Break-even analysis

1. ACC 557: MANAGEMENT
ACCOUNTING
Cost-Volume-profit analysis
(Break-even analysis)
Compiled by
Kwame Oduro Amoako (Ph.D.)
23/08/2023
Kwame Oduro Amoako (PhD)

2. Aims for today
• To understand
what break even
means
•How it can be used
to assist businesses
in their planning
23/08/2023 Kwame Oduro Amoako (PhD)

3. What does break even mean?
• Break even is where a firms TOTAL REVENUE is
the same as its TOTAL COSTS
• At the break even point, a firm is neither making a PROFIT
nor A LOSS
Kwame Oduro Amoako (PhD)
23/08/2023

4. Break-even analysis?
• A break-even analysis is a useful tool for determining at
what point your company, or a new product or
service, will be profitable.
• Put another way, it's a financial calculation used to
determine the number of products or services you need to
sell to at least cover your costs.
• The break even analysis is important to business owners
and managers in determining how many units (or revenues)
are needed to cover fixed and variable expenses of the
business.
23/08/2023 Kwame Oduro Amoako (PhD)

5. Uses of break-even analysis
Break-even analysis enables a business organization to:
• Measure profit and losses at different levels of production
and sales.
• Predict the effect of changes in sales prices on quantities to
be sold.
• Analyze the relationship between fixed and variable costs.
• Predict the effect of cost and efficiency changes on
profitability.
23/08/2023 Kwame Oduro Amoako (PhD)

6. Assumptions of break-even
• All costs are divided into fixed and variable costs.
• Fixed costs will remain constant and will not change according to the
level of production.
• Variable costs will change in direct proportion according to the level
of production.
• Selling price remain constant even though there exists competition or
any change in the volume of production.
• The number of units of production is equal to sales. It means that
there is no opening or closing stock.
• The operating efficiency of the company remains the same.
• There is only one product or product mix in the case of many
products will remain unchanged.
23/08/2023 Kwame Oduro Amoako (PhD)

7. Limitation of break even analysis
• Break-even analysis is based on the assumption that all costs and
expenses can be clearly separated into fixed and variable
components.
• It assumes that fixed costs remain constant at all levels of activity. It
should be noted that fixed costs tend to vary beyond a certain level
of activity.
• It assumes that variable costs vary proportionately with the volume of
output is not true.
• The assumption that selling price remains unchanged gives a straight
revenue line which may not be true.
• The assumption that only one product is produced or that product
mix will remain unchanged is difficult to find in practice.
• It assumes that the business conditions may not change which is not
true.
23/08/2023 Kwame Oduro Amoako (PhD)

8. Methods of conducting break even
analysis
• Graphical method
• Use of contribution margin method
• Use of equation method
23/08/2023 Kwame Oduro Amoako (PhD)

9. Task 2: Draw the break even chart using
your data
1. Label the vertical axis “sales and costs in pounds”.
2. Label the horizontal axis “sales/production (units)”.
3. Draw on the BE point
4. Draw a horizontal line for total fixed costs.
5. Starting at the Total costs point, draw the total cost line going through
the break even point.
6. Starting at zero, draw the total revenue line through the break even.
7. Where the sales revenue crosses the total costs line is the break
even point.
8. Read off the units of sales to give the break even level of sales.
9. The gap between the total costs line and sales revenue line after the
break even point represents the level of profit.
Kwame Oduro Amoako (PhD)
23/08/2023

10. Graphical method of Breakeven
GH¢
Units Sold
23/08/2023 Kwame Oduro Amoako (PhD)

11. Graphic method of Breakeven
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 25 50 75 100 125 150
Fixed Cost
Revenue
Units Sold
GH¢
23/08/2023 Kwame Oduro Amoako (PhD)

12. Graphic method of Breakeven
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 25 50 75 100 125 150
Fixed Cost
Total Cost
Revenue
Units Sold
GH¢
23/08/2023 Kwame Oduro Amoako (PhD)

13. Graphic method of Breakeven
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 25 50 75 100 125 150
Fixed Cost
Total Cost
Revenue
GH¢
Units Sold
23/08/2023 Kwame Oduro Amoako (PhD)

14. 23/08/2023 Kwame Oduro Amoako (PhD)

15. Calculating the break even point
Kwame Oduro Amoako (PhD)
Step 1.
Identify fixed & variable costs – add them together to get the TOTAL
costs
Step 2.
Calculate the TOTAL REVENUE
23/08/2023

