CHAPTER 2

DPB2033 BUSINESS MATHEMATICS

Chapter 2:
Breakeven Analysis

6 hours lecture: 2 hours tutorial

At the end of this lesson, you should be able to
1 Describe the breakeven analysis

1.1 Define the breakeven analysis
1.2 Explain breakeven situation and analysis

2 Explain the sales levels (ringgit/unit), sales price and profit using algebra
2.1 Find contribution margin, contribution margin ratio
2.2 Find the breakeven point, sales price and profit

Definition BEP

The point at which a business generates enough revenue to cover all of its costs without any surplus

is known as the break-even point or break-even quantity.

A point/ situation where TR = TC TR, R(x)

When TR = TC, TC, C(x)

Therefore Profit = 0

When total costs are greater than total revenue the firm makes a loss.
When total costs are less than total revenue the firm will make a profit

**BEP analysis________________________________________________________________________
Purpose of calculating BEP

i. _________________________________________________________________________
ii. _________________________________________________________________________
iii. _________________________________________________________________________

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DPB2033 BUSINESS MATHEMATICS

BEP analysis involve FUNCTIONS of
i. TOTAL COST

Total Cost = Fixed Cost + Total Variable Cost
FC
TC = FC + TVC
@ = FC
C(x) = + VC(x)
@
C(q) + VC(q)

*Bear in mind:
Total Variable Cost=TVC=VC (q) =VC(x)

is
Variable cost per unit x quantity

ii. TOTAL REVENUE

Total Revenue = Price per unit x Quantity
p x q
TR = p x x
@ = p x q
=
R(x)
@

R(q)

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DPB2033 BUSINESS MATHEMATICS

iii. TOTAL PROFIT

Profit = ii - i
-
=

=
=

Analysis
BEP

Calculation Graph

CM CMR PROFIT EQUATION Intersection
i. Contribution ii. contribution margin P(x)=__________ point
TR = TC
margin ratio @

CM=_________ CMR= _____ R(x) = C(x)

BEP (units)= BEP(RM) =

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DPB2033 BUSINESS MATHEMATICS

EXAMPLE 1
BEP Analysis by Calculation
Solve the following
1. Find the break-even quantity and break-even revenue if C(x) = 110x + 40,000 and R(x) = 150x

2. The XYZ Company has a fixed cost of 20,000, a production cost of RM12 for each unit
produced and a selling price of RM20 for each unit produced.
a. Find the break-even point for the firm.
b. If the company produces and sells 2000 units, would they obtain a profit or loss?

c. If the company produces and sells 3000 units, would they obtain a profit or loss?

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DPB2033 BUSINESS MATHEMATICS

3. A bicycle manufacturer experiences fixed monthly costs of RM124,992 and variable costs of
RM52 per standard model bicycle produced. The bicycles sell for RM100 each. How many
bicycles must he produce and sell each month to break even? What is his total revenue at the
point where he breaks even

4. Your college newspaper, The Collegiate Investigator, has fixed production costs of RM70 per
edition, and marginal printing and distribution costs of RM0.40/copy. The Collegiate
Investigator sells for RM0.50/copy. a) Write down the associated
i. cost, revenue, and profit functions.

ii. How many copies should be sold in order to break even?

iii. What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator?

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DPB2033 BUSINESS MATHEMATICS

5. Suppose you intend to open a franchise business to supply a nationally-known line of women’s
shoes. You’ve found a good location in Seremban to open your shop, and have determined
that the average prices and costs of operating the store are:

Price = RM 50 per pair Cost = RM 30 per pair
Rent = RM 2,500 per month Insurance = RM 500 per month
Utilities & Telephone = RM 300 per month

In addition, you plan to hire two sales ladies on a commission basis of 10% in order to provide
them with incentive to sell shoes. You are required determine the breakeven point in RM?

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DPB2033 BUSINESS MATHEMATICS

6. Amazing Kids Day Care Seeing a need for childcare in her community, Iman decided to launch
her own daycare service. Her service needed to be affordable, so she decided to watch each
child for RM25 a day. After doing her homework, Iman came up with the following financial
information:

Selling Price (per child per day) RM
25

Operating Expenses (per month) 500
Insurance 700
Rent 600
Total Operating Expenses

Costs of goods sold 15.00 per unit

The month of June has 20 workdays, Monday through Friday for four weeks. How many
children will Sue need to take care of just to break-even in her new business?

