by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

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1 Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs as ithr fixd or variabl and to stimat th fixd and variabl componnts of mixd costs, is important bcaus it nabls th us of dcision making tchniqus lik cost volum profit analysis (CVP analysis). This is ssntially a short-trm (or tactical) dcision tool which shows th ffct on profit of changs in costs, prics and sals volum in units. W cannot stimat accuratly th impact of ths changs unlss w know which costs ar fixd and which ar variabl. A managr may want th answrs to qustions such as what would b th impact on monthly profit of an incras in production and sals of 100 units pr month, what incras in sals volum is rquird to covr th additional fixd costs of our nw advrtising campaign or how many units of product X do w nd to mak and sll in ordr for it to b profitabl? Ths and othr qustions can b answrd using CVP analysis. CVP analysis is somtims calld brak-vn analysis bcaus it allows th usr to calculat a brak-vn point. This is th lvl of production and sals at which a product or srvic stops losing mony and bcoms profitabl. At th brak-vn point profit quals zro. Onc w know th brak-vn point w can assss th financial viability of a nw product or analys our currnt oprating prformanc. Assumptions Undrlying CVP Analysis A numbr of basic assumptions undrli CVP analysis and ths nd to b kpt in mind whn assssing its usfulnss in a particular dcision making situation. Th assumptions ar: 1. Th bhaviour of sals rvnu and costs is linar throughout th rlvant rang of activity. In othr words, w assum that slling pric pr unit, variabl cost pr unit and th total amount of fixd costs will rmain constant during th tim priod undr considration. 2. Th numbr of units sold is qual to th numbr of units producd during ach priod i.. all th units producd ar sold. 3. Variabl costs chang in total in dirct proportion to th lvl of activity. 4. All costs can b dividd into fixd and variabl lmnts. 5. Labour productivity, production tchnology and markt conditions do not chang. 6. In multiproduct firms, th sals mix rmains constant i.. th numbr of units of ach product sold will rmain a constant prcntag of th total numbr of all th units sold in ach priod (for all products). continud pag 11 10

2 N TARGET CVP analysis is a simplifid modl of rality, howvr, in many cass th stimats that it producs ar accurat nough to b quit usful. Th main dangr is using it whn a larg chang in th lvl of activity will tak oprations outsid th usual or rlvant rang, so that th CVP assumptions may no longr b valid. Contribution Incom Statmnt Th starting point for a CVP analysis is th prparation of a contribution format incom statmnt. This groups togthr all th variabl costs and all th fixd costs for a crtain priod. Most importantly, it shows th amount of contribution margin as an intrmdiat figur instad of th gross profit amount shown on a convntional incom statmnt. Contribution margin is th amount of rvnu rmaining aftr dducting all variabl costs. It can b statd both as a total amount and on a pr unit basis as shown in Illustration 1. blow. [ CVP analysis is a simplifid modl of rality, howvr th stimats that it producs ar accurat nough to b quit usful Illustration 1. A contribution incom statmnt continud pag 12 Run a Bttr Businss 11

