What effect will an increase in fixed costs such as rent or advertising will have on our BEP and our profits?

Transcription

1 Chapter 3 Cst Vlume Prfit (CVP) Analysis January 24, 27, 29, 31, 2014 Fr decisin making must identify the relevant infrmatin, but als the infrmatin by classificatin (behaviur; variable vs. fixed) The Cst Vlume Prfit mdel examines the relatinship between firm cst structure (i.e. relative prprtin f fixed and variable csts) and sales vlume and the effects f this relatinship n the prfitability f a firm Cst structure usually identified by behaviur (variable vs. fixed); can enable apprpriate decisin making The mdel can be used by managers fr the purpses f planning and decisin making This basic mdel cmbines fur imprtant variables vlume f sales, csts, revenue and prfits The basic mdel can be extended t asses the impact f price, cst and vlume chances, alng with changes in prduct mix and incme taxes Fllwing are sme applicatins f CVP analysis What are the ttal sales (either in units r dllars) that the cmpany needs t generate in rder t break even r t attain a desired level f prfit? Hw des change in cst and vlume affect prfit? Breakeven when prfit = 0 (NOT cash = 0) What effect will an increase in fixed csts such as rent r advertising will have n ur BEP and ur prfits? If n sales, then fixed cst, n variable cst lead int lss What effects will changes in perating activities (such as changes in selling price r perating csts) have n the cmpany prfile What effect will increase r decrease in sale price have n the cmpany s prfit? Shuld the cmpany buy r lease a new machine? What effect will adpting a new technlgy that leads t increase in fixed csts by a certain percentage but at the same time leads a reductin f variable csts by a certain percentage will have n BEP r the cmpany s prfit? Dwnsizing a firm utsurce as ppsed t manufacture (n fixed cst, variable cst) Eg/ Purchase units f inventry (variable); d nt need t pay salary, rent, strage etc (fixed csts) Upsizing a firm variable t fixed csts Shuld we prduce mre f prduct A and less f prduct B r vice versa? Effect f incme tax Sensitivity analysis Operating leverage Margin f safety It is imprtant t nte that the CVP analysis is perfrmed at the firm wide level Nn revenue generating department research, HR, accunting etc supprt departments; this department will never breakeven; CVP analysis nt dne fr supprt departments, but the whle firm The Basics f CVP Analysis The CVP margin is simplified by the fllwing assumptins: 1. Bth the revenue functin and the cst functin are linear The selling prices, ttal fixed csts and unit variable csts are knwn with certainty in advance and will remain unchanged during the perid The number f units prduced equals the number f units sld; this suggests that there n changes in the level f inventry during the perid 4. 1 Advanced in the planning phase N inventry; prduce nly what is planned t be sld The prductivity f wrkers is cnstant 5. Related linearly; can make nn linear functin linear by reducing the relevant range Wage wrker prductivity is equal; each wrker prduces same amunt Nt salaried wrkers because they are paid at a fixed amunt Fr multiple prduct analysis, the sales mix is assumed t be knwn in advance and remains cnstant during the perid

2 Mix is knwn in advanced Eg/ Every 2shirts sld, 2 ties and 1 belt is als sld Knwn by experience The Cncept f Cntributin Margin (CM) Cntributin Margin is the amunt remaining frm sales revenue after variable expenses have been deducted; this amunt cntributes twards cvering fixed csts and then twards making prfit Cntributin margin is the net summary f the changes in that perating incme; as the quantity f units sld increases, bth ttal variable csts and ttal revenues increase at the same rate; if revenues increase due t vlume increases, the cntributin margin increases Understanding cntributin margin enables the manager t quickly nte that an increase in selling price withut a crrespnding change in variable cst will increase the cntributin t cver fixed cst and make incme; r a decrease in variable cst withut a crrespnding decease in selling price will cntribute mre t incme and/r the cverage f fixed csts Using revenues and variable csts as per unit measures, the cntributin per unit f prduct sld can prvide a shrtcut t breakeven calculatins r what if questins Each unit f prduct sld cntributes that amunt as it walks ut the dr = unit selling price UVC = unit variable cst = unit cntributin margin Eg/ Pens Prductin csts (functin) DM Variable (behaviur), Direct (traceability) DL Variable Direct VOH Variable, Indirect FMOH Fixed, Indirect Rent UVC 5 TFC 500 > DM, DL, VMOH (prductin functin) > V S&A (selling functin) > FMOH (prductin functin); eg/ rent > F S&A (selling functin); eg/ salaries f sales peple = unit selling price Eg/ Sld 10 pens Sales 10 x 10 VC 10 x 5 CM 50 TFC (500) OI (450) Sell 100 pens cntributin is $500, perating incme is $500; net incme = 0 breakeven pint Sell 1 pen cntributin is $5, perating incme is $495 Cntributin margin f each unit sld, will equally effect prfit Eg/ Sell 1 unit, each unit cntributes t prfit by $5; sell 100 units, each unit cntributes t prfit by $5 Sell 25 ver break even net incme = $125 Sell 100 under break even net incme = $100 If yu knw variable cst f a prduct, and the selling price f the prduct, yu knw the affect n yur prfit exactly, fr a certain number f prducts sld abve r belw breakeven pint Cntributin Margin as lng as it is psitive, it will make mney Even if a lss is being made, and CM is psitive there is hpe fr prfit If CM is negative, fixed csts will never be cvered prfit will never be made Selling price shuld always be greater than variable cst Calculatin f Cntributin Margin There are several ways t calculate and express the CM (cntributin margin) Unit CM = Unit SP Unit VC 2 Ttal CM = Ttal Sales Revenue Ttal Variable Csts Ttal CM = Unit CM x Q