16. Task 1: Calculating break even
Kwame Oduro Amoako (PhD)
• Use the following to
complete the table:
• FC=GH¢2000
• VC=GH¢2 per unit
• Selling price=GH¢4
23/08/2023

17. Task 1: Calculating break even
23/08/2023 Kwame Oduro Amoako (PhD)

18. The break even chart
Kwame Oduro Amoako (PhD)
23/08/2023

19. Margin of safety formula
• The difference between the planned number of
units or actual sales and the number of units of
sales at break even point.
• From the table and chart
They can make:
• 2,000 units potentially – 1,000 actual units at break even
• = 1,000 units Margin of safety
23/08/2023 Kwame Oduro Amoako (PhD)

20. Task 3: Draw the margin of safety
Kwame Oduro Amoako (PhD)
23/08/2023

21. Self test
• KFC operate a hot dog stand
in their branch at Bekwai
Roundabout.
• The wages at the stand costs
GH¢200 per week. Each hot
dog needs one bread roll at
20p, one sausage at 25p and
sauces at 5p.
• The selling price of each hot
dog is GH¢1
23/08/2023 Kwame Oduro Amoako (PhD)

22. Complete the table
At what quantity do total costs = total revenue? (Break even)
What profit is made when they sell 600 hot dogs?
QUANTITY FIXED
COSTS
VARIABLE
COSTS
TOTAL
COSTS
TOTAL
REVENUE
PROFIT OR
LOSS?
100
150
200
250
300
350
400
450
500
550
600
650
23/08/2023 Kwame Oduro Amoako (PhD)

23. Complete the table
At what quantity do total costs = total revenue? (Break even)
What profit is made when they sell 600 hot dogs?
QUANTITY FIXED
COSTS
VARIABLE
COSTS
TOTAL
COSTS
TOTAL
REVENUE
PROFIT OR
LOSS?
100 200 50 250 100 -150
150 200 75 275 150 -125
200 200 100 300 200 -100
250 200 125 325 250 -75
300 200 150 350 300 -50
350 200 175 375 350 -25
400 200 200 400 400 0
450 200 225 425 450 25
500 200 250 450 500 50
550 200 275 475 550 75
600 200 300 500 600 100
650 200 325 525 650 125
23/08/2023 Kwame Oduro Amoako (PhD)

24. Next task
1. Draw a Break Even chart for the Hot Dog business -
Ensure your chart is FULLY and CLEARLY labelled
2. Draw on the margin of safety
3. Explain how the Break even analysis will help Grace
and Joe
4. Discuss what strategies Grace and Joe could use to
enable them to reach their break even point quicker
5. Evaluate which of these strategies would be best for
the business
23/08/2023 Kwame Oduro Amoako (PhD)

25. Break even formulae approach
23/08/2023 Kwame Oduro Amoako (PhD)

26. Contribution Margin
• One of the key relationships in CVP analysis is contribution margin
(CM).
• Contribution margin is the remaining of a product price after
deducting variable cost per unit.
• Contribution margin is a product's price minus all associated
variable costs, resulting in the incremental profit earned for each unit
sold.
• The total contribution margin generated by an entity represents the
total earnings available to pay for fixed expenses and to generate a
profit
• The CM is then available to cover fixed costs and to contribute
income for the company.
23/08/2023 Kwame Oduro Amoako (PhD)

27. Unit Contribution Margin
Views differ as to the best way to express contribution margin
(CM). Some favor a per unit basis.
• At Kuma Wood Videos, the contribution margin is GH¢2.
Unit Selling Price
Unit Variable
Cost
Contribution
Margin
- =
GH¢5 GH¢3 GH¢2
- =
 CM per unit indicates that for every CD sold, Kuma Wood
Video will have GH¢200 to cover fixed costs and
contribute to income.
23/08/2023 Kwame Oduro Amoako (PhD)

28. Contribution Margin
• For example, assume that Kumawood Video sells 100,000 CDs in
one month,
• sales are GH¢500,000 (100,000 x GH¢5) and
• variable costs are GH¢300,000 (100,000 x GH¢3).
• Thus, total contribution is GH¢200,000, computed as follows:
Sales Variable Costs Contribution
- =
GH¢500,000 GH¢300,000 GH¢200,000
- =
23/08/2023 Kwame Oduro Amoako (PhD)

