CHAPTER
3
Trade - Cash
Discounts and Markup Markdown
LEARNING OBJECTIVES
• By the end of this chapter, you should be able to
✔ explain trade discount terms;
✔ calculate trade discount and the net price of goods purchased;
✔ explain chain discount;
✔ fi nd a single discount that is equivalent to a chain discount;
✔ explain cash discount terms;
✔ identify situations where a trader can take a loan to take
cash discounts;
✔ determine the balance after partial payments are made, and
✔ solve problems involving trade and cash discounts.
advantage of
3.1 Introduction
• 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 between the list price and the net price is called
trade discount;
• trade discount = list price – net price
• A manufacturer normally quotes a discount rate in percentage to
the retailer.
• The rate is called the trade discount rate which must be
calculated on the list price.
Example 1
The list price of a leather belt is RM180. A trade discount
of 30% is offered. What is the net price of the belt?
• Solution
List price = RM180
Trade discount = 30% × RM180 = RM54
Net price = list price – trade discount
= RM180 – RM54
= RM126
3.2 Formula for calculating 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%
From net price = list price – trade discount, we get
NP = L – Lr
NP = L(1 – r)
Example 2
Weeny Jean offers a discount of 32% on all the 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% × 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)
NP = 420(1 – 32%)
= 420 (1 – 0.3225)
= RM284.55
Example 3
The net price of a camera with 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 = RM800
Hence, the list price is RM800.
•
Alternatively by using the formula, we get
NP = L(1 – r)
480 = L(1 – 40%)
L = RM800 = list price
Example 4
A bill of RM1,200 including a prepaid handling charge of
RM200 is offered a trade discount of 15%. What is the
net price?
• Solution
Trade discount = 0.15 × RM1,000 = RM150
(It should be noted that the discount is based on the cost
of goods, excluding any other costs.)
Net price = (RM1,000 – 150) + 200
= RM1,050
Example 5
•
Blue Danube sells an item for RM100 less 20% while Yellow River sells the same item for RM120
less 40%.
(a) Find the net prices of the item for the two shops.
(b) What further discount percentage must be offered by the shop that sells at a higher net price
in order to meet the competitor’s price?
•
Solution
(a) Blue Danube: Net price = 100(1 – 20%) = RM80
Yellow River: Net price = 120(1 – 40%) = RM72
(b) Blue Danube sells at a higher net price.
Let the additional discount per cent be r%. Therefore
72 = 100(1 – r)
r = 28%
Hence, Blue Danube must offer an additional 8% to meet its competitor’s price.
3.3 Chain discount
• Multiple discounts are often offered to the retailers
on the same goods by the manufacturers or
wholesalers.
Example 6
• A computer is advertised for RM4,800 less 20% and 10%. Find
(a) the net price, (b) the total discount.
• Solution
(a) List price = RM4,800
Less 20%: 0.20 × RM4,800 = 960
Balance = RM4800 – RM960 = 3,840
Less 10%: 0.10 × RM3,840 = 384
Net price = RM3840 – RM 84 = RM3,456.
• (b) Total discount = RM4,800 – RM3,456 = RM1,344
3.4 Formula for calculating the
net price for a chain discount
• 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)
Example 7
•
A television set with a catalogue price of RM2,500 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 = 2,500 (1 – 30%)(1 – 10%)(1 – 5%)
= 2,500(0.7)(0.9)(0.95)
= RM1,496.25
•
The net price can also be calculated in the following manner.
List price
= RM 2,500.00
Less 30%: 0.30 × RM2,500 = RM
750.00
–
RM 1,750.00
Less 10%: 0.10 × RM1,750 = RM
175.00
–
RM 1,575.00
Less 5%: 0.05 × RM1,575
Net price
= RM
= RM 1,496.25
78.75 –
Example 8
A washing machine is advertised at RM2,000 less 40%, 12% and 2.5%. Find the net price.
•
Solution
From NP = L(1 – r1)(1 – r2)(1 – r3), we get
net price = 2,000 (1 – 40%)(1 – 12%)(1 – 2—1%)
= 2,000(0.6)(0.88)(0.975)
= RM1,029.60
•
Alternatively, the net price can be obtained as follows.
List price
= RM 2,000.00
Less 30%: 0.40 × RM2,000 = RM 800.00 –
RM 1,200.00
Less 12%: 0.12 × RM1,200 = RM 144.00 –
RM 1,056.00
Less 2.5%: 0.025 × RM1,056 = RM
Net price
= RM 1,029.60
26.40 –
3.5 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)
Example 9
• A product is advertised at RM1,500 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
single discount equivalent = 1 – (1 – 0.20)(1 – 0.10)(1 – 0.05)
= 1 – (0.80)(0.90)(0.95)
= 1 – 0.684
= 0.316 = 31.6%
(b) From NP = L(1 – r), we get
net price = 1,500 (1 – 31.6%) = RM1,026
Example 10
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%
3.6 Cash discount
• Wholesalers, manufacturers and even retailers offer
reductions on the amount due to customers 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 perio 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.
