ANALYSIS
This is a tool that
makes use of the contribution concept in order to assess the following measures
for a single product:
·
Contribution to sales
(C/S) ratio
·
Break even point
·
Margin of safety
·
Target profit
1 C/S ratio
The C/S ratio is the
proportion of the selling price that contributes to fixed overheads and profits
and is comparable to gross margin.
|
C/S ratio
|
=
|
Contribution
per unit
|
or
|
Total
contribution
|
|
Selling
price per unit
|
Total
sales revenue
|
Sometimes referred to
as the P/V ratio.
Example 1:
The following
information relates to Product J
|
|
$
|
|
Selling price per unit
|
20
|
|
Variable cost per unit
|
12
|
|
Fixed costs
|
100,000
|
Required:
Calculate the C/S
ratio
Example 2:
The following
information relates to Product Alpha.
|
|
$
|
|
Selling price per unit
|
100
|
|
Variable cost per unit
|
56
|
|
Fixed costs
|
220,000
|
Required:
Calculate the C/S
ratio
2)
Break even point
This is the point at
which neither a profit nor a loss is made. The following situations occur:
·
Total sales revenue =
Total costs
·
Total contribution =
Fixed costs
In terms of sales
units
Break even point in units
|
=
|
Fixed
costs
|
|
Contribution
per unit
|
In terms of sales
revenue
Break even point in sales
|
=
|
Fixed
costs
|
|
C/S
ratio
|
Example 1:
The following
information relates to Product K
|
|
$
|
|
Selling price per unit
|
20
|
|
Variable cost per unit
|
12
|
|
Fixed costs
|
100,000
|
Required:
a)
Calculate the break even point in terms of numbers of units sold.
b)
Calculate the break even point in terms of sales revenue.
The following information relates to Product
Alpha.
|
|
$
|
|
Selling price per unit
|
100
|
|
Variable cost per unit
|
56
|
|
Fixed costs
|
220,000
|
|
|
Required:
a)
Calculate the
breakeven point in terms of units sold.
b)
Calculate the
breakeven point in terms of sales revenue.
3)
Margin of safety
This is the amount by
which the sales in units or a % of budgeted sales can fall below before a loss
is made.
|
Margin of safety in units
|
=
|
Budgeted sales
|
-
|
Breakeven point sales
|
|
Margin of safety as a % of sales
|
=
|
Budgeted
sales
|
-
|
Breakeven
sales
|
x
|
100%
|
|
Budgeted
sales
|
||||||
Example 1:
Arrow Ltd manufactures
Product L to which the following information relates.
|
|
$
|
|
Selling price per unit
|
20
|
|
Variable cost per unit
|
12
|
|
Fixed costs
|
100,000
|
Budgeted sales for the
period are 16,000 units.
Required:
a)
Calculate the margin
of safety in units.
b)
Calculate the margin
of safety as a % of budgeted sales.
Example 2:
The following
information relates to Product Alpha.
|
|
$
|
|
Selling price per unit
|
100
|
|
Variable cost per unit
|
56
|
|
Fixed costs
|
220,000
|
|
Budgeted sales are 7,500 units
|
|
Required:
a)
Calculate the margin
of Safety
b)
Calculate the margin
of safety as a % of budgeted sales.
4)
Target profit
This enables you to
calculate the number of units or sales required in order to earn a certain
level of profit.
|
Sales volume to achieve a target
profit
|
=
|
Fixed
costs
|
+
|
Required
profit
|
=
|
Target
contribution
|
|
Contribution
per unit
|
Contribution
per unit
|
|||||
Example 1:
Arrow Ltd manufactures
Product L and wishes to achieve a profit of $20,000. The following information
relates to Product L.
|
|
$
|
|
Selling price per unit
|
20
|
|
Variable cost per unit
|
12
|
|
Fixed costs
|
100,000
|
Required:
Calculate the sales
volume required to achieve a profit of $20,000.
Example 2:
The following
information relates to Product Alpha.
|
|
$
|
|
Selling price per unit
|
100
|
|
Variable cost per unit
|
56
|
|
Fixed costs
|
220,000
|
|
Budgeted sales are 7,500 units
|
|
Required:
Calculate the unit
sales required to achieve a target profit of $550,000.
The measurements that
we have calculated may be determined by drawing and interpreting graphs.
