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.

21 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS EXHIBIT 3.0 CVP Graph for Small Animal Clinic with Diffrnt Dgrs of Oprating Lvrag Total Rvnu $34,060 Dollars $8,996 $63,800 $9,009 $04,80 Indiffrnc point TC = 4, Q TC = 9, Q $4,000,738 Quantity of Animal Visits,730 3,90 Notic that th indiffrnc point calculation ignors oprational risk. At 3,90 animal visits, th clinic is xpctd to arn th sam profit undr th two cost function altrnativs. Howvr, th clinic s oprational risk is gratr for th cost function having highr fixd costs. Thrfor, th clinic s managr would not ncssarily b indiffrnt btwn th two cost functions if 3,90 animal visits wr xpctd. GUIDE YOUR LEARNING 3.5 Ky Trms Stop to confirm that you undrstand th nw trms introducd in th last svral pags: Margin of safty (p. 03) Dgr of oprating lvrag (p. 04) Margin of safty prcntag (p. 03) Indiffrnc point (p. 05) For ach of ths trms, writ a dfinition in your own words. In rcnt yars, U.S. companis hav incrasingly rlid on tmporary labor (also calld contingnt or contract workrs) to fill positions that in th past would hav bn filld by rgular mploys. Tmporary jobs span th ntir workforc including manufacturing, srvic, farm, and profssional srvics. Managrs gain many bnfits including th following: FOCUS ON ETHICAL DECISION MAKING Tmporary Labor Rduc risk of loss by incrasing th proportion of variabl costs. Quickly incras and dcras mploymnt lvls in rspons to conomic changs. Pay highr wags to skilld workrs without inflating th pay scals of rgular mploys. Pay lowr wags and avoid making hiring commitmnts to low-skilld mploys. Fill positions whil rcruiting prmannt workrs during labor shortags. Many conomists and businss analysts argu that tmporary labor is good for workrs and th conomy. Tmporary work arrangmnts provid th following conomic bnfits:

22 ch03.qxd 9/7/04 4:06 PM Pag 07 MARGIN OF SAFETY AND DEGREE OF OPERATING LEVERAGE 07 Rduc ovrall unmploymnt lvls bcaus mployrs ar lss rluctant to hir tmporary labor than rgular mploys. Incras mploymnt opportunitis for nw workforc ntrants, workrs laid off from jobs, and workrs wanting flxibl work schduls. Improv rgular mploy moral by rducing thir unmploymnt risk. On th othr hand, labor groups, homlss advocacy groups, and othrs bliv that tmporary labor arrangmnts ar socially harmful. Thy argu that th us of tmporary labor contributs to th following issus: Unfairly rducs ovrall pay scals for skilld and unskilld workrs. Incrass unmploymnt risk for th last-skilld and lowst-paid workrs, contributing to povrty and homlssnss. Rducs workr rprsntation as wll as halth car and rtirmnt bnfits. SOURCES: J. C. Coopr and K. Madigan, U.S.: Labor s Nw Flxibility Cuts Two Ways, Businss Wk, Dcmbr 4, 00; and S. N. Housman, A. L. Kallbrg, and G. A. Erickck, Th Rol of Tmporary Hlp Employmnt in Tight Labor Markts, Upjohn Institut Staff Working Papr No. 0-73, July 00. Availabl at Practic Ethical Dcision Making In Chaptr, w larnd about a procss for making thical dcisions (Exhibit.). You can addrss th following qustions to improv your skills for making thical dcisions. Think about your answrs to ths qustions and discuss thm with othrs. Ethical Dcision-Making Procss Idntify thical problms as thy aris. Objctivly considr th wll-bing of othrs and socity whn xploring altrnativs. Clarify and apply thical valus whn choosing a cours of action. Work toward ongoing improvmnt of prsonal and organizational thics. Qustions to Considr about This Ethical Dilmma Dos th hiring of tmporary labor crat an thical problm? Why or why not? Diffrnt viwpoints for this problm wr dscribd in th prcding xampl. What assumptions li bhind ach viwpoint? Is th hiring of tmporary labor a businss issu, a social issu, or both? Explain. Idntify th valus you us to answr th following qustions: Is it fair for mployrs to pay diffrnt wag rats and provid diffrnt bnfits to tmporary and prmannt workrs who prform th sam jobs? Is it fair for businsss to pass thir businss risks dirctly on to th mploys? How can company managrs dtrmin on an ongoing basis whthr thir hiring practics ar thical?

23 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS APPENDIX 3A Spradsht Formulas for Magik Bicycls Spradsht Th following formulas wr usd for th spradsht shown in Exhibit 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 Youth Biks 0, ,700,000 00, Youth Biks =B3 =B3*B4 =B5*B3 =B4-B5 =B6/B3 =B6/B4 =B3/$E3 =B4/$E4 B C D E Youth Biks =B*$E$36 =B36*B4 =B36*B5 =B37-B38 Youth Biks =$E$46*B =B46*B5/B4 =B46-B47 Road Biks 8, (ntr zro for brakvn) Road Biks =C3 =C3*C4 =C5*C3 =C4-C5 =C6/C3 =C6/C4 =C3/$E3 =C4/$E4 Road Biks =C*$E$36 =C36*C4 =C36*C5 =C37-C38 Road Biks =$E$46*C =C46*C5/C4 =C46-C47 Mtn. Biks, Mtn. Biks =D3 =D3*D4 =D5*D3 =D4-D5 =D6/D3 =D6/D4 =D3/$E3 =D4/$E4 Mtn. Biks =D*$E$36 =D36*D4 =D36*D5 =D37-D38 Mtn. Biks =$E$46*D =D46*D5/D4 =D46-D47 Total Biks =SUM(B3:D3) =SUM(B4:D4) =SUM(B5:D5) =SUM(B6:D6) =E6/E3 =E6/E4 =SUM(B:D) =SUM(B:D) =E6 =B7 =E6-E6 =B9*E7 =E7-E8 =B8/(-B9) =B7+E3 Total Biks =E33/E8 =SUM(B37:D37) =SUM(B38:D38) =E37-E38 =B7 =E39-E40 =E4*B9 =E4-E4 Total Biks =E33/E9 =SUM(B47:D47) =E46-E47 =B7 =E48-E49 =B9*E50 =E50-E5 SUMMARY Q What Is Cost-Volum-Profit (CVP) Analysis, and How Is It Usd for Dcision Making? Cost-Volum-Profit (CVP) Analysis A tchniqu that xamins changs in profits in rspons to changs in sals volums, costs, and prics CVP Graph Shows th rlationship btwn total rvnus and total costs; illustrats how an organization s profits ar xpctd to chang undr diffrnt volums of activity

24 ch03.qxd 9/7/04 4:06 PM Pag 09 SUMMARY 09 Uss 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 Discrtionary xpnditurs Product mphasis such as advrtising Slling pric Proportions of fixd Production or activity lvls vrsus variabl costs Employ work schduls Raw matrial purchass Monitor oprations by comparing xpctd and actual: Volums, rvnus, costs, and profits Profitability risk Q How Ar CVP Calculations Prformd for a Singl Product? CVP Formulas CVP analysis in units ndd to attain targt profit: F Profit Q Contribution margin pr unit CVP analysis in rvnus ndd to attain targt profit: F Profit F Profit F Profit Rvnus Contribution margin ratio (P V )/P (TR TVC)/TR Prtax profit ndd to achiv a givn lvl of aftr-tax profit: Aftr-tax profit Prtax profit ( Tax rat) F Profit P V Q3 How Ar CVP Calculations Prformd for Multipl Products? Us CVP Formulas for a Singl Product, Excpt Wightd avrag contribution margin pr unit Wightd avrag contribution margin ratio Total xpctd contribution margin Total xpctd numbr of units Total xpctd contribution margin Total xpctd rvnu Q4 What Is th Brakvn Point? Brakvn Point Lvl of oprating activity at which rvnus covr all fixd and variabl costs, rsulting in zro profit. Calculation St targt profit qual to zro in th CVP formula. Q5 What Assumptions and Limitations Should Managrs Considr Whn Using CVP Analysis? CVP Assumptions Oprations within a rlvant rang of activity Linar cost function Fixd costs rmain fixd. Variabl cost pr unit rmains constant. Linar rvnu function Sals mix rmains constant. Prics rmain constant. Uncrtaintis Actual futur volums, rvnus, and costs ar unknown. CVP assumptions might not hold. In Light of Assumptions and Uncrtaintis, Nd to Evaluat: Quality of data usd in CVP analyss Suitability of CVP analysis for th stting Snsitivity of CVP rsults to changs in data for important uncrtaintis

