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CVP or Breakeven Analysis

» CVP analysis: definition, advantages and disadvantages
Page: 2 - 3
» Contribution, Contribution ratio and Variable cost ratio
Page: 3 - 6
» Expected sales quantity and Expected sales amount
Page: 7 - 12
» Breakeven Point
Page: 12 - 16
» Margin of Safety
Page: 16 - 18
» Limiting factor analysis
Page: 19 - 39
» Make or buy decision
Page: 40 - 43

In this paper we shall discuss about Breakeven or Cost-Volume-Profit (CVP) Analysis
...

CVP analysis (cost-volume-profit) or breakeven analysis refers to determining interrelationships
between cost, quantity and profit at different activity levels
...

Advantages / benefits / importance of CVP or breakeven analysis:
1
...
e
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2
...

3
...

4
...

5
...

6
...
e
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7
...

8
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e
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This enables the company to decide price cuts, sales promotion etc
...
CVP analysis is used to assess if costs are too high for the business to be successful
...
CVP analysis is used to decide if certain product is worth launching in the market or not
...
CVP analysis requires to classify all costs between fixed cost and variable cost
...

2
...
But selling
price may decrease in case of a large sales volume (i
...
trade discount)
...
Variable cost per unit is assumed here to remain the same at any level of output
...

4
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But in practice fixed cost
increases beyond the relevant range
...
CVP analysis ignores variation in machine productivity and labor efficiency
...
CVP analysis ignores any uncertainty in estimating selling price, sales volume, variable cost
and fixed cost etc
...
CVP analysis is applicable only to a single product or a single product mix
...
CVP analysis often assumes that all the produced quantity can be sold in the market
...
As any other management accounting tool, CVP analysis ignores sunk costs
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CVP analysis is absolutely a quantitative technique and ignores any qualitative consideration
...
This is a common word in our daily
life, although the sense it makes in Management Accounting is a bit different
...

Contribution in $

= Total sales – Total variable cost

= Fixed cost + Profit

= (Selling price per unit – Variable cost per unit) × Number of units sold
= Contribution per unit × Number of units sold
If in your exam you are asked to write the definition, you must put the formula also, without saying
...


Page 3 of 43

Contribution per unit = Selling price per unit – Variable cost per unit

Contribution ratio =

Variable cost ratio =

Contribution per unit
Selling price per unit
Variable cost per unit
Selling price per unit

× 100 =

× 100 =

=

Contribution in $
Number of units sold

Contribution in $
× 100 = 100% – Variable cost ratio
Total sales
Total variable cost
Total sales

× 100 = 100% – Contribution ratio

Variable cost ratio + Variable profit ratio = 100%
All the formulas are the different forms of the same thing and are corollary to each other, so perhaps
not difficult to remember
...

Contribution ratio is also known as profit-volume (P/V) ratio, variable profit ratio, marginal income
ratio etc
...

Illustration # 1: Sales is 10,000 units @ $10
...
Find out: (i) Contribution
margin; (ii) Contribution per unit; (iii) Variable profit ratio; and (iv) Variable cost ratio
...
Fixed cost is $50,000
...
Find out
marginal income ratio
...
For example: we
have seen 3 formulas for marginal income or contribution ratio
...
We are left only with formula # 2
...
We need to calculate contribution in $
...
We cannot use formulas # 1, 3 and
4 in this case due to lack of required information
...

For using formula # 2, fixed cost is given in question
...


Page 5 of 43

Illustration # 3: Sales is $100,000
...
Profit is 20% of sales volume
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Solution: Profit = 20% of sales volume = $100,000 = 20% = $20,000
Contribution ratio = Fixed cost + Profit = $50,000 + $20,000 = $70,000
Variable cost ratio = 100% – Contribution ratio = 100% – 70% = 30%
Illustration # 4: The product of XYZ Ltd
...
All of the costs will remain the same
except for material which will increase by 10% and labor by 15%
...
What will be the contribution margin for next year?
Solution: Variable cost structure:
Direct materials [$400 per unit × (100% + 10%)]

= $440 per unit

Direct labor = $30 per unit × (100% + 15%)

= $345 per unit

Variable manufacturing overhead

= $240 per unit

Shipping and handling

= $60 per unit

Total variable cost

= $1,085 per unit

⸫ Contribution margin = (Selling price per unit – Variable cost per unit) × Number of units sold
= ($3,200 per unit – $1085 per unit) × 10,000 units

= $21,150,000

Now we recommend you yourself to solve this math with other formulas of contribution margin
...

Suppose the selling price and the target profit margin are given for a particular product, and you
need to find out the sales volume required
...
Variable cost is $3 per unit and fixed
cost is $30,000
...
Find out the
required sales in units and in $
...
A bit difficult, right?

Illustration # 6: W Limited sells one product for which data is given below:
Selling price

$10 per unit

Variable cost

$6 per unit

Fixed cost

$2 per unit

The fixed costs are based on a budgeted level of activity of 5,000 units for the period
...

