Mathematics of Merchandising

8/10/2019 Mathematics of Merchandising

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Harith Shaari, School of

Management & Business

Math of

Merchandising

44 - 1

Chapter 4



Mathematicsof


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Math of

Merchandising

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Calculate

Learning Objectives

After completing this chapter, you will be able to:

thenet pr iceof an item after single or

multipletrade discounts

asingle discount ratethat is equivalent

to a series of multiple discounts

theamountof the cash discount for

which a payment qualifies

LO 2.

LO 1.

LO 3.


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Math of

Merchandising

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the ordinarydating notationfor the

termsof paymentof an invoice

Understand

merchandise pricing problemsinvolvingmark upsand markdowns

Solve

LO 5.

LO 4.

Learning Objectives


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Merchandising

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Middlemen

Manufacturer

Wholesaler

ConsumerRetailer

Distributor

Middlemen

Receivevarying

levels of

tradediscounts


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Merchandising

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Trade Discount

Calculating

Formula

Amount ofdiscount=dL

Discount Rate L ist PriceD L

NetPrice =L(1d)

NetPrice=L istPriceAmountofDiscounti.e.

FormulaLO 1.


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Merchandising

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Formula Amount ofdiscount=dL

TradeDiscount

The price of office equipment is $3000.The manufacturer offers a

30% trade discount.

Find the netprice and the trade discount amount.Formula NetPrice=L(1d)

=3000(1.3)

30%

=3000(.7)=$2100

= .3* $3000 = $900More


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Math of

Merchandising

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TradeDiscount

An order for power tools has a$2100

netprice aftera 30% trade discount.

What is thelistprice?

Formula NetPrice=L(1d)

L = N/(1d)= 2100 /(1.3)= 2100/(.7)= $3000




Math of

Merchandising

44 - 8

TradeDiscount

For example 15% off first

then 10% off next

then a further 5% off next

Middlemen

Distributor

Note This does not meana TOTAL of 30% Discount!

This refers to the giving of further

discounts as incentives for more sales.

Wholesaler

LO 2.Series Discounts




Math of

Merchandising

44 - 9

The priceof office furniture is $20000.

The series discountsare 20%,10%,5%.

What is the netprice?

Formula N =L(1d)

L(1-d

1

) (1-d2

) (1-d3

)

= 20000(1-.2)(1-.10)(1-.05)

= 20000(.8)(.9)(.95)

= 20000(.6840) = $13680

N =

TradeDiscount




Math of

Merchandising

44 - 10

Find thesinglediscount rate thatis

equivalent to theser ies 15%,10% and5%.

Apply the multiple

discountsto a

List priceof $100

N=L(1d)

(1-d1) (1-d2) (1-d3)

discounts 15% 10% 5%

(.85*= 100 .90* .95)

= 10072.67= $27.33

Calculate the

dollaramount

of the discount

27.33%

N = 100Step1

Step2

TradeDiscount

= 100 (.7268) = 72.68


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The priceof car parts is $20,000.

The ser ies discountsare 20%, 8%,2%.

What is the single equivalentdiscountrate?

= 100(.8)(.92)(.98)

= $72.13Step1

Step2

Calculate the dollaramountof the

discount

discount= 10072.13= 27.87

= 27.87 %

Apply the multiple

discountsto a

List priceof $100

TradeDiscount


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Math of

Merchandising

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100

.98

.8

.92

72.13

Step 1

= 100 (.8)(.92)(.98)

Step 272.13

100

27.87

27.87

27.87 %


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Merchandising

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Math of

Merchandising

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CashDiscount

Invoice

Returned Goods

Freight

Sales Tax&

Trade Discounts

A discount given for theprompt payment

of an account.

No Cash

Discount

LO 3.


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Math of

Merchandising

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May

Discount & Credit Periods

Discount period

Credit period

Period for buyer to

take advantageof

Discount Terms

Period for buyers to

pay invoices

Terms

Within 10 Days

Within 30 Days

CashDiscount


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Math of

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Invoice

Dated May 3

Terms 2/10, n/30

Terms 2/10, n/30

2%discount I Fpaid in 10 daysI FNot then full amount

payable in 30 days

Paid on May 10th

Therefore, discountcan be claimed!

Terms

Net payment

LO 4.

CashDiscount

$500


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Math of

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= $490

Formula N =L(1d)

= 500(1-.02)

= 500(.98)

N

CashDiscount

Invoice

$500

Terms 2/10, n/30


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Math of

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Partial Payments

You owe $400. Your termswere 3/10, n/30.

Within 10 daysyou 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 - .03

= $103.09Amount credited

Step 1

Step 2

OldBalance =$400 - $103.09= $296.91 New Balance


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Merchandising

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Mark

&Mark


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Merchandising

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Manufacturer

Wholesaler

Retailer

Distributor

CostThe price charged

to middlemen inThe Distribution

Chain

SellingPrice

The price charged

to Consumersby Retailers

Consumer

LO 5.


