Breakeven Analysis or Profit Contribution Analysis or Cost-volume-profit (CVP) Analysis

Breakeven analysis – useful in planning, studies the relationship between TC, TR, total losses and profits over the whole range of output

Linear cost and revenue functions

TC = 100 + 10Q, TR = 15Q

Breakeven Q (Qe) TR = TC 20

or PQ=FC+Q.AVC

or FC/P-AVC 20

Operating losses (TC>TR)

Operating profit (TR>TC)

Profit contribution (P-AVC) - revenue on the sale of a unit of output after variable costs are covered represents a contribution towards profit

Contribution margin ratio = P - AVC/P

Criticism of linear functions- linear revenue and non linear cost functions

Non linear costs and revenue functions

TFC

TVC

TRTC

Q1 Q

2Q3

TC

TR,TC, A

B

a

b

C

Dlosses

profits

Managerial uses of breakeven analysis

Margin of safety – refers to the extent to which the firm can afford a decline in sales before it starts incurring losses.

MS = S - BEPwhere MS = margin of safety,S = sales (planned), BEP = breakeven point It reflects resistance capacity to avoid losses

Margin of safety Case -1 MS = 8000 – 5000 = 3000 QOr (S – BEP).100/S = 37.5% Case - 2MS = (4000 – 5000).100/4000 =

25%

Required rate of profit (R) Q

R = PQ - [ (Q.AVC) + FC]

Q = FC + R/P – AVC = 100 + 200/15 –10=60

Change in price P contribution margin and vice

versa P not always demand – it depends on

Ed

Increasing sale price increases MS and vice versaQn = FC + / SPn – AVC

Where Qn = new volume of sales, SPn = new selling price

Case – 1100 +200/15 – 10 = 60Price reduced to 13Qn = 100 + 200/13 – 10 = 100 Case – 2If price increased to 17Qn = 100 + 200/17 – 10 = 44

Change in cost High ratio of TFC to TC allows high

profits with increasing sales Low ratio of TFC to TC has larger

MS

Change in fixed cost New output levelQn = Q + FCn – FC/P – AVC

60 + 150 – 100/15 – 10 = 70 New selling pricePn = P + FCn – FC/Q

= 15 + 150 – 100/60 = 16

Change in variable costs New output levelQn = FC + / P – VCn

= 100 + 200/15 – 12 = 100 The new selling pricePn = P + (VCn + VC)

= 15 + (12 – 10)=17

Operating leverages

A firm is said to be highly leveraged if fixed costs are large relative to variable costs and experiences more variation in profits for a given % ∆ Q than does a less leveraged firm.

Leverage is analyzed using profit elasticity an indicator of risk

Q

Q

QQ

E

SALES UNITIN %

IN % E

Operating leverages

If price is constant, E depends on - the level of output- the level of TFC- AVC = PQ – (AVC) (Q) – TFC

And ∆ = P (∆Q) – (AVC) (∆Q)

Therefore E = [P(∆Q) – (AVC)(∆Q)] / [PQ –

(AVC)(Q) - TFC] /∆Q/QOr E = Q(P – AVC)/ Q(P – AVC) - TFC

Example Operating profit elasticity for two firms

firm a firm b

price = 10 price = 10

AVC = 5 AVC = 2

AFC = 1000 TFC = 4000

Output sale profit E

firm A firm B firm A firm B

1000 4000 4000 1.25 2.00

1500 6500 8000 1.15 1.50

2000 9000 12000 1.11 1.33

2500 11500 16000 1.09 1.25

3000 14000 20000 1.07 1.20

VG/lv/P-II-6

Policy guidelines emanating from break even analysis

– A high BEP indicates vulnerability of the profit position

of the firm

– The higher the contribution margin, the higher is the

endurance of business and vice versa

– During boom, a firm with a higher percentage of fixed

costs to sales earns higher profits as compared to a

business with a higher percentage of variable

expenses to sales. During depression. the leveraged

firm suffers greater losses than others.

VG/lv/P-II-6