The cost volume profit analysis (CVPA) is also known as breakeven analysis.
CVPA determines the breakeven point for different sales volumes and cost structures.
It can be useful for managers for making shortterm business decisions.
CVPA makes several assumptions; sales price, fixed cost and variable cost per unit are constant in CVPA.
CVPA also manages contribution margin.
The contribution margin is the difference between total sales and total variable costs.
The main motive of the business is to earn the profits.
For profit, the contribution margin must be exceed to total fixed costs.
The contribution margin may also be calculated per unit.
Under the cost volume profit analysis, we will study the following:
Contribution margin
Profit volume ratio, contribution margin ratio
Determination of selling price, selling price per unit
Profit calculation at different bases, realize profit
Determination of profit from sales volume, budgeted sales volume
Determination of profit on selling price
Determination of profit on cost price
Profit on margin of safety
Cost volume ratio
Under the breakeven point analysis, we will study the following:
Breakeven analysis under changed situation
Margin of safety
Required sales for desired profit
Cash breakeven point
Application of marginal costing
Contribution means giving or donation.
Here, contribution means to leave sometime for some purpose.
Margin means profit.
Therefore, contribution margin is the excess amount of sales revenue over variable cost; in other words:
Contribution = Sales – Variable cost
The main objective of contribution margin is to recover first fixed cost then remaining amount transfers toward profit.
If the contribution margin is not sufficient to cover fixed cost, then a loss occurs for the period.
There are two methods to calculate contribution margin.
First is unit basis and second is amount basis.
Formula of contribution margin on unit basis:
Contribution margin per unit = SPPU – VCPU
Contribution margin (in unit) = Sales units x Contribution margin per unit
Contribution margin
For 2,000 units
Particulars 
Per Unit 
Amount 
Sales revenue 
250 
500,000 
Less: Variable cost 
150 
300,000 
Contribution 
100 
200,000 
Less: Fixed cost 

100,000 
Earnings before interest and tax (EBIT) 

100,000 
Less: Interest 

10,000 
Earning before tax (EBT) 

90,000 
Less: Tax @ 25% (90,000 @ 25%) 

22,500 
Earning after tax (EAT) 

$67,500 
Contribution margin (in amount) 
= Sales in amount x P/V ratio 
Or 
= Sales revenue – Variable cost 
Or 
= Fixed cost + Profit – Loss 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1A
The extracted data of XYZ Company is given below:
Selling price per unit $50 
Fixed cost $140,000 
Variable cost per unit $30 
Sales units 15,000 
Required: (1) Contribution margin per unit; (2) Contribution margin in rupees; (3) Profit for the period
[Answer: (1) CMPU = $20; (2) CM = $300,000; (3) $160,000]
SOLUTION:
Contribution margin per unit (CMPU)
= SPPU – VCPU
= 50 – 30
= $20
Contribution margin is rupees
Sales amount = 15,000 units x $50 = 750,000
Variable cost = 15,000 units x 30 = 450,000
P/V Ratio = CMPU ÷ SPPU = 20 ÷ 50 = 0.4 or 40%
Now, Contribution margin
= Sales revenue – Variable cost
= 750,000 – 450,000
= $300,000
Alternative,
Contribution margin (in amount)
= Sales in amount x P/V ratio
= 750,000 x 0.4
= $300,000
Profit for the period
Contribution margin 
= Fixed cost + Profit 
300,000 
= 140,000 + Profit 
Profit 
= $160,000 
Alternative,
Sales 
= Variable cost + Fixed cost + Profit 
750,000 
= 450,000 + 140,000 + Profit 
Profit 
= $160,000 
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(Profit volume ratio, contribution sales ratio, variable profit ratio)
It shows the relationship between contribution margin and sales.
When profit volume increases, the earning capacity of the company also increases.
When profit volume ratio decreases, the earning capacity of the company also decreases.
The percentage of contribution margin on the basis of sales is known as contribution margin ratio.
Contribution margin ratio is also known profit volume ratio (P/V Ratio).
But profit volume ratio (P/V Ratio) is not the ratio of net profit to sales revenue.
P/V ratio for amount and units 
Alternatively, 


