business mathematics jerome chapter 04
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Chapter 4Chapter 4
McGraw-Hill Ryerson©
MathemMathematics ofof
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Calculate
Learning ObjectivesLearning
ObjectivesAfter 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 2.
LO 1.LO 1.
LO 3.LO 3.
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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 5.
LO 4.LO 4.
Learning ObjectivesLearning
Objectives
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Middlemen
ManufacturerManufacturer
WholesalerWholesaler
ConsumerConsumerRetailerRetailer
DistributorDistributor
Middlemen
Receive varying levels of
‘trade discounts’
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44 44 Trade DiscountTrade Discount
Calculating
Formula Formula
Amount of discount = dL
Discount RateDiscount Rate List PriceList PriceD L
Net Price = L(1 – d)
Net Price = List Price – Amount of Discounti.e.
FormulaFormula
LO 1.LO 1.
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FormulaFormula Amount of discount = dL
Trade DiscountTrade Discount
The price of office equipment is $3000. The manufacturer offers a 30% trade discount.
Find the net price and the trade discount amount.
FormulaFormula Net Price = L(1 – d) = 3000(1 – .3)
30%30%
= 3000(.7) = $2100
= .3* $3000 = $900More…
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44 44 Trade DiscountTrade Discount
An order for power tools has a $2100 net price after a 30% trade discount.
What is the list price?
FormulaFormula Net Price = L(1 – d)L = N/(1 – d)
= 2100 /(1 – .3)= 2100/(.7)= $3000
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44 44Trade DiscountTrade Discount
For example 15% off first
… then 10% off next… then a further 5% off next
Middlemen
DistributorDistributor
Note This does not mean a TOTAL of 30% Discount!
This refers to the giving of further discounts as incentives for more sales.
WholesalerWholesaler
LO 2.LO 2.
Series Discounts
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The price of office furniture is $20000. The series discounts are 20%,10%, 5%.
What is the net price?
FormulaFormula N = L(1 – d)L (1-d1) (1-d2) (1-d3)
= 20000(1-.2)(1-.10)(1-.05)= 20000(.8)(.9)(.95)
= 20000(.6840) = $13680
N =
Trade DiscountTrade 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
Apply the multiple discounts to a
List price of $100
N = L(1 – d)(1-d1) (1-d2)(1-d3)
discountsdiscounts 15% 10% 5%
(.85*= 100 .90* .95)
= 100 – 72.67 = $27.33
Calculate the
dollar amount of the
discount
Calculate the
dollar amount of the
discount27.33%27.33%
N = 100Step 1Step 1
Step 2Step 2
Trade DiscountTrade Discount
= 100 (.7268) = 72.68
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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 1Step 1
Step 2Step 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
Apply the multiple discounts to a
List price of $100
Trade DiscountTrade Discount
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100
.98
.8
.92
72.13
Step 1Step 1
= 100 (.8)(.92)(.98)
Step 2Step 2
72.13
100
27.87
27.87
27.87 %
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44 44 Cash DiscountCash Discount
Invoice
Returned Goods
Freight
Sales Tax
&
Trade Discounts
A discount given for the prompt payment
of an account.
No Cash Discount
LO 3.LO 3.
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May
Discount & Credit Periods
Discount periodDiscount period
Credit periodCredit period
Period for buyer to take advantage of Discount Terms
Period for buyers to pay invoices
TermsTerms
Within 10 Days
Within 30 Days
Cash DiscountCash Discount
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Invoice
Dated May 3
Terms 2/10, n/30
Terms 2/10, n/30Terms 2/10, n/30
2% discount IF paid in 10 daysIF Not …then full amount
payable in 30 days
Paid on May 10thPaid on May 10th
Therefore, discount can be claimed!Therefore, discount can be claimed!
TermsTerms
Net paymentNet payment
LO 4.LO 4.
