070 (3,800,730) and in rvnus was $64,00 ($8,000 $63,800). Thir margin of safty prcntag was 8.% (,070 3,800, or $64,00 $8,000). In othr words, thir sals volum could drop 8.% from xpctd lvls bfor thy xpctd to incur a loss. Exhibit 3.8 provids a CVP graph for this information. EXHIBIT 3.8 CVP Graph and Margin of Safty for Small Animal Clinic Dollars $8,000 Margin of Safty in Rvnus = $64,00 Total Rvnu Estimatd Surplus = $64,00 Total Costs $63,800 Margin of Safty =,070 visits Brakvn Point =,730 animal visits Quantity of Animal Visits Expctd visits = 3,800 visits

19 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS Dgr of Oprating Lvrag Managrs dcid how to structur th cost function for thir organizations. Oftn, potntial trad-offs ar mad btwn fixd and variabl costs. For xampl, a company could purchas a vhicl (a fixd cost) or it could las a vhicl undr a contract that chargs a rat pr mil drivn (a variabl cost). Exhibit 3.9 lists som of th common advantags and disadvantags of fixd costs. On of th major disadvantags of fixd costs is that thy may b difficult to rduc quickly if activity lvls fail to mt xpctations, thrby incrasing th organization s risk of incurring losss. Th dgr of oprating lvrag is th xtnt to which th cost function is mad up of fixd costs. Organizations with high oprating lvrag incur mor risk of loss whn sals dclin. Convrsly, whn oprating lvrag is high an incras in sals (onc fixd costs ar covrd) contributs quickly to profit. Th formula for oprating lvrag can b writtn in trms of ithr contribution margin or fixd costs, as shown hr. 7 Dgr of oprating lvrag in trms of contribution margin Contribution margin TR TVC Profit Profit Dgr of oprating lvrag in trms of fixd costs F Profit Managrs us th dgr of oprating lvrag to gaug th risk associatd with thir cost function and to xplicitly calculat th snsitivity of profits to changs in sals (units or rvnus): % chang in profit % chang in sals Dgr of oprating lvrag For Small Animal Clinic, th variabl cost pr animal visit was $6.40 and th fixd costs wr $9,009. With budgtd animal visits of 3,800, th managrs xpctd to arn a profit of $46,67. Th xpctd dgr of oprating lvrag using th contribution margin formula is thn calculatd as follows: ($60 $6.40) 3,800 visits $65,680 Dgr of oprating lvrag 3.55 $46,67 $46,67 W arriv at th sam answr of 3.55 if w us th fixd cost formula: $9,009 Dgr of oprating lvrag $46,67 (P V ) Q Profit EXHIBIT 3.9 Advantags and Disadvantags of Fixd Costs Common Advantags Common Disadvantags Fixd costs might cost lss in total than Invsting in fixd rsourcs might divrt variabl costs. managmnt attntion away from th Companis might rquir uniqu assts organization s cor comptncis. (.g., xprt labor or spcializd production Fixd costs typically rquir a longr facilitis) that must b acquird through long- financial commitmnt; it can b difficult to trm commitmnts. rduc thm quickly. Fixd assts such as automation and robotics Undrinvstmnt or ovrinvstmnt in fixd quipmnt can significantly improv oprating costs could affct profits and may not asily fficincy. b changd in th short trm. Fixd costs ar asir to plan; thy do not fluctuat with lvls of activity. 7 To s th rlationship btwn th two formulas, rcall th profit quation: Profit (P V ) Q F, which can b rwrittn as F Profit Contribution margin. In turn, Dgr of oprating lvrag Contribution margin Profit (F Profit) Profit (F Profit).

