COST-VOLUME
PROFIT (C-V-P) ANALYSIS
Cost-volume-profit analysis considers how costs and profits
change with changes in the volume or level of activity.
Cost
– Volume – Profit (CVP) analysis is a technique for analyzing how cost and
profit change with volume of production and sales.
CVP
analysis is the study of the effect of future profit of changes in fixed cost,
variable cost, sales price, quantity and mix.
You should remember from earlier chapters that the variable
cost per unit and the selling price per unit are assumed to be unaffected by a
change in activity level. Hence the total contribution will vary linearly with
the level of activity.
Total fixed costs are not affected by the level of activity
although the costs per unit will fall as more units are produced.
As
a business produces and sells more output during a period, its profit will
increase. This is partly because sales revenue rises as sales volume goes up.
It is also partly because unit costs fall. As the volume of production and
sales go up the fixed cost per unit falls since the same amount of fixed costs
are shared between a large numbers of units.
The importance of contribution in CVP analysis
Contribution
is a key factor in CVP analysis, because if we assume a constant variable cost
per unit and the same selling price at all volume of output, the contribution
per unit is a constant value. Any change in selling price or variable costs
will alter unit contribution, change in fixed costs or profit required will
affect the contribution target.
Unit
contribution = selling price per unit- variable cost per unit.
Total
contribution = volume sales in units X Contribution
OR
Total
sales revenue X contribution /sales ratio.
Contribution/
sales ratio or C/S ratio
Contribution
/sales ratio = contribution per unit/ sales price per unit.
OR
Total
contribution/ Total sales revenue.
Assumptions behind C-V-P analysis
The
major assumptions behind C-V-P analysis are;
- All costs can be resolved into fixed and variable elements
- Fixed costs will remain constant and variable cost vary proportionately with activity
- Over the activity ranges being considered costs and revenues have a linear fashion.
- That the only factor affecting cost and revenue is volume
- That technology, production methods and efficiency remain unchanged.
- Particularly for graphical methods that the analysis relates to one product only or to a constant product mix.
- There are no stock level changes or that stocks are valued at marginal cost only.
USES OF CVP ANALYSIS
CVP
analysis uses many of the principles of marginal costing and is an important
tool in short –term planning. It explores the relationships that exist between
cost, revenue, output levels and resulting profit and is more relevant where
the proposed changes in the level of activity are relatively small.
In
these cases the established cost patterns are likely to continue, so C-V-P
analysis may be useful for decision-making. Applications of C-V-P analysis
include;
1. Estimating future profits
2. Calculating the break-even point
sales
3. Analyzing the margin of safety in
the budget
4. Calculating the volume of sales
required to achieve a target profit
5. Deciding on a selling price for a
product.
ANALYZING THE COST-VOLUME
RELATIONSHIP
This section examines algebraic and graphic analysis of the
cost-volume relationship.
Algebraic Analysis
The assumption of linear cost behavior permits use of
straight-line graphs and simple linear algebra in cost-volume analysis.
Total cost is a semi-variable cost—some costs are fixed, some
costs are variable, and others are semi-variable. In analysis, the fixed
component of a semi-variable cost can be treated like any other fixed cost. The
variable component can be treated like any other variable cost. As a result, we
can say that:
Total Cost = Fixed Cost + Variable Cost
Using symbols:
C = F + V
Where:
C = Total cost
F = Fixed cost
V = Variable cost
Total variable cost depends on two elements:
Variable
Cost = Variable Cost per Unit x Volume Produced
Using symbols:
V
= Vu (Q)
Where:
VU = Variable cost per unit
Q = Quantity (volume) produced
Substituting this variable cost information into the basic
total cost equation, we have the equation used in cost-volume analysis:
C = F + VU
(Q)
Illustration
If you know that fixed costs are Sh.500, variable cost per
unit is Sh.10, and the volume produced is 1,000 units, you can calculate the
total cost of production.
C = F + Vu
(Q)
= 500 + 10 (1000)
= Sh.10500
Given total cost and volume for two different levels of
production, and using the straight-line assumption, you can calculate variable
cost per unit.
Remember that:
- Fixed costs do NOT change no matter what the volume, as long as production remains within the relevant range of available cost information. Any change in total cost is the result of a change in total variable cost.
- Variable cost per unit does NOT change in the relevant range of production.
