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5.3 |
c.
Payment
Terms and Cash Discounts
A cash discount is the amount of discount on the net price (invoice amount) that is offered by a seller
to a buyer to encourage early payment of the invoice. Cash discounts are expressed as a percent of the
net price and have a time limit, after which, the full net price amount is due. A sample invoice with a
description of its payment terms is illustrated in Exhibit 5.3.
Cash discounts apply
to the net price (invoice
amount) before taxes
and shipping charges.
Exhibit 5.3: Sample Invoice with Description of Payment Terms
Cash
Discount (%)
Net
Price
3/10, n/30
Discount
Period
(days)
Credit
Period
(days)
In the invoice from 'Mindswork Electronics' in Exhibit 5.3, the 'payment terms' are 3/10, n/30. This
provides information on cash discount terms, the discount period, and the credit period for the payment.
Payment terms that end without any reference or code indicate that the payment follows 'ordinary
dating', which will be explained later in this section.
The first term, 3/10 (read as three-ten), is the discount period, which implies that the buyer will receive
a cash discount of 3% if the payment is made within 10 days of the invoice date. The buyer will not
receive a discount after the discount period of 10 days.
The second term, n/30 (read as net thirty), is the credit period, which implies that the buyer is expected
to settle the full payment within 30 days of invoice date (in other words, the full payment is expected
within 20 days from the end of the discount period).
To count the days in the payment terms, the invoice date (December 23, 2013) is considered
as day '0', December 24 is day '1', December 25 is day '2', and so on (or simply add 10 days to
December 23, that is, 33 days. December has 31 days so the remaining two days are in January).
Therefore, 10 days from the invoice date is January 02, 2014, and 30 days from the invoice date is
January 22, 2014 as shown in the following time-line diagram:
Chapter 5 | Mathematics of Merchandising
Description of payment terms 3/10, n/30 for the above invoice dated December 23, 2013 are:
■■ 3% discount for payment made on or before January 02, 2014 (discount period).
■■ Net price is due for payment made after January 02, 2014, but on or before January 22, 2014
(credit period).
Note:
■■ If the credit period is not stated, it is understood that the full payment is expected within
twenty days from the end of the discount period: i.e., if only 3/10 is provided in the payment terms,
it is understood that the payment terms are 3/10, n/30.
■■ Determining the time period in days between dates can also be calculated using the days table or
a financial calculator as explained in Chapter 8, Section 8.2, Pages 265 and 266.
Example 5.3(a)
Calculating the Payment Amounts, Given Ordinary Dating Payment Terms
Shawn purchased inventory for his factory and received an invoice for $180,750 dated January 25,
2014 with terms 3/10, 2/30, n/45. What amount will settle the invoice if paid on:
(i) February 03, (ii) February 04, (iii) February 24, (iv) February 25, or (v) March 11?
Solution
From the time-line diagram above,
■■ 3% discount for payment made on or before February 04 (1 discount period).
■■ 2% discount for payment made after February 04, but on or before February 24 (2
st
nd
discount
period).
■■ Net price is due for payments made after February 24, but on or before March 11 (credit period).
(i) If paid on February 03:
He receives a 3% discount on his invoice as it falls within the first 10 days of the
invoice date.
Therefore, he has to pay: 180,750.00 (1 - 0.03) = 180,750.00 # 0.97 = $175,327.50
(ii) If paid on February 04:
He receives a 3% discount on his invoice as it falls on the 10th day of the invoice date.
Therefore, he has to pay: 180,750.00(1 - 0.03) = 180,750.00 # 0.97 = $175,327.50.
(iii)If paid on February 24:
He receives a 2% discount on his invoice as it falls on the 30th day of the invoice date
(which is after 10 days but less than or equal to 30 days).
Therefore, he has to pay: 180,750.00(1 - 0.02) = 180,750.00 # 0.98 = $177,135.00.
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Solution
continued
(iv) If paid on February 25:
The net price has to be paid as it falls after the 30th day of the invoice date.
Therefore, he has to pay: $180,750.00.
(v) If paid on March 11:
The net price has to be paid as it falls on the 45th day (last day of credit period) of the
invoice date.
Therefore, he has to pay $180,750.00.
Payment Terms
There are three ways by which payment terms are generally stated in an invoice.