25 ch03.qxd 9/7/04 4:06 PM Pag 0 0 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS Q6 How Ar Margin of Safty and Oprating Lvrag Usd to Assss Oprational Risk? Margin of Safty 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 Margin of safty prcntag Margin of safty in units Actual or stimatd units Dgr of Oprating Lvrag In trms of contribution margin: Contribution margin TR TVC (P V ) Q Dgr of oprating lvrag Profit Profit Profit In trms of fixd costs: F Dgr of oprating lvrag Profit Snsitivity of profits to changs in sals (units or rvnus): % chang in profit % chang in sals Dgr of oprating lvrag Rlationship Btwn Margin of Safty and Dgr of Oprating Lvrag Margin of safty prcntag Dgr of oprating lvrag Highr Oprating Lvrag (Lowr Margin of Safty) Lads to: Gratr risk of loss Acclratd profits abov th brakvn point Margin of safty in rvnus Actual or stimatd rvnus KEY TO SYMBOLS This qustion rquirs studnts to xtnd knowldg byond th applications shown in th txtbook. This qustion rquirs Stp skills (Idntifying) in Stps 3 4 for Bttr Thinking (Exhibit.0). This qustion rquirs Stp skills (Exploring) in Stps for Bttr Thinking (Exhibit.0). This qustion rquirs Stp 3 skills (Prioritizing) in Stps for Bttr Thinking (Exhibit.0). This qustion rquirs Stp 4 skills (Envisioning) in Stps for Bttr Thinking (Exhibit.0). Q, Q3, Q5, Q6 Slf-Study Problm Slf-Study Problms Cost Function, Targt Profit, Margin of Safty, Oprating Lvrag Coff Cart Suprm slls hot and icd coff bvrags and small snacks. Th following is last month s incom statmnt. Rvnu $5,000 Cost of bvrags and snacks $,000 Cost of napkins, straws, tc. 500 Cost to rnt cart 500 Employ wags, , Prtax profit,000 Taxs Aftr-tax profit 5 0 $ 7 5 0

26 ch03.qxd 9/7/04 4:06 PM Pag SELF-STUDY PROBLEMS A. What is th total cost function for Coff Cart Suprm? B. What is th tax rat for Coff Cart Suprm? C. Calculat th amount of sals ndd to rach a targt aftr-tax profit of $,500. D. What was Coff Cart Suprm s dgr of oprating lvrag last month? E. What was Coff Cart Suprm s margin of safty in rvnu last month? F. What was Coff Cart Suprm s margin of safty prcntag last month? G. Suppos nxt month s actual rvnus ar $8,000 and prtax profit is $,000. Would actual costs b highr or lowr than xpctd? H. Coff costs ar volatil bcaus worldwid coff production varis from yar to yar. Explain how this volatility affcts th quality of th cost function for Coff Cart Suprm. Solution to Slf-Study Problm A. To stimat th cost function, w us judgmnt to classify costs as fixd, variabl, or mixd. For a typical rtail businss, rnt and wags ar likly to b fixd. W stimat fixd costs as th sum of ths two costs ($500 $,000 $,500). It sms rasonabl that th costs of bvrags and snacks ($,000) and napkins, straws, tc. ($500) would vary with rvnus. W us th rvnus as th cost drivr to stimat variabl costs as $,500 $5, , or 50% of rvnus. Thus, th cost function is TC $,500 (50% Rvnu) B. W us incom tax xpns and prtax profit from last month to stimat th tax rat: Tax rat Taxs Prtax profit $50 $,000 5% C. W first calculat th amount of prtax profit ndd to achiv an aftr-tax profit of $,500. Th contribution margin ratio is Targtd prtax profit $,500 ( 0.5) $,000 W thn prform th CVP calculation for rvnus. (5,000,500) 5, or 50% Rvnu ($,500 $,000) 0.50 $3, $7,000 D. W us th rsults of our prvious computations to calculat th contribution margin, and w thn calculat th dgr of oprating lvrag: Contribution margin $5,000 $,500 $,500 Dgr of oprating lvrag Contribution margin Profit Dgr of oprating lvrag $,500 $, E. Bfor calculating th margin of safty, w nd to calculat th brakvn point. Not that th margin of safty must b calculatd in rvnu dollars. W do not hav unit or product mix information. Th brakvn point is calculatd as $, $3,000 in rvnus Currnt rvnus ar $5,000, so th margin of safty is calculatd as Margin of safty $5,000 $3,000 $,000 F. W us th formula to calculat margin of safty prcntag: Margin of safty prcntag $,000 $5,000 40% Not that w can chck our prvious dgr of oprating lvrag computation as follows: Dgr of oprating lvrag Margin of safty prcntag G. Th xpctd and actual costs at $8,000 rvnu ar Expctd Costs $,500 (50% $8,000) $5,500 Actual Costs $8,000 $,000 $6,000 Actual costs ar $500 highr than xpctd.

27 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS H. Whn any costs ar volatil, prdicting thm is problmatic. Worldwid coff prics ar uncrtain for many rasons, such as wathr conditions in coff growing aras, th ability of farmrs to incras crops, and coff dmand pattrns. In addition, broadr factors such as changs in conomis and political uphaval influnc costs. All of ths factors rduc our ability to dvlop a cost function that accuratly prdicts futur costs, which mans that th quality of th cost function is diminishd. Q, Q, Q5 collg/ldnburg Slf-Study Problm Snsitivity Analysis Th spradsht dvlopd for th Magik Bicycls xampls in this chaptr is availabl on th Wb at www. wily.com/collg/ldnburg. Download th tmplat and us th spradsht to answr th following qustions. A printout of th formulas usd in th spradsht is availabl in Appndix 3A. 3 A. Examin th spradsht so that you undrstand how th clls in th data input sction ar rfrncd. Whn all of th dcision variabls ar locatd in on plac in th spradsht, accountants and managrs can asily prform snsitivity analysis by changing valus in th data input sction. Why is it important to b abl to chang th spradsht asily to rflct changs in assumptions? B. Suppos that Magik adds a hlmt to ach youth bik sold. Th hlmts cost $5 ach but incorporat nw matrials and an innovativ dsign that has rducd injuris and daths from childrn s bik accidnts. Magik s managrs bliv that by advrtising th nw hlmt as part of th youth bik packag, sals will incras to 3,000. Howvr, an advrtising campaign will nd to b undrtakn to alrt parnts to th bnfits of th nw hlmt. How much can Magik afford to spnd on advrtising and still xpct to arn th original aftr-tax profit of $455,000? Assum th slling pric rmains at $00 pr bik packag. C. Idntify CVP input factors that you bliv ar uncrtain for this dcision, and us your judgmnt to dtrmin a nw valu for ach factor. Rflct ths changs in th spradsht to s how thy affct th brakvn point and profitability. Choos a bst-cas and worst-cas scnario to prsnt to th managrs of Magik Bicycls. Mak a list of th points you would includ in a mmo xplaining your snsitivity analysis to th managrs. Solution to Slf-Study Problm A. Accountants and managrs will xplor changs in mor assumptions and vary th valus within th spradsht mor radily if it is asy to do. Whn ths changs ar mad and th rsults ar analyzd, managrs bttr undrstand how unplannd changs in futur oprations might affct profitability. This knowldg allows thm to mor radily valuat rsults and adjust oprating plans. B. Exhibit 3. provids rlvant parts of th spradsht with th changs. With incrasd sals of youth biks from 0,000 to 3,000 and an incrasd variabl cost from $75 to $00, xpctd prtax profits incras to $700,000. Comparing $700,000 to $650,000 (Exhibit 3.), Magik can spnd up to $50,000 on advrtising to maintain its currnt lvl of profitability. C. Many diffrnt scnarios could occur. No singl answr is always corrct. Your answr dpnds on th assumptions that you mak. Following ar som xampl assumptions for th bst and worst cass. Your most likly cas should b btwn ths two valus. On bst cas is that th nw stratgy is vry popular with customrs. Mor than 3,000 of th biks ar sold. Th managrs discovr that customrs ar willing to pay a highr pric for th bik, so thy rais th pric. In addition, manufacturing fficincy improvs with th gratr volum, rducing variabl cost pr unit. Also, fixd costs ar lowr than xpctd bcaus th managrs found som costs that could b rducd. On worst cas is that th hlmts fail to attract customrs. In fact, sals fail to mt original xpctations; fwr than 0,000 ar sold. Bcaus th company producd xtra biks xpcting an incras in dmand, th managrs lowr th slling pric to ncourag additional sals. In addition, th company hirs xtra workrs to mt th xpctd dmand, and othr costs such as insuranc and lctricity ar highr than xpctd. Ths changs causd both th variabl and fixd costs to b highr than originally plannd. Your mmo to th managrs should includ th following: Explain th assumptions for th bst cas and worst cas scnarios. Explain th rasoning bhind th most likly cas. Ask managrs to considr bforhand how thy would rspond to th bst- and worst-cas scnarios. Mak suggstions for monitoring th rsults for th youth bik. Encourag th managrs to valuat th advrtising and product rsults, and mak suggstions for improving th opration or dropping th nw hlmt, if plans ar unsuccssful.