Solution: Units to be sold =

Fixed cost + Expected profit
Contribution per unit

Page 7 of 43

=

(5,000 units × $2) + $6,000
$10 − $6

= 4,000 units

Illustration # 7: AB Ltd
...
The company wishes to make
a profit of $16,000 per annum
...

Solution:

Expected sales in units = 14,000 units;

Expected sales in $ = $420,000
...
wishes to sell 14,000 units of a product
...
What is the required selling price per unit?
Discussion: This math can be solved in a number of ways, we are showing here only one way
...
Next we can apply the formula of contribution per unit and find
out selling price per unit
...
Provided below cost structure, find out additional sales quantity required for maintaining
current profit level if selling price is reduced by 10%:
Prime costs

$200,000

Variable overhead

$40,000

Fixed overhead

$100,000

Page 8 of 43

Discussion: You are asked to maintain current profit level
...


Revised selling price = $10 × (100% – 10%) = $9
...
Have we seen any formula for doing so? No
...
Hence what we can do is to calculate expected
sales first
...

Now, for calculating expected sales quantity, fixed cost has been given in the question
...
What about contribution
per unit? We have to calculate variable cost per unit from the information given in the question
...


Is prime cost variable? Of course
...
Both
of these are elements of variable cost
...

For calculating variable cost, you have to use sales quantity instead of production quantity
...

Contribution per unit = Selling price per unit – Variable cost per unit = $9 – $6 = $3
...
The question says
that only selling price will be reduced – nothing is mentioned about variable and fixed costs
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By how much sales volume to change as compared with the original
budgeted level, in order to achieve the original budgeted profit for the period?
Solution: Original budgeted profit = Sales – Total cost = ($10 as selling price per unit - $6 as
variable cost per unit - $2 as fixed cost per unit) × 5,000 units as budgeted activity level = $10,000
Revised selling price per unit = $10 × (100% + 20%) = $12
Revised variable cost per unit = $6 × (100% + 12%) = $6
...
72 = $5
...
28

= 3,788 units

Change in budgeted sales quantity = 5,000 units – 3,788 units = 1,212 units decrease
% of decrease = 1,212 units ÷ 5,000 units × 100 = 24
...
In some cases budgeted sales quantity, actual sales quantity, actual
production quantity etc
...
Following math will clarify your concept in this regard
...
4
$3
...
2) + $12,000

Page 10 of 43

$10 – $4
...
bakes and sells a single type of cake
...
15 per cake and the current sales price is $0
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Fixed costs are $2,600 per month,
and annual profit for the company at current sales volume is $36,000
...
The sales manager wants to raise the sales price by $0
...
Ascertain the fall in monthly sales
volume allowable before affecting current profitability, if the sales manager sticks to his decision
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25 – $0
...
25 + $0
...
15

= 40,000 units

Fall in monthly sales volume allowable = 56,000 units – 40,000 units = 16,000 units
Illustration # 13: AB Ltd
...
Fixed costs are $40,000 per annum, the sales price is $18 per
unit, and the current volume of output and sales is 6,000 units
...
Annual hire costs would be $10,000 and it is expected
that the variable cost of production would fall to $6 per unit
...

(ii) Calculate the annual profit with the machine if output and sales remain at 6,000 units per annum
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Page 11 of 43

(i) Expected sales quantity =

(ii) Sales qty =

Fixed cost + Expected profit ($40,000 + $10,000) + $8,000
=
= 5,800 units
Contribution per unit
$18 − ($6 + $2)

Fixed cost + Profit
Contribution per unit

 Profit = (Sales qty × Contribution per unit) – Fixed cost

Alternatively: Annual profit = Sales – Total cost = [6,000 units as sales volume × ($18 as selling
price per unit – $6 as variable production cost per unit – $2 as variable selling cost per unit)] –
($40,000 as existing fixed cost + $10,000 as machine hire cost)

= $10,000

Illustration # 14: A company is considering launching a new product line
...
Variable cost related to production may
amount in total to $3 per unit
...
The company wants
to make a profit of $30,000 in the first year
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Solution: Units to be sold =

 Contribution per unit =

Fixed cost + Expected profit
Contribution per unit

Fixed cost + Expected profit
Units to be sold

=

$50,000 + $30,000
10,000 units

= $8

Contribution per unit = Selling price per unit – Variable cost per unit
 Selling price per unit = Contribution per unit + Variable cost per unit = $8 + $3 = $11
֍֍֍

֍֍֍

֍֍֍

Now let us move to the next point of discussion: Breakeven point
...
e
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Breakeven sales in $ =

Fixed cost

= Breakeven sales in units × Selling price per unit
Contribution ratio
Fixed cost
Breakeven sales in units =
= Breakeven sales in $ ÷ Selling price per unit
Contribution per unit
Breakeven in percentage =

Breakeven sales quantity
Sales quantity

× 100 =

Breakeven sales revenue
Sales revenue

× 100

You see breakeven sales = expected sales when profit = 0
...