Ordinary Dating
In the previous examples for cash discounts, the payment terms are without any reference or code at
the end of the terms and are called ordinary dating terms. For example, payment terms: 3/20, n/45
refers to ordinary dating where a 3% discount is offered when the payment is made within 20 days
and the payment has to be settled within 25 days from the end of the discount period.
End-Of-Month Dating (E.O.M.)
When E.O.M. is included at the end of the payment terms, it refers to 'end-of-month dating' where the
discount period and credit period start from the end of the month of the invoice date.
For example, if an invoice dated February 12, 2014 has payment terms 3/10, n/30, E.O.M., then the
discount period and credit period start from the last day of the invoice month, which is February 28, 2014.
Therefore, a 3% cash discount is offered if a payment is made on or before 10 days following the endof-month date (with the end-of-month date being day '0'), which is March 10, 2014, and the invoice is
expected to be settled on or before March 30, 2014.
When E.O.M. or R.O.G.
is not specified in the
payment terms of an
invoice, it is ordinary
dating.
E.O.M terms are generally stated without the credit period. If the credit period is not stated, it is understood
that the full payment is expected within twenty days from the end of the discount period: i.e., if 3/10, E.O.M
is provided in the payment terms, it is understood that the payment terms are 3/10, n/30, E.O.M.
Receipt-Of-Goods Dating (R.O.G.)
When R.O.G. is included at the end of the payment terms, it refers to 'receipt-of-goods dating'
where the discount period and credit period start from the date of receipt of goods.
For example, if an invoice dated March 12, 2014 has payment terms: 4/10, n/30, R.O.G. and goods
are received on March 21, 2014, then the discount period and credit period start from March 21, 2014.
Therefore, a 4% cash discount is offered if the payment is made on or before 10 days from the date the
goods were received (with date of the receipt of goods being day '0' or simply add 10 to March 21),
which is March 31, 2014, and the invoice is expected to be settled on or before April 20, 2014.
Note: When E.O.M or R.O.G is specified, any payments made before the start of the first discount
period, will qualify for the first discount rate.
Example 5.3(b)
Calculating the Payment Amounts, Given E.O.M. Dating Payment Terms
An invoice dated March 25, 2014 for $65,000 has payment terms: 2/10, E.O.M. What payment
will settle the invoice if it is paid on: (i) March 28, (ii) April 06, or (iii) April 11?
Solution
E.O.M. is specified at the end of the payment terms. Therefore, the discount period starts from the last
day of the invoice month, which is March 30. As the credit period is not stated, it is understood that the
full payment is expected within 20 days from the end of the discount period, i.e., n/30.
Chapter 5 | Mathematics of Merchandising
Solution
continued
■■ 2% discount for payment made on or before April 10 (discount period).
■■ Net price is due for payments made after April 10, but on or before April 30 (credit period).
(i) If paid on March 28:
The date falls within the 2% discount period.
Therefore, payment amount = 65,000.00 (1 - 0.02) = $63,700.00
(ii) If paid on April 06:
The date falls before the start of the first discount period and will qualify for the
2% discount rate.
Therefore, payment amount = 65,000 .00 (1 - 0.02) = $63,700.00
(iii)If paid on April 11:
The date falls after the discount period, but within the credit period.
Therefore, the net payment is due and the payment amount is $65,000.00.
Example 5.3(c)
Calculating the Payment Amounts, Given R.O.G. Dating Payment Terms
A $50,000 invoice dated March 20 has payment terms 5/10, n/30, R.O.G. However, the goods were
received on March 25.
(i) When does the discount period end?
(ii) When does the credit period end?
(iii)What is the amount of cash discount if the invoice is settled on April 02?
Solution
R.O.G. is specified at the end of the payment terms.
Therefore, the discount period starts from the date
of receipt of the goods, which is March 25.
(i) The discount period ends on April 04, i.e.,
10 days after R.O.G.
(ii) The credit period ends on April 24, i.e.,
20 days after the end of the discount period.
(iii)If the invoice is settled on April 02, it is eligible for a 5% discount as it falls within the 5%
discount period.
Therefore, the amount of cash discount = 50,000.00(0.05) = $2500.00
Partial Payments
A partial payment is a portion of the invoice amount that a buyer
pays within the discount period to take advantage of a cash
discount.
The cash discount is applied to the amount paid. Therefore,
Not all sellers allow buyers to
make partial payments and
receive cash discounts on
the portion of invoice paid.
