Volume-Cost-Pro
Volume-Cost-Profit fit AnalysisAnalysis
Learning Objectives
Learning Objectives
i.
i. ExExplaplain brin breaeak-ek-eveven poin point annt and illd illusustratrate its dte its deteetermirminatnation bion bototh algh algebebrairaicalcally anly andd graphically
graphically ii.
ii. DisDiscuss cuss brebreak-eak-even ven appapplicalicationtions in s in detdetermiermining ning salesales to s to proproduduce dce desiresired ped profrofits,its, additional sales volume to offset a reduction in selling price and so on
additional sales volume to offset a reduction in selling price and so on iii
iii.. UnUndederstrstand cand casash breh breakak-ev-even poen poinint and it and its apts appliplicacatiotions.ns.
Introduction
Introduction
Profit planning is a function of the selling price of a unit of product, the variable cost if Profit planning is a function of the selling price of a unit of product, the variable cost if making and selling the product, the volume of product units sold, and, in the case a making and selling the product, the volume of product units sold, and, in the case a multi-product companies, sales-mix and,
multi-product companies, sales-mix and, finally, the total fixed finally, the total fixed costs. costs. TheThe volumevolume cost-profit (VCP) analysis
cost-profit (VCP) analysis is a management accounting tool to show the relationshipis a management accounting tool to show the relationship betwee
between these ingn these ingredientredients of pros of profit plannifit planning. ng. The enThe entire gamtire gamut of prut of profit plaofit planning nning isis associated wit VCP
associated wit VCP inter-relatiinter-relationships. onships. A widely-used A widely-used technique to study technique to study VCPVCP relationships is break-even analysis.
relationships is break-even analysis.
A break-even analysis is concerned with the study of revenues and costs in relation to A break-even analysis is concerned with the study of revenues and costs in relation to sales volume and, particularly, the determination of that volume of sales at which the sales volume and, particularly, the determination of that volume of sales at which the firm’s revenues and total costs will be
firm’s revenues and total costs will be exactly equal (or net income exactly equal (or net income zero. zero. Thus, theThus, the break-ev
break-even poinen point (t (BEPBEP) may be defined as a point at which the firm's total revenues are) may be defined as a point at which the firm's total revenues are exactly equal to total costs, yielding
exactly equal to total costs, yielding zero income. zero income. The “no-profit, no-loss” point is The “no-profit, no-loss” point is aa break-ev
break-even poinen point or a pt or a point at woint at which lohich losses cease ansses cease and profitd profits begins begin..
Break-even analysis, as a technique, seeks to provide answers to the following Break-even analysis, as a technique, seeks to provide answers to the following questions:
questions: 1.
1. WWhahat st salales es vovolulume me is is nenececessssarary ty to po proroduduce ce anan X X amount of operating profit?amount of operating profit? 2.
2. WWhahat wt wilill tl the he opopereratatining g prprofofit it or or loloss ss atat X X sales volume be?sales volume be? 3
3.. WWhahat pt prroofifit wt wilill rl reessuullt ft frorom am ann X X per cent increase in sales volume?per cent increase in sales volume? 4.
4. WhWhat iat is ths the ade addiditiotional nal salsales ves vololumume ree reququireired to d to mamake gke gooood ad ann X X per centper cent reduction in selling prices so as to maintain the current profit level? reduction in selling prices so as to maintain the current profit level? 5.
5. WhWhat wat will till the efhe effecfect on opt on opereratiating png prorofit bfit be if the if the come compapanyny’s fix’s fixed coed costs hsts havavee increased?
increased? 6.
6. WhWhat wat will till the ehe effeffect on ct on incincomome be if e be if the the firfirm acm achiehieves a rves a rededucuctiotion in vn in varariabiablele costs (say, material or direct labour)?
costs (say, material or direct labour)? 7.
7. WhaWhat is t is the the reqrequireuired sad sales vles voluolume me to cto coveover thr the ade additditionaional fixl fixed ed charcharges ges from from thethe propo
proposed new sed new projectproject?? 8.
8. WhaWhat wt will till the ehe effecffect on t on opeoperatinrating pg profirofit ot of thf the fie firm brm be if e if the the salesales mis mix is x is chachangenged?d? 9.
9. WhWhat wat will till the ehe effeffect on ct on incincomome be if e be if thethere is are is an inn increcrease iase in fixn fixed ced costosts by as by ann X X amount the to new plan but will decrease the labour costs by
amount the to new plan but will decrease the labour costs by Y Y amount per unit?amount per unit? 10.
Section 1 Break-Even Analysis
Section 1 Break-Even Analysis
A break-even analysis shows the relationship between the costs and profits with sales A break-even analysis shows the relationship between the costs and profits with sales volume.
volume. The sales volume wThe sales volume which equates total revenue with hich equates total revenue with related costs and resale inrelated costs and resale in neither profit nor loss is called the
neither profit nor loss is called the break-even volume or point break-even volume or point (BEP)(BEP). . If If all costs all costs areare assumed to be variable with sales volume, the BE
assumed to be variable with sales volume, the BEP would be P would be at zero sales. at zero sales. If all costsIf all costs were fixed, profits would vary disproportionately with sales and the BEP would be at a were fixed, profits would vary disproportionately with sales and the BEP would be at a point w
point where total shere total sales reveales revenue equnue equaled fixed aled fixed costs. costs. HowHowever, buever, but are put are purelyrely hypothetical situations.
hypothetical situations. In actual practice, costs coIn actual practice, costs consist of both nsist of both fixed and fixed and variablevariable elements.
elements.
Break-even point
Break-even point is the sales volume at which revenue equals cost (i.e. no profit nois the sales volume at which revenue equals cost (i.e. no profit no loss).
loss).
The BEP can be determined by two methods: The BEP can be determined by two methods:
1.
1. AlgebAlgebraic methraic methods: (a) ods: (a) ContrContribution ibution margin margin approapproach anach and (b) d (b) EquaEquationtion technique, and
technique, and 2.
2. Graphic Graphic presentapresentation: (ation: (a) Break) Break-even -even chart anchart and (b) d (b) Profit Profit volumvolume grape graph.h.
Algebraic Methods
Algebraic Methods
Contribution Margin
Contribution Margin ApproacApproach:h: The logic underlying the determination of the BEPThe logic underlying the determination of the BEP under the approach can be stated by answering the following question: “How many under the approach can be stated by answering the following question: “How many ice-creams, having a unit cost of Rs 2 and a selling price of Rs 3, much a vendor sell in a creams, having a unit cost of Rs 2 and a selling price of Rs 3, much a vendor sell in a fair to recover the Rs 800 fees paid by him for getting a selling stall and additional cost fair to recover the Rs 800 fees paid by him for getting a selling stall and additional cost of Rs 400 to install the stall?” The answer can be determined to dividing the fixed cost of Rs 400 to install the stall?” The answer can be determined to dividing the fixed cost by the
by the differencdifference betwee between the sellen the selling price ing price (Rs 3) (Rs 3) and cosand cost price (Rt price (Rs 2). s 2). ThusThus,,
cost) cost) able able Unit vari Unit vari -- price price Sales Sales (( expenses) expenses) Stall Stall fees fees (Entry (Entry cost cost Fixed Fixed (units) (units) BEP BEP == ++ (7.1) (7.1) (Rs 800 + Rs 400)/Rs 3 – Rs 2) = 1,200 units (Rs 800 + Rs 400)/Rs 3 – Rs 2) = 1,200 units Or, Or, unit unit per per )) (( in in arg arg m m on on Contributi Contributi costs costs Fixed Fixed (units) (units) BEP BEP CM CM = = (7.2) (7.2) Or, Or,
BEP (amount)/BEP (Sales BEP (amount)/BEP (Sales revenue)/
revenue)/ BESR BESR
= BEP (units) X Selling price (
= BEP (units) X Selling price (SP SP ) per ) per unit unit (7.3)(7.3) = 1,200 X Rs 3 = Rs 3,600 = 1,200 X Rs 3 = Rs 3,600 Or, Or,
ratio) ratio) (P/V (P/V ratio ratio volume volume ofit ofit Pr Pr costs costs Fixed Fixed (amount) (amount) BEP BEP == (7.4) (7.4) unit unit per per price price Selling Selling unit unit per per margin margin on on Contributi Contributi ratio ratio V V // P P 11== (7.5) (7.5) cent cent per per 33 33 .. 33 33 or or 3 3 Re Re 1 1 Re Re = = BEP (amount) = Rs 1,200 ÷ 0.333 = Rs 3,600 BEP (amount) = Rs 1,200 ÷ 0.333 = Rs 3,600 Sum the P/V ratio, the variable cost to volume ratio (
Sum the P/V ratio, the variable cost to volume ratio (V/V V/V ratio) can be easily derived:ratio) can be easily derived: V/V
V/V ratio = 1 – P/V ratioratio = 1 – P/V ratio (7.6)(7.6) In the vendor’s case, it is = 1-1/3 = 2/3 = 66.67 per cent
In the vendor’s case, it is = 1-1/3 = 2/3 = 66.67 per cent The
The V/V V/V ratio, as the name suggests, establishes the relationship between variable costsratio, as the name suggests, establishes the relationship between variable costs (VC) and sales volume in amou
(VC) and sales volume in amount. nt. The direct method of its computation The direct method of its computation is:is:
cent cent per per 66.67 66.67 3 3 Rs Rs 2 2 Rs Rs revenue revenue Sales Sales cost cost Variable Variable = = ÷ ÷ = = (7.7) (7.7) Thus, P/V ratio +
Thus, P/V ratio + V/V V/V ratio = 1 or 100 per centratio = 1 or 100 per cent
(1/3 + 2/3) = 1 (33.33 per cent + 66.67 per cent) = 100 per (1/3 + 2/3) = 1 (33.33 per cent + 66.67 per cent) = 100 per cent
cent
(7.8) (7.8)
Margin of Safety
Margin of Safety The excess of the actual sales revenue (ASR) over the break-evenThe excess of the actual sales revenue (ASR) over the break-even sales revenue (BESR) is know as the
sales revenue (BESR) is know as the margin of safetymargin of safety. . Symbolically, mSymbolically, margin argin of of safetysafety = (ASR – BESR)
= (ASR – BESR)
(7.9) (7.9)
When the margin of safety (amount) is divided by the actual sales (amount), the margin When the margin of safety (amount) is divided by the actual sales (amount), the margin of safety ratio (
of safety ratio ( M/S M/S ratio) ratio) is is obtained. obtained. Symbolically,Symbolically,
ASR ASR BESR) BESR) --(ASR (ASR ratio ratio== M/S M/S (7.10) (7.10) The
The M/S M/S ratio indicates the percentage by which the actual sales may be reduced beforeratio indicates the percentage by which the actual sales may be reduced before they the below
they the below the break-even sales volume. the break-even sales volume. It is important that there should It is important that there should be abe a reasonable margin of safety, lest a reduced level of activity should prove disastrous. reasonable margin of safety, lest a reduced level of activity should prove disastrous. The higher the margin of safety ratio, the better it is from the point of view of the The higher the margin of safety ratio, the better it is from the point of view of the company as it indicates that a “sizeable” sales volume can fall before the BEP is company as it indicates that a “sizeable” sales volume can fall before the BEP is reached.
