7e
Contemporary Mathematics FOR BUSINESS AND CONSUMERS Brechner
Invoices, Trade Discounts,
and Cash Discounts
PowerPoint Presentation by Domenic Tavella, MBA
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
1
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PERFORMANCE OBJECTIVES
Section I The Invoice
7-1: Reading and understanding the parts of an
invoice
7-2: Extending and totaling an invoice
Section II Trade Discounts—Single
7-3: Calculating the amount of a single trade
discount
7-4: Calculating net price by using the net price
factor, complement method
7-5: Calculating trade discount rate when list
price and net price are known
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a publicly accessible website, in whole or in part.
2
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PERFORMANCE OBJECTIVES
continued
Section III Trade Discounts—Series
7-6: Calculating net price and the amount of a trade
discount by using a series of trade discounts
7-7: Calculating the net price of a series of trade
discounts by using the net price factor,
complement method
7-8: Calculating the amount of a trade discount by
using a single equivalent discount
Section IV Cash Discounts and Terms of Sale
7-9: Calculating cash discounts and net amount due
7-10: Calculating net amount due, with credit given
for partial payment
7-11: Determining discount date and net date by
using various terms of sale dating methods
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
3
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The Invoice
invoice
• A document detailing a sales transaction, containing a
list of goods shipped or services rendered, with an
account of all costs.
freight terminology
• F.O.B.—term used in quoting shipping charges
meaning “free on board” or “freight on board.”
• F.O.B. shipping point
– Buyer pays transportation charges from the vendor’s
location.
• F.O.B. destination
– Seller pays shipping charges to the buyer’s store or
warehouse and then bills the buyer for these charges on
the invoice.
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a publicly accessible website, in whole or in part.
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EXHIBIT 7-1
Typical Invoice Format
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a publicly accessible website, in whole or in part.
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EXHIBIT 7-2
Invoice Terminology and Abbreviations
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a publicly accessible website, in whole or in part.
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EXHIBIT 7-3
Shipping Terms
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a publicly accessible website, in whole or in part.
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Extending and Totaling an Invoice
invoice subtotal
• The amount of all merchandise or services on
the invoice before adjustments.
invoice total
• The final amount due from the buyer to the
seller.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
8
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STEPS
TO EXTEND AND TOTAL AN INVOICE
STEP 1 For each line of the invoice, multiply the number of
items by the cost per item.
Extended total = Number of items × Cost per item
STEP 2 Add all extended totals to get the invoice subtotal.
STEP 3 Calculate the invoice total by adding the freight
charges, insurance, and any other charges to the
subtotal.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
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Extending and Totaling an Invoice
From the following invoice, extend each
line to the total column and calculate the
invoice total and subtotal:
Stock #
Quantity
Unit
Merchandise
Description
Unit
Price
R443
125
ea.
Food Processor
89.00
11,125.00
B776
24
ea.
Microwave oven
225.40
5,409.60
Z133
6
dz.
12” Mixer
54.12
324.72
Z163
1
bx.
Mixer Cover
166.30
166.30
Invoice Subtotal
17,025.62
Shipping Charges
194.20
Invoice Total
17,219.82
Total
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
10
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Trade Discounts—Single
trade discount
• Reductions from the manufacturer’s list price
given to businesses that are “in the trade” for
performance of marketing functions.
• Trade discount × List price = Trade discount rate
list price
• Suggested retail selling price of an item, set by the
manufacturer or supplier.
• The original price from which discounts are taken.
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a publicly accessible website, in whole or in part.
11
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Trade Discounts—Single
continued
net price
• The amount a business actually pays for the
merchandise after the discount has been
deducted.
• Net price = List price – Trade discount
net price factor
• The percent of the list price a business pays for
merchandise.
• It is the multiplier used to calculate the net price.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
12
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STEPS
TO CALCULATE NET PRICE BY USING THE NET
PRICE FACTOR
STEP 1 Calculate the net price factor, complement of the
trade discount rate.
Net price factor = 100% – Trade discount rate
STEP 2 Calculate the net price.
