1. QMT 3301 BUSINESS MATHEMATICS
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CHAPTER 6
MATHEMATICS OF SELLING
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6.1 Markup
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In order to gain profit from selling, the company must sell their product at a higher price than the product cost.
The difference between a product’s cost and selling price is refer to as markup.
It can be either in money value or percentage.
The rate of mark-up is known as markup percentage.
Formula: Markup = Selling Price – Cost Price
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6.2 Markup Percent
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Markup is usually expressed as a percent.
It can be expressed as:
a) Markup percent based on retail price
% Mr = M x 100% R
b) Markup percent based on cost price
% Mc = M x 100% C
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Example 1:
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The cost price of a piano is RM What is the
retail price if the seller wants a 15% mark-up
based on
a) Cost price, and
b) Retail price.
Solution:
a) R = C + M
R = RM (RM 4500 x 15%)
R = RM RM 675
R = RM 5175
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b) Let the retail price be X. Then
R = C + M
X = RM X
X – 0.15X = RM 4500
0.85X = RM 4500
X = RM 4500
0.85
X = RM
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6. QMT 3301 BUSINESS MATHEMATICS
Example 2:
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ABC boutique purchases 100 dresses at a cost of
RM 18 each. The boutique expects that 20% of the
dresses will be sold at a reduced price of RM 12
each. If the boutique is to maintain a 65% mark-up
on cost on the entire purchase, find the regular
price of the dresses.
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Solution:
Cost of 100 dresses = RM 18 x 100 = RM 1800
Mark-up 65%
Sale of 100 dresses = RM 1800 x 0.65(RM 1800)
= RM 2970
Sale of 20 dresses = RM 12 x 20 = RM 240
Sale of remaining 80 dresses
= RM 2970 – RM 240
= RM 2730
Regular selling price = RM 2730 = RM per
dress
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Example 3:
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A retailer purchased 150 kg of tomato at RM 1.20
per kg. A 8% spoilage is expected. If he plans to
make a 55% mark-up based on overall cost, what
is the selling price of the tomato?
Solution:
Overall cost = RM 1.20 x 150 kg = RM 180
Amount left after deducting spoilage
= 150 kg – 0.08(150)
= 138 kg
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Mark-up 55%
R = C + M
= RM (RM 180)
= RM 279 (retail price for 138 kg)
Selling price per kg = RM 279
138
= RM 2.02
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10. 6.3 Conversion of Markup Percent
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Markup percent based on retail price:
Since R = C + M
1 + % Mc = 100% + % Mc
Hence :
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Markup percent based on cost price:
Since R = C + M
100% = 1 - % MR + % MR
Hence :
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Example :
a) The mark-up percent on cost price of an item is 20%. What is its mark-up percent based on retail price?
b) The mark-up percent based on retail price of an item is 15%. What is its mark-up percent based on cost price?
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Solution:
a) % Mr = % Mc
1 + % Mc =
= = 16.67%
b) % Mc = % MR
1 - % MR =
= = 17.65%
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6.4 Markdown
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Sometimes retailer may reduce the marked price due to special promotions, festive seasons or the items being obsolete.
Markdown is the reduction from the selling price or marked price, normally in terms of percentage.
Formula:
Markdown Amount = Old Selling Price – New Selling Price
Markdown percent based on old price,
% MD = MD x 100% OP
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Example 1:
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The markdown percent on a handphone is 15%. If
the new retail price is RM 850, find the old retail
price.
Solution:
Let the old price be RM K
% MD = MD x 100%
OP K = 850
0.15 = (K – 850) K = 850 K
0.15K = K – = RM 1000
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Example 2:
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During the year end sales, a department store
marked down a pair of shoes by 25%, making the
selling price RM 270. At this selling price, the
department store made a 18% mark-up on the
selling price. Find
a) The regular price of the shoes.
b) The cost of the shoes.
c) The mark-up percent of the shoes at the regular price.
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Solution:
a) NP = L (1 – r)
270 = L (1 – 0.25)
L = 270
0.75
= RM 360
b) R = C + M
270 = X (270)
X = 270 – 48.6
= RM
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c) Mark-up percent at regular price,
% Mr = M x 100% R
= (Regular price – Cost) x 100%
Regular price
= (360 – ) x 100%
360
= 38.5%
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6.5 Profit and Loss
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Business does not always generate income or profit.
If the business is not managed properly, it may increase operating expense and indirectly increase cost of the product.
The actual cost of the product is the purchase price plus operating expenses.
In accounting, operating expenses include cost of goods sold, official rental, advertising, salary, commission and so on.
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In general, there are three possibilities in business:
a) M = OE : Break-even
b) M > OE : Profit
c) M < OE : Loss
Where:
M = Markup
OE = Operating Expenses
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Formula:
Break-even Price, BEP = Cost Price + OE
Retail Price = Cost + Net Profit + OE
Net Profit / (Loss) = Retail Price – BEP
Gross Profit = NP + OE
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Example :
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A retailer bought a radio for RM 200. Buying
expenses amounted to RM 20. Operating
expenses incurred were 20% of the cost price. If
the retailer made a 25% net profit based on cost,
find
a) The retail price,
b) The gross profit ,
c) The net profit,
d) The breakeven price, and
e) The maximum markdown that could be offered so that there is no profit or loss.
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Solution:
a) Retail price = (220) + 0.2(220)
= RM 319
b) Gross profit = NP + OE
= 0.25(220) + 0.2(220)
= RM 99
c) Net profit = Gross profit – OE
= 99 – 44
= RM 55
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d) Breakeven price = C + OE =
= RM 264
e) Maximum reduction in price = R – BEP
= 319 – 264
= RM 55
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