Example 11
• 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 the 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 12
An invoice dated 2 January 2009 for RM4,010 was offered cash discount
terms of 1/10, n/30. If the invoice was paid on 11 January 2009, what was
the payment?
• Solution
Since the invoice was paid 9 days after the date of the invoice (within the
discount period), the buyer was entitled to a 1% cash discount.
Cash discount = 0.01 × RM4,010 = RM40.10
Payment = invoice amount – cash discount
= RM4,010 – RM40.10
= RM3,969.90
The payment was RM3,969.90.
Example 13
An invoice dated 10 April 2009 for RM2,300 is offered cash discount
terms of 3/10, 2/20, n/60. Find the payment if the invoice is paid on
28 April 2009.
• Solution
Since the invoice is paid 18 days after the date of the invoice, a cash
discount of 2% is obtained. The buyer does not get the 3% cash
discount as the invoice is not paid within the 3% discount period of
10 days.
Net payment = net price – cash discount
= 2,300 – (0.02 × 2,300) = RM2,254
The amount of payment is RM2,254.
Example 14
The total of an invoice with cash discount terms of 3/10, n/30 amounts to
RM2,090 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 = RM2,090.00
Freight charge
=
RM
50.00 –
Cost of goods
= RM2,040.00
Cash discount = 3%(2,040)
= RM
61.20 –
= RM1,978.80
Freight charge
= RM
50.00 +
Amount to be paid
= RM2,028.80
3.7 Borrowing to take advantage
of the cash discount
• Many companies borrow from banks using shortterm loans to take advantage of the cash discounts
offered.
Example 15
Anwar purchases some goods valued at RM2,000 with cash discount terms of 5/10, n/60. What will be the
annualised cost of the credit if the cash discount is not taken?
•
Solution
Cash discount not taken = 5% × 2,000 = RM100
Credit period = 60 – 10 = 50 days
From the formula I = Prt, we get
100 = 1,900 × r × 50/360
r = 37.9%
Hence, the annualised cost of credit is 37.9%.
•
Alternatively, the following formula can be used.
Annualised cost = (Discount per cent)/(100 – Discount per cent)
x 360/(Credit period)
= 5%/95% x 360/50
= 37.9%
Example 16
On 20 May, Mei Lan purchased some goods invoiced at RM3,000 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% × 3,000 = RM90
Principal borrowed = RM3,000 – RM90 = RM2,910
Credit period = 30 days – 10 days = 20 days
Interest incurred on the borrowing = Prt = 2,910 × 0.09 × 20/360
= RM14.55
Amount saved = cash discount – interest
m= RM90.00 – RM14.55
= RM75.45
3.8 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 17
An invoice amounting to RM3,000 and dated 15 July 2012 offers cash discount terms
of 10/15, n/30. Find the amount outstanding if the buyer pays RM1,000 on 20 July
2012.
• Solution
Method 1
Cash discount offered = 10% × 3,000 = RM300
The buyer pays RM1,000 on 20 July 2012. Hence he is entitled to the cash discount
offered. Since the RM1,000 payment could not settle all the amount due, he is only
entitled to a proportionate fraction of the cash discount offered. If he makes a
payment of RM2,700(RM3,000 – RM300), he will receive RM300 cash discount.
Since he pays only RM1,000, he is only entitled to a cash discount of
(1,000/3000) × 300 = RM111.11.
• Hence, the amount outstanding = RM3,000 – RM1,111.11 = RM1,888.89
Continue
• Method 2
The following equation can also be used, that is
Amount paid = (credit given) × (1 – discount rate)
Since the amount paid was RM1,000 and discount rate
was 10%, then
1,000 = (Credit given) × (1 – 10%)
Credit given = 1,000 /(90%) = RM1,111.11
Hence, the amount outstanding = RM3,000 –
RM1,111.11 = RM1,888.89
3.9 Trade and cash discounts
• More often than not, trade and cash discounts are
offered simultaneously to a buyer.
Example 18
An invoice of RM10,000 and dated 18 April 2012 is 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 is paid on 28 April 2012.
•
Solution
(a) Trade discount = 0.25 × 10,000 = RM2,500
(b) Cash discount = 9% (10,000 – 2,500) = RM675
(c) Since the payment date falls within the cash discount period, he
would get the 9% cash discount. Thus,
net payment = 10,000 – (2,500 + 675)
= RM6,825
Example 19
An invoice of RM9,000 dated 19 April 2012 is offered 13%
trade discount and cash discount terms of 3/10, n/30. Find the
net payment if the invoice is paid on 30 April 2012.
