Cost–Volume–Profit (CVP) Analysis
Introduction to Cost–Volume–Profit (CVP) Analysis
Definition
Cost–Volume–Profit (CVP) Analysis is a
managerial accounting technique used to study the relationship between costs,
sales volume, and profit. It helps management understand how
changes in cost structure, selling price, and output level affect a firm’s
profit.
In simple words, CVP analysis answers
three basic questions:
·
How much should we sell to avoid loss?
·
How much should we sell to earn a
target profit?
·
How will profit change if costs, price,
or volume change?
2. Objectives of CVP Analysis
The main objectives of CVP analysis
are:
·
To determine the break-even point
(BEP)
·
To calculate profit or loss at
different levels of output
·
To analyze the impact of changes in
cost and selling price
·
To help in planning,
decision-making, and control
·
To estimate margin of safety
3. Key Assumptions of CVP Analysis
CVP analysis is based on the following
assumptions:
1. Selling price per unit remains constant
2. Variable cost per unit remains constant
3. Fixed costs remain constant within the
relevant range
4. Volume of production equals volume of
sales
5. Costs can be clearly divided into fixed
and variable
6. Productivity and efficiency remain
unchanged
4. Important Components of CVP Analysis
4.1 Fixed Cost
Fixed costs are those costs which do
not change with the level of output.
Examples:
·
Rent
·
Salaries
·
Insurance
·
Depreciation
4.2 Variable Cost
Variable costs change directly with
the level of production.
Examples:
·
Raw material
·
Direct labor (piece-rate)
·
Power (variable portion)
4.3 Contribution Margin
Contribution = Sales – Variable Cost
Contribution helps to:
·
Cover fixed costs
·
Generate profit
Contribution per unit = Selling price
per unit – Variable cost per unit
4.4 Contribution Margin Ratio (P/V
Ratio)
P/V Ratio = Contribution ÷ Sales
This ratio shows how much contribution
is earned from each rupee of sales.
5. Break-Even Analysis
5.1 Break-Even Point (BEP)
Break-even point is the level of sales
at which total revenue equals total cost, resulting in no profit and
no loss.
Formulae:
·
BEP (Units) = Fixed Cost ÷ Contribution
per Unit
·
BEP (Sales Value) = Fixed Cost ÷ P/V
Ratio
6. Importance and Need of CVP Analysis
Importance
·
Helps in profit planning
·
Useful for pricing decisions
·
Assists in cost control
·
Helps management evaluate risk and
uncertainty
·
Essential for short-term decision
making
Need
·
Increasing competition in modern
business
·
Rising fixed costs due to automation
·
Requirement of scientific
decision-making
·
Need to evaluate multiple business
options
7. Current / Modern Benefits of CVP
Analysis
In today’s business environment, CVP
analysis is useful for:
·
Startups for break-even planning
·
E-commerce pricing strategies
·
Manufacturing automation decisions
·
Service sector cost control
·
Budgeting and forecasting using
software tools
·
Scenario analysis and sensitivity
analysis
8. Numerical Problems (Solved Examples)
Example 1: Basic Break-Even Point
A company sells a product for Rs. 500
per unit. Variable cost is Rs. 300 per unit. Fixed costs are Rs. 200,000.
Solution: Contribution per unit = 500 – 300 =
Rs. 200
BEP (Units) = 200,000 ÷ 200 = 1,000
units
BEP (Sales) = 1,000 × 500 = Rs.
500,000
Example 2: Profit at a Given Level of
Sales
Using the above data, calculate profit
if sales are 1,500 units.
Contribution = 1,500 × 200 = Rs.
300,000
Profit = Contribution – Fixed Cost
Profit = 300,000 – 200,000 = Rs. 100,000
Example 3: Sales Required to Earn
Target Profit
Fixed cost = Rs. 300,000 Contribution
per unit = Rs. 150 Target profit = Rs. 150,000
Required sales units:
= (Fixed Cost + Target Profit) ÷
Contribution per unit = (300,000 + 150,000) ÷ 150 = 3,000 units
Example 4: Margin of Safety
Actual sales = Rs. 800,000 Break-even
sales = Rs. 500,000
Margin of Safety = Actual Sales – BE
Sales = 800,000 – 500,000 = Rs. 300,000
Margin of Safety Ratio = 300,000 ÷
800,000 = 37.5%
Example 5: Effect of Change in Selling
Price
Original selling price = Rs. 100
Variable cost = Rs. 60 Fixed cost = Rs. 160,000
New selling price = Rs. 120
New contribution = 120 – 60 = Rs. 60
New BEP = 160,000 ÷ 60 = 2,667 units
(approx.)