Amount Paid = Amount Credited - Amount of Discount
= Amount Credited - (d # Amount Credited)
= Amount Credited(1 - d)
Amount Credited =
[Compare with N = L(1 - d)]
Amount Paid
(1 - d)
The amount credited to the account is the partial payment plus the partial cash discount, as
calculated using the following formula:
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Chapter 5 | Mathematics of Merchandising
Formula 5.3
Amount Credited
Note: The cash discount is only applied on the amount paid within the discount period and not on
the invoice amount. If a payment of $1000 is made within the 10% discount period, the amount
1000 =
credited would be
= $1111.11 (i.e., $1000 payment in the 10% cash discount period
(1 - 0.10)
has the equivalent value of $1111.11).
Example 5.3(d)
Calculating the Payment Amount When a Partial Payment is Made Within the
Discount Period
Rolaxes Industries purchased a large 4-colour printing machine and received an invoice of $150,000
dated March 17, 2014 with terms 2/10, n/30. If it made a partial payment of $50,000 on March 20 and
settled the balance on April 08, calculate the total amount paid for the machine.
Solution
■■ 2% discount for the payment made on or before March 27 (discount period).
■■ Net price was due for payments made after March 27, but on or before April 16 (credit
period).
The payment of $50,000 on March 20 was within the 2% discount period. Therefore, the printing
company would have received a credit equivalent to 50,000 = 51,020.40816... = $51,020.41
(1 - 0.02)
Therefore, the balance that they would then have had to pay,
150,000.00 - 51,020.40816... = 98,979.59184... = $98,979.59
The balance payment on April 08 fell outside the discount period, but within the credit period.
Since the company would not have received any discount on this amount, it would have had to
pay $98,979.59.
Therefore, the total amount paid for the machine = $50,000.00 + $98,979.59 = $148,979.59.
Example 5.3(e)
Calculating the Payment Amount When Two Partial Payments are Made Within the
Discount Periods
Rianna furnished three floors of her office with new furniture and received an invoice dated
January 15, 2014 for $250,000 with the following terms: 3/10, 2/30, n/45.
(i) If she paid $100,000 on January 25, 2014, what was the balance to be paid?
(ii) What was the amount of the second payment made on February 14, 2014 that reduced the
balance to $70,000?
(iii)If she settled the balance on March 01, 2014, what was her total payment for the furniture?
Chapter 5 | Mathematics of Merchandising
Solution
■■ 3% discount for payment made on or before January 25 (1 discount period).
■■ 2% discount for payment made after January 25, but on or before February 14 (2 discount period).
■■ Net price was due for payment made after February 14, but on or before March 01 (credit period).
st
nd
When amounts
represent physical
transactions, they are
generally rounded to
two decimal places
before being used in
further calculations.
(i) $100,000 paid on January 25 was within the 3% discount period
100,000
Amount Paid
=
= 103,092.7835... = $103,092.78
Amount Credited =
(1 - 0.03)
(1 - d)
Balance on that invoice after this payment on January 25:
$250,000.00 - $103,092.78 = $146,907.22
(ii) Since the balance after the second payment was $70,000, the amount credited at the time
the second payment was made should have been:
$146,907.22 - $70,000.00 = $76,907.22
Amount Paid
Amount Credited =
(1 - d)
76,907.22 =
Amount Paid
(1 - 0.02)
76,907.22 =
Amount Paid
(0.98)
Amount paid = 0.98 × 76,907.22 = 75,369.0756 = $75,369.08
Therefore, $75,369.08 was the amount of the second payment she made on February 14.
(iii)Her balance payment of $70,000 on March 01 was not eligible for any discounts and she
should have paid the net price of $70,000.
Therefore, her total payment = $100,000 + $75,369.08 + $70,000 = $245,369.08
5.3 |
Exercises Answers to the odd-numbered problems are available at the end of the textbook
Identify the last date of the discount period and the credit period for the payment terms with ordinary dating in Problems 1 and 2.
1.
Invoice Date
Payment Terms
Last Date of
Discount Period
Last Date of
Credit Period
a.
January 01, 2012
3/10, n/30
?
?
b.
March 15, 2014
2.5/7, n/45
?
?
c.
April 25, 2014
3/10, 1/30, n/45
?
?
d.
July 22, 2014
2.5/10, 1.5/30, n/60
?
?
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2.
Invoice Date
Payment Terms
Last Date of
Discount Period
Last Date of
Credit Period
a.