Assume in the vendor’s case that sales is 2,000 units (Rs 6,000); margin of safety (Rs Assume in the vendor’s case that sales is 2,000 units (Rs 6,000); margin of safety (Rs 6,000 to Rs 3,600) = Rs 2,400; and the M/S ratio is Rs 2,400 ÷ Rs 6,000 = 40 per cent. 6,000 to Rs 3,600) = Rs 2,400; and the M/S ratio is Rs 2,400 ÷ Rs 6,000 = 40 per cent. The amount of profit can be directly determined with reference to the margin of safety The amount of profit can be directly determined with reference to the margin of safety and
and P/V P/V ratio. ratio. Symbolically,Symbolically, Profit = [Margin
Profit = [Margin of safety (amouof safety (amount)] x Pnt)] x P/V ratio/V ratio (7.11)(7.11) Or Profit = [Margin of safety (units) X
Or Profit = [Margin of safety (units) X CM CM per unit]per unit] (7.12)(7.12) In the vendor’s case, profit = Rs 2,400 x 0.3333 (33.33 per cent) = Rs 800 or 800 x Re 1 In the vendor’s case, profit = Rs 2,400 x 0.3333 (33.33 per cent) = Rs 800 or 800 x Re 1 = Rs 800.
= Rs 800.
The reason is that once the total amount of fixed costs has been recovered, profits will The reason is that once the total amount of fixed costs has been recovered, profits will increase by the difference of sales revenue and variable costs.
increase by the difference of sales revenue and variable costs. Equation Technique
Equation Technique This is the most general form of analysis, which can be applied toThis is the most general form of analysis, which can be applied to any cost-volume-profit situation.
any cost-volume-profit situation. It is based on It is based on an income eqan income equation: Sales revenue-uation: Sales revenue-Total costs = Net profit Break up total costs into fixed and variable, Sales revenue – Total costs = Net profit Break up total costs into fixed and variable, Sales revenue – Fixed costs – V
Fixed costs – Variable costs Net profit. ariable costs Net profit. Or sales revenue = Or sales revenue = Fixed costs + VFixed costs + Variable costsariable costs + Net profit.
+ Net profit. If
If S S be the number of units required for break-even and sales revenue (be the number of units required for break-even and sales revenue (SP SP ) and) and variable costs (VC) are on per unit basis, the above equation can be written as follows: variable costs (VC) are on per unit basis, the above equation can be written as follows:
SP(S)
SP(S) = FC + VC= FC + VC (S)(S) ++ NI NI (7.13)(7.13) Where
Where SP SP = Selling price per unit= Selling price per unit S
S = Number of units required to be sold to break-even= Number of units required to be sold to break-even FC = Total fixed costs
FC = Total fixed costs
VC = Variable costs per unit VC = Variable costs per unit NI
NI = Net income (zero)= Net income (zero) SP SP ((S S ) = FC + VC (S) + zero) = FC + VC (S) + zero SP SP ((S S ) – VC () – VC (S S ) = FC) = FC or or S S ((SP SP – VC) = FC– VC) = FC VC VC FC FC − − = = SP SP S S (7.14) (7.14)
It can be seen that Eq. 7.14 is identical to Eq. 7.2 (contribution margin It can be seen that Eq. 7.14 is identical to Eq. 7.2 (contribution margin approach).
approach). Yet, Yet, it it isis specially specially useful in useful in situationsituations in whs in which unit ich unit price anprice and unit d unit variablevariable costs are not clearly identifiable.
costs are not clearly identifiable. Example 7.1
Example 7.1SV SV Ltd, a multi-product company, furnishes you the following dataLtd, a multi-product company, furnishes you the following data relating to the current year:
relating to the current year: Particula
Particularsrs FFiirrsst t hhaallf f oof f tthhe e yyeeaarr SeSeccoonnd d hhaallf f oof f tthhe e yyeeaar r
S
T
Toottaal l ccoossttss 4400,,000000 4433,,000000
Assuming that there is no change in prices and variable costs and that the fixed Assuming that there is no change in prices and variable costs and that the fixed expenses are incurred equally in the two half-year periods, calculate for the year: (i) expenses are incurred equally in the two half-year periods, calculate for the year: (i) The profit-volume ratio (ii) Fixed expenses, (iii) Break-even sales, and (iv) Percentage The profit-volume ratio (ii) Fixed expenses, (iii) Break-even sales, and (iv) Percentage margin of safety.
margin of safety.
Solution
Solution
Sales revenue – Total costs = Net profit Sales revenue – Total costs = Net profit
Rs 45,000 – Rs 40,000 = Rs. 5,000 (first half) Rs 45,000 – Rs 40,000 = Rs. 5,000 (first half) Rs 50,000 – Rs 43,000 = Rs 7,000 (second half) Rs 50,000 – Rs 43,000 = Rs 7,000 (second half)
On a differential basis: Sales revenue, Rs 5,000 – ∆ Total costs, Rs 3,000 = ∆ Total On a differential basis: Sales revenue, Rs 5,000 – ∆ Total costs, Rs 3,000 = ∆ Total profit, R
profit, Rs 2,00s 2,0000
We know that only VC changes with a change in sales volume and, hence, We know that only VC changes with a change in sales volume and, hence, change in total costs are e
change in total costs are equivalent to VC quivalent to VC (Rs 3,000). (Rs 3,000). Accordingly, the additional salesAccordingly, the additional sales of Rs 5,000 has earned a contribution margin of Rs 2,000 [Rs 5,000 (S) – Rs 3,000 of Rs 5,000 has earned a contribution margin of Rs 2,000 [Rs 5,000 (S) – Rs 3,000 (VC)].
(VC)].
P/V ratio = Rs 2,000 ÷ Rs 5,000 = 40 per cent P/V ratio = Rs 2,000 ÷ Rs 5,000 = 40 per cent V/V
V/V ratio = 100 per cent – 40 per cent = 60 per centratio = 100 per cent – 40 per cent = 60 per cent
Accordingly, 60 per cent of the total costs are made up of variable costs and the Accordingly, 60 per cent of the total costs are made up of variable costs and the balance re
balance represents tpresents the total fixhe total fixed costed costs (FC).s (FC).
