3 SLP MKT599

CVP Analysis

Cost, Volum e, Profit

W hat is CVP?

• Uses a specific cost-profit-volum

e form ula to

study the relationship of the costs, price, sales volum

e and profit.

• Profit = (price –

vcost/unit)*Volum e –

Total Fixed Costs.

• Price and vcost are per unit.

Developing the form ula

• Profit = (price –

vcost/unit)*Volum e –

Total Fixed Costs.

• price and vcostare per unit. •

P = (p – c)V –

F (Basic Form ula)

• P = profit

• p = price (per unit)

• c = Variable cost/unit

• F = total Fixed Costs

• V = Sales Volum

e (units sold)

Exam ple Using Basic Form

ula

• P = (p –

c)V – F

• price (p) = $300/unit

• vcost(c) = $100/unit

• Total Fixed Costs = $50,000

• If you sell 1,500 units, w

hat is the profit? •

P = (300 – 100)1500 –

50000 •

= (200)1500 – 50000

• = 300000 –

50000 •

= $250,000

Using CVP

• Breakeven analysis

• Profit, price, Volum

e analysis

Using CVP for Breakeven

Breakeven is the situation w here no profit or

loss is generated. •

Incom e = Costs

• In the Basic Form

ula, Profit = 0 Tw

o w ays to use:

• Breakeven Volum

e: V BE

• Breakeven price: p

BE

Calculating Breakeven Volum e

• Breakeven Volum

e is the quantity that w ill

generate Profit = 0 for given costs and price. •

Using the form ula, w

e need to determ ine w

hat V is w

hen P = 0. •

P = (p – c)V –

F •

0 = (p – c) V

BE – F

• F = (p –

c) V BE

• F/(p –

c) = V BE

• V

BE is being use to denote specifically the

Breakeven Volum e.

Contribution M argin

• V

BE = F/(p – c)

• The breakeven volum

e is calculated by Total Fixed costs divided by price m

inus variable costs.

• (p –

c) is often called the Contribution M argin

(per unit) or Unit Contribution M argin.

• Another w

ay of looking at breakeven is it is the sales volum

e w here Incom

e = Costs.

Breakeven: Incom e = Costs

• Incom

e = Costs •

P = (p – c)V –

F •

0 = (p – c) V

BE – F

• 0 = p V

BE – c V

BE – F

• p V

BE = c V BE + F

• p V

BE is the incom e and c V

BE + F are the total costs, Variable Costs + Fixed Costs.

Exam ple of Breakeven Calculations

• V

BE = F/(p – c)

• price (p) = $300/unit

• vcost (c) = $100/unit

• Total Fixed Costs = $50,000

• W

hat the Breakeven volum e?

• V

BE = 50000/(300 – 100)

• V

BE = 50000/200 •

V BE = 250 units

Check & Validate…

• Check: Incom

e = Total Costs •

p V BE = c V

BE + F ?? •

300(250) = 100(250) + 50000 •

75000 = 25000 + 50000 •

75000 = 75000

Breakeven Graph INCOM

E = pV

FIXED COSTS + VARIABLE COSTS

FIXED COSTS

Breakeven: Incom

e = Total Costs

V BE

Breakeven Price

• Let’s say you know

the volum e and you w

ant to know

the price that w ill generate a

breakeven situation: i.e. P = 0 •

0 = p BE V –

c V – F

• p

BE V = c V + F •

p BE

= (c V + F)/V •

Breakeven price is calculated by dividing the Total Costs by the Volum

e.

Exam ple B

reakeven price •

p B

E = (c V

+ F)/V or c + F/V

• c = 100 (per unit)

• F = 50000

• V

= 1500 units •

p B

E = [100(1500) + 50000]/1500

• = [150000 + 50000]/1500

• = [200000]/1500

• = $133.33/unit

• If you price the item

at $133.33 then if you sell, 1500 units, you w

ill B reakeven.

Exam ple Breakeven price

• p

BE = (c V + F)/V or c + F/V

• c = 100 (per unit)

• F = 50000

• V = 1500 units

• p

BE = $133.33 •

If you price it higher than $133.33, and you sell 1500 units, you w

ill m ake a profit.

U sing X5 from

PDA Sim •

Default Values: •

p = $250 (you can change this after SLP1) •

c = $140 (does not change in the sim ulation)

• U

nit Contr. M argin = $110

• From

Default Run Year 2006: •

R& D costs = 6,666,667

– (33%

of 20,000,000 budget, you decide allocation % )

• O

ther Fixed Costs = 70,000,000 (does not change) •

Total Fixed Costs = 76,666,667 (R& D + O

ther Fixed) •

2006 unit sales volum e: 1,766,216

Using X5 from PDA Sim

• Let’s validate the results in the Sim

and calculate Profit

• P = (p –

c)V – F

• P = (250 –

140) 1,766,216 – 76,666,667

• = (110) 1,766,216 –

76,666,667 •

= 194,283,760 -76,666,667 •

= 117,617,093 •

Profit from Default Sim

for X5 in 2006 = 117,617,097

Using X5 from PDA Sim

• Let’s estim

ate w hat w

ill happen in 2007 if w e low

er R&

D and w e low

er the price. •

R& D%

= 10% (of 20,000,000)