Page 12 of 43

If in your exam you are asked to write the definition, you must put the formula also, without saying
...

Illustration # 15: Expected sales is 10,000 units @ $8
...
Fixed cost is
$21,000
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Solution:

Breakeven sales in units = 7,000 units;

Breakeven sales in $ = $56,000
...
e
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Illustration # 16: Variable cost ratio is 30%
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Find out breakeven point
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How many units
must be sold for making a contribution of $50,000 towards fixed costs?
Discussion: You have to make a contribution of $50,000 towards fixed costs i
...
contribution =
fixed costs = $50,000
...
So you understand
that the number of units must be sold for contribution = fixed cost means breakeven sales in units
...
We need contribution
per unit, which we can calculate easily from the formula of contribution ratio
...
If
fixed cost is $63,000 per annum, calculate the selling price per unit if the company wishes to
breakeven with a sales volume of 12,000 units
...
Let us use its formula and see what happens
...
25
Contribution per unit = Selling price per unit – Variable cost per unit
 Selling price per unit = Contribution per unit + Variable cost per unit = $5
...
25
Page 13 of 43

Illustration # 19: Selling price is $10 per unit and variable cost is $3 per unit
...

Find out the minimum production volume required for avoiding any loss and explain its implication
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This means the company makes no profit
no loss (i
...
merely recovers its expenses) when it produces and sells 5,000 units during a period
...

What is the minimum selling price for avoiding / before incurring any loss?
Answer:

Contribution per unit is $7
...


Illustration # 21: A company is considering launching a new product
...
Annual demand may
be constrained to 4,000 units
...

 Profit = Sales – Total cost

Answer: Sales = Total cost + Profit

 Profit = (4,000 units × $10) – (4,000 units × $3) – $35,000 = $7,000 loss
So the company should not introduce the product
...
Since annual demand is lower than the periodic
breakeven sales quantity, so the company should not introduce the product
...
Historically, the firm has averaged three
bats sold for each glove sold
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Fixed costs
are $170,000 per year
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Tax rate is 20%
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Some information are given for the two
products separately
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e
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So
you understand that it is not possible to calculate breakeven sales for each product separately
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Page 14 of 43

The question is: what is the combination of a set? The question mentions: Historically, the firm
has averaged three bats sold for each glove sold
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We have to convert all information for each set
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Requirement - 2: Expected sales quantity = (Fixed cost + Expected profit) ÷ Contribution per set
= ($170,000 as fixed cost + $85,000 as expected profit) ÷ $17 as contribution per set = 15,000 sets
Number of bats to sold = 15,000 sets × 3 bats per set = 45,000 bats
Number of gloves to be sold = 15,000 sets × 1 glove per set = 15,000 gloves
Expected sales amount = [(3 bats per set × $10 as selling price per bat) + (1 glove per set × $15
per glove)] × 15,000 sets as breakeven sales quantity = $675,000
So we see expected profit is pre-tax profit
...
Hence first
we have to turn the after-tax profit into pre-tax profit
...

Requirement - 3: After-tax profit = Pre-tax profit × (100% – Tax rate)
Pre-tax profit = After-tax profit ÷ (100% – Tax rate) = $85,000 ÷ (100% – 20%) = $106,250
Expected sales quantity = (Fixed cost + Expected profit) ÷ Contribution per set
= ($170,000 as fixed cost + $106,250 as expected profit) ÷ $17 as contribution per set = 16,250 sets
Number of bats to sold = 16,250 sets × 3 bats per set = 48,750 bats
Number of gloves to be sold = 16,250 sets × 1 glove per set = 16,250 gloves
Expected sales amount = [(3 bats per set × $10 as selling price per bat) + (1 glove per set × $15
per glove)] × 16,250 sets as breakeven sales quantity = $731,250

Page 15 of 43

Now let us see some variation in above illustration
...

Solution: Fixed cost apportioned to bat = $170,000 × 60% = $102,000
Fixed cost apportioned to gloves = $170,000 × 40% = $68,000
Contribution per bat = $10 as selling price per bat – $6 as variable cost per bat = $4
Contribution per glove = $15 as selling price per glove – $10 as variable cost per glove = $5
Number of bats to be sold for breakeven = $102,000 as fixed cost apportioned to bat ÷ $4 as
contribution per bat = 25,500 bats
Number of gloves to be sold for breakeven = $68,000 as fixed cost apportioned to gloves ÷ $5 as
contribution per glove = 13,600 gloves
Breakeven sales revenue = (25,500 bats × $10) + (13,600 gloves × $15) = $459,000
Since fixed cost was separable for bats and gloves, so we did not bother about comprising any set
...
Below breakeven means you are at loss
...
The quantity or revenue above BEP is known as margin of safety
...

Margin of safety in units = Sales in units – Breakeven sales in units
Margin of safety in $ = Sales revenue – Breakeven sales revenue
Margin of safety in $ = Margin of safety in units × Selling price per unit
Margin of safety in % =

Margin of safety quantity
Sales quantity

× 100 =

Margin of safety revenue
Sales revenue

× 100

If in your exam you are asked to write the definition, you must put the formula also, without saying
...