28 ch03.qxd 9/7/04 4:06 PM Pag 3 QUESTIONS 3 EXHIBIT 3. Spradsht for Magik Bicycls Youth Hlmt Dcision 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 A Expctd Incom Contribution margin (abov) Fixd costs Prtax incom Incom taxs Aftr-tax incom B C D E Youth Biks 3,000 $00 $00 $4,700,000 $00,000 30% Youth Biks 3,000 $,600,000,300,000 $,300,000 $ % 30.3% 0.48% Road Biks 8,000 $700 $50 (ntr zro for brakvn) Road Biks 8,000 $,600,000 4,500,000 $8,00,000 $ % 4.86% 50.8% Mtn. Biks,000 $800 $300 Mtn. Biks,000 $9,600,000 3,600,000 $6,000,000 $ % 7.9% 38.7% Total Biks 43,000 $4,800,000 9,400,000 $5,400,000 $ % 00.00% 00.00% $5,400,000 4,700, ,000 0,000 $490,000 REVIEW Us th following boxs from th chaptr to rviw ky trms and ky tchniqus, analyz chaptr illustrations, improv your larning of nw concpts, and practic thical dcision making: Guid Your Larning 3.: Ky Trms (p. 9) Guid Your Larning 3.: Th Spottd Cow Cramry (Part ) (p. 93) Guid Your Larning 3.3: Th Spottd Cow Cramry (Part ) (p. 98) Guid Your Larning 3.4: Small Animal Clinic (p. 0) Guid Your Larning 3.5: Ky Trms (p. 06) Focus on Ethical Dcision Making: Tmporary Labor (p. 07) QUESTIONS 3. If a firm has a mixd cost function, a 0% incras in sals volum should incras incom by mor than 0%. Explain why. 3. Explain how to calculat a wightd avrag contribution margin pr unit. 3.3 An organization xprincs a 0% incras in prtax profits whn rvnus incras 0%. Assuming linarity, what do you know about th organization s cost function? 3.4 What is th ffct on a firm s brakvn point of a lowr incom tax rat? 3.5 To stimat rvnus, costs, and profits across a rang of activity, w usually assum that th cost and rvnu functions ar linar. What ar th spcific undrlying assumptions for linar cost and rvnu functions, and how rasonabl ar ths assumptions? 3.6 Explain th rlationship btwn margin of safty prcntag and dgr of oprating lvrag. 3.7 How do volum discounts from supplirs affct our assumption that th cost function is linar? Explain how w incorporat this typ of cost into a CVP analysis. 3.8 Explain th trm sals mix in your own words. How dos sals mix affct th contribution margin? 3.9 How ar CVP analysis and brakvn analysis rlatd? 3.0 Can th margin of safty vr b ngativ? Explain your answr. 3. Dscrib thr uss for CVP analysis. 3. Explain how CVP analysis can b usd to mak dcisions about incrass in advrtising costs. 3.3 Undr what circumstancs will managrs want snsitivity analysis around rsults from a CVP analysis?

29 ch03.qxd 9/7/04 4:06 PM Pag 4 4 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS EXERCISES 3.4 Q, Q4 3.5 Q, Q4 3.6 Q, Q4 Targt profit, not-for-profit brakvn A. Th variabl cost pr gift baskt is $, fixd costs ar $5,000 pr month, and th slling pric of a baskt is $7. How many baskts must b producd and sold in a month to arn a prtax profit of $,000? B. Th Community Clinic (a not-for-profit mdical clinic) rcivd a lump-sum grant from th City of Tucson of $460,000 this yar. Th fixd costs of th clinic ar xpctd to b $36,000. Th avrag variabl cost pr patint visit is xpctd to b $7.64 and th avrag f collctd pr patint visit is $4.64. What is th brakvn volum in patint visits? CVP graph A. Crat a CVP graph using th information in Exrcis 3.4, part (A). Explain th information in th graph. B. Crat a CVP graph using th information in Exrcis 3.4, part (B). Explain th information in th graph. Cost function, brakvn A. Th avrag cost pr unit was $34 at a volum of,00 units and $05 at a volum of,400 units. Th profit was $4,000 at th lowr volum. Estimat th variabl cost pr unit. B. Sparkl Car Wash Supplir slls a hos washr for $0.5 that it buys from th manufacturr for $0.. Variabl slling costs ar $0.0 pr hos washr. Brakvn is currntly at a sals volum of $0,600 pr month. What ar th monthly fixd costs associatd with th washr? C. Monthly fixd costs ar $4,000 whn volum is at or blow 00 units and $36,000 whn monthly volum is abov 00 units. Th variabl cost pr unit is $00 and th slling pric is $300 pr unit. What is th brakvn quantity? 3.7 Q 3.8 Q4 Profit, pric for targt profit Th Martll Company has rcntly stablishd oprations in a comptitiv markt. Managmnt has bn aggrssiv in its attmpt to stablish a markt shar. Th pric of th product was st at $5 pr unit, wll blow that of th company s major comptitors. Variabl costs wr $4.50 pr unit, and total fixd costs wr $600,000 during th first yar. A. Assum that th firm was abl to sll million units in th first yar. What was th prtax profit (loss) for th yar? B. Assum that th variabl cost pr unit and total fixd costs do not incras in th scond yar. Managmnt has bn succssful in stablishing its position in th markt. What pric must b st to achiv a prtax profit of $5,000? Assum that sals rmain at million units. Cost function, brakvn Data for th most rcnt thr months of oprations for th RainBau Salon appar hr: March April May Numbr of appointmnts,600,500, Q, Q4 Hair drssr salaris $4,000 $4,000 $8,000 Manicurist salaris,000,000 6,000 Supplis Utilitis Rnt,000,000,000 Miscllanous 3, , , Total costs $ 3, $ 3, $ 3 9, A gnral cost-of-living salary incras occurrd at th bginning of May. A. What is th total cost function for RainBau Salon? B. If th avrag f pr appointmnt is $5, stimat th appointmnts rquird in Jun to brak vn. Brakvn, targt profit, ROI targt profit Maddn Company projctd its incom bfor taxs for nxt yar as shown hr. Maddn is subjct to a 40% incom tax rat.