Example 6: Multiple Product CVP
(Weighted Average)
Product A contribution = Rs. 40 Product
B contribution = Rs. 60 Sales mix = 2 : 1
Weighted contribution = (40×2 + 60×1) ÷
3 = Rs. 46.67
Fixed cost = Rs. 140,000
BEP units = 140,000 ÷ 46.67 = 3,000
units (approx.)
Example 7: Shutdown Decision
Selling price per unit = Rs. 80
Variable cost per unit = Rs. 65 Fixed cost = Rs. 100,000
Contribution per unit = Rs. 15
Since contribution is positive, the
firm should continue operating in the short run.
9. Real-Life Pakistani Business
Applications of CVP Analysis
9.1 Manufacturing / Factory Example
(Pakistani Context)
Example: Garment Factory in Faisalabad
A garment factory produces school
uniforms.
·
Selling price per uniform = Rs. 2,000
·
Variable cost per uniform = Rs. 1,200
·
Monthly fixed costs (rent, salaries,
utilities) = Rs. 800,000
Contribution per unit = 2,000 – 1,200 =
Rs. 800
Break-even units = 800,000 ÷ 800 = 1,000
uniforms per month
Managerial Insight: The factory must sell at least 1,000
uniforms monthly to avoid loss. Any sale above this level generates profit.
This helps the owner plan production before school seasons.
9.2 Educational Institution / School
Example
Example: Private School in Islamabad
A private school charges monthly fee of
Rs. 6,000 per student.
·
Variable cost per student (books,
stationery, activities) = Rs. 2,000
·
Monthly fixed costs (teachers’
salaries, rent, admin) = Rs. 1,200,000
Contribution per student = 6,000 –
2,000 = Rs. 4,000
Break-even students = 1,200,000 ÷ 4,000
= 300 students
Managerial Insight: The school must enroll at least 300
students to cover costs. CVP analysis helps management decide fee structure,
admissions targets, and expansion plans.
9.3 Service Sector Example (Hospital /
Clinic)
Example: Diagnostic Laboratory in
Lahore
A diagnostic lab charges Rs. 3,000 per
test.
·
Variable cost per test = Rs. 1,800
·
Monthly fixed costs (equipment
depreciation, staff salaries) = Rs. 600,000
Contribution per test = 3,000 – 1,800 =
Rs. 1,200
Break-even tests = 600,000 ÷ 1,200 = 500
tests per month
Managerial Insight: The lab must conduct at least 500
tests monthly to break even. CVP helps in pricing tests and planning
promotional discounts.
9.4 Retail / Small Business Example
Example: General Store in Rawalpindi
Average monthly sales = Rs. 1,000,000
·
Variable cost = 75% of sales
·
Fixed costs (shop rent, electricity,
helper salary) = Rs. 150,000
Contribution = 25% of sales Break-even
sales = 150,000 ÷ 0.25 = Rs. 600,000
Managerial Insight: The shopkeeper knows that sales above
Rs. 600,000 will generate profit. This helps in deciding discounts and stocking
levels.
10. Limitations of CVP Analysis
·
Assumptions may not hold true in real
life
·
Difficult to separate fixed and
variable costs accurately
·
Ignores qualitative factors
·
Suitable mainly for short-term analysis
10. Summary
CVP analysis is a powerful managerial
tool that helps management understand the relationship between cost, volume,
and profit. Despite certain limitations, it plays a vital role in planning,
decision-making, and controlling business operations in modern organizations.
