Cost-Volume-Profit Analysis and Business Decisions

1. Cost-Volume-Profit Analysis
and Business Decisions

2. 2
CVP and Business Decisions
1. Break even analysis
2. Assumptions and Limitations
3. Short-term vs. long term decisions

3. Cost-Volume-Profit
• The Cost-Volume-Profit analysis is an attempt
to measure the effect of changes in volume,
cost, selling price and product mix on profits.
• It explores the relationship between revenue,
cost, and volume and their effect on profits

4. Fixed Costs
• By definition, Fixed Costs are costs
that do not change (in total) in
response to changes in volume or
activity. Examples include
depreciation, supervisory salaries and
maintenance expenses.

5. Variable Costs
• By definition, Variable Costs are costs
that change (in total) in response to
changes in volume or activity. It is
assumed, too, that the relationship
between variable costs and activity is
proportional. That is, if production
volume increases by 10%, then variable
costs in total will rise by 10%.
Examples include direct labor, raw
materials and sales commissions.

6. Cost-Volume-Profit Analysis
• It explores the relationship between
costs (fixed and variable), activity
levels and profits. That is, once the
variable and fixed elements have been
determined using the tools discussed
in the preceding slides, we use the
following profit equation: Profit = SP(x)
- VC(x) – TFC=Net Income

7. 7
ASSUMPTIONS OF BREAK-EVEN ANALYSIS
• Break-even analysis is based on certain
assumptions:
• Some expenses are fixed and some are variable
• Total cost of production can easily be segregated into fixed and variable.
• At each level of production, fixed expenses remain constant.
• Variable costs vary in proportion to volume of production.
• Change in production or sales quantities does not bring any change in
selling price per unit.
• There is no change in general price level.
• There is no change in productivity of workers.
• Only one product is produced or in case of number of products, the sales
mix ratio remains constant.

8. Break-Even Point
• It has been defined by Charles T. Horngren, ‘‘is
that point of activity (sales volume) where
total revenues and total expenses are equal;
it is the point of zero profit and zero loss”.

9. Break-Even Point
• One of the primary purposes of C-V-P is to
calculate the Break-Even Point. It simply
represents the number of units the firm
must sell to generate exactly zero net
income– to earn neither profit nor loss.
Graphically, as shown in the next slide,
Break-Even is the point where the sales
curve and cost curve cross. It should be
noted here that managers are seldom
interested in merely breaking even. But
the Break-Even is an important
benchmark!

10. • Break–even–point can be determined by the
use of mathematical equations and also by
graphical chart
• EQUATION:

11. Break–even–point in units
Break–even–point in units
Break–even–point in units or quantity can be
calculated where the per unit selling price and per
unit variable cost is known along with the total fixed
cost.
Q = F
P - V
where;
Q = Break – even – point in quantity
F = Total fixed costs
P = Selling price per unit
V = Variable cost per unit
11

12. 12
Illustration
The IAA has a fixed cost of shs 150 millions.
The fee collected per student per annum is shs
400,000. The variable cost per student is shs
100,000.
What should be the enrolment of students
where the IAA has no profit no loss?

13. Solution
• Q = F
P – V
= 150,000,000
400,000 – 100,000
= 150,000,000
300,000
500 students
13

14. Break–even–point in Shillings/ Value
It is also known as B.E.P based on revenue (sales) it can be calculated
in either of the following ways:
B.E.P in Shillings = B.E.P in units x selling price per unit
or
B.E.P in Shillings = F x P or F x P
P – V C
where;
C= Contribution per unit i.e. Selling price per unit – Variable cost per unit
or
B.E.P in Shillings = F or F
1 – VC 1 - V
S P
where;
VC = Total variable costs
S = Total sales (Revenue)

15. 15
Example 2
• What would the total amount of Revenue be
collected by IAA on the basis of data given in
the previous illustrated problem, so that it
should not have any profit or loss.