Sales revenue = Fixed costs + Variable costs + Net profit Sales revenue = Fixed costs + Variable costs + Net profit Rs 95,000 = FC + 0.60 X (Rs 95,000) + Rs 12,000 Rs 95,000 = FC + 0.60 X (Rs 95,000) + Rs 12,000 Rs 95,000 = FC + Rs 57,000 + Rs 12,000 Rs 95,000 = FC + Rs 57,000 + Rs 12,000 Rs 95,000 – Rs 69,000 = FC or Rs 26,000 = FC Rs 95,000 – Rs 69,000 = FC or Rs 26,000 = FC BEP (amount) = Rs 26,000 ÷ 0.40 = Rs 65,000 BEP (amount) = Rs 26,000 ÷ 0.40 = Rs 65,000
TABLE 7.1 Verification
TABLE 7.1 Verification
ParticulaParticularsrs AmouAmountnt Per cent Per cent
B
Brreeaakk--eevveen n ssaalleess RRs s 6565,,000000 110000 V
Vaarriiaabbllee ccoossttss 3399,,000000 6600
C
Coonnttrriibbuuttiioonn 2266,,000000 4400
F
Fiixxeeddccoossttss 2266,,000000 5500
Net inco
Net incomeme NilNil NilNil
cent cent per per 58 58 .. 31 31 000 000 ,, 95 95 Rs Rs 65,000) 65,000) Rs Rs --95,000 95,000 (Rs (Rs ratio ratio== == M/S M/S
Break-Even Analysis Applications
Break-Even Analysis Applications
Sales Volume Required to Produce Desired Operating Profit
Sales Volume Required to Produce Desired Operating Profit One application of aOne application of a BE analysis is a determine the required sales volume to generate a budgeted amount of BE analysis is a determine the required sales volume to generate a budgeted amount of profit.
profit. The reThe required saquired sales are gles are given by iven by Eq. 7.Eq. 7.15.15.
(Fixed expenses + Desired operating profit) ÷ P/V ratio
(Fixed expenses + Desired operating profit) ÷ P/V ratio (7.15)(7.15) In Example 7.1, if the desired operating profit of
In Example 7.1, if the desired operating profit of SV SV ltd is Rs 14,000, required salesltd is Rs 14,000, required sales volume = (Rs 26,000 + Rs 14,000)/0.40 = Rs 1,00,000
volume = (Rs 26,000 + Rs 14,000)/0.40 = Rs 1,00,000
A variant of the above approach is that the management may be interested in A variant of the above approach is that the management may be interested in knowing the
knowing the required sales volume to prorequired sales volume to produce the desired profit after taxes. duce the desired profit after taxes. In thisIn this case, the analysis must
case, the analysis must be expanded be expanded slightly. slightly. Assume thatAssume that SV SV ltd wants a net incomeltd wants a net income after taxes of Rs 13,500 and that its current tax rate is 35 per cent, the net income after after taxes of Rs 13,500 and that its current tax rate is 35 per cent, the net income after taxes is 65 per cent of the net income before taxes.
taxes is 65 per cent of the net income before taxes.
ration ration rate)] rate)] tax tax --s/(1 s/(1 after taxe after taxe income income [Desired [Desired costs costs Fixed Fixed volume volume sales sales quired quired Re Re P/V P/V + + = = (7.16) (7.16) 1,16,923 1,16,923 Rs Rs 0.40 0.40 )] )] 35 35 .. 0 0 1 1 /( /( 00 00 ,, 35 35 ,, 1 1 Rs Rs [[ 000 000 ,, 26 26 Rs Rs = = − − + + = = Table 7.2
Table 7.2 VerificationVerification S
Saalleess vvoolluummee RsRs11,,1166,,992233
L
Leessss:: VVaarriiaabbllee ccoossttss 7700,,115544 C
Coonnttrriibbuuttiioonn 4466,,776699
L
Leessss FFiixxeedd ccoossttss 2266,,000000
P
Prrooffiittssbbeeffoorree ttaaxxeess 2200,,776699 L
Leessss:: TTaaxxeess ((00..3355)) 77,,226699
P
Prrooffiitt aafftteerrttaaxxeess 1133,,550000
Operating Profit at a Given Level
Operating Profit at a Given Level of Sales Volumeof Sales Volume [Actual Sales Revenue (ASR) – [Actual Sales Revenue (ASR) – Break-even Sales Revenue (BESR)] X P/V ratio
Break-even Sales Revenue (BESR)] X P/V ratio Effect on Operating Profit of a
Effect on Operating Profit of a Given Increase in Sales VolumeGiven Increase in Sales Volume [Budgeted Sales[Budgeted Sales Revenue (BSR) – BESR] X P/V ratio
Revenue (BSR) – BESR] X P/V ratio (7.18)
(7.18) Suppose that
Suppose that SV SV Ltd forecasts 10 per cent increase in sales next year, the projectedLtd forecasts 10 per cent increase in sales next year, the projected profit wil
profit will be:l be:
(Rs 1,04,500 – Rs 65,000) X 0.40 = Rs 15,800 (Rs 1,04,500 – Rs 65,000) X 0.40 = Rs 15,800
Additional Sales Volume Required to Offset a Reduction in Selling Price
Additional Sales Volume Required to Offset a Reduction in Selling Price The salesThe sales manager on the basis of a market research/survey may report to the management that manager on the basis of a market research/survey may report to the management that
due to increased competition in the market and the liberal import policy of the due to increased competition in the market and the liberal import policy of the government, the present price is
government, the present price is relatively higher. relatively higher. He may He may advise reduction in prices toadvise reduction in prices to stay in competition.
stay in competition. Suppose that
Suppose that SV SV Ltd reduces its selling price form Rs 10 a Ltd reduces its selling price form Rs 10 a unit to Rs 9. unit to Rs 9. The salesThe sales volume needed to offset reduced selling price/maintain a present operating profit of Rs volume needed to offset reduced selling price/maintain a present operating profit of Rs 12,000 would be: 12,000 would be: 1,14,000 1,14,000 Rs Rs 0.3333 0.3333 26,000) 26,000) Rs Rs (12,000 (12,000 Rs Rs 9) 9) Rs Rs // 3 3 (Rs (Rs ratio ratio vised vised Re Re )) (( expenses expenses Fixed Fixed )) (( profit profit Desired Desired = = ÷ ÷ + + = = + + = = P/V P/V FC FC P P
The required sales volume of Rs 1,14,000 represents an increase of about 20 per cent The required sales volume of Rs 1,14,000 represents an increase of about 20 per cent over the present level.
over the present level. The management The management should explore new should explore new avenues of sales potentialavenues of sales potential to maintain the existing amount of profit.
to maintain the existing amount of profit.
On the other hand, if the firm has the opportunity to increase the unit selling price of On the other hand, if the firm has the opportunity to increase the unit selling price of the product, the impact of increased sales price would be that the BEP will be reached the product, the impact of increased sales price would be that the BEP will be reached sooner because an increase in the selling price will raise the contribution margin, sooner because an increase in the selling price will raise the contribution margin, assuming no change
assuming no change in the variable costs. in the variable costs. An increased contribution margin An increased contribution margin willwill decrease the sales volume necessary to reach a desired goals.
decrease the sales volume necessary to reach a desired goals. Assume that the management of
Assume that the management of SV SV Ltd increase the selling price of its product from RsLtd increase the selling price of its product from Rs 10 to Rs 12, the desired sales volume would be:
10 to Rs 12, the desired sales volume would be:
76,000 76,000 Rs Rs 12) 12) Rs Rs 6 6 (Rs (Rs 0.50 0.50 38,000 38,000 Rs Rs ratio ratio vised vised Re Re == ÷÷ ÷÷ == + + P/V P/V P P FC FC
Effect of Changes in Fixed Costs
Effect of Changes in Fixed Costs A firm may be confronted with the situation of A firm may be confronted with the situation of increasing fixed costs.
increasing fixed costs. An increase in the An increase in the total budgeted fixed costs of total budgeted fixed costs of a firm may a firm may bebe necessitated either by external factors, such as, an increase in property taxes, insurance necessitated either by external factors, such as, an increase in property taxes, insurance rates, factory rent, and so on, or by a managerial decision of an increase in salaries of rates, factory rent, and so on, or by a managerial decision of an increase in salaries of executives.
executives. More important than More important than this in the latter category are ethis in the latter category are expansion of the xpansion of the presentpresent plant ca
plant capacity so pacity so as to coas to cope with pe with additioadditional demnal demand. and. The incThe increase in trease in the requhe requirementsirements of fixed costs would imply the computation of the following:
of fixed costs would imply the computation of the following: (a
(a)) RReelalatitive bve brereakak-e-eveven pn poiointntss (b)
(b) ReReququireired sald sales ves vololumume to ee to earn tarn the phe preresensent prt profiofits.ts. (c)
(c) ReRequirquired saled sales voes volumlume to eae to earn the rn the same rsame rate of pate of profrofit on tit on the prohe proposposed exed expanspanskiokionn progr
programme as amme as on the on the existing existing ones.ones.