3 CM% = Ttal CM/Ttal Sales Revenue CM% = Unit CM/Unit SP CM% + VC% = 100% UVC UVC 10 (5) 5 / = Cntributin Margin Percent (prtin f sales that is CM) UVC = CM% Since + UVC = Then CM% + VC% = 1 CM% = 1 VC% CM% + VC% = 1 Eg/ Unit Selling Price () = $20; CM% = 40%; If 100 units are slve abve break even pint, what is the net incme, ignring taxes? Answer: $800 = 40% x 20 = $8 Each unit sld ver breakeven pint will cntribute $8 t net incme $100x8 = 800 Eg/ If ttal fixed cst fr this prduct is $1600, hw many units are needed t sell t break even? Need t sell 200 units t cver fixed cst (breakeven) 200 x $8 = $1600 Eg/ If prfit f $800, hw may units are we selling? 200 t break even 100 t make prfit 300 ttal units sld Sales All VC TCM TFC OI x #Sld UVC x #Sld x #Sld TFC OI Quantity Sld = TFC + OI QTI = TFC + TIBT = TFC + TIBT UVC TIBT = Target Incme BEFORE tax = Operating Incme = EBIT (earnings befre interest and taxes) Fr BEP: OI = 0 QB E = TFC. (Recall: = UVC) $B E = QB E x = TFC x = TFC x UVC = TFC CM% $TI = QTI x = TFC + TIBT CM% CM% = UVC = = CM Rati CM% + UVC % = 1 3

4 Single Prduce Case Mathematical Slutin X (units) = the number f units that shuld be prduced and sld t achieve the desired level f prfit Similarly, the basic equatin can als be expressed in terms f sales dllars using the variable expense rati t drive the frmula fr the dllar Sales needed t achieve target incme as fllws: Eg 1/ C X ($) = the ttal sales revenue that shuld be generated t achieve the desired level f prfit NI = the desired (target) level f prfit SP = selling price per unit VC = variable cst per unit TR = ttal revenues TVC = ttal variable csts FC = ttal fixed csts NI = TR TVC FC = X(SP) X(VC) FC = X(SP VC) FC X(SP VC) = FC + NO X(units) = FC + NI (SP VC) = FC + NI CM/unit The fllwing infrmatin is extracted frm ABC = 36 UVC = 24 TFC = 180,000 Firm wide dn t care whether variable cst cmes frm prductin r sales; want whle cst 1. 4 Hw many units t break even? QBE = TFC/