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DPB2033 BUSINESS MATHEMATICS

7. Amani Sdn Bhd has prepared the following cost analysis for 6 months of trading.

Sales (1800 sets) RM 1,530,000
Materials costs RM 150 per set
Labour costs RM150 per set
Other variable costs RM 150 per set
Overheads RM 600,000 for 6
months operation

Calculate:
i. The profit made in that year

ii. The BEP in units and RM

iii. The units need to be sold to get a profit of RM300,000
iv. The BEP in units if fixed cost decreases by 10 %
v. The BEP in unit if the selling price increases by RM 50.00 per unit.

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DPB2033 BUSINESS MATHEMATICS

8. Megah Sdn Bhd manufactures soft toys for the Selangor market. The costs incurred by the firm
are as follows:

Materials (per toy) RM
Wages (per toy) 5
Packaging (per toy) 4
Rent of premises 3
Machinery hire 5,000
Marketing and administration 3,000
1,000

The soft toys sell for an average price of RM 16. Current capacity of Megah Sdn Bhd is 3000 toys
per year.

Give the formula and compute each of the following:
i. Selling price per kilo, variable expense per kilo and fixed expense.

ii. The breakeven point in kilos.

iii. How many kilos must be sold to make a profit of RM900?

iv. If the variable expenses decrease 5% and selling per kilo increase 5% how many toys must
Megah Sdn Bhd sell his toys to break even?

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DPB2033 BUSINESS MATHEMATICS

9. The following information relates to a company, which produces a single product.

Direct labour per unit RM 22
Direct materials per unit RM 12
Variable overheads per unit RM 6
Fixed costs RM 400,000
Selling price per unit RM 60

i. Find the Break Even Point (BEP) in units and ringgit.

ii. How much is the profit if 3,500 units of products are sold?

iii. If the selling price increasing by 5%, find the new Break Even Point (BEP) in units and
value (RM).

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DPB2033 BUSINESS MATHEMATICS

10. NAZ Air Services Ltd (NAZ) is a new business that will offer helicopter flights from its base at
Subang,Selangor, The entrepreneur behind NAZ – Shafi – has put together some budgeted
financial information as part of her start-up business plan.
Using the financial information provided below, answer the questions that follow
Selected Financial Information
Fixed costs per year
Helicopter leasing & maintenance: RM 250,000
Staff wages & salaries: RM125,000
Marketing: RM60,000
Aerodrome costs: RM125,000
Expected demand revenue and costs per helicopter flight:
Average price per flight RM2,850
Variable cost per flight RM350
Expected number of flights per month 35
Using the information above, calculate:
(1) Total fixed costs for NAZ in the first year

(2) Contribution per flight

(3) The break-even output number of flights for Year 1

(4) The expected profit or loss for NAZ in Year

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DPB2033 BUSINESS MATHEMATICS

At the end of this lesson, you should be able to
3 Show the relationship between cost, revenue and profit as well as the concept of

fixed cost and variable cost using graph
3.1 Prepare the table of fixed cost, variable cost, total cost and total revenue
3.2 Construct the breakeven analysis graph by showing the total revenue, total

cost, total variable cost, fixed cost, equilibrium point, profit and loss areas
4 Illustrate the sales levels (value/unit) and profit area using graph

4.1 Identify the breakeven point
4.2 Identify sales level according to value
4.3 Identify sales level according to unit
4.4 Identify the profit and loss area

EXAMPLE 2

BEP Analysis by Graph

Solve the following
(a) Rose is a massage therapist in Port Dickson. The following information is available about Rose’s
business.

Fixed costs per year (including rent) RM10 000
Variable costs per massage (including essential oils) RM10
Number of massage therapy sessions last year
Price per 60-minute massage 400
RM50

a) Use the breakeven formula and the information above to calculate how many 60-minute
massage therapy sessions Rose has to complete to breakeven.