Cash DiscountCash Discount
$500
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= $490= $490
Formula Formula N = L(1 – d)
= 500(1-.02)= 500(.98)
N
Cash DiscountCash Discount
Invoice
$500
Terms 2/10, n/30Terms 2/10, n/30
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44 44 Partial PaymentsPartial 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/.97 100 - .03100 - .03
= $103.09= $103.09Amount credited
Step 1Step 1
Step 2Step 2
Old Balance =$400 - $103.09 = $296.91 New Balance$296.91 New Balance
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MarkMarkUpUp
&&MarkMark
DownDown
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ManufacturerManufacturer
WholesalerWholesaler
RetailerRetailer
DistributorDistributor
CostCostThe price charged to middlemen in ‘The Distribution
Chain’
Selling PriceSelling Price
The price charged to Consumers by Retailers
ConsumerConsumer
LO 5.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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$1200
Formula 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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33.33%
Mark Mark Up
100%
Selling Price (S) = Cost (C) + Markup (M)
If the MarkUp is to be 33% on Cost then…
+133%
% MarkUp is
The RateCost 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%
Mark Mark Up
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Calculating the Selling Price when …Calculating the Selling Price when …you know Cost & Percent Mark Up on Cost
Mark Mark Up
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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
1.00Selling PriceLess: Cost 150
MarkUp .60
S = C + M
2? 240 ?1.60
90
Mark Mark Up
= $150 + .60($150)= $150 + $90= $240
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Calculating the $MarkUp
and Percent on Cost
Calculating the $MarkUp
and Percent on Cost
Mark Mark Up
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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
$351.40 =
1.40C1.40
? 1.40
C = $25M = S - CM = $35 - $25 M = $10
M = S - CM = $35 - $25 M = $10
(B)
10
Mark Mark Up
25
$ %/100
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Calculating the MarkUp
and Percent on Selling Price
Calculating the MarkUp
and Percent on Selling Price
Mark Mark Up
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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 Formula …on Cost
Selling Price is 100%
The Base
Becomes …on Selling PriceFormula Formula
Cost
Mark Mark Up
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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 PriceDollar Markup
Selling Price = 20%= 20%
$ %/1001.00
= $ .50$ 2.50
.50MarkUp.80 .20
Less: Cost
Mark Mark Up
2.502.00
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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 PriceLess: Cost
MarkUp .60S = C + M
= $150 + .60(S) .40S = $150
2?
225
1.00 1.00- .60 .40
1.00- .60 .40.40
S = $150/.40 = $375
375
M = S - CM = $375 - $150M = $225
M = S - CM = $375 - $150M = $225
(B)
Mark Mark Up
150
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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 PriceLess: Cost
MarkUp .40
S = C + M$35 = C + .40($35)35 1.00
M = S - CM = $35 - $21 M = $14
M = S - CM = $35 - $21 M = $14
(B)
14$35 = C + $14$35 - $14 = C$21 = C
? .60 21
Mark Mark Up
$ %/100
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ConvertingConverting
Mark Mark Up
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ConvertingConverting
% Markup on Selling Price
to % Markup on Cost
% Markup on Selling Price
to % Markup on Cost
% Markup on Cost
to % Markup on Selling Price
% Markup on Cost
to % Markup on Selling Price
% markup on S
1 - % markup on S
Formula Formula
.33
1 - .33 =
.33
.67 = .50 = .50
% markup on C
1 + % markup on C
.50
1+ .50 =
.50
1 .50 = .33 = .33
Formula Formula
Mark Mark Up
33% MU on SP = ? % MU on Cost33% MU on SP = ? % MU on Cost50% MU on Cost = ? % MU on S50% MU on Cost = ? % MU on S
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MarkMarkDownDown
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44 44 MarkDown
Formula 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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*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
= $105.00S(R) = S * (1-d) = 105.00* .60 = $63.00
?
1.00- .45= .55
1.00- .45= .55
$105.00
$ 47.25 .55
Less: Discount Selling Price $105.00 1.00 ?
? $ 63.00
1.00- .40= .60
1.00- .40= .60
42.00 .40.60
MarkDown
* Reduced S
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This completes Chapter 4This completes Chapter 4