CVP Analysis Explained: Break-Even Point, Required Sales Volume, Expected Profit

2013-10-18
1
MANAGEMENT ACCOUNTING
Cost-Volume-Profit Analysis
Zofia Krokosz-Krynke, Ph.D., MBA
zofia.krokosz-krynke@pwr.wroc.pl
Wroclaw University of Technology, Building B4 Room 521
http://www.ioz.pwr.wroc.pl/Pracownicy/krokosz/
2
Zofia Krokosz-Krynke: Management Accounting (Business Information Systems)
QUESTIONS ANSWERED BY CVP ANALYSIS
1. What sales volume is required to break even
2. What sales volume is necessary in order to earn a
desired profit
3. What profit can be expected on a given sales volume
4. How would changes in selling price, variable costs,
fixed costs, and output affect profits
5. How would a change in the mix of products sold affect
the break-even and target income volume and profit
potencial

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3
What sales volume is required to break even
break-even point – the level of sales at which revenue equals expenses and
net income is zero
margin of safety – the planned unit sales less the break-even unit sales
contribution margin (marginal income) – the sales price minus the variable
cost per unit
sales S = X*P
total cost TC = FC + UVC*X
break-even point BEP = X; S = TC
X*P = FC +UVC*X
UVCP
FC
XBEP
−
== PBEPBEPV *=
quantity
$ value
unit Contribution
Margin (CMU)
4
net income
area
total cost
sales
(revenue)
net loss
area
break-even
point
units
$
fixed
expenses
variable
expenses
net income
What sales volume is required to break even cont.
cost-volume-profit graph

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5
conventional and modified
break-even graphs
activity (volume) level
euros
relevant range
of volume
sales
total
expenses
activity (volume) level
euros
relevant range
of volume
sales
total
expenses
6
Assumptions that must be made in constructing the break-even
graph:
1. Expenses may be classified into variable and fixed
categories. Total variable expenses vary directly with activity
level. Total fixed expenses do not change with activity level.
2. The behavior of revenues and expenses is accuratly portrayed
and is linear over the relevant range.
3. Efficiency and productivity will be unchanged.
4. Sales mix (relative proportions or combinations of quantities of
products that constitute total sales) will be constant.
5. The difference in inventory level at the beginning and at the end
of a period is insignificant.
6. The price will be unchanged.
7. Sales and expenses are not the subject of „time value of
money”

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q1
7
q1
q2
$
expenses
plane
revenue
plane
break-even
line
break-even
0
5
10
15
20
0 1 2 3 4 5 6 7 8 9 10
q2
net income
area
net loss
area
cost-volume-profit graph – two products
8
UVCP
DFC
BEPcash
−
−
=
What sales volume is required to cover cash expenses
0
100
200
300
400
500
600
700
Euro
activity level
FC
VC
Sales
total expenses
cash expenses
BEP
BEPcash
Depreciation

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9
-200
-100
0
100
200
300
400
500
600
700
Euro
activity level
What sales volume is necessary in order to earn a desired profit
sales
total costs
net income
net profit
UVCP
taxNPFC
BEPprofit
−
−+
=
)1/(
NP – net profit
tax – tax rate (CIT)
UVCP
taxNP
BEPBEPprofit
−
−
+=
)1/(
or
)1(* taxCMU
NP
BEPBEPprofit
−
+=
or
10
What profit can be expected on a given sales volume
Sales P*units sold
Expenses: variable (CGS) VC* units sold
fixed FC
Income P* units sold – VC* units sold – FC
= (P – VC) *units sold – FC
= CMU * units sold – FC
Profit Income – Tax
= (CMU * units sold – FC) *(1 – tax rate)

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How would changes in selling price, variable costs, fixed costs,
and output affect profits
alternative cost structure
We are going to sell on a fair a software packet „Do-All”. Software we can buy
from the wholesaler for $120 per unit, unsold packet we can return to the
wholesaler. The price of $200 per unit seems to be acceptable. Exibition Center
(fair’s organizer) offers a place we can sell our software according to the
following options:
a) $2000
b) $1400 plus 5% of sales
c) 20% of sales
Which option should we choose?
0
1000
2000
3000
4000
5000
6000
7000
0 5 10 15 20 25 30
option a)
0
1000
2000
3000
4000
5000
6000
7000
0 5 10 15 20 25 30
option b)
0
1000
2000
3000
4000
5000
6000
7000
0 5 10 15 20 25 30
option c)
12
How would changes in selling price, variable costs, fixed costs,
and output affect profits cont.
alternative cost structure
option a) BEP= 2000/(200-120) = 25 units
option b) BEP= 1400/(200-120-200*0.05) = 20 units
option c) BEP= 0/(200-120-200*0.2) = 0 units
-3000
-2000
-1000
0
1000
2000
3000
4000
5000
6000
7000
Dollars
activity level [units]
option a)
option b)
option c)
BEP
BEP
BEP
option c) option b) option a)
net income