·
Traditional breakeven
charts
·
Contribution breakeven
charts
·
P/v charts
1)
Traditional breakeven charts
Has got the fixed cost line. Which is
distinct.
|
|
2)
Contribution breakeven charts
A variation of the
traditional breakeven chart. The difference here is the variable cost line
instead of fixed cost used and that contribution may be read from the
graphs.
|
|
3)
P/V charts
Breakeven charts do
not directly highlight the amounts of profits or losses over various
levels of activity. This is where the P/V chart can clearly illustrate.
|
|
|
|
|
|
|
The chart above shows
the amount of net profit or loss at different levels of (sales) activity.
Example 1
A new product has the
following sales and cost data
Selling Price per unit
$60
Variable Cost per unit
$40
Fixed Cost $25000 per
month
Forecast Sales 1800
units per month
Required:
a)
Prepare Break Even
Chart using the above data
b)
Prepare Profit/volume
chart
Example 2
A product has the
following information
Selling Price per unit
$40
Variable Cost per unit
$30
Fixed Cost $70000
Forecast Sales 8000
units
Required:
a)
Prepare Break Even
Chart using the above data
b)
Prepare Profit/volume
chart
BREAK EVEN ANALYSIS IN MULTI-PRODUCT
ENVIRONMENT
·
To
perform Break even analysis in a multi product organisation, a constant product sales mix must be
assumed or all the products must have the same C/S ratio. That is, we have to assume that whenever X units of product A are sold, Y units of
product B and Z units of product C are
also sold.
·
This
assumption allows us to calculate a weighted average contribution per mix, the
weights being on the basis of the quantities of each product in the constant
Mix.
·
The
only situation when the mix of products don not affect the analysis is when all
the products have the same ratio of Contribution to Sales (C/S Ratio)
Example 1
AB
Ltd produces and sells two products X and Y. X sells for $7 per unit and have a
Variable cost of $2.94 per unit while Y sells for $15 per unit and has a V.C of
$4.50 per unit. The marketing department has estimated that for every 5 units
of X sold, 1 unit of Y is sold. The organisation has a Fixed Costs of $36,000.
Required:
Calculate the
Break Even Point for AB Ltd
Solution
The following steps are involved when calculating BEP in this case:
1. Calculate Contribution per unit
2. Calculate Contribution per mix
3. Calculate Break Even Point in terms
of the number of Mixes
4. Calculate the Breakeven point in
terms of the number of units of the product
5. Calculate the BEP in terms of
revenue
Example
2
Alpha Ltd manufactures and sells three
products: Beta, Gamma and Delta. Information is as follows:
|
|
Beta
|
Gamma
|
Delta
|
|
|
$
per Unit
|
$
per Unit
|
$
per Unit
|
|
Selling Price
|
135.00
|
165.00
|
220.00
|
|
Variable Costs
|
73.50
|
58.90
|
146.20
|
The Fixed Cost was $950,000
The products are sold in the ratio
of 3:4:5
Required: Calculate the BEP of Alpha Ltd
MARGIN OF SAFETY FOR MULTIPLE
PRODUCTS
The margin of
safety for a multi - product organisation = Budgeted sales in std mix – BE
Sales in Std Mix
It may also be
expressed as a percentage of the Budgeted Sales.
Example
1
AB
Ltd produces and sells two products X and Y. X sells for $7 per unit and have a
Variable cost of $2.94 per unit while Y sells for $15 per unit and has a V.C of
$4.50 per unit. The marketing department has estimated that for every 5 units
of X sold, 1 unit of Y is sold. The organisation has a Fixed Costs of $36,000.
Budgeted sales Revenue is $70,000.
Required:
Calculate the MOS
in terms of Sales Revenue and also as a % of Sales
Solution
The following steps are involved when calculating BEP in this case:
1. Calculate Contribution per unit
2. Calculate Contribution per mix
3. Calculate Break Even Point in terms
of the number of Mixes
4. Calculate the Breakeven point in
terms of the number of units of the product
5. Calculate the BEP in terms of
revenue
6. Calculate MOS
Example
2
Alpha Ltd manufactures and sells
three products: Beta, Gamma and Delta. Information is as follows:
|
|
Beta
|
Gamma
|
Delta
|
|
|
$
per Unit
|
$
per Unit
|
$
per Unit
|
|
Selling Price
|
135.00
|
165.00
|
220.00
|
|
Variable Costs
|
73.50
|
58.90
|
146.20
|
The Fixed Cost was $950,000
The products are sold in the ratio
of 3:4:5
Budgeted Sales Revenue is 3,000,000
Required:
Calculate the
MOS in terms of Sales Revenue and also as a % of Sales
TARGET
PROFIT FOR MULTIPLE PRODUCTS
This is the
number of mixes of products required to be sold to achieve a target profit.