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Merchandising

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The X Co. Inc

Gross Sales $ X

Less:Cost of Good Sold XGrossProfit X

(orMargin/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

Computer

$900 $300+

This

side up

SellingPrice (S) = Cost (C) + Markup (M)

=Margin available to

meetExpenses and

make aProfit


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Math of

Merchandising

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33.33%

Mark

100%


If the MarkUpis to be 33%onCostthen

+133%

%MarkUpis

TheRateCost is 100%

TheBase

=

$ MarkUpis

The Portion


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You buySunday newspapers for$1.00.

You plan to sellthem for $1.50.

(A) What is your $ markup?

(B) and your percent markup on cost?

(A) SellingPrice $1.50

Less:Cost 1.00

MarkUp $ .50

(B) Percent markup on cost= DollarMarkup

Cost= $ .50

$1.00=50%

Mark


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Math of

Merchandising

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Calculating the Sell ing Pr icewhen

you knowCost & Percent Mark UponCost

Mark


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Rays Appliances bought a sewing machine for $150.

To make the desired profit, he needs a 60% markup on Cost.

(A) What is Rays $ markup?

(B) What is his Selling price?

$

?

%/100

1.00SellingPrice

Less:Cost 150

MarkUp .60S = C + M

2?240 ?1.60

90

Mark

= $150+ .60($150)= $150 + $90

= $240


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Merchandising

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Calculating the $MarkUpand Percent onCost

Mark


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Merchandising

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?

Janes flower businesssellsfloral arrangementsfor $35. To make her desired profit, Jane needs a

40% markup on cost.

(A) What do the flower arrangements costJane?

(B) What is the dollar markup?

(A)

?

1.00

SellingPrice

Less:Cost

MarkUp .40

S = C + M$35 = C + .40(C)35

$35

1.40=

1.40C

1.40

?1.40

C= $25M = S - C

M = $35- $25

M = $10

(B)

10

Mark

25

$ %/100


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Calculating the MarkUpand Percent onSelling Price

Mark


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Merchandising

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%MarkUpis

TheRate

$ MarkUpis

The Portion

Cost is 100%

TheBase

Selling Price

Formula on Cost

Selling Priceis 100%

The Base

Becomes on Sell ing PriceFormula

Cost

Mark

f


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Merchandising

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You buySunday newspapers for$2.00.You plan to sellthem for $2.50.(A) What is your $markup?

(B) and your percent markup on Sell ing Price?

(A) SellingPrice

(B) % markuponSell ing PriceDollarMarkup

Selling Price= 20%

$ %/100

1.00

= $ .50$2.50

.50MarkUp

.80

.20

Less:Cost

Mark

2.50

2.00

M th f


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Merchandising

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Rays Appliances bought a sewing machine for $150.

To make the desired profit, a 60% markup on Sell ing

Price is needed. (A) What is the Selling price?

(B) What is the $ markup?

(A)

$

?

%/100

SellingPrice

Less:CostMarkUp .60

S = C + M= $150+ .60(S)

.40S = $150

2?

225

1.001.00-.60

.40.40

S = $150/.40 = $375

375

M = S - C

M = $375- $150

M = $225

(B)

Mark

150

M th f

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?

Janes flower businesssellsfloral arrangements for$35. To make her desired profit, Jane needs a 40%

markup on Sell ing Price.

(A) What do the flower arrangements costJane?

(B) What is the dollar markup?

(A)

?

SellingPrice

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

?.6021

Mark

$ %/100

M th f

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Math of

Merchandising

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Converting

Mark

Math of

4 35


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Math of

Merchandising

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Converting

% Markupon Selling Price

to% MarkuponCost

% Markupon Cost

to% Markupon Selling Price

% markupon S

1 - % markupon S

Formula

.33

1 - .33=

.33

.67 = .50

% markupon C

1 + % markupon C

.50

1+ .50=

.50

1 .50= .33

Formula

Mark

33% MU on SP= ? % MUon Cost50% MUon Cost = ? % MUon S

Math of

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Merchandising

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Mark

Math of

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Mark

Formula

%Markdown=$Markdown

Selling Price (original)

Sears marked downa $50tool set to$36.

What is (a) the $markdown and (b) the %markdown?

$Markdown =OldSNewS = $50-$36 =$14 Markdown

%Markdown = Markdown $14$50OldS

= = 28%

Math of

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*S(R)

Ski bindings bought for $57.75were marked up 45%of the Selling Price. When the bindings werediscontinued, they were marked down 40%.

What was the Sale Price afterthe 40% markdown?

?

$ %/100

SellingPrice

Less: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

SellingPrice $105.00 1.00

?

?$ 63.00

1.00

- .40

= .60

42.00 .40.60

Mark

* Reduced S

Math of

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This completes Chapter 4

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Mathematics of Merchandising