1. Mathematics of
Merchandising
Chapter 4
McGraw-Hill Ryerson©

2. Learning Objectives Calculate
After completing this chapter, you will be able to:
Calculate
LO 1.
… the net price of an item after single or multiple trade discounts
LO 2.
… a single discount rate that is equivalent to a series of multiple discounts
LO 3.
… the amount of the cash discount for which a payment qualifies

3. Learning Objectives Understand Solve
LO 4.
…the ordinary dating notation for the terms of payment of an invoice
Solve
LO 5.
…merchandise pricing problems involving mark ups and markdowns

4. The Distribution Chain Receive varying levels of ‘trade discounts’
Middlemen
Middlemen
Manufacturer
Distributor
Receive varying levels of ‘trade discounts’
Wholesaler
Retailer
Consumer

5. Trade Discount Calculating D Discount Rate List Price L
LO 1.
Calculating
Formula
Amount of discount = dL D
Discount Rate
List Price L
Formula
Net Price = L(1 – d)
i.e.
Net Price = List Price – Amount of Discount Q

6. Trade Discount Q Net Price = L(1 – d) 30% = 3000(1 – .3) = 3000(.7)
The price of office equipment is $ The manufacturer offers a % trade discount Find the net price and the trade discount amount.
Formula
Net Price = L(1 – d)
30%
= 3000(1 – .3)
= 3000(.7)
= $2100
Formula
Amount of discount = dL
= .3* $3000 = $900
More…

7. /(1 – .3) Trade Discount = $3000 Q Net Price = L(1 – d) N/(1 – d) L =
An order for power tools has a $2100 net price after a 30% trade discount. What is the list price?
Formula
Net Price = L(1 – d)
N/(1 – d)
L =
/(1 – .3)
= 2100
= 2100/(.7)
= $3000

8. Trade Discount Note Series Discounts Middlemen Distributor Wholesaler
LO 2.
Series Discounts
This refers to the giving of further discounts as incentives for more sales.
Middlemen
Distributor
Wholesaler
For example
15% off first
… then 10% off next
… then a further 5% off next
Note
This
does not mean a TOTAL of 30% Discount!

9. Trade Discount Q N = L(1 – d) L Formula (1-d1) (1-d2) (1-d3) N =
The price of office furniture is $ The series discounts are 20%,10%, 5% What is the net price?
Formula
N = L(1 – d) L
(1-d1)
(1-d2)
(1-d3)
N =
= 20000(1-.2)(1-.10)(1-.05)
= 20000(.8)(.9)(.95)
= 20000(.6840) = $13680

10. Trade Discount Q N = L(1 – d) 27.33%
Find the single discount rate that is equivalent to the series 15%, 10% and 5%.
N = L(1 – d)
Apply the multiple discounts to a List price of $100
Step 1
N = 100
(1-d1)
(1-d2)
(1-d3)
discounts
15%
10% 5%
.90*
= 100
(.85*
.95)
Step 2
Calculate the dollar amount of the discount
= 100
(.7268)
= 72.68
= 100 – = $27.33
27.33%

11. Trade Discount Q = 100(.8)(.92)(.98) = $72.13 Calculator
The price of car parts is $20, The series discounts are 20%, 8%, 2% What is the single equivalent discount rate?
= 100(.8)(.92)(.98)
Apply the multiple discounts to a List price of $100
Step 1
= $72.13
discount =
100 – 72.13
Step 2
Calculate the dollar amount of the discount
= 27.87
= %
Calculator

12. = 100 (.8)(.92)(.98)
Step 1
Step 2
100
72.13
27.87
72.13 .8
100
.92
27.87
.98
27.87 %

13. Cash
Discount

14. A discount given for the prompt payment of an account.
Cash Discount
LO 3.
A discount given for the prompt payment of an account.
Invoice
Returned Goods
Freight
Sales Tax
&
Trade Discounts
No Cash Discount

15. May Cash Discount Discount & Credit Periods Discount period
Within 10 Days
Period for buyer to take advantage of Discount Terms
Within 30 Days
Credit period
Period for buyers to pay invoices
Terms

16. IF Not …then full amount payable in 30 days
Cash Discount
LO 4.
Terms
Invoice
Terms 2/10, n/30
Dated May 3
2% discount IF paid in 10 days
Terms 2/10, n/30
IF Not …then full amount payable in 30 days
Paid on May 10th
$500
Therefore, discount can be claimed!
Net payment

17. Cash Discount N = 500(1-.02) = 500(.98) = $490 N = L(1 – d) $500
Formula
N = L(1 – d)
Invoice
$500
Terms 2/10, n/30 N
= 500(1-.02)
= 500(.98)
= $490

18. Partial Payments Q
You owe $400. Your terms were 3/10, n/30. Within 10 days you sent in a payment of $100. How much is your new balance?
Amount credited L = Amount paid /(1-d)
Step 1
- or -
Amount credited = Payment /(1-d)
= $100/.97
Amount credited
= $103.09
Step 2
Old Balance =$400
- $ =
$ New Balance

19. Mark Up
&
Mark
Down

20. Selling Price Cost Terminology Marketing Manufacturer Distributor
The price charged to Consumers by Retailers
Cost
The price charged to middlemen in ‘The Distribution Chain’
Wholesaler
Retailer
Consumer

21. Terminology Marketing The X Co. Inc Gross Sales $ X
Less: Cost of Good Sold X
Gross Profit X (or Margin/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

