Mathematics of Merchandising

1
Mathematics of Merchandising
Chapter 4
2
Learning Objectives
After completing this chapter, you will be able
to

• Calculate the net price of an item after single
  or multiple trade discounts
• Calculate a single discount rate that is
  equivalent to a series of multiple discounts
• Understand the ordinary dating notation for the
  terms of payment of an invoice
• Calculate the amount of the cash discount for
  which a payment qualifies
• Solve merchandise pricing problems involving
  markup and markdown

3
The Distribution Chain
Manufacturer
Distributor
Wholesaler
Retailer
Consumer
4
Trade Discount Amount Net Price Formulas
Net Price List price - Trade discount
amount L - L d
N L(1 - d)
Re-organize to solve for L
L N / (1 - d)
5
The price of office equipment is 3,000. The
manufacturer offers a 30 trade discount. What
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)
Or N 3000(1 - .3) 3000(.7) 2100
The price of office equipment has a 2,100 net
price and a 30 trade discount. What is the
list price?
L N / (1 - d)
1 -. 30 0.70 L 2,100 / .70 3,000
6
Chain Discounts
Two or more discounts 15/10/5
To calculate discount 15 10 5 30
Find the single equivalent discount rate 1 -
(1-d1)(1-d2)(1-d3) 1 - (.85 .90 .95) 1
- .72675 .2733 27.33
7
The price of a office furniture is 20,000. The
chain discount is 20/10/5. What is the net
price? What is the single equivalent discount
rate?
N L(1-d1)(1-d2)(1-d3)
20000 (.8.9.95) 6320
D 1 - (1-d1)(1-d2)(1-d3)
1- (.8.9.95) .316 31.6
8
Cash Discounts
Discount for prompt payment. Not taken on
freight, returned goods, sales tax, trade
discounts.
9
Ordinary Dating Method
N L(1 - d)
Two ten, net thirty
N 500(1-.02) 500(.98) 490.00
500 invoice dated May 3 terms 2/10, n/30 paid
on May 10.
Discount Period (10 days)
10
Partial Payment
Sara owes 400. Saras terms were 3/10, n/30.
Within 10 days Sara sent in a payment of 100.
How much is her new balance?
Amount credited, L Amount paid, N / (1-d)
or
Amount credited payment / (1 - d)
Amount credited
100 / .97
103.09
- 400 /-
296.91
New balance
11
Terminology
Cost (C) - The price retailers pay to a
manufacturer
Selling Price (SP) - The price retailers charge
customers
Markup, margin, or gross profit (M) - The
difference between the cost of bringing the goods
into the store and the selling price
Operating expenses or overhead (OE) - The
regular expenses of doing business such as rent,
wages, utilities, etc.
Net profit or net income (OP) - The profit
remaining after subtracting the cost of bringing
the goods into the store and the operating
expenses
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Basic Selling Price Formula
Selling price (SP) Cost (C) Markup (M)
Markup (M) Operating Expense (OE)
Operating Profit (OP)
SP C M C OE OP
13
Markup Based on Cost
Dollar markup is the portion
Cost Markup Selling Price 100
33 133
Percent markup on cost is the rate
Cost is 100 - the Base
14
Johnny buys Sundays newspaper for 1.00. He
plans to sell them for 1.50. What is Johnnys
markup? What is his percent markup on cost?
_SP__ 1.50 1.00 ?
(/100) ? - 1.00__ ?
SP - Cost MU
Dollar Markup Selling Price - Cost .50
1.50 - 1.00
Percent Markup based on Selling Price Dollar
Markup Cost .50
50 1.00
15
Calculating Selling Price When You Know Cost and
Percent Markup on Cost
_ 150
(/100) - 1.0__ .60
SP - Cost MU
?
?
?
SP C M SP 150
.60(150) SP 150 90
Dollar Markup
SP 240
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Calculating Dollar Markup and Percent on Cost
SP C M 35 C .40(C) 35
1.40C 1.40 1.40
_ 35 ___
(/100) - 1.0__ .40
SP - Cost MU
?
?
?
25 C
M SP - C M 35 - 25 M
10
17
Markup Based on Selling Price
Dollar markup is the portion
Cost Markup Selling Price 75
25 100
Selling Price is 100 - the Base
Percent markup on selling price is the rate
18
Johnny buys Sundays newspaper for 1.00. He
plans to sell them for 1.50. What is Johnnys
markup? What is his percent markup on selling
price?
_SP__ 1.50 1.00
(/100) 1.00 - ?__ ?
SP - Cost MU
Dollar Markup Selling Price - Cost .50
1.50 - 1.00
?
Percent Markup on Selling Price Dollar Markup
Selling Price .50
33 1.50
19
Calculating Selling Price When You Know Cost and
Percent Markup on Selling Price
_ ? 150 ?
(/100) 1.00 - ?__ .60
SP - Cost MU
SP C M SP 150
.60(SP) 0.4SP 150
M SP - C M 375 - 150 M
225
SP 150/.4 375
20
Calculating Dollar Markup and Percent on Cost
_ 35 _?___ ?
(/100) 1.00 - ?__ .40
SP - Cost MU
SP C M 35 C .40(35) 35
C 14 21 C
M SP - C M 35 - 21 M 14
Dollar Markup
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Formula Conversion For
Percent Markup on Selling Price to Percent Markup
on Cost markup on SP___ .33
.33 .50 1 - markup on SP 1-.33
.67
Percent Markup on Cost to Percent Markup on
Selling Price markup on C___ .50
.50 .33 1 markup on C 1.50
1.50
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Markdowns
Markdown percent ___Dollar markdown
Selling price (original)
Sears marked down a 50 tool set to 36. What are
the dollar markdown and the markdown percent?
50-36 Markdown
14 50 28
23
SP 57.75 / .55 105.00
_ 57.75 ? _____ ?
(/100) .45 ? __ 1.0 - .40__ .60
MU Cost SP - D RSP
RSP .6 105.00 63.00
You could alternatively have found MU, then
added to get SP, and then found the discount and
subtracted from SP