Page 16 of 43

Illustration # 24: In Illustration # 15, determine margin of safety and explain its implication
...


The implication is that actual sales can fall short of expected sales by maximum 3,000 units or
$30,000 in order to reach breakeven point and thus before incurring any loss
...
sells a product which has a variable cost of $30 and selling price of $40
per unit
...
Calculate BEP and margin of safety
...


Illustration # 26: In Illustration # 6, find out margin of safety if fixed cost is 20% higher than budgeted
...
g
...
g
...
Variable cost is $3 per unit
...
Only due to the missing of fixed cost, this entire attempt is abandoned
...
You understand that quantity
to be sold above breakeven point means margin of safety quantity
...

Profit = Margin of safety in $ × Contribution ratio = Margin of safety in units × Contribution per unit
 Margin of safety in units = Quantity to be sold above BEP = Profit ÷ Contribution per unit
= $21,000 as expected profit ÷ ($10 as selling price per unit – $3 as variable cost per unit) = 3,000 units
Page 17 of 43

Illustration # 28: A company sells a product, of which variable cost ratio is 30%
...

You also understand that margin of safety the higher the better, because more profit is earned
...
Production department
estimates that variable cost will be $3 per unit and fixed cost will be $50,400 for a maximum
volume of 10,000 units
...

Answer: From below calculations, it is clear that the product should be launched @ $12 per unit
...
Ultimately you have to calculate profit for making the correct decision
...
Now let us move towards more critical level of managerial decision making
...
Such as: shortage of materials or labor supply,
shortage of machine hours, shortage of demand etc
...

You understand that limiting factor analysis then refers to the determination of maximum profit
potential under the existence of one or more limiting factors
...
Here several products are compared on the basis of their contribution per
unit of limiting factor i
...
contribution margin is divided by the available quantity of the limiting
factor or resource
...

Before entering into mathematical illustrations, let us demonstrate the recommended steps for
limiting factor analysis
...

Step # 2: Calculate contribution per unit and contribution per unit of limiting factor for each product
...

Step # 4: Determine the optimal product mix or profit maximizing production plan or maximum
number of units of each product to be produced according to the ranking in step # 3, after allowing
for any minimum production requirement
...

 Since the steps are sequential, you cannot overlap between them
...
On the other hand, for calculating maximum profit, contribution per unit is used
...


Page 19 of 43

 When demand is unlimited for one or more products, step # 1 becomes undoable
...
Remember, this will get priority over optimal product mix
...

 If the question does not require you to calculate maximum amount of profit or to prepare any
income statement, then step # 5 is to be skipped and fixed cost information is of no use
...
You understand that still you have to conduct limiting factor analysis,
because otherwise maximum profit cannot be calculated
...
Relevant information is as follows:
X

Y

Raw materials required per unit

2 kg

3 kg

Labor hour required per unit

7 hours

8 hours

Selling price per unit

$75

$85

Periodic demand

10,000 pcs
...


Raw materials price is $5 per kg
...
In a certain period, 50,000
kg of raw materials and 200,000 labor hours are available
...
Determine the appropriate product mix as
well as the maximum amount of profit for the period
...
That means,
either raw material or labor hour or both are the limiting factors
...

Solution: Step # 1 - Determining the limiting factor:
Raw materials requirement during the period = (2 kg per pcs
...
as periodic
demand of X) + (3 kg per pcs
...
as periodic demand of Y) = 65,000 kg
Raw materials availability during the period = 50,000 kg
Labor hour requirement during the period = (7 hours per pcs
...
as periodic
demand of X) + (8 hours per pcs
...
as periodic demand of Y) = 190,000 hours
Labor hour availability during the period = 200,000 hours
So we find that raw materials is a limiting factor, but labor hour is not a limiting factor
...

X

Y

Contribution per pcs
...


2 kg

3 kg

= Contribution per kg of raw material

$4
...
as possible
...
)

= Remaining quantity of raw materials

= 30,000 kg

(÷) Raw materials consumption per pcs
...
(full quantity) and Y = 10,000 pcs
...

Step # 5 - Calculating maximum amount of profit:
Contribution per pcs
...
of Y = $6

Total contribution from the optimal product mix = (10,000 pcs × $9) + (10,000 pcs
...
Also consider selling price $80 per unit of X and $100 per unit of Y
...
and Y = 15,000 pcs
...