As a result, we can calculate variable cost per unit (VU)
using the following equation:
VU
= Change in Total Cost
Change in Volume
= C2 – C1
Q2 – Q1
Where:
C1 = Total
cost for Quantity 1
C2 = Total
cost for Quantity 2
Q1 =
Quantity 1
Q2 =
Quantity 2
Illustration
You are analyzing an offeror's cost proposal. As part of the
proposal the offeror shows that a supplier offered 5,000 units of a key part
for Sh.60, 000. The same quote offered 4,000 units for Sh.50, 000. What is the
apparent variable cost per unit?
Vu = C2 –
C1
Q2 – Q1
= 60000 - 50000
5000 – 4000
= Sh. 10
If you know total cost and variable cost per unit for any
quantity, you can calculate fixed cost using the basic total cost equation.
BREAK EVEN ANALYSIS
Break
even analysis is mainly used to explain the relationship between the cost
incurred, the volume operated at and the profit earned. To compute the break
even point we let
S
be selling price per unit
Vu
be variable cost per unit
Q
be break-even quantities
F
be total fixed costs
At Break even point:
Total revenue (TR) = Total Cost
(TC)
Total revenue will be given by SQ
while Total cost (TC) = Vu Q + F
At
break-even point (BEP) therefore
SQ
= Vu Q + F
Q = ___F___
S-
Vu
B.E.P (in units) = F
/ S- Vu
Illustration
Assume
that you are planning to sell badges at the forthcoming Nairobi Show at Sh.9
each. The badges cost Sh.5 to produce and you incur Sh.2000 to rent a booth in
the Show ground.
Required:
a) Compute the breakeven point
b) Compute the margin of safety
c) Compute the number of units that
must be sold to earn a before tax profit of 20%
d) Compute the number of units that
must be sold to earn an after tax profit of Sh.1640, assuming that the tax rate
is 30%.
Solution
a) Break
even point
b)
Break
even point in units =Fixed cost
Contribution per unit
BEP units = 2000/(9-5) = 500
units
BEP
Sh. = 500 x 9 = 4500/-
b) Margin of safety
The
margin of safety is the amount by which actual output or sales may fall short
of the budget without the company incurring losses. It is a measure of the risk
that the company might make a loss if it fails to achieve the target. A high margin of safety means high profit
expectation even if the budget is not achieved. Margin of safety (MOS) can be
computed as follows:
MOS = Expected sales - Break even sales
Expected sales
=
600-500 =
16.7%
600
c) Target
profit before tax profit (Y)
No
of units to earn a target profit
= Fixed
Cost + Target Profit
Contribution per unit
Let X be the number of units to
produce
X
= F +
Y
S -
Vu
X =
2000 + 0.2 (9X)
9-5
X=
2000 + 1.8X
4
X
= 909.09 approximately 910 units.
d) After Tax profit
Let Z be the after tax profit
Y = Z__
I – t
Therefore
X
= F + z/1-t
S – Vu
= 2000
+ 1640/1-0.3
9-5
X
= 1085.71
Approximately
1086 units.
C-V-P
ANALYSIS – MULTIPLE PRODUCTS
If
a company sells multiple products, break even analysis is somewhat more complex
than discussed in the topic break even point calculation. The reason is that the different
products will have different selling prices, different costs, and different
contribution margins. Consequently, the break even point will depend on the mix
in which the various products are sold.
The simple product CVP analysis
can be extended to handle the more realistic situations where the firm produces
more than one product. The objective in
such a case is to produce a mix that maximizes total contribution.
Total
BEP units = Total
fixed cost
Weighted Average CM
CALCULATING THE CONTRIBUTION TO
SALES RATIO IN A MULTI-PRODUCT SITUATIONS.
The
contribution to sales ratio so far we have delt with holds good only for an
organization producing and selling a single product. In reality, firms normally deal in multiple products;
such products could be complementary to each other or independent products.
In
the case of a multi-product company, while the individual product-wise c/s
ratio is an important consideration for certain decision situations, it would
be beneficial to perform a B.E.P analysis for the entire company using the
overall c/s ratio.
This
can be calculated as weighted average of the c/s ratios of all the products the
company deals in. Such analysis is based
on the assumption that sales mix remains constant.
The
B.E.P will shift either upward or downwards if the sales mix changes.