The effect of the increased FCs will be to raise the BEP
The effect of the increased FCs will be to raise the BEP of the firm. of the firm. Assume theAssume the management of SV Ltd decides a major expansion programme of its existing
management of SV Ltd decides a major expansion programme of its existing produc
production caption capacity. acity. It is estimIt is estimated that ated that it will reit will result in esult in extra fixed xtra fixed costs of costs of Rs 8,0Rs 8,000 on00 on advertisement to boost sales volume and another Rs 16,000 on account of new plant advertisement to boost sales volume and another Rs 16,000 on account of new plant facility.
facility. (a)
(a) The relative BEPs will be:The relative BEPs will be:
Present facilities = Fixed costs ÷ P/V ratio = Rs 26,000/0.40 = Rs 65,000 Present facilities = Fixed costs ÷ P/V ratio = Rs 26,000/0.40 = Rs 65,000 Proposed facilities = (Present FC
Proposed facilities = (Present FC s s + Additional FC+ Additional FC s s) ÷) ÷ P/V P/V ratioratio (7.19)
(7.19)
(Rs 26,000 + Rs 24,000)/0.40 = Rs 125,000 (Rs 26,000 + Rs 24,000)/0.40 = Rs 125,000
It may be noted that increase in FCs (from Rs 26,000 to Rs 50,000) has It may be noted that increase in FCs (from Rs 26,000 to Rs 50,000) has caused
caused
disproportionate increase in the BEP (from Rs 65,000 to Rs 1,25,000). disproportionate increase in the BEP (from Rs 65,000 to Rs 1,25,000). (b)
(b) The required sales volume to earn the present profit:The required sales volume to earn the present profit: [Present FC
[Present FC s s + Additional FC+ Additional FC s s + Present profit (+ Present profit ( NI NI ) ÷ P/V ration) ÷ P/V ration (7.20)
(7.20)
= [Rs 26,000 + Rs 24,000 + Rs 12,000] ÷ 0.40 = Rs 1,55,000 = [Rs 26,000 + Rs 24,000 + Rs 12,000] ÷ 0.40 = Rs 1,55,000 (c)
(c) The required sales volume to earn the present rate of profit on investment:The required sales volume to earn the present rate of profit on investment: (Present FC
(Present FC s s + Additional FC+ Additional FC s s + Present return on investment + Return on new+ Present return on investment + Return on new investment)
investment) P/V P/V ratioratio (7.21)
(7.21)
Let us assume that the present investment is Rs 1,00,000 and the new Let us assume that the present investment is Rs 1,00,000 and the new investment will involve as additional financial outlay o
investment will involve as additional financial outlay of Rs 60,0f Rs 60,000. 00. The required salesThe required sales volume will be (Rs 26,000 + Rs 24,000 + Rs 12,000 + Rs 7,200 (0.12 X Rs
volume will be (Rs 26,000 + Rs 24,000 + Rs 12,000 + Rs 7,200 (0.12 X Rs 60,000)/0.40 = Rs 1,73,000
60,000)/0.40 = Rs 1,73,000
These computations may be reported in a summary form to the management as follows These computations may be reported in a summary form to the management as follows (Table 7.3).
(Table 7.3). Table 8.3
Table 8.3 (Effect of Changes in Fixed Costs(Effect of Changes in Fixed Costs Particu
Particularslars Present facilitiesPresent facilities ProspeProspectivective facilities facilities
Increase Increase F
Fiixxeed d ccoossttss RRs s 2266,,000000 RRs s 5500,,000000 RRs s 2244,,000000 B
BEEP P ssaallees s vvoolluummee 6655,,000000 11,,2255,,000000 6600,,000000 B
BEEP P ssaallees s vvoolluumme e ((uunniittss)) 6,,56 50000 1122,,550000 66,,000000 S
Saallees s vvoolluumme e tto o eeaarrn n eexxiissttiinng g pprrooffiitt 9955,,000000 11,,5555,,000000 6600,,000000 S
Saallees s vvoolluumme e iin n uunniitts s tto o eeaarrn n eexxiissttiinng g pprrooffiitt 99,,550000 1155,,550000 66,,000000 S
Saallees s vvoolluumme e tto o eeaarrn n eexxiissttiinng g RROOII 9595,,000000 11,,7733,,000000 7788,,000000 S
Saallees s vvoolluumme e tto o eeaarrn n eexxiissttiinng g RROOI I ((iin n uunniittss)) 9,,5950000 1177,,330000 77,,880000 Effect of Changes in Variable Costs
Effect of Changes in Variable Costs Assuming an increase of VC by Re 1 a unit for Assuming an increase of VC by Re 1 a unit for SV
SV Ltd, the new contribution margin will be: Rs (Rs 10 – Rs 7) and the revised P/VLtd, the new contribution margin will be: Rs (Rs 10 – Rs 7) and the revised P/V ratio 0.30 that is (Rs 3 ÷ Rs 10).
ratio 0.30 that is (Rs 3 ÷ Rs 10).
Revised BEP = (Rs 26,000)/0.30 = Rs 86,667 Revised BEP = (Rs 26,000)/0.30 = Rs 86,667
Desired sales volume to earn existing profit = Rs 38,000/0.30 = Rs 1,26,667 Desired sales volume to earn existing profit = Rs 38,000/0.30 = Rs 1,26,667
Assuming that variable costs of
Assuming that variable costs of SV SV Ltd decline by Re 1 per unit, revised BEP =Ltd decline by Re 1 per unit, revised BEP = Rs 26,000/0.50 = Rs 52,000
Rs 26,000/0.50 = Rs 52,000
Desired sales volume to maintain existing profit = Rs 38,000/0.50 = Rs 76,000. Desired sales volume to maintain existing profit = Rs 38,000/0.50 = Rs 76,000. Effects of Multiple
Effects of Multiple ChangesChanges So far we have assumed that a change takes place in oneSo far we have assumed that a change takes place in one of the three variable affecting profits-cost, price and sales volume.
of the three variable affecting profits-cost, price and sales volume. In case where moreIn case where more than one factor is affected, the BEP
than one factor is affected, the BEP analysisanalysis can be applied as shown below:can be applied as shown below:
)] )] (New (New price price selling selling New New )] )] New New --(New (New unit unit per per margin margin on on Contributi Contributi [[ rate)] rate)] tax tax --(1 (1 // [Desired [Desired (new) (new) SP SP VC VC SP SP NI NI FC FC FC FC ÷ ÷ + + + + (7.22) (7.22)
Assuming the following set of new Figures for
Assuming the following set of new Figures for SV SV Ltd:Ltd: Particula
Particularsrs Existing dataExisting data New dataNew data
S
Seelllliinng g pprriicce e ppeer r uunniitt RRs s 1100 RRs s 1111 F
Fiixxeeddccoossttss 2266,,000000 4400,,000000
V
Vaarriiaabbllee ccoosstt ppeerruunniitt 66 55..5500 C
Coonnttrriibbuuttiioon n mmaarrggiin n ppeer r uunniitt 44 55..5500 D
Deessiirreed d nneet t iinnccoomme e aafftteer r ttaaxxees s ((tto o mmaaiinnttaaiin n tthhe e eexxiissttiinng g RROOII)) 1122,,000000 2255,,000000 T
Taaxxrraattee 3355 ppeerrcceenntt
Solution
Solution Desired sales volume (on the basis of new data) [Rs 26,000 + Rs 14,000 + (RsDesired sales volume (on the basis of new data) [Rs 26,000 + Rs 14,000 + (Rs 25,000 ÷ 0.65)] = 0.50, that is (Rs 5.5 ÷ Rs 11) = (Rs 78,461.5) ÷ 0.50 = Rs 1,56,923 25,000 ÷ 0.65)] = 0.50, that is (Rs 5.5 ÷ Rs 11) = (Rs 78,461.5) ÷ 0.50 = Rs 1,56,923
Desired sales volume on the basis of existing data = [Rs 26,000 + (Rs 12,000 ÷ Desired sales volume on the basis of existing data = [Rs 26,000 + (Rs 12,000 ÷ 0.65)] ÷ 0.40 (Rs 4 ÷ Rs 10) = Rs 44,462 ÷ 0.40 = Rs 1,11,154.
