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Mathematics of Merchandising
Chapter 4
MH Ryerson
4-3
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
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The Distribution Chain
Manufacturer
Distributor
Wholesaler
Retailer
Consumer
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Trade Discount Amount & Net Price
Formulas
Trade discount amount
= List price * discount rate
N = L(1 - d)
Net Price =
List price - Trade discount amount
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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?
N = L(1 - d)
30%
N = 3000(1 - .3)
= 3000(.7)
= $2100
Trade discount = $3,000 x .30 = $900
Net Price = $3,000 - $900 = $2,100
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4-7
The price of office equipment has a
$2,100 net price and a 30% trade
discount. What is the list price?
N = L(1 - d)
L = N / (1 - d)
Re-organize to solve for L
1 -. 30 = 0.70
L = $2,100 / .70
= $3,000
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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
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= .2733 = 27.33%
4-9
The price of a office furniture is
$20,000. The chain discount is
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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4-10
The price of a office furniture is
$20,000. The chain discount is
20/10/5. What is the single equivalent
discount rate?
D = 1 - (1-d1)(1-d2)(1-d3)
If you used storage
in the last question,
now you just need
1 - rcl =
31.6%
Other wise
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.8 * .9 * .95 =
-1 =
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Cash Discounts
Discount for prompt payment. Not taken on freight,
returned goods, sales tax, & trade discounts.
Discount Period
Mar. 1
Mar. 10
Time period buyer has to take advantage of cash discount
Credit Period
Mar. 1
Mar. 31
Time period sellers gives buyers to pay invoices
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Ordinary Dating Method
Two ten, net thirty
N = L(1 - d)
$500 invoice dated May 3; terms
2/10, n/30; paid on May 10.
N = 500(1-.02)
= 500(.98)
= $490.00
May 3
Discount Period
(10 days)
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May 13
Credit Period
(30 DAYS)
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Partial Payment
Sara owes $400. Sara’s 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)
Amount credited = payment / (1 - d)
100 / .97 =
- 400 = +/-
103.09
or
Amount credited
$296.91
New balance
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Terminology
Cost - The price retailers
pay to a manufacturer
Markup, margin, or
gross profit - The difference
between the cost of
bringing the goods into
the store and the
selling price
Selling Price - The price
retailers charge customers
Operating expenses or
overhead - The regular
expenses of doing business
such as rent, wages,
utilities, etc.
Net profit or net income - 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 (S) = Cost (C) + Markup (M)
$1,200
Computer
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$900 - Price
paid to bring
computer
into store
$300 Dollars to
cover
expenses and
profit
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Markup Based on Cost
Dollar markup is
the portion
Cost + Markup = Selling Price
100%
Cost is 100%
- the Base
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33%
133%
Percent
markup 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 his
percent markup on cost?
$ Selling Price
- $ Cost
$ Markup
$1.50
- $1.00
$ .50
Percent Markup based on Cost = Dollar Markup
Cost
= $.50 = 50%
$1.00
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Calculating Selling Price When You Know
Cost and Percent Markup on Cost
Ray’s Appliances bought a sewing machine for $150. To
make desired profit, he needs a 60% markup on cost. What
is Ray’s dollar markup? What is his selling price?
$ _ % (/100)
SP 240
?
?
1.6
- Cost 150 - 1.0__
MU 90
?
.60
S = C + M
S = $150 + .60($150)
S = $150 + $90
S = $240
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Dollar Markup
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Calculating Dollar Markup and Percent on Cost
Jane’s imported flower business sells floral arrangements for
$35. To make her desired profit, Jane needs a 40% markup
on cost. What do the flower arrangements cost Jane? What
is the dollar markup?
S = C + M
$ _ % (/100)
SP 35
?
1.40
25 - 1.0__
- Cost _?___
MU 10
?
.40
$35 = C + .40(C)
$35 = 1.40C
1.40
1.40
$25 = C
M
M
M
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= S - C
= $35 - $25
= $10
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Markup Based on Selling Price
Dollar markup is
the portion
Cost + Markup = Selling Price
75%
25%
100%
Percent markup
on selling price is
the rate
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Selling Price
is 100% - the
Base
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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 his
percent markup on selling price?
Dollar Markup = Selling Price - Cost
$.50
= $1.50 - $1.00
_SP__ % (/100)
SP 1.50 1.00
- Cost 1.00 - ?__
MU .50
?
?
Percent Markup on Selling Price = Dollar Markup
Selling Price
$.50 = 33%
$1.50
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Calculating Selling Price When You Know
Cost and Percent Markup on Selling Price
Ray’s Appliances bought a sewing machine for $150. To make
desired profit, he needs a 60% markup on selling price. What is
Ray’s dollar markup? What is his selling price?
$ _ % (/100)
SP 375
?
1.00
- Cost 150 - .40
?__
MU 225
?
.60
M
M
M
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= SP - C
= $375 - $150
= $225
SP = C + M
SP = $150 + .60(SP)
0.4SP = $150
SP = $150/.4 = $375
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Calculating Dollar Markup and Percent on Cost
Jane’s imported flower business sells floral arrangements for
$35. To make her desired profit, Jane needs a 40% markup
on selling price. What do the flower arrangements cost
Jane? What is the dollar markup?
$ _ % (/100)
SP 35
1.00
21 - ?__
- Cost _?___
MU 14
?
.40
M
M
M
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= S - C
= $35 - $21
= $14
SP = C + M
$35 = C + .40($35)
$35 = C + 14
$21 = C
Dollar Markup
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Conversion
Formula for Converting Percent Formula for Converting
Percent Markup on Cost to
Markup on Selling Price to
Percent Markup on Selling
Percent Markup on Cost
Price
% markup on SP___
1 - % markup on SP
.33 =
1-.33
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.33 = .50
.67
% markup on C___
1 + % markup on C
.50 =
1+.50
.50 = .33
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?
$14
$50
= 28%
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$50-$36
Markdown
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Ski bindings bought for $57.75 were marked up
45% of the selling price. When the binding was
discontinued, it was marked down 40%. What
was the sale price of the binding?
$ _ % (/100)
MU
.45
+Cost 57.75 + ?__
.55
SP 105.00 1.0
- D _____ - .40__
RSP $63.00
??
.60
SP = 57.75 / .55
$105.00
= $105.00
RSP = .6 * 105.00
= $63.00
$63.00
You could alternatively have found MU, then added
to get SP, and then found the discount and subtracted from SP
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