30 ch03.qxd 9/7/04 4:06 PM Pag 5 EXERCISES 5 Sals (60,000 units) $8,000,000 Cost of sals Variabl costs,000,000 Fixd costs Prtax profit 3, 0 0 0, $ 3, 0 0 0, A. What is Maddn s brakvn point in units sold for th nxt yar? B. If Maddn wants $4.5 million in prtax profit, what is th rquird lvl of sals in dollars? C. If Maddn s nt assts ar $36 million, what amount of rvnu must b achivd for Maddn to arn a 0% aftr-tax rturn on assts? 3.0 Q, Q, Q4 3. Q3 3. Q, Q3, Q4 Brakvn, targt profit, cost changs, slling pric Laraby Company producs a singl product. It sold 5,000 units last yar with th following rsults. Sals $65,000 Variabl costs 375,000 Fixd costs 5 0, Incom bfor taxs 00,000 Incom taxs (45%) Aftr-tax profit 4 5, $ 5 5, In an attmpt to improv its product, Laraby s managrs ar considring rplacing a componnt part that costs $.50 with a nw and bttr part costing $4.50 pr unit during th coming yar. A nw machin would also b ndd to incras plant capacity. Th machin would cost $8,000 and hav a usful lif of 6 yars with no salvag valu. Th company uss straight-lin dprciation on all plant assts. A. What was Laraby Company s brakvn point in units last yar? B. How many units of product would Laraby Company hav had to sll in th past yar to arn $77,000 in aftr-tax profit? C. If Laraby Company holds th sals pric constant and maks th suggstd changs, how many units of product must b sold in th coming yar to brak vn? D. If Laraby Company holds th sals pric constant and maks th suggstd changs, how many units of product will th company hav to sll to mak th sam aftr-tax profit as last yar? E. If Laraby Company wishs to maintain th sam contribution margin ratio, what slling pric pr unit of product must it charg nxt yar to covr th incrasd matrials costs? Targt profit, progrssiv incom tax rats, CVP graph Dalton Brothrs pay 5% in taxs on incom btwn $ and $40,000. All incom abov $40,000 is taxd at 40%. Th firm s variabl costs as a prcnt of rvnus ar 60%. Annual fixd costs ar $50,000. A. What lvl of sals must th firm achiv to arn incom aftr taxs of $50,000? B. Prpar a CVP graph for Dalton. Brakvn, slling pric, targt profit with pric and cost changs All-Day Candy Company is a wholsal distributor of candy. Th company srvics grocry, convninc, and drug stors in a larg mtropolitan ara. Small but stady growth in sals has bn achivd by th All-Day Candy Company ovr th past fw yars, but candy prics also hav bn incrasing. Th company is rformulating its plans for th coming fiscal yar. Th following data wr usd to projct th currnt yar s aftr-tax incom of $00,400. Avrag slling pric $4.00 pr box Avrag variabl costs Cost of candy $.00 pr box Slling costs pr box Total $. 40 pr box Annual fixd costs Slling $60,000 Administrativ Total 8 0, $ 4 4 0, Expctd annual sals (390,000 boxs) $,560,000 Tax rat 40%

31 ch03.qxd 9/7/04 4:06 PM Pag 6 6 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS 3.3 Q, Q, Q4, Q6 3.4 Q3 3.5 Q, Q6 Candy manufacturrs hav announcd that thy will incras prics of thir products an avrag of 5% in th coming yar bcaus of incrass in raw matrial (sugar, cocoa, panuts, and so on) and labor costs. All-Day Candy Company xpcts that all othr costs will rmain th sam as during th currnt yar. A. What is All-Day Candy Company s brakvn point in boxs of candy for th currnt yar? B. What avrag slling pric pr box must All-Day Candy Company charg to covr th 5% incras in th variabl cost of candy and still maintain th currnt contribution margin ratio? C. What volum of sals in dollars must th All-Day Candy Company achiv in th coming yar to maintain th sam aftr-tax incom as projctd for th currnt yar if th avrag slling pric of candy rmains at $4.00 pr box and th cost of candy incrass 5%? Brakvn, oprating lvrag, cost function dcision You ar th advisor of a Junior Achivmnt group in a local high school. You nd to hlp th group mak a dcision about fs that must b paid to sll gardning tools at th Hom and Gardn Show. Th group slls a st of tools for $0.00. Th manufacturing cost (all variabl) is $6 pr st. Th Hom and Gardn Show coordinator allows th following thr paymnt options for groups xhibiting and slling at th show:. Pay a fixd booth f of $5,600.. Pay a f of $3,800 plus 0% of all rvnu from tool sts sold at th show. 3. Pay 5% of all rvnu from tool sts sold at th show. A. Comput th brakvn numbr of tool sts for ach option. B. Which paymnt plan has th highst dgr of oprating lvrag? C. Which paymnt plan has th lowst risk of loss for th organization? Explain. D. At what lvl of rvnu should th group b indiffrnt to options and? E. Which option should Junior Achivmnt choos, assuming sals ar xpctd to b,000 sts of tools? Explain. ROI targt profit, forign xchang rats Borg Controls has a nt invstmnt in its Grman subsidiary of $.68 million. Th firm attmpts to arn a 5% prtax rturn on its invstmnt. Variabl costs for th Grman subsidiary ar 60% of rvnus. Annual fixd costs ar 3,000. For th currnt yar, th managr of th Grman subsidiary anticipats rvnus of.7 million. Th xchang rat is xpctd to b. $. A. If oprations mt xpctations, what is th rat of rturn that Borg Controls will arn from its Grman subsidiary? (Hint: Calculat th rat of rturn by dividing prtax incom by th nt invstmnt.) B. What lvl of rvnu in uros would b rquird of th subsidiary for th parnt to arn xactly a 5% rat of rturn in dollars, assuming no changs in th xchang rat? Targt profit, margin of safty, oprating lvrag Th following budgt data apply to Nwbrry s Nutrition: Sals (00,000 units) $,000,000 Costs Dirct matrials $300,000 Dirct labor 00,000 Fixd factory ovrhad 00,000 Variabl factory ovrhad 50,000 Markting and administration 6 0, Total costs 9 0, Budgtd prtax incom $ 9 0, Dirct labor workrs ar paid hourly wags and go hom whn thr is no work. Th markting and administration costs includ $50,000 that varis proportionatly with production volum. Assum that sals and production volums ar qual.

32 ch03.qxd 9/7/04 4:06 PM Pag 7 PROBLEMS Q, Q4, Q6 A. Comput th numbr of units that must b sold to achiv a targt aftr-tax incom of $0,000, assuming th tax rat is 40%. B. Calculat th margin of safty in both rvnus and units. C. Calculat th dgr of oprating lvrag. Brakvn, targt profit, margin of safty, oprating lvrag Pik Strt Taffy maks and slls taffy in a varity of flavors in a shop locatd in th local public markt. Data for a rcnt wk ar as follows: Rvnu (,000 $4.80 pr lb.) $9,600 Cost of ingrdints $3,00 Rnt 800 Wags 4, , Prtax incom 800 Taxs (0%) Aftr-tax incom 6 0 $ Q, Q4, Q6 All mploys work standard shifts, no mattr how much taffy is producd or sold. A. Calculat th brakvn point in units and in rvnu. B. Calculat th numbr of units and th amount of rvnus that would b ndd for aftrtax incom of $3,000. C. Calculat th margin of safty in units and th margin of safty prcntag. D. Calculat th dgr of oprating lvrag. Brakvn, targt profit, margin of safty Vins and Daughtr manufacturs and slls swimsuits for $40 ach. Th stimatd incom statmnt for 005 is as follows: Sals $,000,000 Variabl costs, 0 0, Contribution margin 900,000 Fixd costs 7 6 5, Prtax profit $ 3 5, A. Comput th contribution margin pr swimsuit and th numbr of swimsuits that must b sold to brak vn. B. What is th margin of safty in th numbr of swimsuits? C. Suppos th margin of safty was 5,000 swimsuits in 004. Ar oprations mor or lss risky in 005 as compard to 004? Explain. D. Comput th contribution margin ratio and th brakvn point in rvnus. E. What is th margin of safty in rvnus? F. Suppos nxt yar s rvnu stimat is $00,000 highr. What would b th stimatd prtax profit? G. Assum a tax rat of 30%. How many swimsuits must b sold to arn an aftr-tax profit of $80,000? PROBLEMS 3.8 Q, Q4, Q5 Cost function, brakvn, quality of information, rlvant rang Oystrs Away picks, shucks, and packs oystrs and thn slls thm wholsal to fin rstaurants across th stat. Th incom statmnt for last yar follows: Rvnu (basd on sals of,000 cass of oystrs) $00,000 Expnss: Wags for pickrs, shuckrs, and packrs $00,000 Packing matrials 0,000 Rnt and insuranc 5,000 Administrativ and slling 4 5, , Prtax incom 0,000 Taxs (0%) Aftr-tax incom, $ 8, 0 0 0