29. Contribution Margin Ratio
Others prefer to use a contribution margin ratio.
• At Kuma Wood Video, the contribution margin
ratio is 40%.
Contribution
Margin per Unit
Unit Selling Price
Contribution
Margin Ratio
 =
GH¢2 GH¢5 40%
 =
 The CM ratio means that 40 cents of each sales dollar
(GH¢1 x 40%) is available to apply to fixed costs and
to contribute to income.
23/08/2023 Kwame Oduro Amoako (PhD)

30. Break even formulae approach
• Break-even point (in units) = Fixed Costs
Contribution/unit
• Break-even point (in sales value) = Fixed Costs x S.P
Contribution/unit
OR Break-even point (in units) x Selling price
OR = Fixed Costs x 1
C/S ratio
• C/S ratio = Contribution/unit x 100
Sales price per unit
23/08/2023 Kwame Oduro Amoako (PhD)

31. Break even formulae approach
cont’d
• Level of sales to result in target profit (in units)
= Fixed Costs + Target Profit
Contribution/unit
• Level of sales to result in target profit (in sales value)
= Fixed Costs + Target Profit x Sales Price/unit
Contribution per unit
• Level of sales to result in target profit after tax (units)
23/08/2023 Kwame Oduro Amoako (PhD)

32. Break even formulae approach
cont’d
• Margin of Safety in units = Total Profit
Contribution/unit
• Margin of Safety in sales value
= Total Sales – Break-even point in sales.
OR
Total Profit
C/S ratio
23/08/2023 Kwame Oduro Amoako (PhD)

33. Illustration 1
A company makes a single product with a sales price of GH¢10 and a marginal
cost of GH¢6. Fixed costs are GH¢60,000 p.a. Calculate:
a) Contribution per unit
b) Number of units to break even.
c) Sales at break-even point.
d) C/S ratio
e) What number of units will need to be sold to achieve a profit of GH¢20,000
p.a.
f) What level of sales will achieve a profit of GH¢20,000 p.a.
g) If the taxation rate is 40% how many units will need to be sold to make a
profit after tax of GH¢20,000 p.a.?
h) Because of increasing costs the marginal cost is expected to rise to
GH¢6.50 per unit and fixed costs to GH¢70,000 p.a. If the selling price
cannot be increased what will be the number of units required to maintain
a profit of GH¢20,000 p.a.? (Ignore tax).
23/08/2023 Kwame Oduro Amoako (PhD)

34. Solution
(a)Contribution per unit = Selling price per unit – Variable Cost
= GH ¢10 - GH¢6
= GH¢4
(b) Break-even point (in units) = GH¢60,000
GH¢4 = 15,000 units
(c) Break-even point (in sales value) = GH¢60,000 x GH ¢10
GH¢4 = GH¢150,000
(d) C/S ratio = GH¢4 x 100
GH¢10 = 40%
23/08/2023 Kwame Oduro Amoako (PhD)

35. Solution cont’d
(e) Number of units for target profit = GH¢60,000 + GH¢20,000
GH¢4
= 20,000 units
(f) Sales for target profit = GH¢60,000 + GH¢20,000 x GH¢10
GH¢4
=GH¢200,000
(g) Number of units for target profit after tax =GH¢ 60,000+GH¢20,000
1-0.4
GH¢4
=23,333 unit
(h) Number of units for target profit = GH¢70,000 + GH¢20,000
GH¢3.50
= 25,714 units
23/08/2023 Kwame Oduro Amoako (PhD)

36. Home work
23/08/2023 Kwame Oduro Amoako (PhD)

37. Sales Mix Break-even Point
• Sales mix is the proportion in which two or more
products are sold.
• For the calculation of break-even point for sales
mix, following assumptions are made in addition to
those already made for CVP analysis:
• The proportion of sales mix must be predetermined.
• The sales mix must not change within the relevant
time period.
23/08/2023 Kwame Oduro Amoako (PhD)

38. Sales Mix Break-even Point
• The calculation method for the break-even point of sales mix is
based on the contribution approach method.
• Since we have multiple products in sales mix therefore it is most
likely that we will be dealing with products with different
contribution margin per unit and contribution margin ratios.
• This problem is overcome by calculating weighted average
contribution margin per unit and contribution margin ratio.
• These are then used to calculate the break-even point for sales
mix.
23/08/2023 Kwame Oduro Amoako (PhD)