= (SSPU – VCPU) ÷ SPPU 

= (Fixed cost + Net profit) ÷ Sales 
Or 
= CMPU ÷ SPPU 
Or 
= Difference in profit ÷ Difference in sales 
Or 
= 1 – (VC ÷ Sales) 




Alternatively, 



= Change in contribution margin ÷ Change in sales revenue 


Or 
= Change in net profit ÷ Change in sales revenue 


Or 
= 1 – Variable cost ratio 
Use of profit volume ratio (P/V Ratio)
Profit volume ratio is used for following reason:
Determination of selling price
Find out profit at budgeted sales volume
Find out profit on sales volume
Find out profit on cost
Cost volume ratio
Break even ratio
Find out margin of safety.
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1B
The following information is given:
Sales $500,000
Variable cost $200,000
Fixed cost $50,000
Required: (1) P/V Ratio; (2) Net profit; (3) Contribution margin if sales is $800,000
[Answer: (1) 0.6 or 60%; (2) $250,000; (3) $480,000]
SOLUTION:
Profit volume ratio (P/V Ratio)
= (Sales – Variable cost) ÷ Sales
= ($500,000 – $200,000) ÷ $500,000
= 0.6 or 60%
Net profit
Sales 
= Variable cost + Fixed cost + Profit 
500,000 
= 200,000 + 50,000 + Profit 
Profit 
= $250,000 
Contribution margin if sales is $800,000
= Sales in amount × P/V ratio
= 800,000 × 0.6
= $480,000
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1C
ABC Company has following information:
Particulars 
Year 2020 
Year 2021 
Sales 
$8,00,000 
$10,00,000 
Profit 
$2,00,000 
$3,00,000 
Fixed cost is $3,00,000 for the year 2020
Required: (a) Profit volume ratio (P/V Ratio); (b) Variable cost for year 2020; (c) Contribution margin for year 2021
[Answer: (a) 0.5 or 50%; (b) $300,000; (c) $500,000;
Or (a) 0.625 or 62.5%; (b) $300,000; (c) $625,000]
SOLUTION:
Profit volume ratio (P/V Ratio)
= Difference in profit ÷ Difference in sales
= ($300,000 – $200,000) ÷ ($1000,000 – $800,000)
= $100,000 ÷ $200,000
= 0.5 or 50%
Alternatively,
Profit volume ratio (P/V Ratio)
= (Fixed cost + Profit) ÷ Sales
= ($300,000 + $200,000) ÷ $800,000
= $500,000 + $800,000
= 0.625 or 62.5%
Variable cost for year 2020
Sales 
= Variable cost + Fixed cost + Profit 
800,000 
= Variable cost + 300,000 + 200,000 
Variable cost 
= $300,000 
Contribution margin (CM) for year 2021
= Sales in amount × P/V ratio
= 10,00,000 × 0.5
= $500,000
Alternatively,
Contribution margin (CM) for year 2021
= Sales in amount × P/V ratio
= $10,00,000 × 62.5%
= $625,000
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Selling price is the most sensitive effect in demand, profit and breakeven point.
A small point change in price may cause great change in the operating result.
All the operating expenses and profit depend on selling price.
Selling price is depended on various factors like requisition, competition and return on investment etc.
The following factors are helpful to determine sales price:
Production volume
Variable cost and fixed cost
Desire profit etc.
Selling price 
= Cost of product + Markup profit 
Selling price per unit (SPPU) 
= Contribution ÷ (P/V ratio × Sales units) 
Or 
= Variable cost per unit ÷ (1 – P/V ratio) 
Where:
Markup price is depended on profit percent on sales or cost
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1D
Following is the extracted data of Shiva Manufacturing Company:
Sales 
$800,000 

VCPU 
$6 
P/V Ratio 
0.6 or 60% 

Profit (desire) 
$60,000 
Required: Selling price per unit
[Answer: SPPU = $15]
SOLUTION:
Selling price per unit (SPPU)
= VCPU ÷ (1 – P/V ratio)
= $6 ÷ (1 – 0.6)
= $6 ÷ 0.4
= $15
Sometimes manufacturing company wants to know the profit in advance.
In other words if the manufacturing company sales goods of certain amount or units, what will be the profit?
There are four methods to find out profit; they are:
Determination of profit from sales volume (budgeted sales volume)
Determination of profit on selling price
Determination of profit on cost price
Determination of profit on margin of safety
P/V Ratio = (Fixed cost + Profit) ÷ Sales 



Above formula can be modified as: 

Profit in rupees 
= (Sales x P/V ratio) – Fixed cost 
Fixed cost 
= (Sales x P/V Ratio) – Profit 
Sales 
= (Fixed cost + Desire profit) ÷ P/V ratio 
Keep in Mind (KIM)
This formula can be used to find out sales, profit, profit volume ratio and fixed cost. 