• R&

D = 2,000,000 •

Price p = $225 (dow n from

$250 by 10% )

• Sales Volum

e V = 1,439,609 (from 2007 default run)

• Profit = (225 –

140) 1,439,609 – 72,000,000

• = (85) 1,439,609 –

72,000,000 •

= 122,366,765 – 72,000,000

• = 50,366,765

• Profit = 81,690,327 from

2007, default run

Using X5 from PDA Sim

• So if you low

er your price to $225 and decrease R&

D and the volum e does not

change from the default volum

e, you w ill earn

less profit in 2007 that you did in the default run.

• BUT, if you low

er the price w ill that help to

increase the volum e?

• M

aybe, but w hat does the volum

e need to be to obtain the sam

e profit that w as earned in

2007, default run (81,690,327)

Using X5 from PDA Sim

• Profit, P = 81,690,327

• Volum

e = ? •

P = (p – c)V –

F •

(P + F)/(p – c) = V

• (81,690,327 + 72,000,000)/(85) = V

• 153,690,327 / 85 = 1,808,121.49

• V = 1,808,122 units to achieve the sam

e profit •

If you low er the price to $225 and reduce the

R& D to 10%

, does the reduce price cause an increase in Volum

e so that the profit is the sam e?

D eterm

ining Strategy: X5 Exam ple

• D

efault run 2007

• p = 250

• c = 140

• U

nit Contr. M argin = 100

• R&

D (33% ) = 6,666,667

• O

ther Fixed = 70,000,000

• Profit = 81,690,327

• Volum

e = 1,439,609

• Possible strategy 2007

• p = 225

• c = 140

• ucm

= 85

• R&

D (10% ) = 2,000,000

• O

ther Fixed = 70,000,000

• Profit = 81,690,327

• Volum

e = 1,808,122

If you low er price from

$250 to $225 in 2007, w

ill volum e go up to or higher than 81,690,327

Breakeven Form ulas

• P = (p –

c)V – F

• For Breakeven, set P = 0

Breakeven Volum e

• V

BE = F/(p – c)

Breakeven Price •

p BE

= (c V + F)/V or •

p BE

= c + F/V •

REM EM

BER: in the PDA Sim , you need to consider

that R& D is part of Fixed Costs, so here F = Fo + R

Other CVP Form ulas

Use F = F o + R (PDA sim

fixed costs) •

Price, for a given Profit, Volum e and Costs

• p* = (P + F

o + R + cV) / V

• Volum

e, for a given price, Profit and Costs •

V* = (P + F o + R) / (p –

c)

Application of CVP in the PDA Sim

• W

hen should you use Breakeven? •

How do you deal w

ith m ultiple years?

• How

do you deal w ith m

ultiple products?

• Give these questions som

e thought. •

Experim ent w

ith CVP.

USING THE CVP CALCULATOR

An Exam ple for X5 in the PDA SIM

Default X5 2006 This Year

Last Year %

C hange

R evenue

Sales Volum e

1,766,216 1,448,031

22% R

evenue Volum

e 441,554,008

362,007,649 22%

C ostVariable C

osts 247,270,244

202,724,283 22%

Fixed C osts

70,000,000 70,000,000

0% R

& D

C osts

6,666,667 6,666,667

0% Total C

osts 323,936,911

279,390,950 16%

Profit Total Profit

117,617,097 82,616,699

42% Total Profitability

27% 23%

17%

Price: $250 R&

D% : 33%

X5 Financials for 2006

This Year Last Year

% C

hange

C ustom

er Base Installed B

ase 3,167,351

1,875,622 69%

R em

aining C

ustom ers

2,857,649 4,149,378

-31%

M arket Saturation

53% 31%

69%

Sales Volum e

First-Tim e

C ustom

ers 1,502,270

1,291,729 16%

R epeat Sales

263,946 156,302

69% Total Sales

1,766,216 1,448,031

22%

D efault X5 M

arket R eport for the year 2006

USING CVP Calculator:

R& D Total Budget

$ 20,000,000 R&

D% Allocation

33%

R& D Costs

$ 6,600,000

Fixed Costs $ 70,000,000

Total Fixed Costs $ 76,600,000

Target Profit $117,617,097

Variable Cost/Unit $ 140.00

Variable cost/unit: $140 Price

$ 250.00

Volum e

1,765,610

Sales Revenue $ 441,402,493.18

RO S

26.65%

N ote that the results from

the CVP Calculator are nearly the sam

e as you get in the SIM

. The only difference is because the SIM

m ust be using

33.3333% for the R&

D Allocation and the CVP Calculator is using 33%

. So w e

w ill ignore the difference.

