Introduction to
Accounting
Lectures
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Lectures
Week Date
Topic
Textbook
Management Accounting
7
11 Mar
Cost – Volume – Profit Analysis
Chapter 7
8
18 Mar
Costing
Chapter 7
9
25 Mar
Budgeting
Chapter 9
Learning Outcomes
Cost – Volume – Profit Analysis
Textbook: Chapter 7
• Distinguish between fixed cost and variable cost
• Use this distinction to explain the relationship between cost, volume
and profit
• Deduce the break-even point for some activity and discuss its
usefulness
• Calculate the margin of safety to analyse risk
Financial Accounting & Management Accounting
Management Accounting
1. Identify objectives
2. Search for alternative courses of action
Planning
process
3. Gather data about alternatives
4. Select alternative course of action
5. Implement the decisions
Control
process
6. Compare actual and planned outcomes
7. Respond to divergences from plan
What are the
risks?
What are the
rewards?
CVP Analysis
CVP (cost-volume-profit) analysis is concerned with the
changes in profits in response to changes in sales volumes,
costs and prices.
Cost Behaviour
Costs represent the amount sacrificed to achieve a particular
business objective.
Examining cost behaviour enables us to consider:
• The way in which costs change
• The main factors that influence those changes
Costs can be broadly classified as:
• Fixed costs
• Variable costs
• Mixed costs
Fixed Costs
Fixed costs
• Those costs which remain the same in total (within a given range of
activity and timeframe) irrespective of the level of activity.
• Examples: depreciation, insurance, rent, salaries of permanent staff,
overheads
• Are likely to change as a result of inflation or general price increases.
• Are almost always ‘time-based’, i.e. they vary with the length of time
concerned.
Fixed Costs
When we consider levels of activity in terms of units of output:
• Fixed costs remain the same.
• Fixed costs per unit will decrease as the number of units produced
increases.
Fixed costs per unit = total fixed costs / the number of units
Variable Costs
Variable costs
• Those costs which change in total as the level of activity changes.
• Variable costs per unit: the same per unit of production irrespective of
the number of units produced.
Semi-Fixed (Semi-Variable) Costs
Semi-fixed (semi-variable) costs
• These costs exhibit aspects of both fixed and variable costs.
• Examples: mobile phone bill, electricity bill, advertising costs.
Cost Behaviour with Varying Production
1 unit
10 units
50 units
Total variable costs
Variable cost per unit
£5
£5
£50
£5
£250
£5
Total fixed costs
Fixed cost per unit
£5,000
£5,000
£5,000
£500
£5,000
£100
Total cost
Total cost per unit
£5,005
£5,005
£5,050
£505
£5,250
£105
Contribution
Contribution/Contribution Margin: It is called “contribution” because it contributes
to meeting the fixed cost and, if there is any excess, it then contributes to profit.
Scenario A
Scenario B
Scenario C
Sales Revenue (+)
1,000
1,250
1,500
Variable Costs (-)
(600)
(750)
(900)
Contribution (=)
400
500
600
Fixed Costs (-)
(500)
(500)
(500)
Profit / Loss (=)
(100)
0
100
Contribution
Zero profit:
Total revenues - Variable costs = Fixed costs
Contribution = Fixed costs
Loss-making situation
Contribution < Fixed costs
Profit-making situation
Contribution > Fixed costs
Break-Even Analysis
Break-even is where profit is zero:
Contribution = Fixed Costs
Contribution per unit x the number of unit = Fixed Costs
Break-even units
= Fixed costs / Contribution per unit
= Fixed costs / (Revenue per unit – Variable cost per unit)
Break-Even Analysis
The uses of break-even analysis
• Financial Planning: helps management set realistic sales targets and
pricing strategies.
• Risk Assessment: provides insight into the sales volume needed to
avoid losses.
• Investment Decisions: informs decisions about resource allocation
and potential investments.
• Performance Measurement: allows managers to evaluate how sales
performance compares to required levels.
Break-Even Analysis
The limitations of break-even analysis
• There are non-linear relationships between costs, revenues and
volume.
• There may be stepped fixed costs. Most fixed costs are not fixed over
all volumes of activity.