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13
How would a change in the mix of products sold affect the break-
even and target income volume and profit potencial
( )
∑
∑
∑∑
∑
∑
−
=
+=
+=
=
ii
iii
iiii
ii
ii
qP
qVCUP
FC
BEPVm
FCVCUqPq
FCVCUqTC
PqS
qi – quantity of product i
14
How would a change in the mix of products sold affect the
break-even and target income volume and profit potencial cont.
product i 1 2 3
price P $10 $20 $5
variable cost per unit VC $3 $15 $2
quantity q 30 units 50 units 20 units
fixed cost FC $10 000
product i 1 2 3
price P $10 $20 $5
variable cost per unit VC $3 $15 $2
quantity q 50 units 20 units 30 units
fixed cost FC $10 000
27000$
37,0
10000
20*550*2030*10
20*)35(50*)1520(30*)310(
10000
==
++
−+−+−
=BEPV
19230$
52,0
10000
30*520*2050*10
30*)35(20*)1520(50*)310(
10000
==
++
−+−+−
=BEPV

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Case study
Valtek Company sells three products. The company pays attention to the
budgeting and planning process. The sales budget has been worked out.
even and target income volume and profit potencial cont.
Product
A B C Total
% sales 20% 52% 28% 100%
Sales 150 000 100% 390 000 100% 210 000 100% 750 000 100%
Minus
variable costs
108 000 72 % 78 000 20 % 84 000 40 % 270 000 36 %
contribution margin 42 000 28% 312 000 80% 126 000 60% 480 000 64%
Minus
fixed costs
449 280
Profit 30 720
BEPV = 449 280 / 0,64 = $702 000
16
Assume that according to the plan the sales of $750 000 has been reached, and the sales
on products was as follows: A - $300 000; B - $180 000; C - $270 000.
1. Prepare the income statement for the month.
2. What is the dollars break-even point for the month?
3. The president is shocked with the results of this month – the company’s sale (in dollars)
is exactly the same as planned. Explain the president why the result and the break even
differ from planned.
Product
A B C Total
% sales 100%
Sales 300 000 100% 180 000 100% 270 000 100% 750 000 100%
Minus
variable costs
72 % 20 % 40 %
contribution margin 28% 80% 60%
Minus
fixed costs
449 280
Profit

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Product
A B C Total
% sales 40% 24% 36% 100%
Sales 300 000 100% 180 000 100% 270 000 100% 750 000 100%
Minus
variable costs
72 % 20 % 40 %
contribution
margin
28% 80% 60%
Minus
fixed costs
449 280
Profit
18
Product
A B C Total
% sales 40% 24% 36% 100%
Sales 300 000 100% 180 000 100% 270 000 100% 750 000 100%
Minus
variable costs
216 000 72 % 36 000 20 % 108 000 40 % 360 000 48%
contribution
margin
28% 80% 60%
Minus
fixed costs
449 280
Profit

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Product
A B C Total
% sales 40% 24% 36% 100%
Sales 300 000 100% 180 000 100% 270 000 100% 750 000 100%
Minus
variable costs
216 000 72 % 36 000 20 % 108 000 40 % 360 000 48%
contribution
margin
84 000 28% 144 000 80% 162 000 60% 390 000 52%
Minus
fixed costs
449 280
Profit
20
Product
A B C Total
% sales 40% 24% 36% 100%
Sales 300 000 100% 180 000 100% 270 000 100% 750 000 100%
Minus
variable costs
216 000 72 % 36 000 20 % 108 000 40 % 360 000 48%
contribution
margin
84 000 28% 144 000 80% 162 000 60% 390 000 52%
Minus
fixed costs
449 280
Profit (59 280)
BEPV = 449 280 / 0,52 = $864 000

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Product
A B C Total
% sales 40% 20% 24% 52% 36% 28% 100%
Sales 300 000 150 000 180 000 390 000 270 000 210 000 750 000 750 000
Minus
variable costs
216 000 108 000 36 000 78 000 108 000 84 000 360 000 270 000
contribution
margin
84 000 42 000 144 000 312 000 162 000 126 00 390 000 480 000
Minus
fixed costs
449 280 449 280
Profit (59 280) 30 720
the endthe endthe endthe endthe endthe endthe endthe end

CVP Analysis Explained: Break-Even Point, Required Sales Volume, Expected Profit

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