16. Solution
B.E.P in Sales Value (in shilling) = F x P
P – V
= 150,000,000 x 400,000
400,000 – 100,000
= Shs. 200,000,000
16

17. B.E.P in Sales Value (in shilling) can also be obtained
from = F
P /V Ratio
• Where;
P/V Ratio = Profit volume ratio
Profit volume ratio is also known as Contribution Ratio.
It is a ratio of contribution to sales. Contribution is the
difference between sales (Revenue) and marginal cost
(variable cost)
P/V Ratio = S – VC x 100 or C x 100
S S
or P – V x 100
P

18. Margin of safety
Margin of safety: It is the difference
between Actual sales and the sales at B.E.P
It is used to indicate the amount of sales that
are above the break-even point. In other words,
the margin of safety indicates the amount by
which a company's sales could decrease before
the company will become unprofitable.
M.S = Actual Sales – Sales at BEP

19. 19
PROBLEM
• The IAA runs the following Programs
DAR- Campus PROGRAMS
MBA-LM MBA-IT MSC F&I
•
i. Budgeted No. of students: 25 25 30
ii. Budgeted fee per students: 8,300,00 8,500,000 8,800,000
iii. Budgeted variable cost per stdnt: 500,000 700,000 1,000,000
iv. Budgeted fixed cost (total)160,000,000 180,000,000 225,000,000
You are required to compute B.E.P in quantity, B.E.P in fee for each
program and the margin of safety for each program.

20. BEP- Graph
• Break-even point can also be indicated by graphing. Figure 1 below
is a sample graph for a business. To draw the graph, we should
follow these steps:
• Number of units produced is marked along the horizontal axis and
the total revenue expressed in dollars is set on the vertical axis.
• The sales line is drawn to indicate the sales at each level of
production.
• A horizontal line is drawn at the shs 12,000 level of sales to
represent the fixed costs for our sample business.
• A total cost line is drawn from the point of intersection of the fixed
cost line and the vertical axis to the point of total costs as full
capacity – shs 28,000.
• The intersection of the total cost line with the sales line represents
the break-even point, in this case shs 20,000. The dotted lines
represent the level of production and the total costs at this level of
operation.
• Areas of net loss and of net profit are marked.

22. 22
Break – even – chart
Break–even-point can be find out by the use of graph. Various
levels of output are shown on abscissa X – axis and costs and
revenues are shown on ordinate Y – axis.
• At a point where total sales line interacts the total cost line, is
known as BEP.
• Illustrated Problem
• The following information is available from the records of Mbuni
Soap Factory.
• Variable costs per unit Shs 180
• Total Fixed costs Shs 3,000,000
• Selling Price per unit Shs 350
• Production 50,000 units
• Calculate the B.E.P
•

23. 23
ASSUMPTIONS OF BREAK-EVEN ANALYSIS
• Break-even analysis is based on certain
assumptions:
• Some expenses are fixed and some are variable
• Total cost of production can easily be segregated into fixed and variable.
• At each level of production, fixed expenses remain constant.
• Variable costs vary in proportion to volume of production.
• Change in production or sales quantities does not bring any change in
selling price per unit.
• There is no change in general price level.
• There is no change in productivity of workers.
• Only one product is produced or in case of number of products, the sales
mix ratio remains constant.

24. 24
Limitations of B.E.P
• Total cost line which indicates fixed costs and variable costs,
should not be drawn as straight line as fixed costs may
change after a certain limit.
• Straight line depicting sales revenue also does not give true
picture as increase in volume of production may bring down
the prices
• Break –even chart is only a tool to help the management in
accelerate the management decisions and not to replace the
management.

25. 25
Applications of B.E.P
(a) Calculation of profit at different level of
Turnovers:
Break–even–point assists in ascertaining the profit at
different levels of sales i.e.
Profit = sales – variable – fixed cost
Pt= S – VC – F
Pt= C – F
C = S x P/V Ratio
Pt= S x P/V Ratio – F

26. 26
Illustration (a)
• Simba Plastic Manufacturing Co. is operating at 60%
capacity and manufactures 6000 water tanks per
annum. The present cost break–up of each water
tank is as below:-
Material Shs 10,000
Labour Shs 5,000
Overheads expenses Shs 8,000 (of which 60% is
fixed expenses) or shs. 4800 per unit at full capacity
level
The selling price per water tank is Shs 35,000. What
would be the profit if factory operates at full
capacity?