February 18, 2012
2/10, n/30
?
?
b.
October 06, 2014
3/10, n/45
?
?
c.
February 25, 2012
2/7, 1/30, n/45
?
?
d.
August 23, 2014
3/10, 2.5/30, n/60
?
?
3. Foresteel Inc., a manufacturer of steel tubes, purchased raw materials from Premier Controls Ltd. and received
an invoice for $20,500 dated February 28, 2014 with the following terms: 2/10, 1/30, n/45. What amount does
Foresteel Inc. have to pay to settle the invoice if paid on the following days of 2014:
a. March 10? b. March 11? c. March 30? d. April 14?
4. The purchasing department of a leading information technology company received an invoice of $260,800 for the
purchase of new computers for its software development team. The invoice was dated February 14, 2014 and had
the following payment terms: 2/7, 1.5/30, n/45. What amount does the company have to pay to settle the invoice
on the following days of 2014:
a. February 21? b. February 22? c. March 16? d. March 31?
5. Ella purchased some furniture for her office and received an invoice for $18,800 dated September 16, 2014 with
payment terms 3/7, 2/30, n/60. What amount does she have to pay on October 16, 2014 to settle this invoice?
6. What payment on November 21, 2014 will settle an invoice for $3150 dated October 22, 2014 and payment terms
3/10, 2.5/30, n/60?
7. DCM Clocks received the following two invoices from its supplier: $27,500 on December 19, 2014 and $22,500 on
January 08, 2015. If the payment terms on both the invoices were 2/10, 1/30, n/60, calculate the amount that must
be paid by DCM Clocks to settle both of these invoices on January 18, 2015.
8. A publisher received an invoice for $180,750 on October 20, 2014 and another invoice of $145,000 on November
09, 2014 from its printer. The payment terms on both the invoices were 3/10, 2.5/30, n/45. What amount must be
paid by the publisher to settle both of these invoices on November 19, 2014.
9. Three invoices for the amounts of $35,800, $25,000, and $40,650 were received on March 22, 2014, April 21,
2014, and May 14, 2014, respectively. If the payment terms are 3/7, 2/30, n/60, calculate the amount that must be
paid on May 21, 2014 to settle all three invoices.
10. How much must be paid on December 20, 2014 to settle three invoices of values $125,750, $85,000, and $12,200 that
were received on November 19, 2014, November 20, 2014, and December 10, 2014, respectively. The payment terms
are 3/10, 2/30, n/45.
11. Nina received an invoice for $10,263 dated March 18, 2015 with payment terms 2.5/10, n/30 for the purchase of
fertilizer for her vineyard. If she made a partial payment of $5000 on March 28 and settled the balance amount on
April 17, what was the total amount paid for the fertilizer?
12. A retailer purchased winter clothes from a wholesaler and received an invoice for $40,618 dated November 25,
2014 with payment terms 3/15, n/30. If the retailer made a partial payment of $20,000 on December 10 and settled
the balance on December 23, calculate the total amount paid for the clothes.
13. Suzanne received goods shipped to her from Halifax along with an invoice of $3000 that had payment terms 2.5/10,
n/30. If she made a partial payment of $1000 during the discount period, calculate the balance on the invoice.
Chapter 5 | Mathematics of Merchandising
14. Whitney, the owner of a recording studio, received an invoice for $2500 that had payment terms 1/15, n/30. If she
made a partial payment of $2000 during the discount period, calculate the balance on the invoice.
15. Nancy and Nikki run a very successful bakery in Oshawa, Ontario. On July 29, 2014 they received an invoice of
$1750 with terms 3/7, 1.5/30, n/45 from their flour supplier. If they made a partial payment of $1250 on August
28, 2014, calculate the outstanding balance.
16. If a payment of $5000 was made on October 05, 2014 against an invoice for $30,000 dated September 05, 2014
with terms 3/10, 2/30, n/60, calculate the outstanding balance.
17. Pamela, the purchasing manager, received an invoice for $290,000 dated March 17, 2014 with payment terms 2/7,
1.5/30, n/45. She made a first payment of $140,500 on March 24, a second payment of $100,000 on April 16, and
the balance on May 01.
a. What was the balance amount after the first payment?
b. What was the amount paid on May 01?
