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Mathematics of MerchandisingMathematics of Merchandising

Chapter 4Chapter 4

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Learning ObjectivesLearning Objectives

After completing this chapter, you will be able to:

> Calculate the net price of an item after single ormultiple trade discounts

> Calculate a single discount rate that is equivalent to a series of multiple discounts

> Understand the ordinary dating notation for the terms ofpayment of an invoice

> Calculate the amount of the cash discount for which a payment qualifies

> Solve merchandise pricing problems involving markup and markdown

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The Distribution ChainThe Distribution Chain

Manufacturer

Distributor

Wholesaler

Retailer

Consumer

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Trade Discount Amount & Net PriceTrade Discount Amount & Net PriceFormulasFormulas

Trade discount amount = List price * discount rate

Net Price =List price - Trade discount amount

N = L(1 - d)

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30%

The price of office equipment is $3,000. TheThe price of office equipment is $3,000. Themanufacturer offers a 30% trade discount. Whatmanufacturer offers a 30% trade discount. Whatare the trade discount amount and the net price?are the trade discount amount and the net price?

Trade discount = $3,000 x .30 = $900

Net Price = $3,000 - $900 = $2,100

N = L(1 - d)

N = 3000(1 - .3) = 3000(.7) = $2100

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The price of office equipment has aThe price of office equipment has a$2,100 net price and a 30% trade$2,100 net price and a 30% tradediscount. What is the list price?discount. What is the list price?

1 -. 30 = 0.70

L = $2,100 / .70

= $3,000

N = L(1 - d)Re-organize to solve for L

L = N / (1 - d)

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Chain DiscountsChain DiscountsTwo or more discounts:

15/10/5 To calculate discount

15 + 10 + 5 = 30%

Find the single equivalentdiscount rate:

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

= 1 - (.85 * .90 * .95)

= 1 - .72675

= .2733 = 27.33%

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The price of a office furniture isThe price of a office furniture is$20,000. The chain discount is$20,000. The chain discount is20/10/5. What is the net price?20/10/5. What is the net price?

N = L(1-d1)(1-d2)(1-d3)

.8 * .9 * .95 sto

20000 * rcl =

$6 320

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The price of a office furniture isThe price of a office furniture is$20,000. The chain discount is$20,000. The chain discount is20/10/5. What is the single equivalent20/10/5. What is the single equivalentdiscount rate?discount rate?

D = 1 - (1-d1)(1-d2)(1-d3)

.8 * .9 * .95 =

- 1 =

31.6%

If you used storage in the last question, now you just need

1 - rcl =

Other wise

31.6%

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Cash DiscountsCash Discounts

Discount for prompt payment. Not taken on freight,returned goods, sales tax, & trade discounts.

Time period buyer has to take advantage of cash discount

Mar. 1 Mar. 10

Discount Period

Credit Period

Time period sellers gives buyers to pay invoices

Mar. 1 Mar. 31

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Ordinary Dating MethodOrdinary Dating Method

$500 invoice dated May 3; terms2/10, n/30; paid on May 10.

Two ten, net thirty

May 3 May 13 April2

Credit Period(30 DAYS)

Discount Period(10 days)

N = L(1 - d)

N = 500(1-.02)

= 500(.98)

= $490.00

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100 / .97 =

Partial PaymentPartial PaymentSara owes $400. Sara�s terms were 3/10, n/30. Within 10days Sara sent in a payment of $100. How much is her newbalance?

Amount credited, L = Amount paid, N / (1-d)

Amount credited = payment / (1 - d)or

103.09Amount credited

- 400 = +/- $296.91

New balance

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Terminology TerminologySelling Price - The price

retailers charge customers

Cost - The price retailerspay to a manufacturer

Markup, margin, orgross profit - The difference

between the cost of bringing the goods into

the store and theselling price

Operating expenses oroverhead - The regular

expenses of doing businesssuch as rent, wages,

utilities, etc.

Net profit or net income - The profit remaining aftersubtracting the cost of bringing the goods into the

store and the operating expenses

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Basic Selling Price FormulaBasic Selling Price Formula

Selling price (S) = Cost (C) + Markup (M)

$1,200Computer

$900 - Pricepaid to bring

computerinto store

$300 -Dollars to

coverexpenses and

profit

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Markup Based on CostMarkup Based on Cost

Cost + Markup = Selling Price

100% 33% 133%

Cost is 100%- the Base

Dollar markup isthe portion

Percentmarkup on

cost is the rate

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Johnny buys Sunday�s newspaper for$1.00. He plans to sell them for $1.50.What is Johnny�s markup? What is hispercent markup on cost?