5 = 180,000/(36 24) = 15,000 Hw many units t achieve net incme f $200,000 QTI = TFC + TI = 180, ,000 (36 24) = 31, = 31,667 Repeat Q 1 and 2 fr the amunts rather than number f units Multiple by selling price QBE = TFC/ = 180,000/(36 24) = 15,000 x36 QTI = TFC + TI = 180, ,000 (36 24) = 31, = 31,667 x 36 OR Divide numeratr by CM% CM% = / 36 = V3 = ,000/ (1/3) 180, ,000 / (1/3) 5 Eg 2/Steven Bend wns car service statin in Hamiltn Steve is cnsidering leasing a machine that will allw him t ffer custmers the mandatry Ontari emissins test. Very car in Ontari must be tested every 2 years. The machine csts $6000 per mnth t lease. The variable cst per test (i.e. per car inspectin) is $10. The amunt that Steve can charge each custmer is set by the Prvince law and is currently $40 = 40 UVC = 10 TFC = 6,000 Nte everything is in mnths; in reality, everything culd be in different time perids 1. Hw many inspectins wuld Steve have t perfrm mnthly t break even frm this part f his business? QBE = TFC/ = 6,000/30 = 200 Hw many inspectins wuld Steve have t perfrm mnthly t generate a prfit f $3000 frm this part f his business? QTI = TFC + TI = 6, ,000 (30) = 300 Eg 3/ Alice Waters (age 9) runs a lemnade stand in the summer in Dundas, ON. Her daily fixed csts are $20. Her variable csts are $2 per glass f ice cld, refreshing lemnade. Alice sells an average f 100 glasses per day UVC = 2 TFC = 20 Qsld What price wuld Alice have t charge per glass, in rder t break even per day? Minimum amunt she can charge t breakeven QBE = TFC 100 = 20 P UVC P 2 (P UVC)*100 = P 100UVC = P 200 = P = 220 P = 20 She must charge $20 t break even if she sells 100 glasses What price wuld Alice have t change per glass, in rder t generate prfit f $20 per day QTI = TFC + TI = = 100 (P UVC) (P UVC)*100 = 40 (P 2)*100 = P = 240 P = 40 OR can slve with $TI = TFC + TI CM% CM% = UVC Refer t the infrmatin abut Alice, but n assume that Alice wants t charge $3 per glass f lemnade and at this price, Alice can sell 110 glasses f lemnade daily. What wuld the variable cst per glass have t be, in rder t generate prfits f $200 per day? QTI = TFC + TI = = 110 UVC (3 UVC)

6 220 = (3 UVC)*110 UVC = Eg 4/ Sunshine C. sells a single prduct. The cmpany s mst recent incme statement is given: Cntributin Margin Per Unit 52,000 / 4000 = $13 per unit If sales are dubled t $240,000 ttal variable cst will be equal If sales duble, quantity dubles variable cst dubles $68,000 x 2 = $136,000 If sales are dubled t $240,000, ttal fixed csts will be equal Assume that dubling the number f units is still within the relevant range therwise, fixed cst will change $40,000 If sunshine is past the breakeven pint and 10 mre units are sld, prfit will increase by x Units in excess f breakeven quantity = $130 Cmpute hw any units must be sld t break even QBE = TFC/ = $40,000/$13 = 3,077 units Cmpute hw many units must be sld t achieve a prfit f $20,000 QTI = TFC + TI / = ($40,000 + $20,000)/$13 = 4,615 units Eg/ Aladdin C. manufactured magic lamps. The fllwing infrmatin pertains t the cmpany fr the mst recent accunting perid: Lamps prduced and sld = 40,000 Ttal Cst = $480,000 UFC = $2 CM Rati = 0.59 Target Incme = $5000 Tax Rate = 35% What is the BEP in Q? TFC = 2 x 40,000 = 80,000 TVC = $480,000 $80,000 = $400,000 UVC = $400,000/40,000 = $10 CM% = 50% VC% = 50% Ł VC% = $10 CM%=$10 = $20 QBE =TFC/ UVC = 80,000/$20 $10 = 8,000 The Effect f Incme Tax Operating Incme Tax = Net Incme Tax = tax rate x perating incme Operating Incme (Rate x Operating Incme) Net Incme TIBT = TIAT 1 Tax Rate. TIAT = Target Incme AFTER taxes = Net Incme 6 Organizatins making prfit must pay incme taxes; a business nly gets t keep incme after taxes (net incme); thus, the CVP analysis is mre infrmative if it shws what it will take t generate a target amunt f net incme In rder t calculate the sales vlume needed t achieve a specified amunt f net incme, a tax rate as a percentage f perating incme is assumed; target prfit must be adjusted by incrprating incme tax Mathematically, the amunt f net incme can be expressed as a percentage f perating incme; therefre, the target after tax prfit must be cnverted t its befre tax equivalent using the fllwing frmula:

7 OR Nte that the BEP unaffected by incme taxes becme nt ax is n perating incme Sensitivity Analysis Sensitivity Analysis what if technique managers use t examine hw a result will change if riginal predicted data nt achieved r if an underlying assumptin changes Uncertainty pssibility that an actual amunt will deviate frm an expected amunt Used befre cmmitting csts perfrm analysis f changes in perating incme fr changes underlying assumptins Eg 1/ Selling Price $500 Variable Cst Per Unit $300 Ttal Mnthly Fixed Cst $200,000 Units Sld Per Mnth $1,600 Hw many units d we need t sell t break even? What effect will a 10% discunt n sales price have n BEP in units? New equipment will increase FC by 30%, but decrease VC per unit by 30%; What effect will it have n BEP in units? Purchase f higher quality raw materials will increase VC by $25 per unit, but decrease FC by $17,500; hw many units d we need t sell t maintain perating incme f $120,000? CVP Relatinships in Graphic Frm Axis Y = Ttal cst (eg/ $); X = Cst Driver (eg/ Units) Ttal cst curve begins at ttal fixed cst (Y intercept; a in regressin analysis equatin) Slpe = unit variable cst Revenue curve begins at the rigin Slpe = unit selling price Area between tw curves (under ttal cst, abve revenue) Lss Area between tw curves (abve ttal cst, belw revenues) Prfit Intersectin between tw lines Breakeven Pint Graphs f CVP relatinships can be used t gain insight int the behaviur f expenses and prfits The basic CVP graph is drawn with dllars n the vertical axis and vlume in units n the hrizntal axis Ttal fixed expense is drawn first, then variable expense is added t the fixed expense in rder t draw the ttal expense line Finally, the ttal revenue line is drawn The ttal prfit (r lss) is the vertical difference between the ttal revenue and ttal expense lines The cst vlume prfit graph depicts the relatinships amng cst, vlume and prfits The pint where the ttal revenue line and the ttal cst line intersect is the break even pint Units Sld Eg 1/ ABC Cmpany has a target prfit after tax $12,000 fr 2007; the cmpany pays tax at a rate f 25%; use the next graph t answer the fllwing questins 1. Calculate the SP per unit, VC per unit and CM per unit 7 Hw many units t prduce and sell s as t achieve the target NI fr 2007 If the cmpany prduced and sld 3,500 units during 2007, hw much is the NI after

8 Eg 2/ Use the abve graph t answer the fllwing questins: TFC = $6000 UVC = $6 = 15,000/1500 = $10 At 900 units Ttal Cst Pint = (900x6) = TVC + TFC TC = 15,000 (at 1500 units) Revenue Line pint = 900x10 What is the variable cst per unit? Ttal Revenue Ttal Cst = If fixed csts increased by $3000, what is the new breakeven pint? 8 TVC = 9,000 UVC = $9000/1500 units = $6 What is the net incme if the cmpany sld 900 units? Ttal Revenue Ttal Cst = ,400 What is the net incme f if the cmpany sld 200 units? TFC = 6,000 BEQ = TFC/ = ( )/ (10 6) = 2250 units Eg 3/ The fllwing graph prtrays the CVP activities fr ABC C. fr the year ABC prduced and sld 4000 units during 2006

9 During 2006, ABC prduced and sld 4000 units; cmplete the incme statement fr ABC C. fr 2006 Sales Revenue = x Qsld = 48,000/4000 x 4000 = 48000/4000 = 12 Ttal Variable Cst = UVC x QSld = 8 x 4000 Breakeven pint = 12 x 1000 (due t revenue infrmatin) = 12,000 UVC = DY/DX = (36,000 12,000) / ( ) = 8 Cntributin Margin = (12 8) x 4000 FC = 36,000 32,000 = 4000 TC = 36,000 VC = 8 x 4000 Incme Statement fr the Perid Ended December 31, 2007 Sales Revenue 48,000 Ttal Variable Csts (32,000) = Cntributin Margin 16,000 Ttal Fixed Csts (4000) = Net Incme 12,000 Margin f Safety The margin f safety is the excess f budgeted (r actual) sales ver the break even clumn f sales It is the amunt by which sales can drp befre lsses begin t be incurred The margin f safety cay be cmputed in three ways Margin f safety (in units) = Expected sales (in units) Sales at break even (in units) Margin f safety ($) = Expected sales ($) Sales at break even ($) Margin f safety percentage = Margin f safety ($) / Ttal sales The margin f safety rati is a useful measure f cmparing the relative risk amng alternative prducts r fr assessing the riskiness in any given prduct A relatively lw margin f safety rati fr a prduct is usually an indicatin that the prduct is riskier than higher margin f safety prducts Operating Leverage and Cst Structure Cst Structure Cst structure refers t the relative prprtin f fixed and variable csts in an rganizatin Operating Leverage Operating leverage is named fr the lever effect that cmes frm the use f fixed csts t generate mre prfit 9 The ptimal cst structure fr cmpany depends n many factrs, including the lng run trend in sales, year t year fluctuatins in the level f sales, and the attitudes f wners and managers twards risk Understanding a cmpany s cst structure is imprtant fr decisin making as well as fr analysis f perfrmance If the chice exists t incur fixed r variable cst, and fixed is chsen, then variable cst wuld be less, yielding a larger cntributin margin and the pssibility f larger prfit Once the fixed csts are recvered, the cntributin margin is prfit This effect can be seen n a breakeven graph The intersecting revenue and ttal cst lines create equal and ppsite angles at the intersectin pint One can nte that the risk (dwnside) is equal t the reward (upside) The larger the fixed cst, the wider the intersectin angles usually; the greater the pprtunity fr reward, the greater the pssibility f lss Hw t Measure Operating Leverage Operating leverage is a measure f hw sensitive net incme is t a given percentage change insales vlume