0.65)] ÷ 0.40 (Rs 4 ÷ Rs 10) = Rs 44,462 ÷ 0.40 = Rs 1,11,154. VCP Analysis and a
VCP Analysis and a Segment of the BusinessSegment of the Business The fundamental approach of applyingThe fundamental approach of applying the VCP analysis to a segment of the business is the same as applying it to the business the VCP analysis to a segment of the business is the same as applying it to the business as a whole.
as a whole. The VCP The VCP approach “may be applied to problemapproach “may be applied to problems relative to individuals relative to individual produc
product lines, tet lines, territories, merritories, methods othods of sale, chf sale, channels oannels of distribuf distribution or tion or any paany particular rticular segment of the business which is under scrutiny”
segment of the business which is under scrutiny”22. . In all In all these decisions, fixed these decisions, fixed costscosts and P/V ratio are
and P/V ratio are the required inputs. the required inputs. Where fixed costs are inclusive of Where fixed costs are inclusive of allocated costsallocated costs also, in additional to direct costs, two BEPs may be determined.
also, in additional to direct costs, two BEPs may be determined. Example 7.2
Example 7.2 SV SV Ltd has four Ltd has four sales divisions. sales divisions. The relevant data for its nThe relevant data for its northern divisionorthern division is reproduced below:
is reproduced below:
Direct fixed costs, Rs 10,000 Direct fixed costs, Rs 10,000 P/V ratio, 0.40
P/V ratio, 0.40
Allocated fixed costs from head office, Rs 5,000 Allocated fixed costs from head office, Rs 5,000
The sales volume required to cover direct expenses would be: Direct fixed The sales volume required to cover direct expenses would be: Direct fixed costs/ P/V ratio = Rs 10,000/0.40 = Rs 25,000
costs/ P/V ratio = Rs 10,000/0.40 = Rs 25,000 (7.23)
(7.23)
The total sales volume required to cover all fixed costs would be higher as The total sales volume required to cover all fixed costs would be higher as shown by equation 7.24: shown by equation 7.24: ratio ratio P/V P/V FCs FCs Allocated Allocated FCs FCs Direct Direct ++ (7.24) (7.24) = (Rs 10,000 + Rs 5,000) ÷ 0.40 = Rs 37,500 = (Rs 10,000 + Rs 5,000) ÷ 0.40 = Rs 37,500 Multi-product Firms (Sales-mix)
Multi-product Firms (Sales-mix) So far, we have confined our discussion to a one-So far, we have confined our discussion to a one- produc
product compt company. any. HoweHowever manver many manuy manufacturers facturers make mmake more than ore than one tyone type of prpe of productoduct.. The relative proportion of each product sold in the aggregate sales is known as the The relative proportion of each product sold in the aggregate sales is known as the sales-mix.
sales-mix. A change in A change in the mix of the mix of products sold usually affects the weighted products sold usually affects the weighted averageaverage P/V ratio and, hence, the BEP
P/V ratio and, hence, the BEP. . Thus when the Thus when the products have different P/V ratios,products have different P/V ratios, changes in the sales-mix/product-mix will affect the BEP and the results from changes in the sales-mix/product-mix will affect the BEP and the results from operation.
Example 7.3
Example 7.3 The Garware Paints Ltd presents to you the following income statementThe Garware Paints Ltd presents to you the following income statement in a condensed form for the first quarter ending March 31:
in a condensed form for the first quarter ending March 31: Particu
Particularslars PPrroodduucctt TToottaall X
X Y Y XX
S
Saalleess RRs s 11,,0000,,000000 RRs s 6600,,000000 RRs s 4400,,000000 RRs s 22,,0000,,000000 V
Vaarriiaabblle e ccoossttss 8800,,000000 4422,,000000 2244,,000000 11,,4466,,000000 C
Coonnttrriibbuuttiioonn 2200,,000000 1188,,000000 1166,,000000 5454,,000000 F
Fiixxeeddccoossttss 2277,,000000
Net inco
Net incomeme 27,0027,0000
P
P//VVrraattiioo 00..2200 00..3300 00.. 4400 00..2277 B
Brreeaakk--eevveenn ssaalleess 11,,0000,,000000
S
Saalleess--mmiix x ((ppeer r cceenntt)) 00..5500 00..3300 00.. 2200 110000 If Rs 40,000 of the sales shown for product
If Rs 40,000 of the sales shown for product X X could be shifted equally to productscould be shifted equally to products Y Y and
and Z Z , the profit and the BEP would change as shown in Table 7.4., the profit and the BEP would change as shown in Table 7.4. Table 7.4
Table 7.4 Break-even PointBreak-even Point Particu
Particularslars PPrroodduucctt TToottaall X
X Y Y XX
S
Saalleess RRs s 6600,,000000 RRs s 8800,,000000 RRs s 6600,,000000 RRs s 22,,0000,,000000 Less:
Less: VVaarriiaabblle e ccoossttss 4488,,000000 5566,,000000 3366,,000000 11,,4400,,000000 C
Coonnttrriibbuuttiioonn 1122,,000000 2244,,000000 2244,,000000 6600,,000000 Less:
Less: FFiixxeedd ccoossttss 2277,,000000
Net inco Net incomeme 33,0033,0000 P P//VVrraattiioo 00..2200 00..3300 00..4400 00..3333 B BEEssaalleess 9900,,000000 S
Saalleess--mmiix x ((ppeer r cceenntt)) 00..3300 00..4400 00..3300 110000 Example 7.3 shows that by increasing the mix of high P/V products (
Example 7.3 shows that by increasing the mix of high P/V products ( Y Y from 30from 30 to 40 per cent,
to 40 per cent, Z Z from 20 to 30 per cent) and decreasing the mix of a low P/V productfrom 20 to 30 per cent) and decreasing the mix of a low P/V product (( X X from 50 from 50 to 30 per to 30 per cent), the company cent), the company can increase its overall profitability. can increase its overall profitability. In fact, itIn fact, it can further augment its total profits, if it can make, and the market can absorb, more can further augment its total profits, if it can make, and the market can absorb, more quantities of
quantities of Y Y andand Z Z , say Rs 1 lakh each (Table 7.5)., say Rs 1 lakh each (Table 7.5).
Table 7.5
Table 7.5
Particu
Particularslars PPrroodduucctt TToottaall
Y
Y Z Z
S
Saalleess RRs s 11,,0000,,000000 RRs s 11,,0000,,000000 RRs s 22,,0000,,000000 Less:
Less: VVaarriiaabblle e ccoossttss 7700,,000000 6060,,000000 11,,3300,,000000 C
Coonnttrriibbuuttiioonn 3300,,000000 4400,,000000 7700,,000000 Less:
Less: FFiixxeedd ccoossttss 2277,,000000
Net inco Net incomeme 43,0043,0000 P P//VVrraattiioo 00..3300 00..4400 00..3355 B BEEssaalleess 7777,,114433 S
From the above, it can be generalized that, other things being equal, management From the above, it can be generalized that, other things being equal, management should stress product with hig
should stress product with higher contribution margins. her contribution margins. For individual product For individual product lineline income statements, fixed costs should not be allocated or apportioned.
income statements, fixed costs should not be allocated or apportioned.
Finally, it may be stressed that there is a need for a closer study of cost structures of Finally, it may be stressed that there is a need for a closer study of cost structures of individual product line/department within the same firm or of two different companies. individual product line/department within the same firm or of two different companies. It may be possible that the two departments/companies may have the same profits but It may be possible that the two departments/companies may have the same profits but very different cost structures.
very different cost structures. For instance, observe the FFor instance, observe the Figures in Table 7.6 igures in Table 7.6 of twoof two departments of
departments of SV SV Ltd.Ltd.
Table 7.6
Table 7.6
P
Paarrttiiccuullaarrss DDeeppaarrttmmeennt t XX DDeeppaarrttmmeennt t Y Y
Amou
Amountnt Per cent Per cent Amount Amount Per cent Per cent S
Saallees s rreevveennuuee RRs s 11,,0000,,000000 ((110000)) RRs s 11,,0000,,000000 ((110000)) L
Leessss: : VVaarriiaabblle e ccoossttss 7700,,000000 ((7700)) 2200,,000000 ((2200)) C
Coonnttrriibbuuttiioon n / / PP//V V rraattiioo 3300,,000000 ((3300)) 8080,,000000 ((8800)) L
Leessss: : FFiixxeed d ccoossttss 2200,,000000 7700,,000000 P
Prrooffiitt 1100,,000000 1100,,000000
B
BEEP P ((aammoouunntt)) 6666,,666677 8877,,550000 M
Maarrggiin n oof f ssaaffeetty y ((MMSS)) 3333,,333333 1122,,550000 M
Maarrggiin n oof f ssaaffeetty y rraattiioo 00..33333333 00..112255 Department
Department Y Y is operating closer to the BEP than Departmentis operating closer to the BEP than Department X X . Department. Department Y Y has ahas a narrower margin of safety (12.5 per cent) compared to 33.33 per cent of
narrower margin of safety (12.5 per cent) compared to 33.33 per cent of X X . . The The marginmargin of safety ratio signifies that if the sales of
of safety ratio signifies that if the sales of Y Y decreases by more than 12.5 per cent, it willdecreases by more than 12.5 per cent, it will operate at a loss.
operate at a loss. In other woIn other words, the margin/cushion of rds, the margin/cushion of safety is relatively smaller.safety is relatively smaller. X X will not operate at a loss unless its sales volume drops by more than 33.33 per cent. will not operate at a loss unless its sales volume drops by more than 33.33 per cent.