So you see, product that gives higher contribution per unit (i
...
product X) may or may not give
higher contribution per unit of the limiting factor
...
The common raw
material is available up to 6,000 kg during a period
...
5

2
...
6

Fixed cost per unit ($)

1
...
2

2
...
3

0
...
8

Find out the profit maximizing production mix as well as the maximum amount of profit
...
3 kg per unit of X × 4,000 units as maximum
demand of X) + (0
...
8 kg per unit
of Z × 5,000 units as maximum demand of Z)

= 6,400 kg

Raw materials availability during the period = 6,000 kg
So we find that raw materials is the limiting factor
...
3
kg as raw materials required per unit of X × $1
...
55
Contribution per unit of Y = Selling price – Variable cost = $4 as selling price per unit of Y – [(0
...
4 as raw materials price per kg for Y) = $3
...
8
kg as raw materials required per unit of Z × $2
...
92
Page 22 of 43

Step # 3 - Ranking products on the basis of contribution per unit of the limiting factor:
X

Y

Z

Contribution per unit

$2
...
04

$2
...
3 kg

0
...
8 kg

= Contribution per kg of raw material

$8
...
6

$3
...

Raw materials available

= 6,000 kg

(–) Raw materials consumption for producing full quantity of X

= 1,200 kg (4,000 units × 0
...
4 kg)

= Remaining quantity of raw materials

= 3,600 kg

(÷) Raw materials consumption per unit of Z

= 0
...

Step # 5 - Calculating maximum amount of profit:
Total contribution from the optimal production mix = (4,000 units of X × $2
...
04 as contribution per unit of Y) + (4,500 units of Z × $2
...
8 as fixed cost per unit of X) + (3,000
units as maximum demand of Y × $2
...
4 as fixed cost per unit of Z)

= $25,800

We know: Contribution = Fixed cost + Profit
 Profit = Contribution – Fixed cost

= $32,460 – $25,800 = $6,660

Note carefully: fixed cost is calculated on the basis of maximum demand, not optimal product mix
...
:
Particulars

X

Y

Maximum demand (units)

3,000

5,000

Selling price per unit ($)

26

17

Raw materials cost per unit ($0
...
Labor hour is available up to 8,000 hours and
raw materials is available up to 50,000 kg
...

Solution: Step # 1 - Determining the limiting factor:
Particulars

X

Y

Raw materials cost per unit

$1

$3

(÷) Raw materials price per kg

$0
...
5

= Raw materials requirement per unit

2 kg

6 kg

Raw materials requirement during the period = (2 kg per unit of X × 3,000 units as maximum
demand of X) + (6 kg per unit of Y × 5,000 units as maximum demand of Y)

= 36,000 kg

Raw materials availability during the period = 50,000 kg
So we find that raw materials is not a limiting factor
...

Page 24 of 43

Step # 2 - Calculating contribution per unit for each product:
Contribution per unit of X = Selling price – Variable cost = $26 as selling price per unit – ($1 as
raw materials cost per unit + $18 as labor cost per unit + $1 as overhead cost per unit)

= $6

Contribution per unit of Y = Selling price – Variable cost = $17 as selling price per unit – ($3 as
raw materials cost per unit + $9 as labor cost per unit + $1 as overhead cost per unit)

= $4

Step # 3 - Ranking products on the basis of contribution per unit of the limiting factor:
Remember that labor hour is the limiting factor
...

Labor hours available

= 8,000 hours

(–) Labor hour requirement for producing full quantity of Y

= 5,000 hours (1 hour × 5,000 units)

= Remaining quantity of labor hours

= 3,000 hours

(÷) Labor hour requirement per unit of X

= 2 hours

= Quantity of X can be produced

= 1,500 units

⸫ Optimal production mix: X = 1,500 units (partial quantity) and Y = 5,000 units (full quantity)
...

And if there is more than one limiting factor, then the optimal production mix is determined by
using linear equation
...

We told earlier that, if the question mentions a minimum production requirement for one or more
products, this will get priority over the optimal product mix
...

Illustration # 34: Redo Illustration # 33, assuming that 500 units of each of products X and Y are to
be produced under a contracted supply
...

Solution: Steps # 1, 2 and 3 - same as above
Maximum demand includes the minimum production requirement:
Step # 4 - Determining the optimal product mix:
First we have to fulfill the minimum production requirement under the contracted supply
...

Labor hours available

= 8,000 hours

(–) Labor hour required for minimum production quantity:
X: (500 units × 2 hours per unit)

= 1,000 hours

Y: (500 units × 1 hour per unit)

= 500 hours

= Remaining quantity of labor hours

= 6,500 hours

(–) Labor hour required for producing remaining quantity of Y

= 4,500 hours (1 hour × 4,500 units)

= Remaining quantity of labor hours

= 2,000 hours

(÷) Labor hour requirement per unit of X

= 2 hours

= Quantity of X can be produced

= 1,000 units

⸫ Optimal production mix: X = 1,500 units (partial quantity) and Y = 5,000 units (full quantity)
...
Next,
with the remaining quantity of labor hours, we should produce Y before producing X
...


So we arrive at the following conclusion:
No minimum quantity given

Minimum quantity given,

Minimum quantity given, but

and included into demand

not included into demand

Optimal production mix is same under these two situations

Optimal production mix changes

Remember that optimal production mix is same under first two situations as long as:
Optimal production quantity ≥ Minimum production requirement
...