N ow

let’s develop a Revised Strategy

N ow, let’s try to develop a different price and R&

D allocation for 2006 for our Revised Strategy using the

• CVP Calculator. Should w

e low er R&

D or increase it? Should w

e low er the price or increase it? How

m uch

profit do w e w

ant? How m

uch w ill w

e sell? •

Let’s low er the R&

D% , say dow

n to 15% -w

hy? I w ill

leave that up to you decide w hy w

e m ight w

ant to do this.

• Let’s leave the price the sam

e for this first estim ate:

$250. •

And let’s shoot for the sam e profit: $117,617,097

• If you put these into the CVP Calculator, this says you need less volum

e: 1,732,883 units.

Price: $250 R&

D : 15%

à Volum

e: 1,732,883

R& D

Total Budget $ 20,000,000

R& D

% A

llocation 15%

R& D

Costs $ 3,000,000

Fixed Costs $ 70,000,000

Total Fixed Costs $ 73,000,000

Target Profit $117,617,097

Variable Cost/U nit

$ 140.00

Price $ 250.00

Volum e

1,732,883

Sales Revenue $ 433,220,675.00

RO S

27.15%

W h

at p rice

if V o

lu m

e d

o e

s n o

t

ch a

n ge

?

• P

rice =

?

• Sa

m e

vo lu

m e

a s

d e

fa u

lt ru n

• Sa

m e

p ro

fit a s

d e

fa u

lt ru n

• R

& D

% : 1

5 %

V o

lu m

e 1

,7 6

5 ,6

1 0

P rice

$ 2

4 7

.9 6

Sa le

s R e

ve n

u e

$ 4

3 7

,8 0

2 ,4

9 7

.0 0

R O

S 2

6 .8

7 %

Price = $247.96

W hat happens in SIM

? •

Let’s run the sim

w ith our

revised strategy for X5 for 2006.

• Price: $248

• R&

D% :

15%

This Year Last Year

% Change

Revenue Sales Volum

e 1,835,367

1,448,031 27%

Revenue Volum

e 455,170,904

362,007,649 26%

CostVariable Costs 256,951,317

202,724,283 27%

Fixed Costs 70,000,000

70,000,000 0%

R & D Costs

3,703,704 6,666,667

-44% Total Costs

330,655,021 279,390,950

18%

Profit Total Profit

124,515,884 82,616,699

51% Total Profitability

27% 23%

20%

X5 Financials for 2006

R e

s u

lts d

o n

o t m

a tc

h !!

• V

o lu

m e

s o

ld : 1

,8 3

5 ,3

6 7

• P

ro fit e

a rn

e d

: 1 2

4 ,5

1 5

,8 8

• W

e d

o n

’t g e

t th e

s a

m e

re s u

lts th

a t w

e re

p re

d ic

te d

b y

th e

C V

P !!

In th

e C

V P

w e

u s e

d a

V o

lu m

e o

f: 1 ,7

6 5

,6 1

0

B u

t in th

e S

IM , w

h e

n w

e lo

w e

re d

th e

p ric

e ju

st a

b it d

o w

n to

$ 2

4 8

, w e

g o

t a v

o lu

m e

o f:

1 ,8

3 5

,3 6

7 .

W e

w ill g

e t th

is s

a m

e re

s u

lt in th

e C

V P

c a

lc u

la to

r

if w e

p u

t in th

e a

c tu

a l p

ro fit e

a rn

e d

in th

e S

IM

CVP Calculator w ith Revised Strategy Results

R& D

Total Budget $ 20,000,000

R& D

% Allocation

15%

R& D

Costs $ 3,000,000

Fixed Costs $ 70,000,000

Total Fixed Costs $ 73,000,000

Target Profit $124,515,884

Variable Cost/U nit

$ 140.00

Price $ 248.00

Volum e

1,828,851

Sales Revenue $ 453,554,992.89

RO S

27.45%

W hy does the SIM

not m atch your

predictions w ith the CVP Calculator?

• The SIM

gives you the results based on your inputs of price and R&

D% •

It w ill determ

ine how m

uch you sell based on the price –

usually a low er price w

ill generate a higher sales volum

e and vice versa, depending on the price elasticity.

• The CVP calculator does not know

the price:dem

and curve – it is sim

ply telling you how

m uch you need to sell for a given Price

and a Target Profit.

Som e final thoughts

• So w

hat is m issing is the relationship betw

een price and dem

and. •

Dem and is based on based price and the perform

ance (how

m uch is being spent on R&

D). •

You need to use CVP to help you determ ine or predict a price in

your revised strategy. •

Then based on the results you get, you can begin to understand the price:dem

and relationship.

• That is w

hy you get to run the SIM several tim

es as you learn m

ore about price:dem and.

• And of course dem

and is related to how m

uch you spend on R&

D. •

And each product is m ore or less sensitive to price and product

developm ent efforts.