This type of profit analysis for two different companies is of special This type of profit analysis for two different companies is of special
significance from the point of view of outside investor who want to invest in one of the significance from the point of view of outside investor who want to invest in one of the two
two companies. companies. Assuming Assuming companiescompanies X X andand Y Y in place of the departmentsin place of the departments X X andand Y Y inin the above tabulation, Company
the above tabulation, Company X X is certainly less risky than Companyis certainly less risky than Company Y Y ..
Graphic Presentation
Graphic Presentation
Under the algebraic technique of break-even analysis, separate computations were Under the algebraic technique of break-even analysis, separate computations were needed to arrive at
needed to arrive at the above set of the above set of figures. figures. The utility of the The utility of the graphical technique is thatgraphical technique is that such a set of figures can be determined without involving any separate calculations. such a set of figures can be determined without involving any separate calculations. Break-Even Chart/Volume Cost Profit (VCP) Graph
Break-Even Chart/Volume Cost Profit (VCP) Graph TheThe break even chartbreak even chart is ais a graphic relationship between volume, costs and profits.
graphic relationship between volume, costs and profits. It shows not only It shows not only the BEP butthe BEP but also the effects of costs and
also the effects of costs and revenue at varying levels orevenue at varying levels of sales. f sales. The break-even chartThe break-even chart can, therefore, be more appropriately called the volume-cost-profit graph (VCP graph). can, therefore, be more appropriately called the volume-cost-profit graph (VCP graph).
Assumptions Regarding the VCP Graph are
Assumptions Regarding the VCP Graph are
1.
1. CosCosts can be bits can be bifurcfurcated inated into varto variable aiable and fixend fixed comd componponentents.s. 2.
3.
3. Variable Variable cost per ucost per unit will nit will remain cremain constant donstant during turing the relevhe relevant voluant volume rangme range of e of graph.
graph. 4.
4. Selling Selling price pprice per unit er unit will rewill remain comain constant nstant irrespectivirrespective of te of the quahe quantity sontity soldld within the relevant range of the graph.
within the relevant range of the graph. 5.
5. In the In the case of case of multi-prmulti-product oduct compacompanies, in nies, in additioaddition to n to the abothe above fouve four r assumptions, it is assumed that the sales-mix remains constant.
assumptions, it is assumed that the sales-mix remains constant. 6.
6. FinFinallyally, prod, productiuction anon and saled sales volus volumes are emes are equalqual.. The VCP g
The VCP graph may be prepared in raph may be prepared in a simple or elaborate manner. a simple or elaborate manner. Figure 7.1 is anFigure 7.1 is an example of a simple and traditional form.
example of a simple and traditional form. In Figure 7.1, sales are shown oIn Figure 7.1, sales are shown on then the
horizontal axis; the vertical axis measures costs and revenues corresponding to varying horizontal axis; the vertical axis measures costs and revenues corresponding to varying volume of sales.
volume of sales. Sales are expressed in terms of Sales are expressed in terms of units, rupees and percentage level ounits, rupees and percentage level of f activity.
activity. The VCP The VCP relationships portrayed in such a relationships portrayed in such a graph are valid ograph are valid only within thenly within the relevant range that underlies the construction of
relevant range that underlies the construction of the graph. the graph. The importance of The importance of aa
relevant range should be recognized because in practice most firms will progressively relevant range should be recognized because in practice most firms will progressively reduce fixed costs as the
reduce fixed costs as the volume tends to volume tends to decrease towards zero activity. decrease towards zero activity. Similarly,Similarly, fixed costs are to be increased beyond a certain volume.
fixed costs are to be increased beyond a certain volume. Accordingly, in Figure 7.1 Accordingly, in Figure 7.1 thethe lower limit and upper limit of the VCP have been drawn.
lower limit and upper limit of the VCP have been drawn. The BEP lies at the point
The BEP lies at the point of intersection of the sales line and the total cost line. of intersection of the sales line and the total cost line. TheThe vertical distance between the sales revenue and the total cost line measures the
vertical distance between the sales revenue and the total cost line measures the
estimated net income (after the BEP) and the estimated net loss (before the BEP) at the estimated net income (after the BEP) and the estimated net loss (before the BEP) at the related sales volume.
related sales volume. The The fixed cost fixed cost line is line is parallel to the parallel to the horizontal axis. horizontal axis. The variableThe variable cost line is superimposed on the fixed cost line and moves upward uniformly with sales cost line is superimposed on the fixed cost line and moves upward uniformly with sales volume at
volume at the variable cost to the variable cost to volume ratio. volume ratio. This is total This is total cost line. cost line. The sales revenueThe sales revenue line starts from the point of origin and mo
line starts from the point of origin and moves upward uniformly with vves upward uniformly with volume. olume. TheThe meeting point of the total cost line and sales line is the BE
meeting point of the total cost line and sales line is the BEP. P. At the point, an angle isAt the point, an angle is formed known as the
formed known as the angle of incidence. angle of incidence. The management objective should be The management objective should be to haveto have an angle of as large a size as possible because a high angle is a sign of a high rate of an angle of as large a size as possible because a high angle is a sign of a high rate of profit afte
profit after the fixer the fixed costs hd costs have beeave been coven covered; the nred; the narrower aarrower angle wngle will signify ill signify thatthat profits aft
profits after the fixeer the fixed costs d costs have behave been coven covered; the ered; the narrowenarrower angle wr angle will signify ill signify thatthat profits w
profits will increaill increase at a lowse at a lower rate afteer rate after the BEr the BEP, shoP, showing twing that variabhat variable costs fole costs form arm a large part of cost of
large part of cost of sales. sales. Figure 7.1 is Figure 7.1 is based on based on the following data relating tothe following data relating to Hypothetical Ltd (Example 7.4).
Hypothetical Ltd (Example 7.4).
Example 7.4
Example 7.4
S
Seelllliinngg pprriiccee ppeerruunniitt RRss 1100 F
Fiixxeeddccoossttss 6600,,000000
V
Vaarriiaabbllee ccoossttssppeerruunniitt 55
Relevant range (units) Relevant range (units)
L
Loowweerrlliimmiitt 66,,000000
U
Uppppeerrlliimmiitt 2200,,000000
Break-up
Break-up of variaof variable costs ble costs per uniper unit:t: D
Diirreecctt mmaatteerriiaall RRss22 D
Diirreecctt llaabboouurr 11..5500
D
Diirreecctt eexxppeennsseess 11
S
Seelllliinngg eexxppeennsseess 00..5500 Actual sales, 18,000 units (Rs 1,80,000)
Actual sales, 18,000 units (Rs 1,80,000) Plant capacity, 20,000 units (Rs 2,00,000) Plant capacity, 20,000 units (Rs 2,00,000)
Tax rate, 50 per cent Tax rate, 50 per cent
Figure 7.1 Volume-Cost-Profit Graph (Traditional) Figure 7.1 Volume-Cost-Profit Graph (Traditional)
Figure 7.1 has been drawn by using a sales line and a total cost line (including both Figure 7.1 has been drawn by using a sales line and a total cost line (including both fixed and variable costs).
fixed and variable costs). The steps involved in drawing The steps involved in drawing the VCP graph the VCP graph are enumeratedare enumerated as follows:
as follows: 1.
1. Select an Select an appropappropriate scale foriate scale for sales vor sales volume olume on the hon the horizontal arizontal axis, sayxis, say, 2,00, 2,000 units0 units (Rs 20,000) per square, and plot the point for total sales revenues at relevant
(Rs 20,000) per square, and plot the point for total sales revenues at relevant volume: 6,000 units X Rs 10 = R
volume: 6,000 units X Rs 10 = Rs 60,000. s 60,000. Draw the sales line from the origin to RsDraw the sales line from the origin to Rs 2,00,000 (the u
2,00,000 (the upper limit of the pper limit of the relevant range). relevant range). Ensure thatEnsure that all the pointsall the points, 0, Rs, 0, Rs 60,000 and Rs 2,00,000
60,000 and Rs 2,00,000 fall in t fall in the same he same lineline. . This should This should be ensured for be ensured for the totalthe total cost line also.
cost line also. 2.