P/V Ratio = (Fixed cost + Profit) ÷ Sales 



Above formula can be modified as: 

(a) Profit in rupees 
= (Sales x P/V ratio) – Fixed cost 
(b) Fixed cost 
= (Sales x P/V Ratio) – Profit 
(c) Sales 
= (Fixed cost + Desired profit) ÷ P/V ratio 
Profit in rupees can be found out with help of profit volume ratio.
For this purpose, these amounts should be given in the question (predetermined):
Sales amount (units x SPPU)
Variable cost
Fixed cost
Profit 
= (Sales x P/V ratio) – Fixed cost 
Or 
= Sales – Variable cost – Fixed cost 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1E
Following data is given from Ultra Manufacturing Company for one month:
Sales units 20,000
Selling price per unit $20
Variable cost per unit $8
Fixed cost $50,000
Required: (a) P/V Ratio; (b) Profit for the month
[Answer: P/V ratio = 60%; Profit = $190,000]
SOLUTION:
Profit volume ratio (P/V Ratio)
= (SPPU – VCPU) ÷ SPPU
= ($20 – $8) ÷ $20
= $8 ÷ 20
= 0.6 or 60%
Profit for the month
Sales = 20,000 units × $20 = $400,000
VC = 20,000 units × $8 = $160,000
P/V Ratio 
= (Fixed cost + Profit) ÷ Sales 
0.6 
= ($50,000 + Profit) ÷ $400,000 
$400,000 x 0.6 
= $50,000 + Profit 
$240,000 
= $50,000 + Profit 
$240,000 – $50,000 
= Profit 
Profit 
= $190,000 
Alternatives,
Sales 
= Fixed cost + Variable cost + Profit 
400,000 
= 50,000 + 160,000 + Profit 
Profit 
= $190,000 
Or 

Profit (in rupees) 