Whether minimum production requirement is included or not into maximum demand – if this is
not mentioned in the question, you should consider it as included
...
makes two products: A and B
...
Variable cost per unit is $35 for A and $40 for B
...
In the forthcoming period the availability of raw materials is limited to
2,000 kg
...
is contracted to supply 500 units of A
...

Demand for A is unlimited
...


We said earlier that when demand is mentioned as unlimited for one or more products, step # 1
becomes undoable because we cannot calculate the required quantity of the constrained resource
...
So we cannot calculate the required quantity
of raw materials
...


Illustration # 36: ABC Ltd
...

A

B

C

Maximum demand

100 units

100 units

100 units

Selling price

$15

$20

$10

Variable costs

$9

$12

$7

Required time in heat treat per unit

1
...
5 hours

1 hour

The heat treating equipment has 400 hours available during the period
...

(ii) A = 100 units (full quantity); B = 60 units (partial quantity); C = 100 units (full quantity)
...
And sales demand is limited to 15,000 units for each product
...


Illustration # 38: You are provided with following information about three products of ABC Ltd
...
has formulated the following production schedule, based on contribution per unit:

Contribution per unit
Production priority
Expected production

A
$40
3rd
Nil

B
$50
2nd
500 units

C
$60
1st
Full quantity

Assess if the above formulation is maximizing profit or not
...
The profit maximizing formulation is:

Contribution per kg of raw materials
Production priority
Expected production

A
$8
1st
Full quantity

Page 29 of 43

B
$6
...
makes three products: A, B and C by using the same machine
...
You are required to calculate:
(i) The shortfall in machine hours and production; (ii) Maximum profit earnable during the period
...
75

$2
...
20

Ranking

1st

2nd

3rd

Page 30 of 43

Total machine hours available

= 2,96,500 hours

(–) Machine hours used for producing full quantity of A

= 1,00,000 hours (5,000 units × 20 hours)

= Remaining machine hours

= 1,96,500 hours

(–) Machine hours used for producing full quantity of B

= 1,65,000 hours (7,500 units × 22 hours)

= Remaining machine hours

= 31,500 hours

(÷) Machine hour consumption per unit of C

= 25 hours

= Quantity of C can be produced

= 1,260 units

⸫ The shortfall in production for each product is as follows:
A and B = No shortfall since full quantity will be produced;
C = 2,500 units – 1,260 units = 1,240 units shortfall
Calculating the maximum profit earnable during the period:
Contribution margin from the optimal product mix = (5,000 units of A + 7,500 units of B + 1,260
units of C) × $55 as contribution per unit of all products

= $756,800

Fixed cost = $200,000 for A + $315,000 for B + $130,000 for C

= $645,000

Maximum profit

= $111,800

Illustration # 40: Survey Ltd
...
The company
manufactures and sells three products: A, B and C
...
The company
has 228,000 labor hours available for the budgeting period
...
A recent market survey
reveals following demand:

A = 24,000 units;

B = 15,000 units;

C = 60,000 units
...
After thorough discussion the board decided that a minimum of 10,000 units of each
product should be produced
...

Prepare a statement which shows the maximum profit which could be achieved in the year
...

֍֍֍

We have discovered the mechanism of maximizing profit under constrained situations
...

This may be possible sometimes, but often at higher cost
...
For example: when raw
material is not available locally for meeting entire demand, we may buy additional raw materials
from abroad
...
In the
same way, we may increase labor hour availability up to a certain limit by deploying the workers
for extra hours
...
Thus the available quantity of a limiting factor may be increased to a certain extent at a higher
cost
...
The general formula is:
Extra price allowable for each additional unit of the restricted resource = Contribution per unit of
the finished product ÷ Quantity of the restricted resource required per unit of the finished product

Page 32 of 43

In illustration # 40, we have curtailed the production of A and B due to the shortage of labor hours
...

Extra labor hour required for producing full quantity of A = 2,000 units as curtail in the production
of A × 4 labor hours required per unit of A = 8,000 hours
Extra labor hour required for producing full quantity of B = 5,000 units as curtail in the production
of B × 8 labor hours required per unit of B = 40,000 hours
The conclusions are as follows:
 We need minimum 4 additional labor hours for increasing production of A and only in that
case, extra hourly rate will be worth paying
...
For <4 additional labor hours available, we should
not pay anything (not even the regular rate of $6, because no extra unit of A can be produced)
...

This is because 8,000 additional labor hours are required for producing full quantity of A and 8
additional labor hours are required for producing any extra unit of B
...