Net price = List price × Net price factor
Note: This procedure can be combined into one step by
the formula
Net price = List price(100% – Trade discount rate)
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
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Trade Discount Example
Find the amount of the trade discount on an
MP3 player that has a list price of $249.95
less a trade discount of 20%
Trade discount = List price × Trade discount rate
Trade discount = 249.95 × .20 =
49.99
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a publicly accessible website, in whole or in part.
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Net Price—Complement Method
Example
A beauty salon has ordered for beauty supplies from
a wholesaler. The list price of the order is $2,800. If
the vendor offers a trade discount of 46%, what is
the net price of the order?
Net price = List price × Net price factor
Net price factor = 100 – 46 = 54%
Net price = 2,800 × .54 = 1,512
Alternate Method:
Net price = 2,800 (100% – 46%)
= 2,800(.54)
= 1,512
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a publicly accessible website, in whole or in part.
15
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STEPS
FOR CALCULATING TRADE DISCOUNT RATE
STEP 1 Calculate the amount of the trade discount
Trade discount = List Price – Net Price
STEP 2 Calculate the trade discount rate.
Trade discount rate = Trade discount
List Price
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a publicly accessible website, in whole or in part.
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Trade Discount Rate Example
A watch has a list price of $889 and can be
bought by the jewelry store for a net price of
$545.75. What is the amount of the trade
discount and the trade discount rate?
Trade discount amount = List price – Net price
Trade discount rate
=
Amount of trade discount
List price
Trade discount amount = 889.00 – 545.75 = 343.25
Trade discount
rate
=
343.25
889.00
= .3861 = 38.61%
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a publicly accessible website, in whole or in part.
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Trade Discounts—Series
chain, or series, trade discount
• Term used when a vendor offers a buyer more
than one trade discount.
reasons for multiple discounts:
• Position or level in the channel of distribution
• Volume buying
• Advertising and display
• Competition
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a publicly accessible website, in whole or in part.
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Trade Discounts—Series Example
Calculate the net price and trade discount
amount for merchandise with a list price of
$4,000 less trade discounts of 10/15/25.
4,000
x .10
400
4,000
- 400
3,600
3,600
x .15
540
3,600
- 540
3,060
3,060
x .25
765
3,060
- 765
2,295
Trade discount amount = List price – Net price
Trade discount amount = 4,000 – 2,295 = 1,705
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a publicly accessible website, in whole or in part.
19
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STEPS
FOR CALCULATING NET PRICE BY USING THE
NET PRICE FACTOR
STEP 1 Find the complement of the trade discount rates in
the series by subtracting each from 100% and
converting them to decimal form.
STEP 2 Calculate the net price factor of the series by
multiplying all the decimals together.
STEP 3 Calculate the net price by multiplying the list price
by the net price factor.
Net price = List price × Net price factor
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a publicly accessible website, in whole or in part.
20
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Trade Discounts—Series Net Price
Factor Example
Calculate the net price and trade discount
amount for merchandise with a list price of
$4,000 less trade discounts of 10/15/25.
100%  10%  90%  .90
100%  15%  85%  .85
100%  25%  75%  .75
.9  .85  .75  .57375
4,000  .5738  2,295
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a publicly accessible website, in whole or in part.
21
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STEPS
TO CALCULATE THE SINGLE EQUIVALENT DISCOUNT
AND THE AMOUNT OF A TRADE DISCOUNT
STEP 1 Calculate the net price factor as before by
subtracting each trade discount from 100% and
multiplying them all together in decimal form.
STEP 2 Calculate the single equivalent discount by
subtracting the net price factor in decimal form
from 1.
Single equivalent discount = 1 – Net price factor
STEP 3 Find the amount of the trade discount by
multiplying the list price by the single equivalent
discount.
Trade discount = List price × Single equivalent discount
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a publicly accessible website, in whole or in part.
22
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Trade Discounts—Series Single
Equivalent Discount Example
Motor City received an order of satellite radios
listing for $9,500 and trade discounts of 25/13/8.
Calculate the single equivalent discount and the
trade discount.
100%  25%  75%  .75
100%  13%  87%  .87
100%  8%  92%  .92
.75  .87  .92  .6003
1.0000  .6003  .3997
Trade Discount  9,500  .3997  3,797.15
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a publicly accessible website, in whole or in part.
