11CHAPTER 62Cost-Volume-Profit Analysis3• Firms study relationship between their C-V-P levels• Part of planning process– Answers common questions4• “How many units does Firm have to produce & sell in order to BE?”• “Can Firm obtain this level of production & sales?”5• “How many units does Firm have to sell to produce a target income?”• “If Firm increases its sales volume by 50%, what will be the impact on my OP?” 6Break-Even Point27P=Selling Price Per Unitx=Units Produced and SoldV=Variable Cost Per UnitF= Total Fixed CostsOP = Operating Profits-Before Taxt = Tax rate8• Sales Revenue = Px • Total Costs = Vx + F • When Firm Breaks Even (BE)Sales Revenue – Total Costs = 09Revenue=Total CostsPx=Vx + FPx - Vx=Fx(P - V)=Fx=__F__(P -V)(FORMULA "A")10x =__F__(FORMULA "A")CMU• Denominator called CMU11E.g., Assume Firm has following costs, revenues and tax rates:P=$200V=$120F = $2,000Tax Rate (t) = 40%12x =2,000(200 - 120)x = 2,00080x = 25 unitsX = F/(P-v)313• This is common sense• Firm makes $80 every time it sells a unit.x =$2,000= 25 units8014x =_F__ (Formula “A”)(P-V)Px =F x P(P-V)`Px =__F__ (FORMULA "B")(P-V)P15• Denominator called CMR: Px =__F__ (FORMULA "B")CMR• What is CMR? 16• CMR gives % of Sales Price that goes to pay off FC & generates profits (after you pay VC): (P-V)/PP/P - V/P1 - V/P(1 – part of price that pays VC)17Px =__2,000__(200 - 120)200Px = 2,000.40Px = $5,000Px = F/((P-V)/P)18• Why do we need Formula B?419Revenue: $100K(Px)Less VCs: -30K(Vx)CM: $ 70K(Px – Vx)Less FCs: -50K(F)OP: $ 20K(Px - Vx – F)• E.g., What is BE Point for Co.?20• What is BE?–We do not know the # of units sold–We do not know P or VC per unit–We cannot use Formula “A”21• We can calculate the CMR– So we can use Formula “B”CM=Px - VxRevenue Px=(P-V)x=(P-V)Px P22• The CMR is .70 (70,000/100,000)• The BE Point in Sales Revenue is:Px = F/CMR = 50,000/.70 = $71,428.5723Revenue: $100KLess VCs: -30KCM: $ 70KLess FCs: -50KOP: $ 20K24OLD REVISEDRev $100KPx $71.4KVC(30%) -30K-Vx -21.4KCM: $ 70K$50KFC: -50K-$50KOP: $ 20K$ 0525Targeted Operating Profits26OP = Revenue - CostsOP = Px - Vx - FPx = Vx + F + OP 27Px = Vx + F + OPPx - Vx = F + OPx(P - V) = F + OPx = (F + OP)Modified Formula “A”(P - V)x = (F + OP)CMU28x = (F + OP)(P - V)Px = (F + OP)P(P - V)Px = _(F + OP)_Modified Formula “B”(P - V)PPx = (F + OP)CMR29• Same E.g.• Assume Co wants Target OP of $40Kx =(2,000 + 40,000)(200 - 120)x =42,00080x = 525 units30• Again, this is common sense• Firm makes $80 for every unit–Needs to sell 25 units to BE (2,000/80)–Needs to sell 500 units to generate OP of $40K (40,000/80)–Needs to sell 525 units ($42,000/80)631• OP do not include tax expense• OP – Tax Expense = NI • What if given Targeted NI?32• E.g., Given target NI (after-tax) of $50K & tax rate of 40%• Convert $50K NI into OP:OP - Taxes = NIOP - .4 (OP) =50,000.6 (OP) =50,000OP = 50,000/ .6OP = 83,33433• You can check this:OP: $83,334Taxes (40%): -33,334NI: $50,00034What if Target OP is given as % of Revenue?Px = (F+OP)/((P-V)/P)Px = (2,000 + .1 Px) / [(200 -120)/200]Px = (2,000+.1Px) / .40.4 Px = 2,000 + .1Px.3 Px = 2,000Px = 2,000/.3Px = $6,66735Revenue: $6,667Less VCs (60%): -4,000CM: $2,667Less FCs: -2,000OP: $ 66736Multiple Products737• Firm has >1 product• Same analysis but use composite:– CMU (Formula A) or – CMR (Formula B)38• If using CMR (Formula B)• Need to calculate CMR for entire Company– CMR = CM/Sales39• If using composite CMU–Basket (Package) Method–Weighted Average CM Method40• Need to assume sales mix/ product mix doesn’t change41E.g., Co sells 3 Bananas for each Orange that it sells (75% vs. 25%) Bananas OrangesPrice: $2 $4VC per Unit: $1 $2CMU: $1 $2Common Fixed Costs: $2,000 42• Basket Method: (75%:25%)• Basket 3 Bs & 1 Or: CMB= 3 CMban+ 1CMorCMB= 3 (1) + 1 (2)CMB=5843• Now, plug CMBinto BE formula• Gives you BE Point in Baskets:Baskets = F/CMBBaskets = 2,000/ 5Baskets =400 Baskets44Bananas: 3 x 400 Baskets = 1200Oranges: 1 x 400 Baskets = 40045• Weighted Average MethodCMWA=.75 CMban+ .25 CMorCMWA=.75 (1) + .25 (2)CMWA= .75 + .5 = $1.2546x = F/CMWAx = 2,000/ 1.25x =1600 units• The BE Point in units is:47Bananas: .75 (1600) = 1200 Oranges: .25 (1600) = 400 48Margin of Safety949• Margin Of Safety Amount that actual sales (dollars or units) exceed BE Point–If BE Point is 25 units (or $5,000) & Co actually sells 40 units ($8,000)–Margin Of Safety is 15 units (or $3,000)50Operating Leverage51• Operating Leverage (OL)–Divide CM by OP• OL is a multiplier• If you multiply Co’s OL by % increase in Co’s Sales –You get % increase in Co’s OP52• E.g.,Revenue: $ 8,000 (200x40) (Px)VCs: -$4,800 (120x40) (Vx)CM: $ 3,200FCs: -$2,000OP: $1,20053CM=$3,200= 2.67OP $1,200• Operating Leverage:54• Common to ask – If we increase our sales by so much, what will be our new OP?– OL gives you the answer quickly1055• If Sales increases by 50%• OL x Sales↑% = OP↑%• 2.67 x 50% = 133%• OP of $1,200 will increase by $1,600 (1.33 x $1,200) –New OP $2,80056OLDRev: $ 8,000 (200 x 40 units)VCs: -$4,800 (120 x 40 units)CM: $ 3,200 (80 x 40 units)FCs: -$2,000OP: $1,20057NEWRev: $12,000 (200 x 60 units)VCs: -$7,200 (120 x 60 units)CM: $4,800 (80 x 60 units)FCs: -$2,000OP: $2,800The increase in Rev is assumed to be due to increase in
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