33 ch03.qxd 9/7/04 4:06 PM Pag 8 8 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS 3.9 Q, Q3, Q Q3, Q4, Q5 Pickrs, shuckrs, and packrs ar mployd on an hourly basis and can b laid off whnvr ncssary. Salspopl mostly dlivr th product and ar paid on a salarid basis. A. Estimat th cost function for Oystrs Away. B. What is th brakvn point in cass for Oystrs Away? C. Th managr thinks that th company will harvst and sll 3,000 cass of oystrs nxt yar. Estimat th aftr-tax incom. D. Oystrs Away harvstd and sold,000 cass in ach of th last svral yars. What dos this suggst about th quality of th incom information you calculatd in part (C)? E. Dscrib rasons why th cost function dvlopd for th rlvant rang up to,000 cass might not hold for,00 to 3,000. Rlvant information, brakvn, targt profit, pric, uncrtaintis Francsca would lik to las a coff cart in Aspn, Colorado. Th las is $800 pr month and a city licns to sll food and bvrags costs $0 pr month. Th lssor of th stand has shown Francsca rcords indicating that gross rvnus avrag $3 pr hour. Th out-of-pockt costs for ingrdints ar gnrally about 40% of gross rvnus. Last yar sh paid 5% of hr incom in fdral taxs. Francsca pays $,000 pr month for hr condominium. Sh could stor th cart ovrnight in th condo s garag, which is currntly unusd. Ral stat dvloprs in Aspn stimat that about 0% of th cost of a rsidntial building is for th garag. At prsnt, Francsca is arning $,400 pr month as a ski instructor for on of th big ski aras. In th summrtim sh arns about th sam incom as a kayaking instructor. A. List ach pic of quantitativ information in this problm. For ach itm, indicat whthr it is rlvant to Francsca s dcision and xplain why. B. If Francsca lass th cart and works 30 days in a month, how many hours will sh hav to work ach day, on avrag, to b at last as wll off financially as sh is in hr currnt job? C. If Francsca wants to work only 5 days pr month, how much will rvnus hav to incras for hr to work 4 hours pr day and b as financially wll off as sh is in hr currnt job? D. Can Francsca b crtain that hr rvnus will avrag $3 pr hour? Why or why not? E. What othr information might hlp Francsca with this dcision? Sals mix, multipl product brakvn, uncrtaintis, quality of information Knr producs two products: rgular boomrangs and prmium boomrangs. Last month,00 units of rgular and,400 units of prmium wr producd and sold. Avrag prics and costs pr unit for th month ar displayd hr. Rgular Prmium Slling pric $.5 $45.30 Variabl costs Product lin fixd costs Corporat fixd costs Oprating Profit $ $ Product lin fixd costs can b avoidd if th product lin is droppd. Corporat fixd costs can b avoidd only if th firm gos out of businss ntirly. You may want to us a spradsht to prform calculations. A. Assuming th sals mix rmains constant, how many units of prmium will b sold ach tim a unit of rgular is sold? B. What ar th total fixd product lin costs for ach product? C. What ar th total corporat fixd costs? D. What is th ovrall corporat brakvn in total rvnu and for ach product, assuming th sals mix is th sam as last month s? E. What is th brakvn in rvnus for rgular boomrangs, ignoring corporat fixd costs? F. Why is th brakvn for rgular boomrangs diffrnt whn w calculat th individual product brakvn vrsus th combind product brakvn? (continud)

34 ch03.qxd 9/7/04 4:06 PM Pag 9 PROBLEMS 9 G. Whn managrs monitor th profitability of rgular boomrangs, ar corporat fixd costs rlvant? Explain. H. CVP analysis assums that th sals mix will rmain constant. Explain why managrs gnrally cannot know for crtain what thir sals mix will b. I. What is th ffct of uncrtainty about th sals mix on th quality of th information obtaind from CVP analyss? 3.3 Q, Q, Q4 3.3 Q, Q, Q4, Q5 Cost function, marginal cost, opportunity cost, usfulnss of CVP A nighbor askd for your hlp prparing a grant for a not-for-profit aftr-school art program that would bnfit lmntary school childrn in th nighborhood. H wants to charg low fs for most childrn, but also offr som scholarships for low-incom childrn. H nds to hav on staff prson for vry six childrn to mt stat rgulations. H can us high school studnt voluntrs for two of ths positions, but is concrnd about potntial absncs on thir part if h rlis on thm for th stat count. H would lik th program to srv at last 30 childrn, and mor, if possibl. H wants you to hlp him dcid on th fs to charg and also to dtrmin how many studnts could rciv scholarships. A. Think about th costs involvd in an aftr-school program. Assum that your nighbor can us th local lmntary school for fr.. List costs that will b incurrd for th program, and catgoriz thm as fixd, variabl, or mixd.. For ach variabl cost, choos a potntial cost drivr. Explain your choic. B. Do you think th cost structur would b primarily fixd or primarily variabl? Explain. Rmmbr, vn though staff work only part tim, thy will hav a rgular schdul to mt th stat rgulations of six childrn pr staff mmbr. C. Suppos on of th staff mmbrs has only on child to hlp. What is th marginal cost for thr scholarships? D. Suppos th program is fully subscribd by f-paying childrn. What is th opportunity cost pr scholarship? E. Will CVP analysis hlp your nighbor choos a f that would covr at last 0 scholarships? Explain how you would st up a spradsht so that your nighbor could prform snsitivity analysis to mak mor informd dcisions. Brakvn, CVP, potntial cost structur chang, mploy raction Ersatz manufacturs a singl product. Th following incom statmnt shows two diffrnt lvls of activity, which ar assumd to b within Ersatz s rlvant rang. You may want to us a spradsht to prform calculations. Ersatz, Inc. Incom Statmnt Activity Lvls Volum,000 units,500 units $00 ach $00,000 $50,000 Lss variabl xpnss $40 ach 40,000 60,000 $0 ach 0,000 5,000 $6 ach 6, , Contribution margin 44,000 66,000 Lss fixd xpnss Manufacturing 0,000 0,000 Slling,000,000 Administration Prtax incom 0, $ 3, , $ 5, A. What is Ersatz s brakvn point in units? B. Draw a CVP chart showing th two lvls of activity and th brakvn point. C. If Ersatz plans to sll,300 units, what will prtax incom b? (continud)

