chapter 6

TRADE DISCOUNT

Consumers buy goods from retailers, who in turn, purchase goods from wholesalers, manufactures or other retailers. Some wholesalers and manufactures issue catalogue describing the products sold by them. These catalogues also include the list prices (catalogue prices) of the products.

Retailers usually pay for the goods at prices lower than the list prices. The prices that the retailers pay after reduction in prices are called the net prices. The difference the list price and net price is called trade discount, that is

Trade discount = List price – Net price

A manufacturer normally quotes a discount rate in percentage to the retailer. The rate is called trade discount rate. The trade discount rate must be calculated on the list price.

Example:

If the list price of an article is RM500 and the trade discount is 20% then the amount of trade discount is RM500 X 20% = RM100

Hence the formula to calculate the amount of trade discount is given as

Amount of trade discount = List price X Trade discount rate

Example

The list price of a leather belt is RM180. A trade discount of 30% is offered. What is the net price of the belt?

List price = RM180
Trade discount = 30% X RM180
                       = RM54

Net price = List price – Trade discount
               = RM180 – RM54
               = RM126

FORMULA FOR FINDING THE NET PRICE

As an alternative to the method discussed above, the formula,

NP = L(1 – r)
can be used to find the net price. The derivation of the formula is discussed as follows

Let
Net price = NP
List price = L
Trade discount = r%

Net price = List price – Trade discount, we get

NP = L – Lr
      = L (1 – r)

Example

Nur Kaelyn Elmira offers a discount of 32 ¼% on all jeans it sells. What is the net price of a pair of jeans that is listed at RM420?

Solution

List price = RM420
Trade discount = 32 ¼% X RM420
                       = RM135.45

Net price = List price – Trade discount
               = RM420 – RM135.45
               = RM284.55

Alternatively by using the formula, we get

NP = L (1 – r)
      = 420 (1 – 32 ¼&)
      = 420 (1 – 0.3225)
      = RM284.55

Example

The net price of a camera with a 40% trade discount is RM480. What is the list price?.

Solution

Let the list price be RMX. Hence
Trade discount = 0.4X

Net price = List price – Trade discount
480 = X – 0.4X
480 = 0.6X
X = 480 ÷ 0.6
X = RM800

Hence the list price is RM800

Alternatively by using the formula, we get

NP  = L (1 – r)
480 = L (1 – 40%)
       = RM800

Example

A bill of RM1200 including prepaid handling charge of RM200 is offered a trade discount of 15%. What is the net price?

Trade discount = 0.15 X RM1000 = RM150
(It should be noted that the discount is based on the cost of goods, excluding any other costs)

Net price = (1000 – 150) + 200
               = RM1050

Example

Nur Alesya Adriana sells an item for RM100 less 20% while Nur Harisya Adlina sells the sell item for RM120 less 40%

i. Find the net prices of the item for two shops

ii. What further discount percent must be offered by the shop that sells at a higher net price in order to meet the competitor’s price?


Solution

Nur Alesya Adriana : Net price = 100 (1 – 20%) = RM80
Nur Harisya Adlina : Net price = 100 (1 – 40%) = RM72
Nur Alesya Adriana sells at a higher net price. Let the additional discount percent be r%. Therefore

72 = 80 (1 – r)
     = 28%

Nur Harisya Adlina must offer an additional 8% to meet its competitor’s price.


CHAIN DISCOUNT

Price of goods may go up or down within a period due to supply and demand situations. As such, multiple discounts are offered to the retailers on the same goods by the manufacturers or wholesalers. For instance, a wholesaler may offer trade discounts may offer trade discounts of 10%, 5% and 2%. Such multiple discounts are termed chain discount or series discount. In a chain discount, each discount rate is calculated on the successive net amount.

Example

A computer is advertised for RM4800 less 20% and 10%. Find

a. The net price
b. The total discount

Solution

List price = RM4800
Less 20% : 0.2 X RM4800 = RM960
= RM3840

Less 10% : 0.1 X RM3840 = RM384

Net price = RM3456

Total discount = RM4800 – RM3456
= RM1344

It should be noted that the chain discount of 20% and 10% is not the same as 30% since the 10% is based on the net amount (RM3840) after the first discount of 20% and not on the list price of RM4800. If a single discount of 30% is given in example 4, the net price is 70% of the list price, that is

Net price = 70% X RM4800
= RM3360

Thus, we see that chain discount of 20% and 10% is less than a single discount of 30%.


FORMULA FOR FINDING THE NET PRICE FOR A CHAIN DISCOUNT

When a chain discount is offered, the net price can be calculated more quickly by using the following formula.
For an item listed at L ringgit less r1%, r2% and r3% the net price, NP is given by

NP = L (1 – r1) (1 – r2) (1 – r3)

The formula is derived as follows

List price = L
Net price after first discount = L – Lr1
= L (1 – r1)

Net price after second discount = L (1 – r1) – L (1 – r1)r2
= L (1 – r1) (1 – r2)

Net price, NP = L (1 – r1) (1 – r2) – L (1 – r1) (1 – r2) r3
= L (1 – r1) (1 – r2) (1 – r3)

If there are two discount rates, r1 and r2 in the chain discount, the formula becomes
NP = L (1 – r1) (1 – r2)

Consider the following example.