3 Studnt Nots [ Using th CMR nabls managrs to quickly dtrmin th ffct on profit from any plannd chang in sals Th incom statmnt for th Widmark Clock Company shows that contribution margin pr unit ($200) is qual to th slling pric pr unit ($500) lss th variabl cost pr unit ($300). W will assum that th trm cost includs all costs and xpnss prtaining to th production and sal of th product. Hnc variabl costs includ variabl manufacturing costs plus variabl slling and administrativ xpnss. W can s that for vry clock that Widmark maks and slls it will hav $200 to covr fixd costs and contribut towards profit. Bcaus total fixd costs ar $80, 000 pr month, Widmark must gnrat at last $80, 000 of contribution margin ach month bfor it starts arning any profit. Its monthly sals must xcd 400 clocks ($ $200). This is Widmark s brak-vn point as shown in Illustration 2. blow. If Widmark sold 401 clocks in a month its profit bfor tax for that month would b $200. Onc th sals volum of a product passs th brakvn point, contribution margin pr unit is qual to profit bfor tax pr unit. Contribution Margin pr Unit Illustration 2. A contribution incom statmnt at th brak-vn point Contribution Margin Ratio Th contribution margin ratio (CMR) is th proportion of th slling pric pr unit rprsntd by contribution margin pr unit. For xampl, if th slling pric is $10 pr unit and this yilds $8.50 in contribution margin, th CMR is 85 pr cnt or Altrnativly, th CMR is th proportion of total sals rvnu rprsntd by th total contribution margin amount. For th Widmark Clock Company th CMR is $200 $500 or 40 pr cnt. Out of ach sals dollar 40 cnts is availabl to apply to fixd costs and to contribut to profit. If Widmark s sals rvnu incrasd by $20, 000 from $200, 000 in August to $220, 000 in Sptmbr its profit bfor tax would incras from zro to $8 000 ($ x 40 pr cnt). Using th CMR nabls managrs to quickly dtrmin th ffct on profit from any plannd chang in sals providd that th chang dos not tak th lvl of activity outsid th rlvant rang. If this occurs, total fixd costs and/or variabl cost pr unit may chang. Th rlvant rang is an important limitation on CVP analysis. If w wr considring an infinitly larg rang of output and sals, starting from zro, all costs would tnd to b variabl. Th assumptions that total fixd costs will rmain constant and that variabl cost pr unit dos not chang ar only valid within th normal or rlvant rang. Not that th contribution margin ratio plus th variabl cost ratio (total variabl costs sals rvnu) quals 100 pr cnt i.. CMR + VCR = 100 pr cnt (or 1.0) continud pag 13 12

4 N TARGET Calculating th Brak-Evn Point Th brak-vn point can b calculatd in thr ways: 1. Th graphical mthod 2. Th quation mthod 3. Th contribution margin mthod 1. Th Graphical Mthod A CVP graph nabls us to visualis th rlationships btwn sals rvnu, total cost, th numbr of units sold and profit. Illustration 3. blow shows a CVP graph basd on th rvnu and cost information for th Widmark Clock Company. Sals volum is rcordd along th horizontal axis whil sals rvnu and total costs ar shown on th vrtical axis. Th sals rvnu (SR) lin starts at th origin (whr th two axs intrsct) and passs through th brak-vn point which, as w saw in Illustration 2., is 400 units or $200, 000 of sals rvnu. For vry clock that Widmark slls, rvnu incrass by th slling pric pr unit of $500 which w assum rmains constant. This is th gradint or slop of th sals rvnu lin. Sa ls R SR v nu Profit Ara TCC an d Co sts Brak- Evn $ Point Loss Ara $$ TFC $$ R R v nu Units Sold $R Illustration 3. Th CVP graph for th Widmark Clock Company v Th amount of total nfixd costs is dpictd by a horizontal lin (TFC) which starts at a point u on th vrtical axis R rprsnting $80, 000. W assum that th rlvant rang xtnds from zro to at last 800 vunits so fixd costs rmain unchangd in total. Th total cost (TC) lin starts at th sam nu point as th TFC lin and has a uniform gradint qual to variabl cost pr unit ($300). On th graph, th amount of total variabl cost is rprsntd by th vrtical distanc btwn th total cost lin and th total fixd cost lin. Profit at any lvl of activity is th diffrnc btwn sals rvnu and total costs, and whr th SR lin crosss th TC lin profit quals zro. This is th brak-vn point. 2. Th Equation Mthod This mthod is basd on th following quation: Sals rvnu = Variabl costs + Fixd costs + Profit Bcaus at th brak-vn point profit is zro, brak-vn occurs whn sals rvnu is xactly qual to variabl costs plus fixd costs. Th brak-vn point in units can b calculatd by insrting in th quation th amounts for slling pric pr unit, variabl cost pr unit and total fixd costs. So for th Widmark Clock Company: continud pag 14 [ A CVP graph nabls us to visualis th rlationships btwn sals rvnu, total cost, th numbr of units sold and profit Run a Bttr Businss 13