2. Select an Select an appropappropriate scale foriate scale for costs ar costs and salend sales revenues revenues on the s on the vertical axvertical axis, say, Ris, say, Rss 10,000 per square.
10,000 per square. Draw the line showing Draw the line showing Rs 60,000 fixed coRs 60,000 fixed cost parallel to thest parallel to the horizontal axis.
horizontal axis. 3.
3. DetermDetermine the vine the variable poariable portion ortion of costs af costs at two vt two volumes olumes of scales (bof scales (beginneginning anding and ending): 6,000 units X Rs 5 = Rs 30,000; 20,000 units X Rs 5 = Rs 1,00,000. ending): 6,000 units X Rs 5 = Rs 30,000; 20,000 units X Rs 5 = Rs 1,00,000. 4.
4. Variable cVariable costs are to be aosts are to be added to fidded to fixed costxed costs (Rs 30,0s (Rs 30,000 + RS 600 + RS 60,000,000 = Rs 90,00 = Rs 90,000).00). Plot the point at 6,000 units sales volume and Rs 1,00,000 + Rs 60,000 = Rs
Plot the point at 6,000 units sales volume and Rs 1,00,000 + Rs 60,000 = Rs 1,60,000.
1,60,000. Point is to Point is to be plotted be plotted at 20,000 at 20,000 units sales volume. units sales volume. This obviously This obviously is theis the total cost line.
5.
5. The pThe point ooint of interf intersection osection of the f the total cototal cost line st line and saand sales line les line is the is the BEP. BEP. To tTo the righe rightht of BEP, there is a profit area and to the left of it, there is a loss area.
of BEP, there is a profit area and to the left of it, there is a loss area. 6.
6. Verification:Verification: FC ÷FC ÷ CM CM per unit = Rs 60,000 ÷ Rs 5 per unit = 12,000 units or Rsper unit = Rs 60,000 ÷ Rs 5 per unit = 12,000 units or Rs 1,20,000
1,20,000
Figure 7.1 has been drawn using different scales for the horizontal and vertical axis. Figure 7.1 has been drawn using different scales for the horizontal and vertical axis. Figure 7.2 has been draw
Figure 7.2 has been drawn on a un on a uniform scale for both axes. niform scale for both axes. Since the scales are theSince the scales are the same, the 45º
same, the 45º line will always be the proxy of the sales line.line will always be the proxy of the sales line. Any amount of salesAny amount of sales revenue on the horizontal axis will correspond to costs and revenue on the vertical revenue on the horizontal axis will correspond to costs and revenue on the vertical axis.
axis. Let us Let us illustrate taking two illustrate taking two sales levels.sales levels. 1.
1. Rs 60 Rs 60,000:,000: FC = Rs 60,000FC = Rs 60,000
VC = 30,000 (50 per cent variable cost to volume VC = 30,000 (50 per cent variable cost to volume ratio)
ratio)
TC
TC = 90,000= 90,000 Loss = 30,000 (
Loss = 30,000 (TC TC , Rs 90,000 – Rs 30,000, sales, Rs 90,000 – Rs 30,000, sales revenue)
revenue)
Thus, Rs 60,000 – Rs 60,0
Thus, Rs 60,000 – Rs 60,000 + Rs 30,000 – Rs 3000 + Rs 30,000 – Rs 30,000. ,000. Point A in Figure 7.2Point A in Figure 7.2 clearly shows these three relevant figures at the sales volume of Rs 60,000.
clearly shows these three relevant figures at the sales volume of Rs 60,000. 2. 2. Rs 1,8 Rs 1,80,0000,000:: FFC C = = RRss 6600,,000000 VC VC = = 90,00090,000 TC TC == 11,,5500,,000000 P Prrooffiitt == 3300,,000000 Figure 7.2
Thus, Rs 1,80,000 = Rs 60
Thus, Rs 1,80,000 = Rs 60,000 (FC) + Rs 90,000 (VC) + R,000 (FC) + Rs 90,000 (VC) + Rs 30,000 (Profit). s 30,000 (Profit). PointPoint B
B in Figure 7.2 portrays these three relevant figures at the sales volume of Rs 1,80,000.in Figure 7.2 portrays these three relevant figures at the sales volume of Rs 1,80,000. The VCP graph in Figure 7.3 is drawn with the details of the individual segment The VCP graph in Figure 7.3 is drawn with the details of the individual segment of variable cost and is
of variable cost and is more informative. more informative. The steps involved The steps involved in drawing in drawing the graphthe graph include an additional step of
include an additional step of adding variable costs to adding variable costs to the fixed cost. the fixed cost. This is to This is to bebe
repeated four times for four different components: material, labour, direct expenses and repeated four times for four different components: material, labour, direct expenses and selling expenses.
selling expenses. In fact, In fact, fixed costs fixed costs can also can also be further be further split-up into split-up into parts. parts. Such aSuch a graph provides a
graph provides a bird’s-eye view of the entire cost bird’s-eye view of the entire cost structure to the management. structure to the management. ByBy drawing a line perpendicular from any volume (horizontal axis), the corresponding cost drawing a line perpendicular from any volume (horizontal axis), the corresponding cost and profit variables can be
and profit variables can be ascertained on the vertical axis. ascertained on the vertical axis. For instance, at 20,000 For instance, at 20,000 unitunit level, following are the various cost figures, as shown by the VCP graph.
level, following are the various cost figures, as shown by the VCP graph. F
Fiixxeeddccoossttss RRss 6600,,000000
Variable costs: Variable costs: M Maatteerriiaall 4400,,000000 L Laabboouurr 3300,,000000 D
Diirreecctt eexxppeennsseess 2200,,000000
S
Seelllliinngg eexxppeennsseess 1100,,000000
P
Prrooffiitt bbeeffoorree ttaaxxeess 4400,,000000
Application of the P/V Ratio
Application of the P/V Ratio
1.
1. DetDetermerminatination ion of Bof BEP EP = FC = FC ÷ P/÷ P/V raV ratiotio 2.
2. DetermDetermination ination of proof profit at gfit at given/buiven/budgeted dgeted sales vosales volume = lume = (Actual (Actual sales – sales – BE BE sales)sales) X
X P/V P/V ratioratio 3.
3. DetDetermerminatination of salion of sales voles volume to eume to earn buarn budgedgeted proted profit = (FC +fit = (FC + DP DP ) ÷ P/V ratio) ÷ P/V ratio 4.
4. DetermDetermination oination of change f change is sales vis sales volume tolume to mainto maintain the cain the current leurrent level of prvel of profit if ofit if there is (a) a change is sales price, (b) change in variable cost = (FC +
there is (a) a change is sales price, (b) change in variable cost = (FC + DP DP ) ÷) ÷ Revised P/V ratio.
Revised P/V ratio. 5.
5. DetermDetermination oination of the perf the percentage ocentage of net prof net profit with fit with the helthe help of map of margin of rgin of safety ratsafety ratioio = (P/V ratio X
= (P/V ratio X MS MS ratio)ratio) (7.25)
(7.25)
Cash Break-Even Point
Cash Break-Even Point
The VCP relationship can also be u
The VCP relationship can also be used to show the liquidity position of sed to show the liquidity position of the firm. the firm. ThisThis is done through the computation of
is done through the computation of cash break-even pointcash break-even point or cash break-even salesor cash break-even sales revenue (CBEP
revenue (CBEP / C/ CBESR). BESR). Algebraically:Algebraically: Cash break-even point
Cash break-even point is total cash fixed cost divided by contribution margin per unit.is total cash fixed cost divided by contribution margin per unit.
unit unit per per margin margin on on Contributi Contributi )) (( cost cost fixed fixed cash cash Total Total CFC CFC CBEP CBEP == (7.26) (7.26)
ratio ratio cost cost fixed fixed cash cash Total Total P/V P/V CBESR CBESR== (7.27) (7.27) Graphically, the CBEP is determined at the point of intersection of total cash cost Graphically, the CBEP is determined at the point of intersection of total cash cost line and total sales line.
line and total sales line. The area to The area to the left of the the left of the curve signifies cash losses and thecurve signifies cash losses and the area on the right side is indicative of cash profits.
area on the right side is indicative of cash profits.
Assuming for Example 7.4, the cash fixed cost to be Rs 15,000, the CBESR Assuming for Example 7.4, the cash fixed cost to be Rs 15,000, the CBESR using Equation 7.27 would be Rs 30,000 = Rs 15,000 ÷ 0.50
using Equation 7.27 would be Rs 30,000 = Rs 15,000 ÷ 0.50
Figure 7.4 portrays the graphic presentation of the cash break-even sales Figure 7.4 portrays the graphic presentation of the cash break-even sales revenue.
revenue.