35 ch03.qxd 9/7/04 4:06 PM Pag 0 0 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS 3 D. Your boss askd you to draft an -mail rspons to Ersatz s major stockholdr, who wants to know why prtax incom incrass by mor than 800% whn sals incras by just 50%. Both your boss and th stockholdr ar busy popl and xpct short answrs. E. Managmnt xpcts that variabl costs and slling prics will ris by 3%, but fixd costs will not chang. What will th nw brakvn point b? Explain th rsult. F. Managmnt wants to chang th way that sals rprsntativs ar paid. At prsnt, sals rprsntativs ar paid $,000 $0 pr unit. Managmnt will rplac this formula with a paymnt of $0 pr unit. At what lvl of sals will it mak no diffrnc in incom which cost function is usd? G. Add th nw cost function to th prcding CVP chart. H. Which of th two cost functions will minimiz slling xpnss assuming that sals ar abov th indiffrnc lvl calculatd in part (F)? I. How would sals rprsntativs b likly to rspond to th nw paymnt systm? J. Discuss th pros and cons to th company of changing th way sals rprsntativs ar paid Q, Q, Q4, Q5, Q6 Brakvn, avoidabl fixd costs, pric, CVP assumptions, oprating risk Last yar s incom statmnt for King Salmon Sals follows. Rvnu (00,000 lbs.) $800,000 Expnss Fish $00,000 Smoking matrials 0,000 Packaging matrials 30,000 Labor (wags) 300,000 Administrativ 50,000 Sals commissions 0, Total xpnss 7 0, Incom $ 9 0, Q, Q, Q4, Q5 Th fishing sason is only thr to four months long, so labor costs (wags) ar for mploys who ar collg studnts and work in th summr. Thy ar hird only as ndd. A. Th stat govrnmnt curtaild fishing bcaus of low fish counts. Bcaus of this rstriction, King Salmon Sals can only buy 50,000 pounds. Assum th administrativ cost is incurrd only if th company slls salmon. Assuming th managrs will dcid to oprat if th company can at last brak vn, should thy oprat this yar? (Hint: Calculat th brakvn quantity.) Provid calculations and xplain your answr. B. Now assum that th administrativ costs continu rgardlss of whthr th company slls salmon. Assuming th managrs will dcid to oprat if th company can at last brak vn, should thy oprat this yar? Provid calculations and xplain your answr. C. Bcaus of th salmon shortag, suppos that rtail salmon prics ar incrasing. What is th brakvn pric for King Salmon? Assum that administrativ costs continu rgardlss of whthr th company slls salmon. D. Suppos th managrs rly on th prcding CVP analysis to dcid whthr to oprat th businss. What assumptions ar thy making? E. How rasonabl ar ths CVP assumptions? F. Suppos th ownr of King Salmon Sals askd you about th company s cost structur. Bcaus volums of fish fluctuat a grat dal from on yar to th nxt, th ownr is wondring if som way can b found to rduc th risk of an oprating loss. Writ a brif mmo to xplain how th proportion of fixd and variabl costs affcts th risk of loss whn oprations ar clos to th brakvn point. Cost function, brakvn, targt profit, uncrtaintis and bias, intrprtation Jo Davis is thinking about starting a company to produc carvd woodn clocks. H lovs making th clocks. H ss it as an opportunity to b his own boss, making a living doing what h liks bst. Jo paid $300 for th plans for th first clock, and h has alrady purchasd nw quipmnt costing $,000 to manufactur th clocks. H stimats that it will cost $30 in matrials (wood,

36 ch03.qxd 9/7/04 4:06 PM Pag PROBLEMS ANALYZE INFORMATION WRITTEN ASSIGNMENT 3.35 Q, Q5 clock mchanism, and so on) to mak ach clock. If h dcids to build clocks full tim, h will nd to rnt offic and manufacturing spac, which h thinks would cost $,500 pr month for rnt plus anothr $300 pr month for various utility bills. Jo would prform all of th manufacturing and run th offic, and h would lik to pay himslf a salary of $3,000 pr month so that h would hav nough mony to liv on. Bcaus h dos not want to tak tim away from manufacturing to sll th clocks, h plans to hir two salspopl at a bas salary of $,000 ach pr month plus a commission of $7 pr clock. Jo plans to sll ach clock for $5. H blivs that h can produc and sll 300 clocks in Dcmbr for Christmas, but h is not sur what th sals will b during th rst of th yar. Howvr, h is fairly sur that th clocks will b popular bcaus h has bn slling similar itms as a sidlin for svral yars. Ovrall, h is confidnt that h can pay all of his businss costs, pay himslf th monthly salary of $3,000, and arn at last $4,000 mor than that pr month. (Ignor incom taxs.) Th following qustions will hlp you analyz th information for this problm. Do not turn in your answrs to ths qustions unlss your profssor asks you to do so. A. Prform analyss to stimat th numbr of clocks Jo would nd to manufactur and sll ach yar for his businss to b financially succssful:. List all of th costs dscribd and indicat whthr ach cost is (a) a rlvant fixd cost, (b) a rlvant variabl cost, or (c) NOT rlvant to Jo s dcision.. Calculat th contribution margin pr unit and th contribution margin ratio. 3. Writ down th total cost function for th clocks and calculat th annual brakvn point in units and in rvnus. 4. How many clocks would Jo nd to sll annually to arn $4,000 pr month mor than his salary? B. Idntify uncrtaintis about th CVP calculations:. Explain why Jo cannot know for sur whthr his actual costs will b th sam dollar amounts that h stimatd. In your xplanation, idntify as many uncrtaintis as you can. (Hint: For ach of th costs Jo idntifid, think about rasons why th actual cost might b diffrnt than th amount h stimatd.). Idntify possibl costs for Jo s businss that h has not idntifid. List as many additional typs of cost as you can. 3. Explain why Jo cannot know for sur how many clocks h will sll ach yar. In your xplanation, idntify as many uncrtaintis as you can. C. Discuss whthr Jo is likly to b biasd in his rvnu and cost stimats. D. Explain how uncrtaintis and Jo s potntial biass might affct intrprtation of th brakvn analysis rsults. Suppos Jo has askd for your advic. Turn in your answrs to th following. 3 E. Us th information you larnd from th prcding analyss to writ a mmo to Jo with your rcommndations. Attach to th mmo a schdul showing rlvant information. As appropriat, rfr to th schdul in th mmo. CVP snsitivity analysis, bias, quality of information Jasmin Krishnan has bn taking ntrprnurship courss as part of hr businss dgr. Sh dvlopd a plan to start a travl agncy spcializing in spring brak trips for studnts. Sh larnd how to dvlop CVP analysis in hr cost accounting class. Now sh is prparing pro forma (i.., forcastd) incom statmnts for a brochur about hr plans for th travl agncy. Sh wants to us th information from th CVP as a basis for th statmnts. Hr ntrprnurship profssor criticizd hr businss plan bcaus Jasmin includd too small an amount for liability insuranc. Howvr, whn sh includd th amount suggstd by hr fathr s insuranc agnt, sh had to st prics quit high, cut back on th amount sh plannd as hr salary, find lowr quality hotls for th studnts, or tak som combination of ths actions. Sh thought that hotl quality and prics would affct sals volums ngativly and did not want to risk incurring losss from low rvnus during hr first fw yars. Sh also ndd a bas lvl of salary to at last pay for hr living xpnss.

37 ch03.qxd 9/7/04 4:06 PM Pag CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS 3.36 Q, Q4, Q5 collg/ldnburg 3.37 Q, Q3, Q4, Q5, Q6 Sh dcidd to ask frinds and rlativs to invst in hr travl agncy to nsur sh had nough capital for th first fw yars. Onc hr rputation was wll stablishd, sh assumd that highr customr volums would covr all of hr xpctd costs. Sh was confidnt that hr plannd trips would attract nough studnts ach yar to covr most of hr costs. From focus groups on campus, sh larnd which typs of trips wr most appaling to othr studnts. Now sh plannd to us snsitivity analysis to solv for volums that would mak th pro forma statmnts look attractiv to invstors. 3 A. In gnral, what information do w hop to gain from prforming snsitivity analyss? Explain. B. Explain how bias might ntr into Jasmin s snsitivity analyss. C. How might Jasmin s bias affct th quality of th invstmnt brochur information? D. Idntify a potntial thical problm for Jasmin. E. Whn you considr th wll-bing of Jasmin s family and frinds, how would you rcommnd that Jasmin us snsitivity analysis for hr brochur? Explain. Small businss ownrs, CVP rsarch on th intrnt Th Intrnt provids many rsourcs to hlp small businss ownrs succssfully manag thir businsss. Rsourcs includ information about common tchniqus usd for planning and managing oprations. 3 A. Why ar small businss ownrs oftn unawar of common businss tchniqus such as CVP analysis? B. Why might CVP analysis b vn mor usful to small businss ownrs than to managrs of larg organizations? (Hint: Considr whthr information about th margin of safty and siz of potntial losss might b spcially important for popl who own small businsss.) C. Us an Intrnt sarch ngin to locat Wb sits that provid information about th trms brakvn analysis and cost-volum-profit analysis. Also sarch for ths trms on Wb sits dsignd xplicitly to hlp small businss ownrs, such as th U.S. Small Businss Administration ( Summariz what your rsarch tlls you about th uss and usfulnss of brakvn and CVP analysis. D. Suppos you ar trying to hlp a small businss ownr larn to us brakvn and CVP analysis. Writ a mmo to th ownr xplaining what you think th ownr should do and includ appropriat rfrncs to Intrnt rsourcs that would b usful to th ownr. Assum that you hav alrady had a brif convrsation with th ownr about brakvn and CVP analysis, and th ownr xprssd an intrst in larning mor. Focus on communicating ffctivly by avoiding unncssarily tchnical languag and concntrating on th most important points. Cost function, oprating lvrag, kping or dropping a businss Th univrsity s Wildcat Lair catrs to studnts and srvs sandwichs and bvrags. It has bn rporting losss in past months. In July, for xampl, th loss was $5,000. Rvnu $ 70,000 Expnss Purchass of prpard food $,000 Srving prsonnl 30,000 Cashirs 5,500 Administration 0,000 Univrsity surcharg 7,000 Utilitis Loss, , $ ( 5, ) Th Lair purchass prpard food dirctly from Univrsity Food Srvics. This charg varis proportionatly with th numbr and kind of mals srvd. Prsonnl paid by th Lair srv th food, tnd th cash rgistr, bus and clan tabls, and wash dishs. Th staffing lvls rarly chang; th xisting staff can usually handl daily fluctuations in volum. Administrativ costs ar primarily th salaris of th managr and hr offic staff. Bcaus th univrsity provids support srvics for th

