McGraw-Hill Ryerson© Math of Merchandising Math of Merchandising 4 4 4 - 1 Chapter 4 McGraw-Hill Ryerson© Mathem of Mathematics of

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McGraw-Hill Ryerson©

Math of

Merchandising

Math of

Merchandising

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Chapter 4Chapter 4


MathemMathematics ofof

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Math of

Merchandising

Math of

Merchandising

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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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Math of

Merchandising

Math of

Merchandising

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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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Math of

Merchandising

Math of

Merchandising

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Middlemen

ManufacturerManufacturer

WholesalerWholesaler

ConsumerConsumerRetailerRetailer

DistributorDistributor

Middlemen

Receive varying levels of

‘trade discounts’

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Math of

Merchandising

Math of

Merchandising

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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Math of

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Math of

Merchandising

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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Math of

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Math of

Merchandising

44 44Trade DiscountTrade Discount

For example 15% off first

… then 10% off next… then a further 5% off next

Middlemen


Note This does not mean a TOTAL of 30% Discount!

This refers to the giving of further discounts as incentives for more sales.


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 =


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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


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


= 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 %


List price of $100


List price of $100


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Merchandising

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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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Merchandising

Math of

Merchandising

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Merchandising

Math of

Merchandising

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.


$500

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= $490= $490

Formula Formula N = L(1 – d)

= 500(1-.02)= 500(.98)

N


Invoice

$500

Terms 2/10, n/30Terms 2/10, n/30

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Math of

Merchandising

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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Math of

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MarkMarkUpUp

&&MarkMark

DownDown

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Math of

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ManufacturerManufacturer


RetailerRetailer


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%


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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Math of

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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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Math of

Merchandising

Math of

Merchandising

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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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Merchandising

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 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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Math of

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Math of

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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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Math of

Merchandising

Math of

Merchandising

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% 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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Math of

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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 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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Math of

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Math of

Merchandising

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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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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 Selling Price. (A) What do the flower arrangements cost Jane?

(B) What is the dollar markup?

(A)

?


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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Math of

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ConvertingConverting

Mark Mark Up

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Math of

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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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Math of

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MarkMarkDownDown

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Math of

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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


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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Math of

Merchandising

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Merchandising

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This completes Chapter 4This completes Chapter 4

Documents

McGraw-Hill Ryerson© Math of Merchandising Math of Merchandising 4 4 4 - 1 Chapter 4 McGraw-Hill Ryerson© Mathem of Mathematics of