• Multi-product businesses have problems in allocating fixed costs to
particular activities.
Break-Even Analysis
Find out break-even units.
Analysis:
1. Revenue
2. Fixed costs
3. Variable costs
4. Per unit
Break-Even Analysis
Information
Revenue per unit
150
Charged fee per player
Variable cost per unit
(increase as the number of players increase)
25
Nomination fees per player
35
Kit bag per player
30
Lunches and drinks per player
1200
Coach for the event
600
Bus hire for the event
Fixed cost
(regardless of the number of players)
Break-Even Analysis
Information
Revenue per unit
150
Charged fee per player
Variable cost per unit
(increase as the number of players
increase)
25
Nomination fees per player
35
Kit bag per player
30
Lunches and drinks per player
1200
Coach for the event
600
Bus hire for the event
Fixed costs
(regardless of the number of players)
Contribution per unit
= revenue per unit - variable cost per unit
= 150 – (25+35+30)
= 60
Break-even units
= fixed costs/contribution per unit
= (1200 + 600)/60
= 1800/60
= 30 players
Break-Even Analysis
Determine activity level required to cover all costs associated with the
business if those costs are changing.
Break-even (zero profit):
Break-even units = fixed costs/contribution per unit
= (1200 + 600)/(150 – (25+35+30))
= 1800/60
= 30 players
• Fixed costs are decreased by 200
• Variable cost per unit is increased by 10 per unit
Break-even units = fixed costs / Contribution per unit
= (1800 - 200) / (150 – (25+35+30+10))
= 1600/50
= 32 players
Break-Even Analysis
It is possible to build a desired profit level into this analysis and thereby
calculate the units required to be sold to achieve a particular profit.
Break-even (zero profit):
Break-even units = fixed costs/contribution per unit
= (1200 + 600)/(150 – (25+35+30))
= 1800/60
= 30 players
• Desired profit: 600
Desired profit units = (fixed costs + desired profit) / Contribution per unit
= (1800 + 600) / 60
= 40 players
Margin of Safety
CVP analysis provides the opportunity for ‘what if’ analysis.
Assess margin of safety – difference between break-even volume and
budgeted/actual output, provides indication of risks involved.
•
•
If the margin of safety is small, managers may put more emphasis on
reducing costs and increasing sales to avoid potential loss.
A larger margin of safety gives managers more confidence in making plans
such as incurring additional fixed costs.
Margin of safety (as %)
= (sales volume - break-even sales volume)/sales volume x 100%
Margin of Safety
£
Sales Revenue
100,000 units x £2
200,000
Variable Costs
100,000 units x £0.60
(60,000)
Contribution
140,000
Fixed Costs
125,000
Profit
15,000
Breakeven is 125,000/(140,000/100,000)= 89,285.7 units
(round the result to the nearest unit)
Margin of safety
= (100,000 – 89,286) / 100,000 x 100%
= 0.10714 x 100%
= 11%
Break-Even Analysis and Marginal Analysis –
Example
A sports equipment company produces and sells two differing products: 120 units of Product A and 250 units of
Product B. The financial details are as follows:
Product A:
• Total Selling Price: £7,500
• Total Variable Cost: £2,800
Product B:
• Total Selling Price: £18,500
• Total Variable Cost: £3,500
The total fixed costs for the business amount to £10,500.
Required:
1. Break-even Analysis: Calculate the number of units required for Product A and Product B, respectively, to reach the break-even point.
Round the result to the nearest unit. Assess the strengths and limitations of break-even analysis.
2. Profit Target Calculation: The company targets a profit of £14,500. Calculate the number of units required for Product A and Product
B, respectively, to achieve the target profit. Round the result to the nearest unit.
3. Strategic Changes for Profitability: To enhance profitability and reach the £14,500 target profit, the company need to refine Product A
that increases its cost by £20 per unit and expand warehouse that increases a fixed cost of £30,000. Calculate the revised number of
units required for Product A and Product B, respectively, to still achieve the target profit. Round the result to the nearest unit.
4. Margin of Safety Calculation: The company projects actual sales of 170 units of Product A and 260 units of Product B. Calculate the
margin of safety for both products.