27. Solution
27
Total capacity = 6,000 x 100 or 10,000 units
60
Sales value at 100% capacity
= 10,000 units x 35,000
= 350,000,000
Profit at 100% capacity
Profit = S x P/V – F
P/V Ratio = (35,000 – 18,200) x 100
35,000
= 16,800 x 100 or 48%
35,000
F = shs 4,800 x 10,000 or shs 48,000,000
S = 10,000 x 35,000
= shs 350,000,000
Profit = (shs 350,000,000 x 48) – shs 48,000,000
100
= shs 168,000,000 – 48,000,000
= shs 120,000,000

28. 28
b. Calculation of Sales at a Target profit
If a management wants to earn a fixed amount of profit
it would like to know the volume of sales (In shillings
and in quantity) to be made.
Sales in units = F + Pt
P – V
Sales in Shillings = F + Pt
1 – V
P

29. 29
Illustration b
• Comafric Co is manufacturing Radiators. The following
information is available from its records:
• Sales 5,000 units @ shs 30,000 shs 150,000,000
• Marginal cost (variable cost) 80,000,000
• Contribution 70,000,000
• Fixed Expenses 50,000,000
• Profit 20,000,000
• The company wants to make a profit of Shs 40,000,000.
What should be its sales in units? What would be the amount
of sales to earn a profit of shs 10,000,000?

30. Solution
30
Sales in units = F + Pt
P – V
= 50,000,000 + 40,000,000
30,000 – 16,000
= 90,000,000 or 6428.6 units or 6429 units
14,000
Sales in shillings = F + Pt or F + Pt x P
1 – V P – V
P
= 50,000,000 + 10,000,000
1 – 16,000
30,000
= 60,000,000
1-.5333
= 60,000,000
.4667
= Shs 128,562.25

31. 31
c. Determining the Selling Price per unit for a given B.E.P :
What would be the selling price per unit at a given B.E.P? In order
to find selling price per unit, the following formula is used.
• Selling Price = V + C per unit
• C per unit = F
• B.E.P in units
Illustration c
From the following particulars find the selling price per unit, if the
B.E.P is 40,000 units.
• Fixed cost Shs 20,000,000
• Variable cost 3,000 per unit

32. Solution
32
Selling price per unit = V + C per unit
C per unit = F
B.E.P in units
= 20,000,000 or shs 500
40,000
Selling price per unit = V + C per unit
= 3000 + 500
= Shs. 3,500

33. 33
d. Impact of the Variations of Fixed and Variable Costs on
Profit and Sales:
• The impact of changes of fixed and
variable costs on profit & sales can be
ascertained as the levels of B.E.P would
change.

34. 34
Illustration d
• The following information is obtained from the records of National
Manufacturing Co.
• Sales shs 20,000,000
• Variable cost 8,000,000
• Fixed cost 5,000,000
• Required:
(i) P/V Ratio
• (ii) B.E.P in value
• (iii) Margin of safety
• b) Calculate the effect of the following on the P/V
ratio, B.E.P in value and Margin of safety.
• (i) 20% increase in the fixed costs
• (ii) 10% increase in the fixed costs; and
10% increase in the variable costs
• (iii) 30% increase in the fixed costs; and
10% decrease in variable cost

35. Solution
35
(i) P/V Ratio = S – VC x 100
S
= 20,000,000 – 8,000,000 x 100
20,000,000
= 12,000,000 x 100
20,000,000
= 60%
(ii) B.E.P in Shs = F
P/V Ratio
= 5,000,000 x 100
60
= Shs 8,333,333
(iii) Margin of safety = AS – S BEP
= 20,000,000 – 8,333,333
= 11,666,667

36. Continued…
36
(i) P/V ratio is not going to be effected, it will remain 60%.
F = 5,000,000 + 20% of 5,000,000
= Shs. 6,000,000
B.E.P in shillings = F/ P.V Ratio = 6,000,000 x 100
60
= Shs 10,000,000
Margin of safety = A.S – Sales at BEP
= 20,000,000 – 10,000,000
= 10,000,000

37. Continued….
37
(i) VC = 8,000,000 + 10% of shs 8,000,000
= Shs 8,800,000
F = 5,000,000 + 10% of shs 5,000,000
= Shs 5,500,000
P/V Ratio = S – VC x 100
S
= 20,000,000 – 8,800,000 x 100
20,000,000
= 11,200,000 x 100
20,000,000
= 56%
B.E.P in shillings = F
P/V Ratio
= 5,500,000 x 100
56
= Shs 9,821,428.50 or 9,821,429
Margin of safety = AS- Sales at BEP
= 20,000,000 – 9,821,429
= Shs 10,178,571

38. Continued….
38
(i) F = 5,000,000 + 30% of shs 8,000,000
= Shs 6,500,000
VC = 8,000,000 – 10% of shs 800,000
= 8,000,000 – 800,000
= shs 7,200,000
P/V Ratio = S – VC x 100
S
= 20,000,000 – 7,200,000 x 100
20,000,000
= 12,800,000 x 100
20,000,000
= 64%
B.E.P in shilling = F
P/V Ratio
= 6,500,000 x 100
64
= Shs 10,156,250
Margin of safety = AS – Sales at BEP
= 20,000,000 – 10,156,250
= Shs 9,843,750