4. Numerical Questions and Solutions
Question 1: Break-even Point in Units
**Data:**
Selling Price per Unit = Rs. 50
Variable Cost per Unit = Rs. 30
Fixed Costs = Rs. 40,000
**Formula:**
Break-even Units = Fixed Costs / (Selling Price – Variable Cost)
**Solution:**
40,000 / (50 − 30) = 2,000 units
✅ Answer: 2,000 units
Question 2: Break-even Sales in Rupees
**Data:**
Selling Price per Unit = Rs. 100
Variable Cost per Unit = Rs. 60
Fixed Costs = Rs. 80,000
**Formula:**
Contribution Margin Ratio = (100 − 60) / 100 = 0.4
Break-even Sales = Fixed Costs / Contribution Margin Ratio
**Solution:**
80,000 / 0.4 = Rs. 200,000
✅ Answer: Rs. 200,000
Question 3: Target Profit Sales in Units
**Data:**
Selling Price = Rs. 75
Variable Cost = Rs. 50
Fixed Cost = Rs. 30,000
Target Profit = Rs. 15,000
**Formula:**
Target Sales (Units) = (Fixed Cost + Target Profit) / (Selling Price − Variable
Cost)
**Solution:**
45,000 / 25 = 1,800 units
✅ Answer: 1,800 units
Question 4: Margin of Safety
**Data:**
Actual Sales = Rs. 300,000
Break-even Sales = Rs. 200,000
**Formula:**
Margin of Safety = Actual Sales − Break-even Sales
**Solution:**
300,000 − 200,000 = Rs. 100,000
✅ Answer: Rs. 100,000
Question 5: Profit Calculation
**Data:**
Selling Price = Rs. 60
Variable Cost = Rs. 40
Fixed Cost = Rs. 50,000
Units Sold = 4,000
**Formula:**
Profit = (Selling Price − Variable Cost) × Units Sold − Fixed Costs
**Solution:**
20 × 4,000 − 50,000 = Rs. 30,000
✅ Answer: Rs. 30,000
3. Solved Numerical Questions
✅ Example 1: Break-Even Point
(Units)
A small bakery in Lahore sells cupcakes.
- Selling
Price per unit = Rs. 200
- Variable
Cost per unit = Rs. 120
- Fixed
Costs = Rs. 160,000
Step 1: Calculate Contribution Margin (CM)
CM = 200 – 120 = Rs. 80
Step 2: Break-Even Units
BEP = 160,000 ÷ 80 = 2,000 units
📌 The bakery must sell
2,000 cupcakes to break even.
✅ Example 2: Break-Even in Rupees
Using the same data:
- CM
Ratio = 80 / 200 = 0.40
Break-Even Sales (Rs.)
BEP = 160,000 ÷ 0.40 = Rs. 400,000
📌 The bakery needs Rs.
400,000 in sales to break even.
✅ Example 3: Target Profit
A T-shirt seller in Karachi wants a profit of Rs. 100,000.
- Selling
Price = Rs. 600
- Variable
Cost = Rs. 350
- Fixed
Cost = Rs. 200,000
Step 1: CM per unit
CM = 600 – 350 = Rs. 250
Step 2: Required Units
Required Units = (200,000 + 100,000) ÷ 250
Required Units = 300,000 ÷ 250 = 1,200 units
📌 Must sell 1,200
T-shirts to earn Rs. 100,000 profit.
✅ Example 4: Margin of Safety
A business has:
- Actual
Sales = Rs. 1,000,000
- Break-Even
Sales = Rs. 700,000
Margin of Safety
= 1,000,000 – 700,000
= Rs. 300,000
📌 Sales can drop by Rs.
300,000 before the business becomes unprofitable.
✅ Example 5: CVP with tax
A company wants after-tax profit of Rs. 210,000.
Tax rate is 30%.
- SP =
Rs. 500
- VC =
Rs. 300
- FC =
Rs. 240,000
Step 1: Convert after-tax profit to before-tax profit
Before-tax profit = 210,000 ÷ (1 – 0.30)
= 210,000 ÷ 0.70
= Rs. 300,000
Step 2: CM per unit
CM = 500 – 300 = 200
Step 3: Required Units
Required Units = (240,000 + 300,000) ÷ 200
= 540,000 ÷ 200
= 2,700 units
📌 Must sell 2,700
units to earn the desired after-tax profit.
4. Real-Life Examples Relevant to Pakistan
1. Daraz Seller
A seller selling mobile covers uses CVP to decide:
- How
many covers to sell to cover delivery charges + ads
- Whether
increasing price increases profit
2. Samosa Shop in Rawalpindi
CVP helps determine if buying a frying machine reduces
variable cost.
3. Textile Unit in Faisalabad
Managers use break-even to plan production quantity.
4. Startup in Islamabad
Entrepreneurs use CVP to calculate how many customers they
must reach to survive.
5. Importance of CVP Analysis
For Students and Entrepreneurs:
- Helps
understand profit planning
- Assists
pricing decisions
- Helps
businesses avoid losses
- Useful
for budgeting and forecasting
- Shows
the effect of cost changes on profit
- Helps
determine minimum sales required
- Aids
in deciding whether to introduce or drop a product
For Businesses:
- Essential
for cost control
- Helps
evaluate new projects
- Useful
in “what-if” analysis
- Reduces
risk in decision-making
6. Conclusion
CVP Analysis is a powerful tool for profit planning,
pricing decisions, and cost control.
It helps entrepreneurs understand how changes in cost, selling price, and sales
volume impact profitability.
Every business large or small should use CVP to avoid losses and make smarter
financial decisions.
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