22. Margin available to meet Expenses and make a Profit
Terminology
Marketing
Formula
Selling Price (S)
= Cost (C) +
Markup (M)
$1200
$900
$300
This side up
Computer = +
Margin available to meet Expenses and make a Profit

23. + = Up Mark 133% If the MarkUp is to be 33% on Cost then…
Selling Price (S)
= Cost (C) +
Markup (M)
100%
33.33% + =
133%
% MarkUp is
The Rate
Cost is 100% The Base
$ MarkUp is
The Portion

24. Mark Up Q
You buy Sunday newspapers for $ You plan to sell them for $ (A) What is your $ markup? (B) …and your percent markup on cost?
(A) Selling Price $1.50
Less: Cost
MarkUp $ .50
Percent markup on cost…
(B) =
Dollar Markup =
$ .50
= 50%
Cost
$ 1.00

25. Calculating the Selling Price when …
Mark Up
Calculating the Selling Price when …
you know Cost & Percent Mark Up on Cost

26. Mark Up Q
Ray’s Appliances bought a sewing machine for $ To make the desired profit, he needs a 60% markup on Cost (A) What is Ray’s $ markup? (B) What is his Selling price? $
%/100
240 2? ?
1.60
Example
Selling Price
150
Less: Cost
1.00
MarkUp
.60 90 ?
S = C M
= $ ($150)
= $ $90
= $240

27. Calculating the $MarkUp and Percent on Cost

28. Up Mark Q S = C + M (A) 35 1.40 $35 = C + .40(C) 25 1.00 1.40C 1.40
Jane’s flower business sells floral arrangements for $35. To make her desired profit, Jane needs a % markup on cost.
(A) What do the flower arrangements cost Jane?
(B) What is the dollar markup? $
%/100
S = C + M
(A)
Selling Price 35
1.40 ?
$35 = C (C)
Less: Cost 25 ?
1.00
1.40C
1.40
$35
1.40 =
MarkUp 10
.40 ?
C = $25
(B)
M = S C
M = $35 - $25
M = $10

29. Calculating the MarkUp and Percent on Selling Price

30. Up Mark Reminder Becomes …on Selling Price Formula Formula …on Cost
Selling Price (S)
= Cost (C) +
Markup (M)
% MarkUp is
The Rate
$ MarkUp is
The Portion
Cost is 100% The Base
Selling Price
Selling Price is 100%
The Base
Cost

31. Up Mark Q (A) Selling Price 2.50 1.00 Less: Cost 2.00 .80 MarkUp .50
You buy Sunday newspapers for $ You plan to sell them for $ (A) What is your $ markup? (B) …and your percent markup on Selling Price? $
%/100
(A) Selling Price
2.50
1.00
Less: Cost
2.00
.80
MarkUp
.50
.20
% markup on Selling Price
(B)
= 20%
Dollar Markup
Selling Price
$ .50
$ 2.50 =

32. Mark Up Q
Ray’s Appliances bought a sewing machine for $ To make the desired profit, a 60% markup on Selling Price is needed. (A) What is the Selling price? (B) What is the $ markup? $
%/100
1.00
.60
.40
(A)
375 2?
1.00
Selling Price
150
.40
Less: Cost
MarkUp
225
.60 ?
S = C M
(B)
M = S C
M = $375 - $150
M = $225
= $ (S)
.40S = $150
S = $150/.40 = $375

33. Up Mark Q S = C + M (A) 35 1.00 $35 = C + .40($35) 21 .60
Jane’s flower business sells floral arrangements for $35. To make her desired profit, Jane needs a 40% markup on Selling Price.
(A) What do the flower arrangements cost Jane?
(B) What is the dollar markup? $
%/100
S = C + M
(A)
Selling Price 35
1.00
$35 = C ($35)
Less: Cost 21 ?
.60 ?
$35 = C + $14
MarkUp 14
.40 ?
$35 - $14 = C
(B)
M = S C
M = $35 - $21
M = $14
$21 = C

34. Mark Up
Converting

35. % Markup on Selling Price to % Markup on Selling Price
Converting
50% MU on Cost = ? % MU on S
33% MU on SP = ? % MU on Cost
% Markup on Selling Price to
% Markup on Cost
% Markup on Cost to
% Markup on Selling Price
Formula
Formula
% markup on S
% markup on C
1 - % markup on S
1 + % markup on C
.33 =
.33
.50 =
.50
= .50
= .33
.67
1+ .50
1 .50

36. Mark
Down

37. Mark Down $Markdown %Markdown = Q Formula Selling Price (original)
Sears marked down a $50 tool set to $ What is (a) the $markdown and (b) the %markdown?
$Markdown =
Old S – New S = $50 - $36 = $14 Markdown
%Markdown =
Markdown
$ $50
= 28% =
Old S

38. Mark Down Q S = Cost/(1 - .45) S = $57.75 / .55 = $105.00 $105.00 1.00
Ski bindings bought for $57.75 were marked up 45% of the Selling Price. When the bindings were discontinued, they were marked down 40% What was the Sale Price after the 40% markdown? $
%/100
S = Cost/( )
S = $57.75 / .55
= $105.00
1.00
.45
= .55
$105.00
1.00
Selling Price ?
Less: Cost
57.75
.55 ?
MarkUp $
.45 ?
Selling Price $
S(R) = S * (1-d) = * = $63.00
1.00
.40
= .60
Less: Discount
42.00 ?
.40
$ 63.00
.60
*S(R) ?
* Reduced S

39. This completes Chapter 4