39. 39
e. Ascertaining the Sales value in case of Decrease in
Prices
When ever the management decides to reduce the selling
price per unit but interested to maintain same level of profit,
it has to sell more number of units.
Illustration e:
• The following information is provided concerning a firm:-
• Selling Price per unit Shs 2,000
• Variable cost per unit Sh 900
• Fixed cost Shs 300,000
• No. of unit produced & sold 1,000
• The management of the firm wants to reduce the price to
1,800 but interested to maintain same level of profit as
before. Calculate the no. of units to be produced & sold.

40. Solution
40
When sales are shs 2,000,000 i.e. 1,000 x 2,000
Pt = S x P/V ratio – F and P/V Ratio = P-V X 100 or 2000-900 x 100 0r 1100 x 100
P 2000 2000
= 2,000,000 x 1,100 x 100 – 300,000
2,000
= 2,000,000 x 55% - 300,000
= 2,000,000 x 55 - 300,000
100
= 1,100,000 – 300,000
= Shs 800,000
New P/V Ratio = P-V x 100
P
900 x 100
1,800
= 50%
Sales in Shs = F + Pt
New P/V ratio
= 300,000 + 800,000
50
100
= 1,100,000 x 100
50
= Sh 2,200,000
Number of units to be sold= 2,200,000 or 1222 units
1,800

41. Example
• The National Art and Craft Industries Ltd.
makes handbags for ladies. The fixed cost of
operating the workshop for a month totals to
£500. Each handbag requires materials that
cost £2 and takes one hour to make. The
business pays the handbag makers £10 an hour.
The handbag makers are all on contracts such
that if they do not work for any reason, they
are not paid. The handbags are sold to
customers for £14 each.
41

42. Continued…..
• The business expects to sell 500 handbags a month. The business
has the opportunity to rent a handbag-making machine. Doing so
would increase the total fixed cost of operating the workshop for a
month to £3,000. Using the machine would reduce the labour time
to half an hour per handbag. The handbag makers would still be
paid £10 an hour.
• What is the BEP for handbag making for the business without the
machine?
• What is the BEP if the machine is rented?
• How much profit would the business make each month from selling
handbags:
• without the machine; and
• with the machine?
• What do you notice about the figures that you calculate?
42

43. Example
• Black Ltd. can render three different types of services (Alpha, Beta and
Gamma) using the same staff. Various estimates for the next year have
been made as follows:
• SERVICES
• Alpha Beta Gamma
• Selling price (£/unit) 30 39 20
• Variable material cost (£/unit) 15 18 10
• Other variable costs (£/unit) 6 10 5
• Share of fixed cot (£/unit) 8 12 4
• Staff time required (hours) 2 3 1
• Fixed cost for next year is expected to total £40,000
43

44. Required
(a) If the business were to render only service Alpha next year, how many
units of the service would it need to provide in order to break even?
Assuming there is no effective limit to market size and staffing level.
(b) If the business has limited staff hours available next year, in which order
of preference would the three services come?
(c)The maximum market for next year for the three services is as follows:
• Alpha 3,000 units
• Beta 2,000 units
• Gamma 5,000 units
• Black Ltd has a maximum of 10,000 staff hours available next year.
What quantities of each service should the business provide next year and
how much profit would this expected to yield?
44

45. Illustrated Example 6.8
• A business makes three products A, B and C. All three products require the use of two types
of machines: cutting machines and assembling machines. Estimates for the next year
include the following:
•
• Product
• A B C
• Selling price (£ per unit) 25 30 18
• Sales demand (units) 2,500 3,400 5,100
• Material cost (£ per unit) 12 13 10
• Variable production cost (£ per unit) 7 4 3
• Time required per unit on cutting machines (hrs) 1 1 0.5
• Time required per unit on assembling machines (hrs) 0.5 1 0.5
•
• Fixed cost for next year is expected to total £42,000.
• The business has cutting machine capacity of 5,000 hours a year and assembling
machine capacity of 8,000 hours a year.
45

46. Required
• State, with support workings, which products
in which quantities the business should plan
to make next year on the basis of the above
information first determining which machines
will be limiting factor.
• State the maximum price per product that it
would be worth the business paying to a
subcontractor to carry out that part of the
work that could not be done internally.
46