business mathematics. Mathematic of merchandising

business mathematics

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Math of
Merchandising
44
Chapter 4
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MathemMathematics
ofof

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Math of
Merchandising
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Calculate
Learning Objectives
After completing this chapter, you will be able to:
… the net price of an item after single or
multiple trade discounts
… a single discount rate that is equivalent
to a series of multiple discounts
… the amount of the cash discount for
which a payment qualifies
LO 2.
LO 1.
LO 3.

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Math of
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…the ordinary dating notation for the
terms of payment of an invoice
Understand
…merchandise pricing problems
involving mark ups and markdowns
Solve
LO 5.
LO 4.
Learning Objectives

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Math of
Merchandising
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Middlemen
Manufacturer
Wholesaler
ConsumerRetailer
Distributor
Middlemen
Receive
varying
levels of
‘trade
discounts’

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Math of
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Trade Discount
Calculating
Formula
Amount of discount = dL
Discount RateList PriceD L
Net Price = L(1 – d)
Net Price = List Price – Amount of Discounti.e.
Formula
LO 1.

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Math of
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FormulaAmount of discount = dL
Trade Discount
The price of office equipment is $3000.
The manufacturer offers a
30% trade discount.
Find the net price and the trade discount
amount.
FormulaNet Price = L(1 – d)
= 3000(1 – .3)
30%
= 3000(.7)
= $2100
= .3* $3000 = $900
More…

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Math of
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Trade Discount
An order for power tools has a $2100
net price after a 30% trade discount.
What is the list price?
FormulaNet Price = L(1 – d)
L =N/(1 – d)
= 2100/(1 – .3)
= 2100/(.7)
= $3000

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Trade Discount
For example15% off first
… then 10% off next
… then a further 5% off next
Middlemen
Distributor
NoteThisdoes not mean a TOTAL of 30% Discount!
This refers to the giving of further
discounts as incentives for more sales.
Wholesaler
LO 2.
Series Discounts

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Math of
Merchandising
44
The price of office furniture is $20000.
The series discounts are 20%,10%, 5%.
What is the net price?
Formula N = L(1 – d)
L(1-d
1)(1-d
2)(1-d
3)
= 20000(1-.2)(1-.10)(1-.05)
= 20000(.8)(.9)(.95)
= 20000(.6840) = $13680
N =
Trade Discount

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Find the single discount rate that is
equivalent to the series 15%, 10% and 5%.
Apply the multiple
discounts to a
List price of
$100
N = L(1 – d)
(1-d
1)(1-d
2)(1-d
3)
discounts15%10%5%
(.85*= 100 .90*.95)
= 100 – 72.67 = $27.33
Calculate the
dollar amount
of the
discount
27.33%
N = 100
Step
1
Step
2
Trade Discount
= 100(.7268)= 72.68

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Math of
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The price of car parts is $20,000.
The series discounts are 20%, 8%, 2%.
What is the single equivalent
discount rate?
= 100(.8)(.92)(.98)
= $72.13
Step
1
Step
2
Calculate the dollar
amount of the
discount
discount = 100 – 72.13
= 27.87
= 27.87 %
Apply the multiple
discounts to a
List price of
$100
Trade Discount

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Math of
Merchandising
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100
.98
.8
.92
72.13
Step 1
= 100 (.8)(.92)(.98)
Step 2
72.13
100
27.87
27.87
27.87 %

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Math of
Merchandising
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Math of
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Invoice
Returned Goods
Freight
Sales Tax
&
Trade Discounts
A discount given for the
prompt payment
of an account.
No Cash
Discount
LO 3.

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May
Discount & Credit Periods
Discount period
Credit period
Period for buyer to
take advantage of
Discount Terms
Period for buyers to
pay invoices
Terms
Within 10 Days
Within 30 Days
Cash Discount

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Invoice
Dated May 3
Terms 2/10, n/30
Terms 2/10, n/30
2% discount IF paid in 10 days
IF Not …then full amount
payable in 30 days
Paid on May 10th
Therefore, discount can be claimed!
Terms
Net payment
LO 4.
Cash Discount
$500

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= $490
Formula N = L(1 – d)
= 500(1-.02)
= 500(.98)
N
Cash Discount
Invoice
$500
Terms 2/10, n/30

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Math of
Merchandising
44 Partial Payments
You owe $400. Your terms were 3/10, n/30.
Within 10 days you sent in a payment of $100.
How much is your new balance?
Amount credited L = Amount paid /(1-d)
- or -
Amount credited = Payment /(1-d)
= $100/.97100 - .03
= $103.09Amount credited
Step 1
Step 2
Old Balance =$400 - $103.09 =$296.91 New Balance

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Math of
Merchandising
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Mark
Up
&
Mark
D
o
w
n

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Math of
Merchandising
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Manufacturer
Wholesaler
Retailer
Distributor
Cost
The price charged
to middlemen in
‘The Distribution
Chain’
Selling
Price
The price charged
to Consumers
by Retailers
Consumer
LO 5.