5 Studnt Nots Sals rvnu = Variabl costs + Fixd costs + Profit $500Q = $300Q + $80,000 + $0 Whr: Q = Numbr of clocks sold $500 = Slling pric pr unit $300 = Variabl cost pr unit $80,000 = Total fixd costs Now solv for th valu of Q: $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 $200 Q = 400 clocks This is th brak-vn point in trms of units sold. To find th sals rvnu ndd to brak-vn, w multiply th numbr of units sold at th brak-vn point by th slling pric pr unit: 400 x $500 = $200, 000 (brak-vn sals rvnu) 3. Th Contribution Margin Mthod Th third mthod of calculating th brak-vn point is drivd from th quation mthod dscribd abov. Whn w solvd for th valu of Q, th last stp involvd dividing total fixd costs by th contribution margin of $200 pr unit to giv brakvn units (Q = 400). This simpl calculation can b xprssd thus: Brak-vn point in units sold = Total fixd costs Contribution margin pr unit 400 = $80,000 $200 To calculat th amount of brak-vn sals rvnu w us th contribution margin ratio instad of contribution margin pr unit: Brak-vn point in dollars of sals rvnu = Total fixd costs Contribution margin ratio $200, 000 = $80, Th contribution margin mthod can b xtndd to giv th numbr of sals units or sals dollars rquird to rach a crtain targt profit figur simply by adding th targt profit to th total fixd cost amount in th brak-vn formula. Not that th targt profit figur w must us is th profit rquird bfor tax has bn dductd. If you ar givn a targt profit figur aftr tax, dividing it by (1 th tax rat) will convrt it into th largr bfor tax amount: Targt profit bfor tax = (targt profit aftr tax) (1 t) whr t dnots th incom tax rat. CVP Analysis with Multipl Products So far w hav considrd situations involving singl products. Howvr, th rality is that thr ar vry fw singl product organisations. CVP analysis can b adaptd for situations whr thr is mor than on product bing mad and sold. For xampl, assum that th Contx Calculator Company producs two typs of calculator: Modl A and Modl B. Thir dtails ar as follows: Modl A Modl B Slling Pric Pr Unit $30 $50 Variabl Cost pr Unit Contribution Margin Pr Unit $15 $30 Sals Mix 2 1 Contx typically slls two Modl A calculators for ach Modl B that is sold. Th sals mix is, thrfor, two to on. Assum that Contx s total fixd costs ar $100, 000. W can now calculat th wightd avrag contribution margin (WACM) pr unit using th sals mix numbrs as wights. Sinc two Modl As ar sold for ach Modl B, th contribution margin of A is multiplid by 2, and th contribution margin of B is multiplid by 1. Th sum of th answrs is thn dividd by 3 (th sum of th wights) to giv th wightd avrag contribution margin pr unit of $20. WACM pr unit = ($15 x 2) + ($30 x 1) 3 = $20 Th wightd avrag contribution margin pr unit can now b usd to calculat th brak-vn point in units: Brak-vn sals in units = Total fixd costs WACM pr unit = $100, 000 $20 = 5, 000 Ths 5, 000 units would consist of 3, 333 units of Modl A (two-thirds of 5, 000) and 1, 667 units of Modl B (on-third of 5, 000). Chck: TCM = (3, 333 x $15) + (1, 667 x $30) = $100, 005 = TFC ($5 rounding rror) Although th mthod w hav just usd is appropriat for situations whr th sals mix is constant, in rality a constant sals mix is vry rar. If a firm s sals mix dos vary ovr tim, on of th main assumptions undrlying CVP analysis bcoms invalid and th rsults it producs bcom lss rliabl. 14

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