• Solution
Trade discount = 0.13 × 9,000 = RM1,170
The buyer does not receive any cash discount since the last date
to receive cash discount is 29 April 2012. He only receive the
trade discount. Thus,
net payment = RM9,000 – RM1,170
= RM7,830
SUMMARY
1.
Trade discount = list price – net price
Or
Net price = list price – trade discount
2.
Net price, NP = L (1 – r)
where,
L = list price
r = trade discount
3.
For chain discounts r1, r2, r3,
net price, NP = L (1 – r1)(1 – r2)(1 – r3)
4.
Single discount equivalent, r, for a chain discount of r1, r2, and r3 is
r = 1 – (1 – r1)(1 – r2)(1 – r3)
5.
Cash discount 2/10, 1/30, n/60 means 2% of the net price may be deducted if the invoice is paid within ten days of
the invoice date; 1% may be deducted if the invoice is paid between the 11th and 30th day; and the full amount must
be paid by the 60th day.
Continue
6. Borrowing to take advantage of the cash discount:
Amount saved = cash discount – interest
Interest = (Invoice amount – cash discount) × r × credit
period
7. Partial payment of invoice:
Amount paid = credit given × (1 – discount rate)
Amount outstanding = Invoice amount – credit given
Markup and Markdown
• An important principle in retail business is the
proper pricing of its merchandise. A wrong decision
on pricing may lead to small profits or heavy losses.
• A retailer should be able to mark up his goods to
obtain a reasonable profit or markdown his goods to
clear old stock.
LEARNING OBJECTIVES
• By the end of this chapter, you should be able to
✔ explain retail price, cost price, mark-up and
markdown;
✔ compute mark-up per cent;
✔ compute markdown per cent, and
✔ compute gross profi t, operating expenses, net
profi t and breakeven price.
3.10 Mark-up
• The cost price is the original price of the goods paid by the retailer.
• The retailer must add an additional amount called mark-up to the cost of
the goods to cover the business expenses and to generate a profit.
• The sum of this cost and mark-up is the retail (selling) price.
• Mark-up (gross profit or gross margin) is the difference in the retail price
and the cost that is
• R = C + M or M = R - C
where R = retail price
C = cost price
M = mark-up
3.11 Mark-up per cent
• Mark-up is usually expressed as a percentage.
• It can be expressed as
(a) mark-up per cent based on retail price
%Mr = (M/R) × 100%.
(b) mark-up per cent based on cost price
%Mc = (M/C) × 100%.
Example 1
The cost price of an antique table is RM5,000. What is the retail price if the seller
wants a 20% mark-up based on (a) cost price, (b) retail price?
• Solution
(a) Let the retail price be RMx. Then
R
=
C
+
RM5,000
M
0.2(RM5,000)
Retail price = 5,000 + 0.2(5,000) = RM6,000
The retail price is RM6,000.
(b) Let the retail price be x. Then
R =
C
+
M
x = 5,000 + 0.2x
0.8x = 5,000
x = 5,000 / 0.8 = RM6,250
Example 2
Mariam’s shop purchased 90 shirts at a cost of RM20 each. The shop expects that 10% of the
shirts will be sold at a reduced price of RM15 each. If the shop is to maintain a 75% mark-up on
cost on the entire purchase, find the regular price of the shirts.
•
Solution
Cost of the 90 shirts = 20 × 90 = RM1,800
The shop maintains a 75% mark-up on cost. Then,
R
=
C
RM1,800
+
M
0.75(RM1,800)
Sale of 90 shirts = 1,800 + 0.75(1,800) = RM3,150
Sale of 9 shirts (10% × 90 shirts) = 15 × 9 = RM135
Sale of other 81 shirts (90 – 9) = RM3,150 – RM135 = RM3,015
Regular selling price of a shirt = 3,015 ÷ 81 = RM37.22
Example 3
A retailer purchased 200 kg of cucumber at 50 cents per kilogram. A 5%
spoilage is expected. If he plans to make a 40% mark-up based on overall
cost, what is the selling price of the cucumber?
• Solution
Total cost of cucumbers = 0.50 × 200 = RM100
Amount left after deducting spoilage = 200 – 5%(200) = 190 kg
The retailer wants a 40% mark-up on cost. Thus,
R = C
RM100
+
M
0.40(RM100)
• Selling price of 190 kg = 100 + 0.40(100) = RM140
Selling price of 1 kg = 140 ÷ 190 = RM0.74
3.12 Conversion of mark-up per
cent
•
Mark-up per cent based on retail can be converted to mark-up per cent based on cost and vice
versa as follows.