20 ch03.qxd 9/7/04 4:06 PM Pag 05 MARGIN OF SAFETY AND DEGREE OF OPERATING LEVERAGE 05 Th dgr of oprating lvrag and margin of safty prcntag ar rciprocals. Margin of safty prcntag Dgr of oprating lvrag Dgr of oprating lvrag Margin of safty prcntag If th margin of safty prcntag is small, thn th dgr of oprating lvrag is larg. In addition, th margin of safty prcntag is smallr as th fixd cost portion of total cost gts largr. As th lvl of oprating activity incrass abov th brakvn point, th margin of safty incrass and th dgr of oprating lvrag dcrass. For Small Animal Clinic, th rciprocal of th margin of safty prcntag is 3.55 ( 0.8). Th rciprocal of th dgr of oprating lvrag is 0.8 ( 3.55). CURRENT PRACTICE Bfor 983, Mdicar usd costbasd paymnt. Hospitals had high oprating lvrag bcaus risk of loss was low. Aftr Mdicar changd to a flat f pr patint, managrs lowrd thir oprating lvrag. 8 Using th Dgr of Oprating Lvrag to Plan and Monitor Oprations Managrs nd to considr th dgr of oprating lvrag whn thy dcid whthr to incur additional fixd costs, such as purchasing nw quipmnt or hiring nw mploys. Thy also nd to considr th dgr of oprating lvrag for potntial nw products and srvics that could incras an organization s fixd costs rlativ to variabl costs. If additional fixd costs caus th dgr of oprating lvrag to rach what thy considr an unaccptably high lvl, managrs oftn us variabl costs such as tmporary labor rathr than additional fixd costs to mt thir oprating nds. For xampl, th tchnicians at th Small Animal Clinic ar paid a salary and work 40-hour wks. Suppos Lticia could hir part-tim tchnicians at $0.00 pr hour instad of hiring full-tim tchnicians at th currnt salaris of $78,009. If ach visit rquirs about an hour of tchnician tim, th nw cost function would b TC ($9,009 $78,009) ($6.40 $0.00)Q $4,000 $36.40Q. Th brakvn point dcrass considrably to,738 animal visits [$4,000 ($60.00 $36.40) pr animal visit] or $04,80. Profit at Q 3,800 animal visits is $48,680 [$8,000 $4,000 (3,800 animal visits $36.40 pr animal visit)]. Oprating lvrag at 3,800 animal visits bcoms.84 [($4,000 $48,680) ], which is much lowr than th 3.55 whn tchnicians ar a fixd cost. Although oprating lvrag improvd, th cost for tchnicians incrasd from $8.75 pr hour [$78,009 ( tchnicians,080 hours pr tchnician pr yar)] to $0.00 pr hour. Th advantag of having tchnicians as hourly workrs is that thy can b schduld only for hours whn appointmnts ar also schduld. Whn businss is slow fwr tchnician hours ar ndd, which mans lss risk of incurring losss if th numbr of visits drops. Exhibit 3.0 provids a CVP graph of th two options. Risk dcrass considrably whn th brakvn point is so much lowr. On th othr hand, it may b mor difficult to hir qualifid and dpndabl tchnicians unlss work hours and pay can b guarantd. An indiffrnc point is th lvl of activity at which qual cost or profit occurs across multipl altrnativs. To provid Lticia with additional information as sh considrs changing th cost structur, Josh calculats th indiffrnc point. Using th budgtd assumptions, Josh sts th two cost functions qual to ach othr and thn solvs for Q as follows: $4,000 $36.40Q $9,009 $6.40Q $0Q $78,009, so Q 3,90 Whn visits ar fwr than 3,90, th clinic profit will b gratr using mor variabl cost. Whn visits xcd 3,90, th clinic is bttr off using mor fixd costs, assuming that th fixd costs rmain constant up to 4,000 visits. Whn visits xcd 4,000, w know that additional fixd costs will b incurrd, and thn a nw indiffrnc point will nd to b calculatd. 8 S. Kallapur and L. Eldnburg, Uncrtainty, Ral Options, and Cost Bhavior: Evidnc from Washington Stat Hospitals, Univrsity of Arizona Working Papr, 003.