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The X Co. Inc
Gross Sales $ X
Less: Cost of Good Sold X
Gross Profit X
(or Margin/MarkUp)
Less: Operating Expenses X
Net Profit (Income) $ X
Operating Expenses are the expenses the
company incurs in operating the business,
e.g. rent, wages and utilities

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Math of
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$1200
Formula
Computer
$900 $300+
This
side up
Selling Price (S)= Cost (C) +Markup (M)
=
Margin available to
meet Expenses and
make a Profit

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Math of
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33.33%
MarkUp
100%
Selling Price (S)= Cost (C) +Markup (M)
If the MarkUp is to be 33% on Cost then…
+133%
% MarkUp is
The Rate
Cost is 100%
The Base
=
$ MarkUp is
The Portion

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You buy Sunday newspapers for $1.00.
You plan to sell them for $1.50.
(A) What is your $ markup?
(B) …and your percent
markup on cost?
(A) Selling Price$1.50
Less: Cost 1.00
MarkUp $ .50
(B)Percent markup on cost…
=
Dollar Markup
Cost
=
$ .50
$ 1.00
= 50%
MarkUp

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Math of
Merchandising
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Calculating the Selling Price when …
you know Cost & Percent Mark Up on Cost
MarkUp

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Ray’s Appliances bought a sewing machine for $150.
To make the desired profit, he needs a 60% markup on Cost.
(A) What is Ray’s $ markup?
(B) What is his Selling price?
$
?
%/100
1.00
Selling Price
Less: Cost 150
MarkUp .60
S = C + M
2? 240 ?1.60
90
MarkUp
= $150 + .60($150)
= $150 + $90
= $240

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Math of
Merchandising
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Calculating the $MarkUp
and Percent on Cost
MarkUp

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Math of
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?
Jane’s flower business sells floral arrangements
for $35. To make her desired profit, Jane needs a
40% markup on cost.
(A) What do the flower arrangements cost Jane?
(B) What is the dollar markup?
(A)
?
1.00
Selling Price
Less: Cost
MarkUp .40
S = C + M
$35 = C + .40(C)35
$35
1.40
=
1.40C
1.40
? 1.40
C = $25
M = S - C
M = $35 - $25
M = $10
(B)
10
MarkUp
25
$%/100

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Math of
Merchandising
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Calculating the MarkUp
and Percent on Selling Price
MarkUp

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Math of
Merchandising
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Selling Price (S)= Cost (C) +Markup (M)
% MarkUp is
The Rate
$ MarkUp is
The Portion
Cost is 100%
The
Base
Selling Price
Formula …on Cost
Selling Price is 100%
The Base
Becomes …on Selling PriceFormula
Cost
MarkUp

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Math of
Merchandising
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You buy Sunday newspapers for $2.00.
You plan to sell them for $2.50.
(A) What is your $ markup?
(B) …and your percent markup on Selling Price?
(A) Selling Price
(B)% markup on Selling Price
Dollar Markup
Selling Price
= 20%
$%/100
1.00
=
$ .50
$ 2.50
.50MarkUp
.80
.20
Less: Cost
MarkUp
2.50
2.00

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Ray’s Appliances bought a sewing machine for $150.
To make the desired profit, a 60% markup on Selling
Price is needed. (A) What is the Selling price?
(B) What is the $ markup?
(A)
$
?
%/100
Selling Price
Less: Cost
MarkUp .60
S = C + M
= $150 + .60(S)
.40S = $150
2?
225
1.00
1.00
- .60
.40.40
S = $150/.40 = $375
375
M = S - C
M = $375 - $150
M = $225
(B)
MarkUp
150

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Math of
Merchandising
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?
Jane’s flower business sells floral arrangements for
$35. To make her desired profit, Jane needs a 40%
markup on Selling Price.
(A) What do the flower arrangements cost Jane?
(B) What is the dollar markup?
(A)
?
Selling
Price
Less: Cost
MarkUp .40
S = C + M
$35 = C + .40($35)
35 1.00
M = S - C
M = $35 - $21
M = $14
(B)
14
$35 = C + $14
$35 - $14 = C
$21 = C
? .60 21
MarkUp
$%/100

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Math of
Merchandising
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Converting
MarkUp

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Math of
Merchandising
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Converting
% Markup on Selling Price
to
% Markup on Cost
% Markup on Cost
to
% Markup on Selling Price
% markup on S
1 - % markup on S
Formula
.33
1 - .33
=
.33
.67
= .50
% markup on C
1 + % markup on C
.50
1+ .50
=
.50
1 .50
= .33
Formula
MarkUp
33% MU on SP = ? % MU on Cost 50% MU on Cost = ? % MU on S

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Math of
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Mark
D
o
w
n

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Mark
D
o
w
n
Formula
%Markdown =
$Markdown
Selling Price (original)
Sears marked down a $50 tool set to $36.
What is (a) the $markdown and (b) the %markdown?
$Markdown = Old S – New S = $50 - $36 = $14 Markdown
%Markdown = Markdown




$14

$50
Old S
= = 28%

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Math of
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*S(R)
Ski bindings bought for $57.75 were marked up 45%
of the Selling Price. When the bindings were
discontinued, they were marked down 40%.
What was the Sale Price after the
40% markdown?
?
$%/100
Selling
PriceLess: Cost
MarkUp .45
1.00
?
57.75
S = Cost/(1 - .45)

S = $57.75 / .55
= $105.00
S(R) = S * (1-d)
= 105.00* .60
= $63.00
?
1.00
- .45
= .55
$105.00
$ 47.25
.55
Less: Discount
Selling Price $105.00 1.00
?
? $ 63.00
1.00
- .40
= .60
42.00.40
.60
Mark
D
o
w
n
* Reduced S

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Math of
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This completes Chapter 4