Mathematics of Merchandising - mheducation.ca of Merchandising Chapter 4. 4-3 ... desired profit, he...
Transcript of Mathematics of Merchandising - mheducation.ca of Merchandising Chapter 4. 4-3 ... desired profit, he...
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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
14
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