Keeping these two points in mind, we will find out the extra hourly rate payable
...
Then:
Maximum profit = (22,001 units of A × $40 as contribution margin per unit of A) + (10,000 units
of B × $60 as contribution margin per unit of B) + (60,000 units of C × $12 as contribution margin
per unit of C) - $1,300,000 as fixed cost

= $900,040
Page 33 of 43

Increase in maximum profit = $900,040 – $900,000 = $40 = Contribution margin per unit of A
Highest hourly premium (i
...
extra cost) allowable per additional labor hour = Contribution per
unit of the finished product ÷ Quantity of the restricted resource required per unit of the finished
product = $40 as contribution per unit of A ÷ 4 labor hours required per unit of A = $10
Highest hourly rate allowable for extra labor hours = $6 as regular rate + $10 as premium = $16
That means, for producing the 22001st unit of A, we are ready to pay maximum @ $16 per labor
hour, before incurring any loss
...

Please note, for producing the Optimal production quantity (i
...
A = 22,000 units, B = 10,000 units
and C = 60,000 units), labor hour rate is $6
...
In
other words, labor hour rate is $6 for up to 228,000 hours and $16 maximum for next 8,000 hours
...
What about if more than 236,000 labor hours are available?
Definitely we will increase the production of B beyond the minimum quantity
...
If, say 236,006 labor hours are available,
we cannot increase the production of B
...
e
...
50
Highest hourly rate allowable for extra labor hours = $6 as regular rate + $7
...
50
So labor hour rate is $6 for up to 228,000 hours and $16 maximum for next 8,000 hours and $13
...
After that, entire demand is fulfilled
...


Page 34 of 43

Illustration # 41: In Illustration # 40, assume that additional 10,000 labor hours may be available
by working overtime
...
5 times the normal pay rate
...

Solution: Step # 1 - Calculating the optimal production mix:
Contribution per unit of A = $40

Labor hour requirement per unit of A = $24 ÷ $6 = 4 hours

Highest hourly premium allowable for each extra labor hour = $40 ÷ 4 hours = $10
Highest hourly rate allowable for each extra labor hour = $6 as regular rate + $10 as premium = $16
Hourly rate actually payable for each extra labor hour = $6 × 2
...
should increase production of A
...
So we can produce the full quantity of A
...
can use these hours for producing B, if it is worth paying the extra hourly rate
...
50
Highest hourly rate allowable for each extra labor hour = $6 as regular rate + $7
...
50
Highest hourly rate actually payable for each extra labor hour = $6 × 2
...
should not increase production of B, and only 8,000 extra labor hours should be used
...


Step # 2 - Calculating the maximum profit:
Maximum profit under original situation

=

$900,000

(+)

Contribution from additional quantity of A (2,000 units × $40)

=

$80,000

(–)

Overtime premium [8,000 hours × ($15 – $6)]

=

($72,000)

=

Maximum profit under original situation

=

$908,000

Illustration # 42: In Illustration # 40, assume that additional labor hours are available as follows:
Additional labor hour

Hourly premium

1 hour - 5,000 hours

$5

5,001 hours - 10,000 hours

$6

10,001 hours - 12,000 hours

$7

12,001 hours - 15,000 hours

$8

Find out the optimal production mix and the maximum profit under the changed situation
...
can produce full quantity of A and some additional quantity of B, if the increased
production is worth paying the hourly premium
...
50

Page 36 of 43

Actual hourly premium for each extra labor hour:
1 hour - 5,000 hours

= $5

5,001 hours - 10,000 hours

= $6

10,001 hours - 12,000 hours

= $7

12,001 hours - 15,000 hours

= $8

So Survey Ltd
...

And Survey Ltd
...

Additional production quantity of B = 4,000 extra labor hours ÷ 8 hour per unit = 500 units
Optimal production mix:

A = 24,000 units;

B = 10,500 units;

C = 60,000 units
...
Additional 40,000 labor hours
may be available for an hourly premium of $8
...
can accomplish production as follows:
A = 15,000 units (partial quantity); B = 10,000 units (minimum quantity); C = 60,000 units (full quantity)
...

Extra labor hour required for producing full quantity of A = (24,000 units as maximum demand –
15,000 units as optimized production quantity) × 4 labor hours required per unit = 36,000 hours
Extra labor hour required for producing full quantity of B = (15,000 units as maximum demand –
10,000 units as minimum production quantity) × 8 labor hours required per unit = 40,000 hours
Total extra labor hours required = 76,000 hours

Extra labor hours available = 40,000 hours

So Survey Ltd
...

In case of A, highest hourly premium allowable for each extra labor hour = $10
In case of B, highest hourly premium allowable for each extra labor hour = $7
...
should use 36,000 extra labor hours for producing full quantity of A
...

Optimal production mix:

A = 24,000 units;

B = 10,000 units;

C = 60,000 units
...
More 20,000 labor hours may
be available by working for extra hours
...
5 times the normal hourly pay rate
...
can accomplish production as follows:
A = 24,000 units (full quantity); B = 10,500 units (partial quantity); C = 60,000 units (full quantity)
...
should increase the production of B by using 20,000 extra labor hours
...
50
Actual premium for each extra labor hour = $9 [⸪ overtime pay rate = normal hourly pay rate × 2
...
should not produce any additional quantity of B
...