38 ch03.qxd 9/7/04 4:06 PM Pag 3 PROBLEMS 3 Lair, such as payroll, human rsourcs, and othr administrativ support, th univrsity chargs a surcharg of 0% of its rvnus. Utility costs ar th costs of cooling, hating, and lighting during its normal oprating hours. Th univrsity s managmnt is considring closing th Wildcat Lair bcaus it has bn oprating at a loss. ANALYZE INFORMATION WRITTEN ASSIGNMENT Th following qustions will hlp you analyz th information for this problm. Do not turn in your answrs to ths qustions unlss your profssor asks you to do so. A. What is th brakvn point for Wildcat Lair from th univrsity s prspctiv (including th univrsity surcharg)? What is th brakvn point from Wildcat Lair s prspctiv (xcluding th univrsity surcharg)? B. Dfin and calculat th dgr of oprating lvrag for th Lair, ignoring th univrsity surcharg. C. From th prspctiv of univrsity managmnt, is th univrsity surcharg a rlvant cost in dciding whthr to clos th Lair? Why or why not? D. Idntify possibl ways that oprations could b modifid so that som of th fixd costs bcom variabl costs. E. Givn th Lair s cost function and oprating lvrag, dscrib possibl bnfits of modifying oprations so that som of th fixd costs bcom variabl costs. Turn in your answrs to th following. 3 F. From th prspctiv of univrsity managmnt, dscrib th pros and cons of closing th Wildcat Lair. G. Suppos you ar th managr of th Wildcat Lair. Writ a mmo to prsuad th univrsity managmnt to kp th club opn Q, Q, Q4, Q5, Q6 Not-for-profit brakvn pric, budgt altrnativs Th Eldr Clinic, a not-for-profit organization, provids limitd mdical srvics to low-incom ldrly patints. Th managr s summary rport for th past four months of oprations is rproducd hr. March April May Jun Total Patint visits ,90 Patint fs $ 4, 30 $ 4, 80 $ 3, 875 $ 4, 60 $ 6, 545 Mdical staff salaris 3,54 3,56 3,54 4,5 53,879 Mdical supplis usd 3,8 3,077,934 3,75,368 Administrativ salaris 3,97 3,98 3,97 3,4 3,004 Rnt,000,000,000,00 4,00 Utilitis ,457 Othr xpnss Total xpnss, , 0 9, , 6 8 5, 6 7 3, 3 7 7, 8 8 4, 8 5 6, 9 9 5, Oprating surplus (loss) $ ( 9, ) $ ( 9, ) $ ( 9, 5 0 ) $ ( 0, ) $ ( 7 9, 3 9 ) Th clinic rcivs an oprating subsidy from th city, but unfortunatly, th oprating loss incurrd through Jun ($79,39) is largr than anticipatd. Part of th problm is th salary incras that wnt into ffct in Jun, which had bn ovrlookd whn th budgt was submittd to th city last yar. To compound th problm, th warm summr months traditionally bring with thm an incras in hat-rlatd halth problms. Thus, th clinic is likly to xprinc an incras in patint visits during July. Th accountant mad th following assumptions in dvloping th cost function: Salaris ar fixd, and Jun valus ar usd. Mdical supplis vary with patint visits. Rnt and utilitis ar fixd, and last priod s costs ar usd. Othr xpnss ar mixd and using rgrssion, fixd cost is $70 and variabl cost is $.53 pr patint visit.

39 ch03.qxd 9/7/04 4:06 PM Pag 4 4 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS Clinic managmnt is considring an incras in patint fs to rduc losss. A. Dvlop a cost function for this data. You may hav don this for Chaptr, and in that cas us that cost function. Solv for th avrag patint f ncssary to brak vn assuming thr ar 940 patint-visits using th cost function you dvlopd. Compar this nw f with th avrag patint f chargd during March through Jun. B. Suppos th clinic raiss its patint fs to brak vn. What problms do you s from th ldrly patints prspctiv if th f is raisd? C. In this stting, would an incras in fs b likly to affct patint volum? What problms do you s from th clinic s prspctiv if th f is raisd? D. Othr than raising th f, what idas might th clinic considr to balanc th budgt? 3.39 Q, Q3, Q4, Q5, Q6 Cost function, targt profit, oprating lvrag, CVP graph, ownr goals Elina Siljandr owns Elina s Staind Glass in Hlsinki, Finland. Th businss producs and slls thr diffrnt typs of staind glass windows: small, mdium, and larg. Elina has two full-tim mploys who work rgular schduls to cut glass and assmbl th windows. Sh borrowd mony from th bank to start th businss and pay living xpnss. Sh is concrnd that hr cash flows might not b high nough ithr to pay hrslf or to rpay th bank loan. Sh would lik to gnrat approximatly 0,000 (uros) in prtax profit ach month to covr hr living xpnss and rpay th loan. Th following rvnu and cost information covrs th past four months: 3 Jun July August Sptmbr Rvnus 9,050 0,53,946 6,6 Raw matrials and supplis,745,433 3,074 4,09 Labor 3,880 4,04 4,46 4,8 Rnt,000,000,000,00 Miscllanous Profit 9 0 0, 3 5 6, , 8 A. Dvlop a cost function for Elina s Staind Glass. B. Dtrmin th lvl of rvnu Elina s Staind Glass must gnrat to achiv th targtd profit of 0,000 pr month. C. Calculat Elina s dgr of oprating lvrag for Sptmbr. D. Intrprt Elina s dgr of oprating lvrag. E. Crat a CVP graph showing th brakvn point, targt profit, and margin of safty. F. Writ a mmo to Elina with rcommndations about ways sh might achiv hr goals Q, Q3, Q4, Q5 Building and using a CVP financial modl Toddlr Toy Company slls baby dolls, tddy bars, and toy cars. Th managrs stablishd a prliminary budgt using th following assumptions. Thy would now lik to valuat th snsitivity of budgtd rsults to diffrnt sts of assumptions. Toddlr Toy Company Assumptions for Coming Yar Baby Dolls Tddy Bars Toy Cars Volum 00,000 5,000 5,000 Pric $ 3.50 $.75 $ 3.5 Variabl costs $.05 $.75 $.45 Fixd costs $65,000 $5,000 $35,000 Targt prtax incom $0 Invstmnt $ million Capacity million units A. Crat a spradsht that th managrs can us for snsitivity analysis. (Hint: Us th Magik Bicycls spradsht in Exhibit 3. and Appndix 3A to hlp you st up a spradsht with a data input box.) Modify input data in th spradsht to answr th following parts of this problm. You may wish to add cll rfrncs for prcntag changs in prics, volums, and costs. (continud)