= (Sales x P/V ratio) – Fixed cost 

= 400,000 x 0.6 – 50,000 

= 240,000 – 50,000 

= $190,000 
Sometime manufacturing company determines profit on selling price.
Profit volume ratio is used for it.
This profit can be calculated from unit basis and cash basis.
Profit (in rupees from units) 
= (Actual sales units – BEP units) × Contribution units 
Profit (in rupees from rupees) 
= (Actual sales – BEP sales) × P/V ratio 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1F
The extracted data are taken from AL Rice Mill for one month:
Sales 20,000 kg
Selling price per kg $30
Variable cost per kg $20
Break even sales 10,000 kg
Required: (1) Actual sales; (2) BEP sales; (3) P/V Ratio; (4) Profit for the month from units and amount; (5) Fixed cost per month
[Answer: (1) $600,000; (2) $300,000;
(3) 1/3 or 0.3333; (4) $100,000; (5) $60,000]
SOLUTION:
Given and working note:
Contribution per unit
= SPPU – VCPU
= 30 – 20
= $10
Actual sales
= Sales units × SPPU
= 20,000 × $30
= $600,000
BEP sales
= BEP sales units × SPPU
= 10,000 × $30
= $300,000
Profit volume ratio (P/V Ratio)
= (S – V) ÷ S
= ($30 – $20) ÷ $30
= $10 ÷ 30
= 1/3 or 0.3333 or 33.33%
Profit for the month
Profit (from units)
= (Actual sales units – BEP sales units) × Contribution units
= (20,000 – 10,000) × $10
= 10,000 × 10
= $100,000
Profit (from amount)
= (Actual sales – BEP sales) x P/V ratio
= ($600,000 – $300,000) x 1/3
= 300,000 x 1/3
= $100,000
Fixed cost
Sales 
= Variable cost + Fixed cost + Profit 
600,000 
= (22,000 kg x $20) + Fixed cost + 100,000 
600,000 
= 440,000 + fixed cost + 100,000 
Fixed cost 
= $60,000 
Most of the companies charge profit on cost.
For this purpose variable cost, variable cost ratio and profit volume ratio are needed.
Fixed cost is ignored under this method while calculating profit.
Variable cost ratio = 1 – P/V ratio
Again,
Profit = (Variable cost x P/V ratio) ÷ Variable cost ratio
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1G
BS Industries (P) Ltd has following information:
Sales 20,000 units
Selling price per unit $40
Variable cost per unit $18
Required: (a) P/V Ratio; (b) Variable cost ratio; (c) Profit per unit
[Answer: (a) 0.55; (b) 0.45; (c) $22]
SOLUTION:
Profit volume ratio (P/V Ratio)
= (S – V) ÷ S
= ($40 – $18) ÷ $40
= $22 ÷ $40
= 0.55 or 55%
Variable cost ratio (V/C ratio)
= 1 – P/V Ratio
= 1 – 0.55
= 0.45 or 45%
Profit per unit
= (Variable cost x P/V ratio) ÷ Variable cost ratio
= ($18 x 0.55) ÷ 0.45
= $22
Sometime, manufacturing company charges profit on margin of safety basis.
In such a condition, profit volume ratio is multiplied to margin of safety.
Profit (on margin of safety) = Margin of safety × P/V ratio
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1H
The extracted data are taken from BD Corporation for one month:
Sales $12,00,000
Variable cost $800,000
Margin of safety $900,000
Required: (1) P/V Ratio; (2) Profit from margin of safety
[Answer: (1) 1/3; $300,000]
SOLUTION:
Profit volume ratio (P/V Ratio)
= (S – V) ÷ S
= ($12,00,000 – $8,00,000) ÷ $12,00,000
= $4,00,000 ÷ $12,00,000
= 1/3 or 0.333
Profit from margin of safety
= Margin of safety × P/V Ratio
= 900,000 × 1/3
= $300,000
All manufacturing company or organizations have to do expenses.
These expenses are related to factory, office, administrative, selling and distribution.
The main purpose of organization is to earn profit.
To earn profit, company does expenses.
There are mainly three types of cost/expenses.
They are variable cost, semivariable cost and fixed cost.
These costs are incurred for sales revenue or service revenue.
Cost volume ratio = 1 − profit volume ratio 
Variable cost ratio = Variable cost ÷ Sales 
Fixed cost ratio = Fixed cost ÷ Sales 
Total cost ratio = Total cost ÷ Sales 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 1I
BD Cottage Industries has following extracted on 31^{st} December 2021:
Variable cost $400,000
Fixed cost $300,000
Sales $10,00,000
Required: (a) Profit volume ratio; (b) Cost volume ratio; (c) Variable cost ratio; (d) Fixed cost ratio; (e) Total cost ratio;
(f) Profit for the period
[Answer: (a) 60%; (b) 40%; (c) 40%; (d) 30%; (e) 70%; (f) $300,000]
SOLUTION:
Profit volume ratio (P/V ratio)
= (Sales – Variable cost) ÷ Sales
= ($10,00,000 – $4,00,000) ÷ $10,00,000
= $6,00,000 ÷ $10,00,000
= 0.6 or 60%
Cost volume ratio (C/V ratio)
= 1 – P/V ratio
= 1 – 0.6
= 0.4 or 40%
Variable cost ratio (V/C ratio)
= Variable cost ÷ Sales
= $4,00,000) ÷ $10,00,000
= 0.4 or 40%
Fixed cost ratio (F/C ratio)
= Fixed cost ÷ Sales
= $3,00,000 ÷ $10,00,000
= 0.3 or 30%
Total cost ratio (T/C ratio)
= Total cost ÷ Sales
= $7,00,000 ÷ $10,00,000
= 0.7 or 70%
Profit for the year
Sales 
= Variable cost + Fixed cost + Profit 
10,00,000 
= 400,000 + 300,000 + Profit 
Profit 
= $300,000 
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