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Cash Discounts and Terms of Sale
terms of sale
• The details of when an invoice must be paid, and if a
cash discount is being offered.
credit period
• The time period that the seller allows the buyer to pay
an invoice.
net date, due date
• The last day of the credit period.
cash discount
• An extra discount offered by the seller as an incentive
for early payment of an invoice.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
24
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Cash Discounts and Terms of Sale
continued
invoice date
• The date an invoice is written.
• The beginning of the discount and credit periods when
ordinary dating is used.
cash discount period
• The time period in which a buyer can take advantage
of the cash discount.
discount date
• The last day of the discount period.
net amount
• Amount of money due from the buyer to the seller.
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a publicly accessible website, in whole or in part.
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EXHIBIT 7-4
Terms of Sale
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a publicly accessible website, in whole or in part.
26
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EXHIBIT 7-5
Terms of Sale Time Line
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a publicly accessible website, in whole or in part.
27
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STEPS
STEP 1
TO CALCULATE CASH DISCOUNT AND NET
AMOUNT DUE
Calculate the amount of the cash discount by multiplying the
cash discount rate by the net price of the merchandise.
Cash discount = Net price × Cash discount rate
STEP 2
Calculate the net amount due by subtracting the amount of the
cash discount from the net price.
Net amount due = Net price – Cash discount
Note: As with trade discounts, buyers are frequently more interested in
the net amount due than the amount of the discount. When that
is the case, we can simplify the calculation by using the
complement method to determine the net amount due.
Net amount due = Net price(100% – Cash discount rate)
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a publicly accessible website, in whole or in part.
28
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Cash Discounts and Net Amount
Due Example
A retailer buys merchandise with an invoice amount
of $7,000. The terms of sale are 2/10, n/30. What is
the amount of the cash discount? What is the
amount due if the bill is paid by the 10th?
Cash discount  Net price  Cash discount rate
Cash discount  7,000  .02  140
Net amount due  Net price - Cash discount
Net amount due  7,000 - 140  6,860
Alternate Method:
Net amount due = 7,000 (100% – 2%)
= 7,000 (.98)
= 6,860
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a publicly accessible website, in whole or in part.
29
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Calculating Net Amount Due, with
Credit Given for Partial Payment
partial payment
• When a portion of the invoice is paid within the
discount period.
partial payment credit
• The amount of the invoice paid off by the partial
payment.
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a publicly accessible website, in whole or in part.
30
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STEPS
TO CALCULATE PARTIAL PAYMENT CREDIT AND
NET AMOUNT DUE
STEP 1 Calculate the amount of credit given for a partial
payment by dividing the partial payment by the
complement of the cash discount rate.
Partial payment
Partial payment credit =
100% – Cash discount rate
STEP 2 Calculate the net amount due by subtracting the
partial payment credit from the net price.
Net amount due = Net price – Partial payment credit
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a publicly accessible website, in whole or in part.
31
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Net Amount Due, with Credit Given
for Partial Payment Example
Metro Wireless purchased $28,900 in phones on
November 25 with terms of sale of 4/20, 3/30, n/60.
What is the net amount due if Metro Wireless sends a
partial payment of $5,000 on December 20?
November 25 to December 20  25 days
3% discount applies
5,000
5,000
Partial


 5,154.64
.97
payment credit 100%  3%
Net due amount  28,900  5,154.64  23,745.36
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a publicly accessible website, in whole or in part.
32
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STEPS
TO FINDING A FUTURE DATE USING A DAYS-IN-AYEAR CALENDAR
STEP 1 Find the “day number” of the starting date.
Note: In leap years, add 1 to the day numbers beginning
with March 1.
STEP 2 Add the number of days of the discount or credit
period to that day number.
Note: If the new day number is over 365, subtract 365.
This means the future date is in the next year.
STEP 3 Find the date by looking up the new day number
from Step 2.
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a publicly accessible website, in whole or in part.
33
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EXHIBIT 7-6
Days-In-A-Year Calendar
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34
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Finding the Net Date Example
If an invoice is dated
March 25 and is due
in 85 days, what is
the net date?