Fixed
costs are one of the important aspects of the C.V.P analysis. In a multi-product scenario, there could be
some fixed costs that are product specific while the others are common to all
products.
The
product specific costs can be avoided if that product is not produced at
all, but common fixed costs cannot be
avoided.
Under
the multi-product scenario, weighted average contribution margin is derived by
multiplying the product’s contribution rate with the proportion of the product
in total sales.
Weighted
average contribution margin (WACM)
= c/s ratio of product A x proportion of
A in total sales) + c/s ratio of product B x proportion of product B in total
sales) + c/s ratio of product C x proportion of product C in total sales).
B.E.P
in terms of units = Fixed
costs .
Weighted
average contribution
Margin
per unit.
or
Fixed costs
Contribution per mix
Example
KK
produces and sells two products. The P
sales for $7 per unit and has a total
variable cost of $2.94 per unit , while the
L sells for $15 per unit and has a total
variable cost of $4.50 per unit. The
marketing department has estimated that for every five units of P sold, one
unit of L will be sold. The organization
fixed cost total $36,000.
Required:
Calculate
the break even point for KK.
Solution
Calculate
contribution per unit
P L
Selling
Price 7 15
Variance
Cost 2.94 4.5
Contribution 4.06 10.50
Calculate
Contribution per mix
= ($4.06x5)+ ($10.50x1)= $30.80
Calculate
break even point in term of mixes
= Fixed costs
Contribution per mix
= $36,000
30.80
= 1,169 mixes
Calculate
the break even point in terms of the number of units of the products.
(1169 x 5) = 5844 units of P
(1169 x 1) = 1169 units of L
Calculate
the B.E.P in terms of revenue
(5845 x $7)+ (1169 x $15)
= $40,915 of P and $17,535 of L
= $58,450
It
is important to note that the B.E.P is not $58,450 of revenue, whatever the mix
of products.
The
breakeven point is $58,450 provided that the sales mix remains 5:1. Likewise the breakeven point is not at a
production/sales level of (5845 + 1169) 7014 units.
Rather,
it is when 5845 units of P and 1169 units of L are sold, assuming a sales mix
of 5:1.
Question
Grammer
manufactures and sells three products, the beta, the gamma and the delta. Relevant information is as follows:
Beta Gamma Delta
Selling price $ 135 165 220
Variance cost $ 73.50 58.90 146.20
Total
fixed costs are $950,000.
An
analysis of past trading patterns indicates that the products are sold in the ratio
3: 4 : 5
Required:
Calculate breakeven
point in terms of revenue for the products.
Breakeven point in
terms of dollars
Breakeven point in (terms of
sales dollars) = Fixed
costs
Weighted
average contribution margin ratio
Example
The
smiles curvature store produces two products: lipsticks and lip-gloss. These account for 40% and 60% of the total
sales of the company respectively.
Variable costs (as percentage of sales) are 40% for lipsticks and 50%
for lip-gloss. Total fixed costs are
$540,000
Required:
Calculated break
even point in dollars.
Weighted
average contribution margin can be calculated as follows:
The
contribution margin ratio for lipsticks is 60% of sales and the contribution
margin ratio for lip-gloss is 50% of sales.
The
WACM ratio is:
=
(c/s ratio of lipsticks X proportion of lipsticks in total sales) + c/s ratio
of lip-gloss X proportion of lip gloss in total sales)
=
(60% x 40%) + 50% x 60%
24%
+ 30%
=
54%
B.E.P
in terms of dollars = Fixed costs
Weighted average contribution
margin ratio
=
$540,000
54%
=
$1,000,000
Question
ABC
Ltd produces two products, product A and B and the following budget has been
prepared.
|
|
A
|
B
|
Total
|
|
|
120,000
|
40,000
|
160,000
|
|
Sales
in units
|
Sh.
|
Sh.
|
Sh.
|
|
|
|
|
|
|
Sales
@5/-, 10/-
|
600,000
|
400,000
|
100,000
|
|
Variable
cost @ 4/-, 3/-
|
480,000
|
120,000
|
600,000
|
|
Contribution
@ 1/- 7/-
|
120,000
|
280,000
|
400,000
|
|
Total
fixed cost
|
|
|
300,000
|
|
Profit
|
|
|
100,000
|
Required:
a) Compute the
break-even point in total and for each of the products.
b) The company
proposes to change the sales mix in units to 1:1 for products A and B.