Example

A television set with a catalogue price of RM2500 is offered a chain discount of 30%, 10% and 5%. Calculate the net price

Solution

From NP = L (1 – r1) (1 – r2) (1 – r3), we get

Net price = 2500 (1 – 30%) (1 – 10%) (1 – 5%)
= 2500 (0.7) (0.9) (0.95)
= RM1496.25

The net price can also be calculated in the following manner

List price = RM2500.00
Less 30% : 0.3 X RM2500 = RM750.00
= RM1750.00

Less 10% : 0.1 X RM1750 = RM175.00
= RM1575.00

Less 50% : 0.05 X RM1575 = RM78.78
Net price = RM1496.25

Example

A washing machine is advertised at RM2000 less 40%, 12% and 2 ½%. Find the net price.

Solution

From NP = L (1 – r1) (1 – r2) (1 – r3), we get

Net price = 2000 (1 – 40%) (1 – 12%) (1 – 2 ½%)
= 2000 (0.6) (0.88) (0.975)
= RM1029.60

Alternatively, the net price can be obtained as follows

List price = RM2000.00
Less 30% : 0.4 X RM2000 = RM800.00
= RM1200.00

Less 12% : 0.12 X RM1200 = RM144.00
= RM1056.00

Less 2 ½% : 0.025 X RM1056= RM26.40

Net price = RM1029.60


SINGLE DISCOUNT EQUIVALENT

A single discount equivalent is a single discount which is equivalent to a chain discount. The single discount equivalent, r for a chain discount of r1, r2 and r3 is given by

R = 1 – (1 – r1) (1 – r2) (1 – r3)

The formula is derived as follows
We have discuss that the net price of an item listed at RM L less r1, r2 and r3 is given as

NP = L (1 – r1) (1 – r2) (1 – r3)

Now let the single discount equivalent to the chain discount be r. Then

NP = L (1 – r)

Equating equations 1 and 2, we get

L (1 – r) = L (1 – r1) (1 – r2) (1 – r3)

Solving for r, we get
r = 1 – (1 – r1) (1 – r2) (1 – r3)

if there are two discount rates in the chain discount, then the above equation becomes r = 1 – (1 – r1) (1- r2).

Example

A product is advertised at RM1500 less 20%, 10% and 5%. Find

a. The single discount equivalent
b. The net price

Solution

a. From r = 1 – (1 – r1) (1 – r2) (1 – r3), we get
b. From NP = L(1 – r), we get

Net price = 1500 (1 – 31.6%)
= RM1026

Example

Find the single discount equivalent of 10% and 3%

Solution

From r = 1 – (1 –r1) (1 – r2), we get

r = 1 – (1 – 10%) (1 – 3%)
  = 12.7%


CASH DISCOUNT

Wholesalers, manufactures and even retailers offer reduction on the amount due to customer s who pay their bills within a stipulated period of time. This is to encourage prompt payment of bills. The credit terms which comprise the cash discount rate and the credit period are usually shown in the invoice. If the bill is settled within the specified period, the buyer needs only to pay the net amount after deducting the cash discount from the amount in the invoice.

For example, a supplier may offer terms 3/10, net 20, which means that a 3% discount is given for payment within 10 days or the full amount is due in 20 days. If the buyer pays within 10 days from the date of the invoice, he is entitled to the 3% cash discount. This is the most common type of cash discount terms and is called ordinary dating. Other dating (which are not discussed here) include end-of-month dating, receipts of goods dating and extra dating.

Example

Explain the cash discount terms

a. 2/10, 1/30, n/60
b. Net 30

Solution

a. This term means 2% of the net price may be deducted if the invoice is paid within 10 days of the date of the invoice; 1% may be deducted if the invoice is paid between 11th and 30th day and the full amount must be paid by the 60th day. After the 60th day, the bill is overdue

b. Net 30 means payment is due within 30 days of the invoice date.

Example

An invoice dated 2 January 1995 for RM4010 was offered cash discount terms of 1/10, n/30. If the invoice was paid on 11 January 1995, what was the payment?

Solution

Since the invoice was paid 9 days after the date invoice (within the discount period) the buyer was entitled to a 1% cash discount

Cash discount = 0.01 X RM4010 = RM40.10

Payment = Invoice amount – Cash discount
              = RM4010 – RM40.10
              = RM3969.90

The payment was RM3969.90

Example

An invoice dated 10 April 1995 for RM2300 was offered cash discount terms of 3/10, 2/20, n/60. Find the payment if the invoice was paid on 28 April 1995.