Step # 2 - Calculating the maximum profit:
Contribution margin from the optimal production mix:
A (24,000 units × $40 per unit)

$960,000

B (10,500 units × $60 per unit)

$630,000

C (60,000 units × $12 per unit)

$720,000

Total contribution
(–)

Fixed cost

=

Total profit

$2,310,000
($1,300,000)
$1,010,000

֍֍֍

֍֍֍

Page 39 of 43

֍֍֍

So far we have dealt with all final products
...
g
...
In such a case, the question will mention in-house
production cost of the inputs and purchase price of the same from local or outside source, or
subcontracting price
...

If the question mentions:
Selling price of the final product

→

Purchase price of inputs from local source →

Production preference is defined on the basis of:
Contribution per unit of the constrained resource
Variable cost saved from in-house production
per unit of limiting factor

For your information, this type of analysis is known as make or buy decision
...
5 kg
8,000 units
$8

Assuming 32,000 kg of raw materials are available during the period, determine the optimal plan
...

Solution: Raw materials requirement = (10,000 units of Standard product × 2 kg per unit) + (8,000
units of Premium product × 2
...
So raw materials is the limiting factor
...
5

Premium
($8 – $4) = $4
2
...
6

So production preference is first the Standard product and then the Premium product
...
manufactures and sells a single product: ABC
...
ABC Ltd
...

For the upcoming period, ABC Ltd
...
of each component
...

Variable cost per pcs
...

Purchase price per pcs
...

Determine the optimal manufacturing plan and total variable cost to be incurred for the period
...

B = 4,000 pcs
...

C = 1,000 pcs
...

Illustration # 47: In Illustration # 46, consider following additional information:
Sales projection of the final product ABC is 4,000 units at $250 per pcs
...

Estimate the maximum profit for the upcoming period
...

B = 4,000 pcs
...

C = 1,000 pcs
...
of
ABC × $100 as assembling cost per pcs
...
of ABC × $250 as selling price per pcs
...
manufactures two products – A and B
...
5 hours
$17

Annual demand
Variable cost
Labor hour requirement per unit
Local subcontracting price

B
12,000 units
$15
8 hours
$25

Labor hour availability is limited to 87,500 hours during the period
...
manufacture in order to maximize profit?
Answer:

Optimal manufacturing plan:

A = 9,000 units

Page 41 of 43

B = 7,000 units

Illustration # 49: Following information relates to the six products as manufactured by a company:
A

B

C

D

E

F

Cost of parts

$1,200

$1,375

$1,450

$500

$375

$690

Labor hour requirement

150 hours

100 hours 200 hours 50 hours 150 hours 100 hours

Machine hour requirement

170 hours

30 hours

70 hours

30 hours

70 hours

70 hours

Subcontractor price

$3,950

$2,700

$4,900

$1,800

$2,700

$2,400

Labor is paid $8 per hour
...
Only 400 labor hours are available
...

Solution: Labor hour requirement = 150 hours for A + 100 hours for B + 200 hours for C + 50
hours for D + 150 hours for E + 100 hours for F = 900 hours
Labor hour availability = 400 hours
...


(+)
(+)
=
(–)
=
(÷)
=

Cost of parts
Labor cost @ $8 per hour
Machine overhead @ $1 per hour
Total variable cost
Subcontractor price
Difference
Labor hour requirement
Variable cost saved from in-house
production per labor hour
Ranking

A
$1,200
$1,200
$170
$2,570
$3,950
$1,380
150 hours

B
C
D
E
F
$1,375
$1,450
$500
$375
$690
$800
$1,600
$400
$1,200
$800
$30
$70
$30
$70
$70
$2,205
$3,120
$930
$1,645
$1,560
$2,700
$4,900
$1,800
$2,700
$2,400
$495
$1,780
$870
$1,055
$840
100 hours 200 hours 50 hours 150 hours 100 hours

$9
...
95

$8
...
40

$7
...
40

2nd

6th

3rd

1st

5th

4th

Labor hour available

= 400 hours

(–)

Labor hour requirement for D

= 50 hours

=

Remaining labor hours

= 350 hours

(–)

Labor hour requirement for A

= 150 hours

=

Remaining labor hours

= 200 hours

(–)

Labor hour requirement for C

= 200 hours

=

Remaining labor hours

= Nil

Therefore: A, C and D should be manufactured
...

Page 42 of 43

Illustration # 50: In Illustration # 48, consider following information and calculate maximum profit:
To maintain quality and schedule of production, a supervisor has been appointed at following pay:
5% of the sale value of the goods produced, or $20,000 – whichever is higher
...
Selling price of A and B is $20 and $25 respectively
...
Hence what the company can do is to obtain the highest possible benefit from them
...
Here products are ranked on the basis of either
“contribution per unit of limiting factor” or “variable cost saved from in-house production per unit
of limiting factor” instead of simple “contribution per unit”
...
And products with lower contribution or variable cost saving may be subcontracted outside
...

Part of a work may be subcontracted outside when an organization has shortage of resources for
producing all the products
...


Page 43 of 43



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