18. A company received an invoice dated October 20, 2014 with terms 1.5/10, 0.5/30, n/60 for an amount of $150,860.
It made a first payment of $65,500 on October 30, 2014, a second payment of $40,250 on November 19, 2014, and
the balance on December 19, 2014.
a. What was the balance amount after the first payment?
b. What was the amount paid on December 19, 2014?
Identify the last date of the discount period and the credit period for the payment terms with E.O.M. and R.O.G. dating
in Problems 19 and 20.
19.
Invoice Date
Payment Terms
Date Goods Were
Received (R.O.G.)
Last Date of
Discount Period
Last Date of
Credit Period
a.
August 12, 2014
3/10, E.O.M.
August 15, 2014
?
?
b.
July 01, 2014
1.5/10, E.O.M.
July 05, 2014
?
?
c.
February 21, 2012
3/7, n/30, R.O.G.
February 28, 2012
?
?
d.
June 12, 2012
2.5/10, n/45, R.O.G.
July 16, 2012
?
?
Last Date of
Discount Period
Last Date of
Credit Period
20.
Invoice Date
Payment Terms
Date Goods Were
Received (R.O.G.)
a.
June 30, 2014
2/10, E.O.M.
July 05, 2014
?
?
b.
October 18, 2014
1.5/10, E.O.M.
October 25, 2014
?
?
c.
April 20, 2012
2/7, n/30, R.O.G.
May 10, 2012
?
?
d.
August 02, 2012
1.5/10, n/45, R.O.G.
August 23, 2012
?
?
21. An invoice for $120,800 dated January 27, 2014 for a shipment of furniture has payment terms 3/15, E.O.M. What
payment will settle the invoice if it is paid on:
a. January 31?
b. February 15? c. March 01?
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22. Built-in Installers received an invoice dated February 24, 2014 for $83,500 for electrical appliances that it
purchased. If the payment terms on the invoice were 2/10, E.O.M., what payment would settle the invoice if it is
paid on:
a. February 27? b. March 10? c. March 30?
23. Meghan, the owner of a brewery in Toronto, receives a shipment of barley on May 05, 2014 with an invoice dated
May 01, 2014 valued at $30,600 and cash discount payment terms 3/10, n/30, R.O.G. What cash discount would she
receive if the invoice is settled on the following dates:
a. May 10?
b. May 15?
c. June 04?
24. Starlight, a Kingston based production company, shipped a truck-load of lighting equipment to a client in Halifax.
The invoice of $175,000 for the equipment was dated August 02, 2014. The equipment was received by the client
on September 10, 2014. If the payment terms were 2.5/10, n/45, R.O.G., what cash discount would the client receive
if the invoice is settled on the following dates:
a. September 10? b. September 25? c. October 10?
25. A purchasing manager of a beverage bottling factory received a shipment of raw materials with an invoice for $132,500
with terms 3/10, n/30. What payment should he make within the discount period to reduce the balance to $50,000?
26. An invoice for $56,000 has terms 1.25/15, n/45. What payment should be made within the discount period to reduce
the balance to $25,000?
27. The purchasing department of a manufacturing company received an invoice for $280,550 with payment terms
2/10, n/30. What payment should be made within the discount period to reduce the balance by $30,000?
28. A purchasing manager received a shipment of raw materials with an invoice for $120,000 with terms 2.5/10, n/30.
What payment should he make within the discount period to reduce the balance by $100,000?
29. Markus received an invoice dated April 25, 2014 for $22,760 with the following terms: 3/10, 2/30, n/45.
a. If he paid $10,000 on May 05, what is the outstanding balance?
b. After making the first payment on May 05, calculate the amount of the second payment made on May 25
that reduced the balance to $5000.
c. What was the total payment (assuming that the balance was paid during the non-discount period)?
30. Lucy was in charge of sourcing chemicals for her pharmaceutical company. She received 300 shipments of chemicals
for $280,400 with an invoice dated October 12, 2014 and payment terms 2/10, 1/30, n/45.
a. If she pays $100,000 on October 22, what is the outstanding balance?
b. What was the amount of the second payment that she made on November 11 if it reduced the balance to $69,288.89?
c. What was her total payment for the chemicals (assuming that the balance was paid during the non-discount period)?
5.4 |
Markup
Markup (M) is the amount that a business adds to the cost (C) of the product to arrive at the
selling price (S) of the product.
The relationship is expressed by the formula:
Formula 5.4(a)
Selling Price
S=C+M