40 ch03.qxd 9/7/04 4:06 PM Pag 5 PROBLEMS 5 B. Assum that th volum of dolls sold incrass to 5,000 units with no chang in fixd or variabl costs. What is th nw prtax incom? Dos th numbr producd by your financial modl appar to b rasonabl? (Manually stimat th incras in prtax incom if volum incrass and fixd costs rmain constant. Compar this figur to your spradsht rsult.) C. Basd on th original assumptions, what is th ffct on prtax incom if variabl costs incras by 5% for ach of th thr product lins? Assum that nothing ls changs. D. Rturn to th original assumptions. Assum that a sals managr proposd a nw advrtising campaign to boost sals volum. Th campaign would cost $30,000 and is stimatd to incras th volum of ach product as follows: Baby doll sals incras by 0,000 units. Tddy bar sals incras by 7,500 units. Toy car sals incras by 30,000 units. What would b th ffct on prtax incom if this plan wr adoptd? E. Rturn to th original assumptions. Now assum that du to comptition, Toddlr Toys must cut prics on ach of its thr products by 0%. In addition, a nw advrtising campaign costing $45,000 must b institutd to countract bad publicity. Givn ths assumptions, what is th nw brakvn point? F. Rturn to th original assumptions. What would b th prtax incom if Toddlr Toys incrass th pric of all thr products by 0% and th volum of ach product lin dcrass by 5%? G. Givn th sam assumptions as in part (F), how many units must Toddlr Toys sll to arn a targt prtax incom of $00,000? A targt prtax incom of $50,000? A prtax rturn on invstmnt (ROI) of 0%? (Hint: To dtrmin th targt prtax incom, multiply 0% tims amount invstd.) H. Spradshts for financial modling allow snsitivity analysis of rvnus, costs, and quantitis such as stimatd product volums.. Explain why it is not possibl to prfctly stimat rvnus, costs, and quantitis.. Explain how snsitivity analysis can hlp managrs valuat th pros and cons of altrnativs. 3. Explain how managr bias might influnc stimats of rvnus, costs, and quantitis. 3.4 Q, Q3, Q4, Q5 Building and using a CVP financial modl Th following information for Pt Palac, a larg rtail stor that slls pt-rlatd mrchandis, was rcordd for th first quartr. Th stor tracks mrchandis according to product typ. Th catgory Othr includs accssoris such as dog bds, lashs, kitty littr boxs, bird cags, and so on. Th company is considring svral diffrnt stratgis to improv oprations for th nxt quartr. Input Data Food Toys Pts Othr Total Rvnu $500,000 $50,000 $75,000 $00,000 $95,000 Variabl cost 00,000 50,000 60,000 50, ,000 Fixd cost 550,000 Tax rat 5% A. Crat a spradsht that Pt Palac managrs can us for snsitivity analysis. Modify information in th data input sction and answr th qustions in th following parts. B. What is Pt Palac s brakvn point? What total rvnu is ncssary for a targt aftrtax incom of $00,000? C. Pt Palac managrs ar considring thir advrtising campaign for th nxt priod. Thy bliv thy could spnd an additional $0,000 on advrtising for a product lin and incras sals by 0%. On managr wants to incras advrtising on pts bcaus that product lin is currntly th smallst. Anothr managr blivs th ads should promot th most profitabl products, but thy ar not sur which products thos would b. What is th aftr-tax incom if pts ar promotd? What is th most profitabl product? What is th aftr-tax incom if that product is promotd? D. What factors, othr than th quantitativ rsults, might influnc managrs dcisions to incras advrtising?

41 ch03.qxd 9/7/04 4:06 PM Pag 6 6 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS BUILD YOUR PROFESSIONAL COMPETENCIES 3.4 Q, Q, Q3, Q4, Q5, Q6 DEFINITION: Focus on Profssional Comptncy: Dcision Modling Modl building for dcision making, quality of analysis Rviw th following dfinition and lmnts for th Dcision Modling comptncy. 9 Individuals prparing to ntr th accounting profssion must b abl to us stratgic and critical approachs to dcision-making. Thy must objctivly considr issus, idntify altrnativs, and choos and implmnt solution approachs in ordr to dlivr srvics and provid valu. ELEMENTS FOR THIS COMPETENCY INCLUDE Lvl Lvl Lvl 3 Lvl 4. Idntifis problms, potntial solution approachs, and rlatd uncrtaintis. Objctivly idntifis strngths, waknsss, opportunitis, and thrats associatd with a spcific scnario, cas, or businss activity 3. Uss quantitativ tchniqus to xplor th liklihood of altrnativ scnarios 4. Organizs and valuats information, altrnativs, cost/bnfits, risks and rwards of altrnativ scnarios 5. Employs modl-building tchniqus to quantify problms or tst solutions 6. Links data, knowldg, and insights togthr for dcisionmaking purposs 7. Engags in continuous improvmnt and constructs nw modls ovr tim 8. Maks dcisions ovr tim as a rsult of ngaging in continuous improvmnt and constructing nw modls A. Focus on th comptncy lmnts, 4, 6, and 8, which rlat to th us of information in managmnt dcision making. Answr th following qustions:. What typs of managmnt dcisions wr addrssd in Chaptr 3?. What typs of quantitativ analyss wr usd in Chaptr 3 to addrss ths dcisions? 3. Wr quantitativ rsults th only information usd by managrs to mak dcisions? Why or why not? 4. Rviw th dcision-making illustrations in Chaptr 3. Provid an xampl whr data, knowldg, and insights wr linkd togthr. Explain. 5. Rviw th dcision-making illustrations in Chaptr 3. Provid an xampl whr an improvmnt in analysis ld to improvd dcision making. Explain. B. Focus on comptncy lmnt 5, which addrsss th us of modl-building tchniqus. Explain how CVP analysis (a modl-building tchniqu) can b usd to () quantify problms and () tst solutions. C. Focus on comptncy lmnts and 3, which rlat to th us of quantitativ tchniqus to xplor altrnativ scnarios. Answr th following qustions:. What is CVP snsitivity analysis? How is it usd to quantitativly xplor th liklihood of altrnativ scnarios?. What is th dgr of oprating lvrag? How is it usd to quantitativly xplor th liklihood of altrnativ scnarios? D. Focus on comptncy lmnt 6, which rlats to th us of information in dcision making. Suppos you plan to prform CVP analysis for an organization.. What typs of data do you nd to prform th CVP analysis?. Why is knowldg about th organization critical to your ability to prform a highquality analysis? What do you nd to know? 9 Th dfinition and lmnts ar rprintd with prmission from AICPA; copyright & 003 by Amrican Institut of Crtifid Public Accountants. Th AICPA s Cor Comptncy Framwork can b accssd at ca.aicpasrvics.org.

42 ch03.qxd 9/7/04 4:06 PM Pag 7 BUILD YOUR PROFESSIONAL COMPETENCIES Q, Q, Q5 Intgrating Across th Curriculum: Economics and Markting Nonlinar rvnu, maximiz profits, CVP assumptions Hollis Company manufacturs and markts a rgulator usd to maintain high lvls of accuracy in timing clocks. Th markt for ths rgulators is limitd and highly dpndnt upon th slling pric. Basd upon past rlationships btwn th slling pric and th rsulting dmand, as wll as an informal survy of customrs, managmnt drivd th following dmand function, which is highly rprsntativ of th actual rlationships. D,000 P whr D Annual dmand in units P Pric pr unit Th stimatd manufacturing and slling costs for th coming yar ar as follows: Variabl costs Manufacturing Slling Fixd costs Manufacturing Slling $75 pr unit $5 pr unit $4,000 pr yar $6,000 pr yar collg/ldnburg A. Writ th function for total rvnu. [Hint: Rcall that total rvnu quals pric tims quantity (P Q), and th dmand function dtrmins th quantity sold (Q).] B. Writ th total cost function, substituting th dmand function for Q. C. Prform a sarch on th Intrnt to find a quadratic quation calculator or go to www. wily.com/collg/ldnburg. Us th calculator to find th brakvn points. (Hint: St th rvnu function qual to th cost function and algbraically convrt th quation to quadratic form: AP BP C 0.) D. Draw a graph with total rvnu and total cost for Q btwn zro and,000 units. Mark th brakvn points. E. Dtrmin th slling pric that Hollis Company should charg pr rgulator and th numbr of rgulators th company should sll to maximiz th company s profits for th coming yar. (Hint: Rcall that profit is maximizd whn marginal rvnu quals marginal cost. You must b abl to diffrntiat a simpl function to answr this qustion.) F. Which CVP assumption dos this situation violat? Explain. G. For th past svral yars, assum th company sold rgulators at th pric you calculatd in part (E) and that volum varid btwn 375 and 45 units pr yar. In this situation, discuss whthr it would b appropriat to us CVP analysis to stimat th company s profits.