10 It is affected by the relative mix f fixed and variable csts This trade ff affects the amunt by which prfits will change as sales fluctuate and is measured by the degree f perating leverage (CM/Prfits) using a given level f sales as the reference pint Once the degree f perating leverage (DOL) is cmputed, the percentage change in prfits is cmpuated by multiplying the percentage change in prfits by the DOL The degree f perating leverage at a given level f sales is cmputed as fllws: Hw t Use Operating Leverage A cmpany with high perating leverage wuld have high FC, lw VC, and high CM Such a cmpany wuld experience a large change in perating incme fr a small change in sales, as cmpared with a cmpany which have lw perating leverage The DOL can be used t measure the percentage f change in prfit that results frm a percentage f change in sales The higher degree f perating leverage, the greater the change in prfit when sales change Percentage change in prfit = DOL x percentage change in sales Thus given that there is n change in FC, the degree f perating leverage prvides a quick way t predict the percentage effect n prfits f a given percentage increase in sales The higher the degree f perating leverage, the larger the increase in net incme Nte the degree f perating leverage is nt cnstant Degree f perating leverage = cntributin margin/net incme It changes as the level f sales change Eg/ at the break even pint, the degree f perating leverage is infinite since the denminatr wuld be zer Therefre the degree f perating leverage shuld be used with sme cautin and shuld be recmputed fr each level f starting sales Eg/ The fllwing data are related t tw identical cmpanies with different cst structure: Bth cmpanies sell same prduct at same price; while cmpany A is mre labr intensive, cmpany B is mre capital intensive Calculate the BEP in dllar fr bth cmpanies Calculate the degree f perating leverage fr bth cmpanies What effect will a 20% increase in sales have n bth cmpanies perating incme? Multiple Prduct Analysis Sales Mix The term sales mix means the relative prprtins in which a cmpanys prducts are sld Ost cmpanies prduce a number f different prducts with different selling prcis, css and cntributin margins This, changes in the sales mix can cause variatns in a cmpanys prfits As a result, the break even pint in a multi prduct cmpany is dependent n the mix in which the varius prducts are sld Cnstant Sales Mix Assumptin CVP analysis with multiple prducts assumes that sales will cntinue at the same mix f prducts, expressed in either sales units r sales dllars; in essense, the assumptin is made that the firm has nly ne prduct that cnsists f a basket (package) f its varius prducts in a specified prprtin This assumptin is essential, because a change in the prduct mix will prbably change The weighted average variable cst The weighted average cntributin margin The sales mix can be expressed either in terms f units r dllars f sales revenue Thus, we can calculate the sales revenues (in units r dllars) t achieve a certain level f target prfit in ne r three different equatins as fllws: 1. # f packages that the cmpany shuld prduce and sell t achieve an verall target prfit 10 The weighted average sales price # f units f each prduct that the cmpany shuld prduce and cell t achieve an verall target prfit

11 Eg/ Califrnia C. Prduces tw prducts A&B; ttal fixed csts per mnth fr the cmpany is $200,000 Fllwing infrmatin is extracted frm the cmpany s recrds: Prduct Mix Price/Unit VC/Unit A 3 $10 $5 B Hw many units f each prduct t breakeven? 11 Ttal sales revenue ($) that the cmpany shuld generate frm all prduct t achieve an verall target prfit Hw much is ttal sales revenus t breakeven?