Advice the Co. on whether this change is
desirable.
Question
Tom
produces and sells two products, the MK and KL.
The organization expects to sell I MK for every 2 KLs and have monthly
sales revenue of $150,000. The MK has a
c/s ratio of 20% whereas the KL has a c/s ratio of 40%. Budgeted monthly fixed
costs are $30,000.
Required:
What is the
budgeted break even sales revenue?
Margin of safety
for multiple products
Margin
of safety for multi produced organization is equal to the budgeted sales in the
std mix less the breakeven sales in the std mix.
Question
ABC
produces and sells two products. The W
sells for $8 per unit and has a total variable cost of $3.80 per unit, while
the R sells for $14 per unit and has a total variable cost of $4.20. For every five units of W sold, six units of
R are sold. ABC’s fixed costs are
$43,890 per period.
Budgeted
sales revenue for next period is $74,400, in the std mix.
Required:
Calculate
the margin of safety in terms of sale revenue and also as a percentage of
budgeted sales revenue.
Solution:
Determine
first the B.E.P
Calculate
contribution per unit
W R
Selling
price $ 8 14
Variable
cost $ 380 4.20
Contribution 4.20 9.20
Contribution
per mix
=
($4.20 x 5) + (9.2 x 6) = $79.80
Breakeven
point in terms of number of mixes
Fixed
costs = $43,890
Contributions
per mix $79.80
=
550 mixes
Breakeven
point in terms if the number of units of the products
(550 x 5) 2750 units of W
(550
x 6) 3300 units of R
Breakeven
point in terms of revenue.
(2750
units x 8) + (3300x14)
=
$22000 of W and $46200 of R = 68,200.
Margin
of safety
=
Budgeted sales – Breakeven sales in std mix
=
$74,890 - $68,200
=$6200.
As
percentage
6200
x 100%
74890
= 8.3% of budgeted sales
Target profits for
multiple products
Here,
sales mix will be derived by using the following formulae:
Target
sales mix = Fixed costs + target profit
Contribution per mix
Target
sales mix in dollars = WACM
= Fixed costs + target profit
Average contribution/sales ratio
After
deriving the total sales mix, it needs to be divided into individual products
in the proportion of the budgeted sales mix
Question
The
following are the products from which a company needs to earn a profit of
$50,000, after deducting fixed costs of $90,000.
Products
selling price variable costs budgeted units
$ $
X 100 64 500
Y 150 76.50 1250
The
proportion of budgeted sales mix 500:1250 i.e. 2:5
Required
Calculate the
required sales value of each product in order to achieve this target profit.
Solution
X Y
Selling
price 100 150
Variable
costs 64 76.50
Contribution
36 73.50
Contribution
per mix/WACM
=
(2 /7x 36) + (5 /7x 73.50) 439.50
10.29
+ 52.5 = $62.79
Target
sales mix = Fixed costs + Target profit
WACM
= 90,000 + 50,000
$62.79
= 2230 units
Product
X (2/7 x 2230) = 637 units
Product
Y 5/7 x 2230 = 1593 units
LIMITATIONS OF
BREAKEVEN PROFIT CHARTS
1.
A break even chart is based upon a number of
assumption discussed above which may not hold good under all circumstances. For
example fixed costs do not remain constant after a certain level of activity
variable costs do not always vary in direct proportion to changes in the volume
of output because of the laws of diminishing and increasing returns ; selling
prices do not remain the same forever and for all level of output due
competition and changes in the general price level; etc.
2.
A break even chart provides only limited
information. We have to draw a number of charts to study the effects of changes
in the fixed costs variable costs and selling price on the profitability.
3.
Break even charts present only cost volume profit
relationships but ignore other important consideration such as the amount of
capital investment marketing problems and government policies etc.
4.
A break even chart does not suggest any action or
remedies to the management as a tool of management decisions
5.
Moiré often a break even chart presents only a
static view of the problem under consideration.
C-V-P ANALYSIS UNDER UNCERTAINTY
A
major limitation of the basic C.V.P analysis is the assumption that the unit
variable cost, selling price and the fixed costs are constant and can be
predicted with certainty. These factors
however are variables with expected values and standard deviations that can be
estimated by management.