Percent Markup based on Cost = Dollar Markup Cost

= $.50 = 50% $1.00

$ Selling Price- $ Cost $ Markup

$1.50- $1.00 $ .50

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Calculating Selling Price When You KnowCost and Percent Markup on Cost

S = C + MS = $150 + .60($150)S = $150 + $90

Dollar Markup

SP- Cost MU

$ _ ? 150 ?

% (/100) ?- 1.0__ .60

1.6

90

240

Ray�s Appliances bought a sewing machine for $150. Tomake desired profit, he needs a 60% markup on cost. Whatis Ray�s dollar markup? What is his selling price?

S = $240

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Calculating Dollar Markup and Percent on CostCalculating Dollar Markup and Percent on Cost

S = C + M$35 = C + .40(C)$35 = 1.40C1.40 1.40

M = S - CM = $35 - $25 M = $10

SP- Cost MU

$ _ 35 _?___ ?

% (/100) ?- 1.0__ .40

25

10

1.40

Jane�s imported flower business sells floral arrangements for$35. To make her desired profit, Jane needs a 40% markupon cost. What do the flower arrangements cost Jane? Whatis the dollar markup?

$25 = C

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Markup Based on Selling PriceMarkup Based on Selling Price

Cost + Markup = Selling Price

75% 25% 100% Selling Priceis 100% - the

Base

Dollar markup isthe portion

Percent markupon selling price is

the rate

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Johnny buys Sunday�s newspaper forJohnny buys Sunday�s newspaper for$1.00. He plans to sell them for $1.50.$1.00. He plans to sell them for $1.50.What is Johnny�s markup? What is hisWhat is Johnny�s markup? What is hispercent markup on selling price?percent markup on selling price?

Dollar Markup = Selling Price - Cost

$.50 = $1.50 - $1.00

Percent Markup on Selling Price = Dollar Markup Selling Price

$.50 = 33%$1.50

SP- Cost MU

_SP__ 1.50 1.00 ?

% (/100) 1.00- ?__ ?.50

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Calculating Selling Price When You KnowCost and Percent Markup on Selling Price

SP = $150/.4 = $375

SP- Cost MU

$ _ ? 150 ?

% (/100) 1.00- ?__ .60

M = SP - CM = $375 - $150M = $225

.40375

225

SP = C + MSP = $150 + .60(SP)0.4SP = $150

Ray�s Appliances bought a sewing machine for $150. To makedesired profit, he needs a 60% markup on selling price. What isRay�s dollar markup? What is his selling price?

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Calculating Dollar Markup and Percent on CostCalculating Dollar Markup and Percent on Cost

SP = C + M$35 = C + .40($35)$35 = C + 14

$21 = CM = S - CM = $35 - $21M = $14

SP- Cost MU

$ _ 35 _?___ ?

% (/100) 1.00- ?__ .40

21

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Dollar Markup

Jane�s imported flower business sells floral arrangements for$35. To make her desired profit, Jane needs a 40% markupon selling price. What do the flower arrangements costJane? What is the dollar markup?

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ConversionConversion

Formula for Converting PercentMarkup on Selling Price toPercent Markup on Cost

% markup on SP___1 - % markup on SP

.33 = .33 = .50 1-.33 .67

Formula for ConvertingPercent Markup on Cost toPercent Markup on SellingPrice

% markup on C___ 1 + % markup on C

.50 = .50 = .33 1+.50 1.50

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MarkdownsMarkdowns

Sears marked down a $50 tool set to $36. What arethe dollar markdown and the markdown percent?

$14$50= 28%

$50-$36Markdown

Markdown percent =___Dollar markdown Selling price (original)

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MU+Cost SP - D RSP

$ _

57.75

_____ ??

% (/100) .45+ ?__ 1.0- .40__

.55

.60

SP = 57.75 / .55

= $105.00$105.00

105.00

RSP = .6 * 105.00

= $63.00$63.00

You could alternatively have found MU, then addedto get SP, and then found the discount and subtracted from SP

Ski bindings bought for $57.75 were marked upSki bindings bought for $57.75 were marked up45% of the selling price. When the binding was45% of the selling price. When the binding wasdiscontinued, it was marked down 40%. Whatdiscontinued, it was marked down 40%. Whatwas the sale price of the binding?was the sale price of the binding?

$63.00

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