No of Mixes of products = Fixed
Costs + Target Profit
Contribution/Mix
Example
1
An organisation makes and sells 3
products F, G and H. the products are sold in the proportion of F:G:H as 2:1:3
respectively. The organisation’s Fixed Costs are $80,000 per month and details
of the products are as follows:
|
Product
|
Selling
Price
|
Variable
Cost
|
|
|
$
per unit
|
$
per unit
|
|
F
|
22
|
16
|
|
G
|
15
|
12
|
|
H
|
19
|
13
|
The organisation wishes to earn a
profit of $52,000 next month.
Required
Calculate the
required sales value of each product in order to achieve target profit.
Solution
The following steps are involved:
1. Calculate Contribution per unit
2. Calculate Contribution per mix
3. Calculate required number of mixes
4. Calculate the required sales in
terms of the number of units of the products and sales revenue of each product
NB: Alternatively, C/S Ratio can be used
to determine the required sales:
The following steps are involved
1. Calculate Revenue per mix
2. Contribution per mix
3. Average C/S Ratio
4. Required total revenue
5. Revenue ratio of mix
6. Required sales
C/S RATIO FOR MULTIPLE PRODUCTS
Average C/S Ratio = Ratios x
Individual C/S Ratios
Total of
Ratios
Example
An organisation sells two products A
and B in the ratio of 2:5. The C/S ratio of A is 10% where as C/S ratio of B is
50%.
Required
Calculate
Average C/S ratio
BREAK EVEN POINT INTERMS OF SALES
REVENUE (alternative
method)
The BEP
interms of Sales Revenue can be calculated as follows
BEP (Revenue) = Fixed
Costs
Average C/S Ratio
Example
AB
Ltd produces and sells two products X and Y. X sells for $7 per unit and have a
Variable cost of $2.94 per unit while Y sells for $15 per unit and has a V.C of
$4.50 per unit. The marketing department has estimated that for every 5 units
of X sold, 1 unit of Y is sold. The Organisation has a Fixed Costs of $36,000.
Required:
Calculate the
Break Even Point in terms of Revenue for AB Ltd
Solution
Steps Involved are as follows:
1. Calculate Revenue per mix (S.P x
Ratio) Totals
2. Calculate Contribution per mix
(Cont/Unit x Ratio)
3. Calculate Average C/S Ratio (Step 2
divided by Step 1)
4. Calculate the Total BEP ( Fixed Cost
divided by Average C/S )
5. Calculate Revenue Ratio of Mix (S.P x Ratio) Don’t use totals
6. Calculate BEP in terms of Revenue
(Step 5 x Ratio Proportions)
MULTI PRODUCT BREAK EVEN CHARTS
These are
charts which indicates approximate profits or losses at different levels of
sales volume within a limited range.
Break even
charts for multiple products can be drawn if a constant product sales mix is
assumed (if there are ratios).
These charts can be plotted when:
1. The products are made in a constant
Mix
2. The products are made in a sequence
Example
1
AB ltd sells three products X, Y and
Z which have a variable unit cost of $3, $4 and $5 respectively. The sales
price of X is $8, Y is $6 and Z is $6. Fixed Costs per annum are $10,000.
Budgeted sales are 2000 units of X, 4000 units of Y and 3000 units of Z.
Required
a) Prepare the Break Even Chart when
1. The products are made in a constant
Mix
2. The products are made in a sequence
b) Prepare the PV Chart in a single
chart when the products are made in a constant mix and also in a sequence
Example
2
A company sells three products X, Y
and Z. Costs and sales data for one period are as follows:
|
|
X
|
Y
|
Z
|
|
Sales Volume
|
2000
units
|
2000
units
|
2000
units
|
|
Selling Price/unit
|
$3
|
$4
|
$2
|
|
Variable Costs/unit
|
$2.25
|
$3.50
|
$1.25
|
Total Fixed Costs $3,250
Required
A.
Prepare
the Break Even Chart when
1. The products are made in a constant
Mix
2. The products are made in a sequence
B.
Prepare
the PV Chart in a single chart when the products are made in a constant mix and
also in a sequence
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