To conclude, the uses of break-even analysis, as a technique for profit planning, To conclude, the uses of break-even analysis, as a technique for profit planning, have been discussed in
have been discussed in detail in this chapter. detail in this chapter. In brief, break-even analysis shows In brief, break-even analysis shows thethe interplay of profit factors, that is, cost, revenue and volume in a way, which assists interplay of profit factors, that is, cost, revenue and volume in a way, which assists management in choosing the best feasible alternative now and in the future. “The management in choosing the best feasible alternative now and in the future. “The break-even system is at once an X-ray, exploratory and planning tool intended for frequent even system is at once an X-ray, exploratory and planning tool intended for frequent use and a proper cost-volume-profit analysis supported by the break-even chart can use and a proper cost-volume-profit analysis supported by the break-even chart can eliminate many of the time-consuming reports now being prepared at the company.” eliminate many of the time-consuming reports now being prepared at the company.”33
The graphs can be used to analyse the impact of various alternative proposals under The graphs can be used to analyse the impact of various alternative proposals under consideration on the
consideration on the profit structure. profit structure. Thus, the Thus, the break-even system provides break-even system provides moremore readily understandable facts than conventional accounting or statistical data regarding readily understandable facts than conventional accounting or statistical data regarding the profit structure of the company
Figure 7.4
Figure 7.4 Cash Break-even pointCash Break-even point
However, it is important to recognize its limitations which originate from the However, it is important to recognize its limitations which originate from the given assumptions.
given assumptions. The greater the deviation The greater the deviation of actual facts from the of actual facts from the givengiven
assumptions, the more imperfect, incorrect and invalid are the break-even calculations. assumptions, the more imperfect, incorrect and invalid are the break-even calculations. These limitations limit the usefulness of the break-even chart and must be borne in These limitations limit the usefulness of the break-even chart and must be borne in mind by
mind by those who prepare othose who prepare or interpret the break-even chart. r interpret the break-even chart. These limitations suggestThese limitations suggest that the validity of the break-even chart is in proportion to the validity of the
that the validity of the break-even chart is in proportion to the validity of the assumptions.
assumptions. One of tOne of the assumptions of the he assumptions of the break-even analysis is that an enterprise’sbreak-even analysis is that an enterprise’s cost are either perfectly variable or absolutely fixed over all ranges of operating
cost are either perfectly variable or absolutely fixed over all ranges of operating volume.
volume. In other words, In other words, variable cost is a linear function variable cost is a linear function of volume: fixed of volume: fixed costs arecosts are assumed not to
assumed not to be affected by vbe affected by volume at all. olume at all. In practice, these assumptions are notIn practice, these assumptions are not likely to be valid over all ranges of volum
likely to be valid over all ranges of volume. e. Even within the relevant range of volumeEven within the relevant range of volume,, there is a likelihood of some degree of imprecision and to that extent validity of the there is a likelihood of some degree of imprecision and to that extent validity of the results is affected.
results is affected. For instance, variable costs For instance, variable costs are likely to are likely to increase as the firmincrease as the firm approaches full capacity.
approaches full capacity. The reason may The reason may be due be due to less efficient labour or costlyto less efficient labour or costly overtime having been
overtime having been resorted to. resorted to. This limitation can be This limitation can be overcome by studovercome by studying theying the relationship between total costs and volume, non-linear, to correspond with economic relationship between total costs and volume, non-linear, to correspond with economic reality.
reality.
Another assumption of the break-even analysis is that it is possible to classify Another assumption of the break-even analysis is that it is possible to classify total costs of an enterprise as either fixed
total costs of an enterprise as either fixed or variable. or variable. Many costs defy Many costs defy clear divisionclear division because t
because they are hey are partly fixpartly fixed and ed and partly vpartly variable. ariable. These cThese costs are kosts are known nown asas semi- semi-variable costs.
Yet another assumption of the break-even analysis is that selling price per unit Yet another assumption of the break-even analysis is that selling price per unit remains unchanged, irrespective of volume.
remains unchanged, irrespective of volume. In other words, In other words, total sales revenue istotal sales revenue is perfectly
perfectly variable wvariable with its phith its physical salysical sales volues volume. me. For soFor some firmme firms, operats, operating in ting in thehe seller’s market, this assumption may be perfectly valid.
seller’s market, this assumption may be perfectly valid. For most otFor most others, however, it ishers, however, it is not a realistic assumption because price reductions may be necessary to increase the not a realistic assumption because price reductions may be necessary to increase the sales volume.
sales volume. Once again, this limitation can be Once again, this limitation can be remedied by studying remedied by studying the relationshipthe relationship betwee
between total salen total sales revenus revenue and coe and costs.sts.
Summary
Summary
Profit planning is a function of coordinating the selling price of a unit of product,Profit planning is a function of coordinating the selling price of a unit of product, the variable cost per unit of making and selling the product, the volume of sales, the variable cost per unit of making and selling the product, the volume of sales, sales-mix in the case of multiple-product firms and the total fixed cost.
sales-mix in the case of multiple-product firms and the total fixed cost.
The volume-cost-profit analysis (VCP) is a tool to show the relationship betweenThe volume-cost-profit analysis (VCP) is a tool to show the relationship between these ingredients of profit planning. A widely-used technique to study VCP
these ingredients of profit planning. A widely-used technique to study VCP relationship is break-even analysis (BE).
relationship is break-even analysis (BE).
The break-even analysis shows the relationship between costs and profits withThe break-even analysis shows the relationship between costs and profits with the sales volume.
the sales volume. The sales volume tThe sales volume that equates the total revenues with hat equates the total revenues with the totalthe total related costs and results in neither profit nor loss is called the BE sales/point. In related costs and results in neither profit nor loss is called the BE sales/point. In other words, the no-profit-no-loss point is BEP at which losses cease and beyond other words, the no-profit-no-loss point is BEP at which losses cease and beyond which profits begin.
which profits begin.
The BPE can be determined by two methods: (1) Algebraic, comprising, (a)The BPE can be determined by two methods: (1) Algebraic, comprising, (a) Contribution margin approach, (b) Equation technique, and (2) Graphic Contribution margin approach, (b) Equation technique, and (2) Graphic presenta
presentation. tion. AccordAccording to ing to the contthe contributioribution margn margin approin approach, Bach, BEP is coEP is computemputedd on the basis of the relationship between the fixed costs and the contribution on the basis of the relationship between the fixed costs and the contribution margin (CM).
margin (CM). The CM The CM represents the differences between sales revenue represents the differences between sales revenue andand variable costs.
variable costs.
The equation technique is specially useful in situations in which unit price andThe equation technique is specially useful in situations in which unit price and unit variable costs are
unit variable costs are not clearly identifiable. not clearly identifiable. The excess oThe excess of actual sales over f actual sales over thethe BE sales is the margin of safety.
BE sales is the margin of safety. When the margin oWhen the margin of safety is divided by actualf safety is divided by actual sales, we get the margin of safety radio which indicates the percentage by which sales, we get the margin of safety radio which indicates the percentage by which actual sales may decline without the firm suffering a loss.
actual sales may decline without the firm suffering a loss.
Under the Under the algebraic technique, separate computations are algebraic technique, separate computations are required. required. The utility of The utility of the graphic techniques/presentation lies in the fact that a set of figures can be the graphic techniques/presentation lies in the fact that a set of figures can be determined without separate calculations.
determined without separate calculations.
The VCP The VCP chart portrays the relationship between sales, costs and chart portrays the relationship between sales, costs and profits. profits. It notIt not only shows BE sales but also the effect of costs and revenues at varying sales only shows BE sales but also the effect of costs and revenues at varying sales levels.
levels. It is, therefore, also It is, therefore, also referred to as referred to as the volume-cost-profit chart graph).the volume-cost-profit chart graph).
Both the algebraic and graphic approaches can be applied to analyse the VCPBoth the algebraic and graphic approaches can be applied to analyse the VCP relationship profit planning to reflect changes in fixed costs, variable costs and relationship profit planning to reflect changes in fixed costs, variable costs and selling price.
selling price. The following The following are the are the more specific applications:more specific applications:
Sales volume required to produce desired profitSales volume required to produce desired profit
Operating profit at a given level of sales volumeOperating profit at a given level of sales volume
Effect on operating profits of a given percentage change in salesEffect on operating profits of a given percentage change in sales
Additional sales volume required to offset reduction in selling priceAdditional sales volume required to offset reduction in selling price
Effect of changes in fixed costsEffect of changes in fixed costs
Effect of changes in variable costsEffect of changes in variable costs