• March 25 = 84
• Due days = 85
• Total days = 169
• Due date = June 18
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a publicly accessible website, in whole or in part.
35
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Terms of Sale—Dating Methods
ordinary dating
• When the discount period and credit period start
on the invoice date.
end-of-month (EOM or proximo) dating
• Depending on invoice date, terms of sale start at
the end of the month of the invoice or the end of
the following month.
receipt of goods (ROG) dating
• Terms of sale begin on the date the goods are
received by the buyer.
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a publicly accessible website, in whole or in part.
36
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Terms of Sale—Dating Methods
continued
extra, ex, or x dating
• The buyer receives an extra discount period as an
incentive to purchase slow-moving or out-of-season
merchandise.
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a publicly accessible website, in whole or in part.
37
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Ordinary Dating Example
An invoice is dated May 5 with terms of 4/15,
n/30. What are the discount date and net
date?
Discount date = May 5 + 15 days = May 20
Net date =
=
=
May 5 + 30 days
26 days remaining in May
4 days in June
June 4
Alternate calendar method:
May 5 = 125 + 30 = 155 = June 4
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a publicly accessible website, in whole or in part.
38
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EOM Dating Example
EOM Dating:
• For invoices dated between the 1st of the month and
the 25th, terms begin the beginning of the following
month. For invoices dated after the 25th, skip a
month and the terms begin the beginning of the
following month.
Example: An invoice is dated August 29 with terms of
4/15 EOM. What are the discount date and the net
date? After the 25th of the month, terms of sale begin after the end
of the following month.
Discount date = October 15
Net date = October 15 + 20 days = November 4
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a publicly accessible website, in whole or in part.
39
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ROG Dating Example
An invoice dated January 15 has terms of 3/20
ROG. The goods are delayed in shipment and
arrive March 2. What are the discount date and
the net date?
• Discount date = March 2 + 20 = March 22
• Net date = March 22 + 20 days = April 11
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a publicly accessible website, in whole or in part.
40
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Extra Dating Example
What are the discount date and the net date
for an invoice dated November 6, with terms
4/15, 30 extra?
Discount date =
November 6 + 15 days + 30 days = December 21
Net date = December 21 + 20 =
December 21 = 355 + 20 days = 375 – 365 = January 10
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a publicly accessible website, in whole or in part.
41
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CHAPTER REVIEW PROBLEM 1
Solve the following word problem:
• Lawn and Garden buys lawnmowers that list for
$889.95 less a 30% trade discount. What are the
amount of the trade discount and the net price of
each lawnmower?
Trade discount = 889.95 × .30 =
Net price = 889.95 – 266.99 =
266.99
$622.96
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a publicly accessible website, in whole or in part.
42
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CHAPTER REVIEW PROBLEM 2
Solve the following word problem:
• If Warner Co. sends a $1,350 partial payment for
an invoice of $4,609.29 with terms of 3/10, n/30,
by the discount date, what is the balance due on
the invoice?
Partial
payment credit
1,350
1,350


 1,391.75
100%  3% .97
Net due amount  4,609.29  1,391.75  3,217.54
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a publicly accessible website, in whole or in part.
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CHAPTER REVIEW PROBLEM 3
What is the net price factor for trade
discounts of 25/15/10?
100%  25%  75%  .75
100%  15%  85%  .85
100%  10%  90%  .90
.75  .85  .90  .57375
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a publicly accessible website, in whole or in part.
44
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CHAPTER REVIEW PROBLEM 4
What is the single equivalent discount for
this trade discount series: 20/15/11?
100%  20%  80%  .80
100%  15%  85%  .85
100%  11%  89%  .89
.80  .85  .89  .6052
1.0000  .6052  .3948
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a publicly accessible website, in whole or in part.
45
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CHAPTER REVIEW PROBLEM 5
Solve the following word problem:
• A firm orders merchandise on May 4. Terms of
sale are 2/10, n/30 EOM. What are the discount
date and the net date?
Date is between the 1st and the 25th.
Discount date: June 10
Net date: June 10 + 20 days = June 30
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a publicly accessible website, in whole or in part.
46