Solution

Since the invoice was paid 18 days after the date invoice a cash discount of 2% was obtained. The buyer did not get the 3% cash discount as the invoice was not paid within the 3% discount period of 10 days.

Net payment = Net price – Cash discount
= RM2300 – 0.02 X RM2300
= RM2254

The payment was RM2254

Example

The total of an invoice with cash discount terms of 3/10, n/30 amounts to RM2090 which includes a prepaid freight charge of RM50. Find the amount that is needed to pay the invoice within the cash discount period.

Solution

Total amount including freight charge = RM2090.00
Freight charge = RM50.00
Cost of goods = RM2040.00

Cash discount = 3%(2040) = RM61.20
                      = RM1978.00

Freight charge = RM50.00

Amount to be paid = RM2028.80



BORROWING TO TAKE ADVANTAGE OF THE CASH DISCOUNT

Not many businesses have sufficient cash in hand to take advantage of the cash discount offered. Many of these companies borrow from banks on short term loans to take advantage of the offer

Consider the following example

Example

Anwar purchases some goods valued at RM2000 with a cash discount terms of 5/10, n/60. What will be the annualized cost of the credit if the cash discount is not taken?

Solution

Cash discount not taken = 5% X RM2000
                                     = RM100

Credit period = 60 – 10 days
                     = 50 days

From the formula I =Prt, we get

100 = 1900 X r X 50 ÷ 360
r = 37.9%

Hence the annualized cost of credit is 37.9%

Alternatively, the following formula can be used

Annualised cost = Discount percent X 360
100 – Discount percent Credit period
= (5% ÷ 95%) X (360 ÷ 50)
= 37.9%

Example

On 20 May, Nur Irdina Darwisya purchased some goods invoiced at RM3000 with cash discount terms of 3/10, n/30. In order to pay the invoice on 30 May, she borrowed the money for 20 days at 9% per annum simple interest. How much did she save by borrowing to take advantage of the discount?

Solution

Cash discount = 3% X RM3000 = RM90

Principal borrowed = RM3000 – RM90 = RM2910

Credit period = 30 days - 10 days = 20 days

Interest incurred on the borrowing = Prt
= RM2910 X 0.09 X 20 ÷ 360
= RM14.55

Amount saved = Cash discount – Interest
                       = RM90 – RM14.55
                       = RM75.45


PARTIAL PAYMENT OF INVOICE

If a buyer pays only part of the invoice within the discount period, he receives a proportionate fraction of the cash discount that is offered. He will only receive the full amount of the cash discount if he settles all the payment.

Example

An invoice amounting to RM3000 and dated 15 July 2004 offered cash discount terms of 10/15, n/30. Find the amount outstanding if the buyer paid RM1000 on 20 July 2004.

Solution

Method 1

Cash discount offered = 10% X 3000 = RM300

The buyer paid RM1000 on 20 July 2004. Hence he was entitled to the cash discount offered. Since the RM1000 payment could not settle all the amount due, he was only entitled to a proportionate fraction of the cash discount offered. If he had made a payment of RM2700 (RM3000 – RM300), he would have received RM300 cash discount. Since he paid only RM1000, he was only entitled to cash discount of

(1000 ÷ 2700) X 300 = RM111.11

Hence, the amount outstanding = RM3000 – RM1111.11
                                               = RM1888.89

Method 2

The following equation can also be used, that is

Amount paid = (credit given) X (1 – discount rate)

Since the amount paid was RM1000 and discount rate was 10%, then

1000 = (Credit given) X (1 X 10%)

Credit given = 1000 ÷ 90% = RM1111.11

Hence the amount outstanding = RM3000 – RM1111.11
                                              = RM1888.89



TRADE AND CASH DISCOUNTS

More often than not, trade and cash discounts are offered simultaneously to a buyer. We shall discuss two examples where trade and cash discounts are offered at the same time.

Example

An invoice of RM10 000 and dated 18 April 2005 was offered 25% trade discount and cash discount terms of 9/10, n/30. Find

a. The trade discount offered
b. The cash discount offered
c. The net payment if the invoice was paid on 28 April 2005

Solution

Trade discount = 0.25 X 10000
                       = RM2500

Cash discount = 9% (10000 – 2500)
                      = RM675

Since the payment date fell within the cash discount period, he would get the 9% cash discount. Thus

Net payment = 10000 – (2500 + 675)
                    = RM6825

Example

An invoice of RM9000 dated 19 April 2005 was offered 13% trade discount and cash discount terms of 3/10, n/30. Find the net payment if the invoice was paid on 30 April 2005.

Solution

Trade discount = 0.13 X 9000
                       = RM1170

The buyer did not receive any cash discount since the last date to receive cash discount was 29 April 2005. He only received the trade discount. Thus,

Net payment = RM9000 – RM1170
                    = RM7830