5. Risk and Reward Evaluation: Evaluate the risks and rewards associated with each product.
Break-Even Analysis and Marginal Analysis –
Example
Break-even Analysis:
Step 1: Determine Per-Unit Values
Product A:Total Selling Price: £7,500 for 120 units; Total Variable Cost: £2,800 for 120 units.
• Selling Price per Unit : 7,500/120=62.50≈63
• Variable Cost per Unit : 2,800/120=23.33≈23
• Contribution per Unit : 63−23=40
Product B:Total Selling Price: £18,500 for 250 units; Total Variable Cost: £3,500 for 250 units.
• Selling Price per Unit : 18,500/250=74
• Variable Cost per Unit : 3,500/250=14
• Contribution per Unit : 74−14=60
Step 2: Break-even Analysis
Break-even Quantity=Fixed Costs/Contribution per Unit
• Product A:10,500/40=262.5≈263 units
• Product B:10,500/60=175 units
Thus, the company must sell 263 units of Product A or 175 units of Product B to break even.
Break-Even Analysis and Marginal Analysis –
Example
The uses of break-even analysis:
• Helps management set realistic sales targets and pricing strategies.
• Provides insight into the sales volume needed to avoid losses.
• Informs decisions about resource allocation and potential investments.
• Allows managers to evaluate how sales performance compares to required levels.
The limitations of break-even analysis:
• There are non-linear relationships between costs, revenues and volume.
• There may be stepped fixed costs. Most fixed costs are not fixed over all volumes of activity.
• Multi-product businesses have problems in allocating fixed costs to particular activities.
Break-Even Analysis and Marginal Analysis –
Example
Profit Target Calculation:
Required Sales=(Fixed Costs + Target Profit )/Contribution per Unit
Profit​ Target Profit = £14,500
• Product A: (10,500+14,500)/40=625 units
• Product B: (10,500+14,500)/60=25,000/60=416.66≈417 units
Thus, to achieve a profit of £14,500, the company must sell:625 units of Product A or 417 units of Product B.
Break-Even Analysis and Marginal Analysis –
Example
Strategic Changes for Profitability:
Changes:
• Increase in Product A variable cost by £20 per unit → New Variable Cost: £23 + £20 = £43
• Increase in Fixed Cost by £30,000 → New Fixed Cost: £10,500 + £30,000 = £ 40,500
New Contribution per Unit for Product A:63−43=20
New Required Sales for Target Profit:(40,500+14,500)/Contribution per Unit
• Product A: 55,000/20=2,750 units
• Product B: 55,000/60=916.66≈917 units
Thus, after these changes, the company must sell: 2,750 units of Product A or 917 units of Product B.
Break-Even Analysis and Marginal Analysis –
Example
Margin of Safety Calculation:
(Projected Sales−Break-even Sales)/Projected Sales×100%
Projected Sales units:
• Product A: 170 units
• Product B: 260 units
Break-even units:
• Product A: 263 units
• Product B: 175 units
Thus, the Margin of Safety is:
• Product A:(170−263)170×100%=−55%
• Product B: (260−175)/260×100%=33%
Break-Even Analysis and Marginal Analysis –
Example
Risk and Reward Evaluation: A sports equipment company
Product A
Rewards:
• Lower selling price (£63 per unit): potentially higher sales volume if demand exists.
• Possible cost reductions over time: manufacturing improvements or bulk purchasing of raw materials could lower costs
in the future.
Risks:
• Higher break-even point (263 units): More units need to be sold to recover fixed costs, making profitability harder.
• Margin of safety (-55%): Indicates a current loss situation, increasing financial risk.
Product B
Rewards:
• Higher contribution per unit (£60 per unit): Makes each sale significantly more profitable.
• Lower break-even point (175 units): Easier to reach profitability.
• Positive margin of safety (32.69%): Indicates current sales levels exceed break-even, making it a financially safer
product.
Risks:
• Higher selling price (£74 per unit): Might limit demand as fewer customers can afford it.
• More frequent production updates need: If the product needs improvements every few years, additional costs may
arise.