39. Illustration:
Following information is related to sales mix of product A, B
and C. Calculate the break-even point in units and in dollars.
Product A B C
Sales Price per
Unit
GH¢15 GH¢21 GH¢36
Variable Cost
per Unit
GH¢9 GH¢14 GH¢19
Sales Mix
Percentage
20% 20% 60%
Total Fixed Cost GH¢40,000
23/08/2023 Kwame Oduro Amoako (PhD)

40. Solution
Step 1: Calculate the contribution margin
Product A B C
Sales Price per
Unit
GH¢15 GH¢21 GH¢36
− Variable Cost
per Unit
GH¢9 GH¢14 GH¢19
Contribution
Margin per Unit
GH¢6 GH¢7 GH¢17
23/08/2023 Kwame Oduro Amoako (PhD)

41. Solution cont’d
Step 2
Calculate the weighted-average contribution margin per unit for
the sales mix using the following formula:
• Product A CM per Unit × Product A Sales Mix Percentage
+ Product B CM per Unit × Product B Sales Mix Percentage
+ Product C CM per Unit × Product C Sales Mix Percentage
= Weighted Average Unit Contribution Margin
23/08/2023 Kwame Oduro Amoako (PhD)

42. Solution cont’d: Step 2
Product A B C
Sales Price per Unit GH¢15 GH¢21 GH¢36
− Variable Cost per Unit GH¢9 GH¢14 GH¢19
Contribution Margin per Unit GH¢6 GH¢7 GH¢17
× Sales Mix Percentage 20% 20% 60%
Weighted contribution per
unit
GH¢1.2 GH¢1.4 GH¢10.2
Sum: Weighted Average CM
per Unit
GH¢12.80
23/08/2023 Kwame Oduro Amoako (PhD)

43. step 3: Calculate total units of sales mix required to break-even using
the formula:
Break-even Point in Units of Sales Mix = Total Fixed Cost ÷ Weighted
Average CM per Unit
Total Fixed Cost GH¢40,000
÷ Weighted Average CM
per Unit
GH¢12.80
Break-even Point in Units
of Sales Mix
3,125
23/08/2023 Kwame Oduro Amoako (PhD)

44. Step 4: Calculate the number units of product A, B
and C at break-even point:
Product A B C
Sales Mix Ratio 20% 20% 60%
× Total Break-even Units 3,125 3,125 3,125
Product Units at Break-
even Point
625 625 1,875
23/08/2023 Kwame Oduro Amoako (PhD)

45. Step 5: Calculate Break-even Point in dollars as follows:
Product A B C
Product Units at
Break-even Point
625 625 1,875
× Price per Unit GH¢15 GH¢21 GH¢36
Product Sales in
Dollars
GH¢9,375 GH¢13,125 GH¢67,500
Sum: Break-even
Point in Dollars
GH¢90,000
23/08/2023 Kwame Oduro Amoako (PhD)

46. Self test in class
23/08/2023 Kwame Oduro Amoako (PhD)

47. Self test: Solution
Weighted average selling price:
= (GH¢200 × 20%) + (GH¢100 × 30%) + (GH¢50 × 50%)
= GH¢40 + GH¢30 + GH¢25
= GH¢95
Weighted average variable expenses:
= (GH¢100 × 20%) + (GH¢75 × 30%) + (GH¢25 × 50%)
= GH¢20 + 22.50 + 12.50
= GH¢55
The company will have to sell 1,250 units to break-even. Now I would
compute the number of units of each product to be sold:
Product X (1,250 × 20%): 250 units
Product Y (1,250 × 30%): 375 units
Product Z (1,250 × 50%): 625 units
Total: 250 units + 375 units + 625 units = 1,250 units
23/08/2023 Kwame Oduro Amoako (PhD)

48. Alternatively: Fast track
• You can also use the break even formula:
23/08/2023 Kwame Oduro Amoako (PhD)

49. Self test: Solution cont’d
23/08/2023 Kwame Oduro Amoako (PhD)

50. • As the number of units of each individual product to
be sold have been computed, I can compute the
break-even point in dollars as follows:
• Product X (250 units x 200) 50,000
• Product Y (375 units x 100) 37,500
• Product Z (625 units x 50) 31,250
• Break even point in cedis 118,750
23/08/2023 Kwame Oduro Amoako (PhD)