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DPB2033 BUSINESS MATHEMATICS

b) Construct a breakeven chart using the information above to illustrate how many 60-minute
massage therapy sessions Rose has to complete to breakeven.

(b) The Pinky T-shirt Company sells t-shirts for children as discounted prices. The owner, Shakir,
prides herself in the affordability of the t-shirts she sells, which are all RM10. Shakir has fixed
costs amounting to RM120 000 a year. The average cost of each t-shirt is RM4 and Shakir has
other variable costs of RM1 per unit. Shakir aims to sell 30 000 in the next 12-month, based on
sales in previous years.
a) Use the breakeven formula and the information above to calculate how many t-shirts Shakir
needs to sell in order to break even.

b) Construct a breakeven chart using the information above to illustrate how many t-shirts
Shakir needs to

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DPB2033 BUSINESS MATHEMATICS

(c) Mirror Glass Corporation is a company that produces glass-based products. To produce each
unit, the company determines that the variable cost (material) is RM 700 while the fixed cost is
RM 45,000. The other variable cost (wage) is RM 300 and the product has a selling price of RM
4,000 each.
You are required to:
i. Formulate the Cost Function, Total Revenue Function and Profit Function.

ii. by using calculation find the Break Even Point (BEP) in unit and RM

iii. By using the appropriate scale, construct a table and draw on the graph paper the fixed
cost, the variable cost and the total cost and the total revenue curves.

iv. From the graph, show the Break Even Point (BEP), profit and loss area.
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DPB2033 BUSINESS MATHEMATICS

v. Determine the number of units that must be sold for the company to earn a profit of RM
90,000.

vi. If the variable cost per unit increases RM 500 from the original value, what is the new
Break Even Point in unit?

(d) The following data show the information from a factory in Bandar Alor Setar, Kedah.

Selling price per unit = RM 600

Total cost function = 8q2 + 10 000

i. Find the total revenue function and the profit function.

ii. Find the breakeven point (unit and price)

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DPB2033 BUSINESS MATHEMATICS

iii. Draw a graph to show the total revenue, total cost and breakeven point

(e) HappyToys Limited is a producer and retailer of toys for children. They are an established
business and have been trading for 30 years and have a large factory in Klang Valley. They have
24 retail outlets around the Malaysia

Cost, revenue and profits for HappyToys Limited - 2020

Sales Revenue RM 6,000,000

Fixed Costs RM 2,000,000

Variable Costs RM 2,250,000

Total Costs RM 4,250,000

Profit RM 1,750,000

They currently sell 750,000 products per year at an average price of RM 8.00 per product.

1. Define the term ‘contribution’.

2. How many products does the business have to sell to break even in 2020?

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DPB2033 BUSINESS MATHEMATICS

3. On the break even chart supplied, you are to:
(a) draw the ‘revenue line
(b) draw the ‘fixed cost line’
(c) draw the ‘variable cost line’
(d) draw the total cost line’
(c) label the break even point

4. If sales for 2021 were 1,000,000 units, what level of profit would HappyToys earn? [Assume
that fixed costs, variable costs per unit and average selling price are unchanged.]

5. Evaluate why the management of HappyToys would use break even analysis.

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DPB2033 BUSINESS MATHEMATICS

(f) The output information for 75 000 units products of Syarikat Laila Majnun for
The year 2020 are shown below

Material cost RM 12,500

Labor cost RM 10,000

Rent RM 3,000
Machine RM 10,000

Revenue RM 30,000

As an industrial student in this company, you are required to:
i. Find the Break-Even Point (in RM and unit) by plotting in a graph

ii. Plot a profit area in the graph

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DPB2033 BUSINESS MATHEMATICS

(g) Price of the new coco product is given RM10.00 per unit. Meanwhile the total units sold are 5,000
units. If the total cost function is given as C=3,500 + 4.5x.
You are required to find:
i. Total revenue function.
ii. Variable cost function.

iii. Breakeven point in unit and value.

iv. Draw a breakeven point graph (inclusive a variable and a fixed cost curve), and shade
the profit and loss area in the graph.

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DPB2033 BUSINESS MATHEMATICS

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