There are various ways of dealing
with uncertainty. Examples include:
- Sensitivity analysis
- Point estimate of probabilities
- Continuous probability distribution e.g. normal distribution
- Simulation analysis
- Margin of safety
Point Estimate of Probabilities
This approach requires a number
of different values for each of the uncertain variables to be selected. These might be values that are reasonably
expected to occur but usually 3 values are selected. These are:
The
worst possible outcome
The
most likely outcome
The
best possible outcome
For each of these 3 values, a
probability of occurrence will be estimated.Illustration
Assume that a Management
accountant of a Company that makes and sells product X has made the following
estimate:
|
|
Selling
price Sh.10
|
|
Unit
variable cost
|
|
|
|||
|
|
Sales
demand
|
|
Condition
|
|
|
|||
|
Condition
|
Unit
|
Prob.
|
|
Cost
|
Sh.
|
|||
|
Worst possible
|
45000
|
0.3
|
Best possible
|
3.5
|
0.30
|
|||
|
Most likely
|
50000
|
0.6
|
Most likely
|
4.0
|
0.55
|
|||
|
Best possible
|
55000
|
0.1
|
Worst possible
|
5.5
|
0.15
|
|||
|
Fixed cost = Sh.240,000
|
|
|
|
|
|
|||
|
Unit selling price =Sh.10
|
|
|
|
|
||||
Required:
a.
Compute
the expected profit
b.
Compute
the prob. that the company will fail to break even
c.
If
the Company has a profit targets of Sh.60, 000 what is the probability that the
company will not achieve this target.
Solution
a)
E(Demand)
= (45000 x 0.3) + (50000 x 0.6) + (55000 x 0.1) = 49000
E(variable
cost) = (3.5 x 0.3) x (4 x 0.55) + (55 x
0.15) = Sh.4.075
E(Profit) = (10-4.075) 49000 –
240000 = Sh.50325
This can
be worked out differently as shown below:
A B C D E F G (FxG)
Demand Prob. Unit VC Prob. Contr Profit Joint weighted Prob. Profit
45000 0.3 3.5 0.30 292500
52500 0.09 4725
4.0 0.55 270000
30000 0.165 4950
5.5 0.15 202500 (37500) 0.045 (1687.5)
50000 0.6 3.5 0.3 325000
85000 0.18 15300
4.0 0.55 300000 60000 0.33 19800
5.5 0.15 225000 (15000) 0.09 (1350)
55000 0.1 3.5 0.3 357500 117500 0.33 3525
4.0 0.55 330000 90000 0.055 4950
5.5 0.15 247500 7500 0.015 112.5
Expected
profit 50325
b)
The P (Profit <0 0.045="" 0.09="" span="">
= 0.135
Note:
This
can be read from the above table
c) P(profit < 60000)
= 0.3 + 0.09 + 0.015
= 0.405
Continuous Probability Distribution (Use of normal distribution)
In
reality the C-V-P variables might take any values in a continuous range. It could therefore be more appropriate to use
a continuous probability distribution such as the normal distribution with an
estimated mean and standard deviation.
Estimates may be made of the expected sales volume, the expected selling
prices, the expected variable cost and the expected fixed costs together with
their probabilities.
It
would therefore be possible to compute the expected profit and the likelihood
that the company would break even or achieve a given target profit.
Illustration
Assume
that the selling price of a product is estimated to be Sh.100, the variable
cost Sh.60, and budgeted fixed cost is Sh.36000. The demand is normally
distributed with a mean of 1000 units and a standard deviation of 90 units
Required
a.
Compute
the expected profit and standard deviation of profit
b.
Compute
the prob. that the company would not break even
c.
Compute
the prob. that a loss >Sh.1400 will
occur
a) E(profit) = Contribution margin x
E(D) - F.C
= (100-60) 1000 –36000
= Sh.4000
δ(profit) =δ demand x CM =
90 x 40 =Sh.3600
b) P(profit <0 span="">
z = x – u = 0
- 4000 = -1.11
δ 3600
From the Z tables the value =
0.1335
Therefore P(profit<0 span=""> =
0.1335
c) P (profit < - 1400)
Z
= -1400 – 4000 = -1.5
3600
From the Z tables the value = 0.0668
Therefore P(profit <-1400 0.0668="" span="">
No comments:
Post a Comment