•
Mark-up per cent based on retail price
R=C+M
1 + %Mc = 100% + %Mc
%M Mark-up per cent based on retail price =
%M r = %Mc /(1 + %Mc)
•
Mark-up per cent based on cost price
R
=
C
+
M
100% = (1 – %Mr) + %Mr
•
Mark-up per cent based on cost price
%Mc = %Mr/(1 – %Mr)
Example 4
(a) The mark-up per cent based on cost price of an item is 20%.
What is its mark-up per cent based on retail price?
(b) The mark-up per cent based on retail price of an item is 15%. What is its mark-up
per cent based on cost price?
• Solution
From %M r = %Mc /(1 + %Mc) we get
%M r = 20%/(1 + 20%)
= 16.67%
• From %Mc = %Mr/(1 – %Mr) we get
= 15%/(1 – 15%)
= 17.65%
3.13 Markdown
• Markdown is a decrease in the selling price. It is the difference between the old retail
price and the new retail price; that is,
MD = OP – NP
where MD = markdown
OP = old retail price
NP = new retail price
• Prices are sometimes marked down due to many reasons: to face stiff competition, to
encourage purchases in bulk, to dispose off old, damaged or obsolete stocks and to
close a line of merchandise.
• The markdown per cent, %MD, is based on old price OP and is expressed as follows.
%MD = (MD/OP) × 100%
Example 5
The markdown per cent on a TV set is 10%. If the new retail price is
RM900, find the old retail price.
• Solution
Let the old price be RM K.
From %MD = (MD/OP) × 100%, we get
10%K= (K-900/K)
0.1K = K – 900
K – 0.1K = 900
K = RM1,000
The old selling price is RM1,000.
Example 6
During a clearance sale, an appliance department marked
down a microwave oven by 12%, making the selling price
RM400. At this
selling price, the department made a 30% mark-up on the
selling price. Find
(a) the regular price of the oven,
(b) the cost of the oven,
(c) the mark-up per cent of the oven at the regular price.
Solution
(a) From NP = L(1 – r), we get
400 = L(1 – 12%)
L = RM454.55
Hence, the regular price of the oven is RM454.55.
(b) When the appliance was sold for RM400, the department made a 30% mark-up based on the selling
price.
Let the cost be RM x.
Thus, R
=
C
+
M
400 = x + 0.30(400)
x = 400 – 0.30(400) = RM280
The cost of the appliance is RM280.
(c) Mark-up per cent at the regular price
= [(Regular price – Cost)/Regular price] × 100%
= [(454.55 – 280)/454.55] X 100%
= 38.4%
Example 7
A retailer wants to sell an item that costs RM200 at a price less 15% discount that will give him a 28% mark-up
based on cost. Find
(a) the actual selling price, (b) the list price.
•
Solution
(a) The retailer wants a 28% mark-up on cost. Thus,
R
=
C
+
M
RM200
0.28(RM200)
Actual selling price = 200 + 0.28(200) = RM256
(b) Let the list price be L.
From
NP = L(1 – r), we get
256 = L(1 – 0.15)
L = 256/0.85
= RM301.18
Hence, the list price is RM301.18.
3.14 Profit and loss
• Not all businesses make money.
• A business incurs operating expenses such as rent, lighting, wages,
commissions, bonus and other operating expenses.
•
•
•
•
•
The mark-up must be able to cover the operating expenses.
If mark-up is greater than operating expenses, net profit is achieved.
However, if mark-up is less than operating expenses, loss is incurred.
Thus, if M > OE, net profit is obtained
if M < OE, loss is incurred
where M = mark-up
OE = overhead expenses
Continue
• If the retail price just covers the cost price and the operating
expenses, then it does not make any profit nor incur any loss.
This price is called the breakeven price; that is,
Breakeven price = cost price + operating expenses
• The mark-up equation, retail price = cost + mark-up
can be expressed as:
Retail price = Cost + Net profit + Operating expenses
or in abbreviation
R = C + NP + OE
Example 8
A retailer bought a radio for RM200. Buying expenses amounted to
RM20. Operating expenses incurred were 20% of the cost price. If
the retailer made a 25% net profit based on cost, find
(a) the retail price,
(b) the gross profit,
(c) the net profit,
(d) the breakeven price,
(e) the maximum markdown that could be offered so that there is
no profit or loss,
(f) the net profit or loss if the retail price was RM280.
Solution
• Actual cost of the radio = RM200 + RM20 = RM220
From
R
=
C
RM220
+
NP
+
OE
0.25(RM220)
0.20(RM220)
(a) Retail price = 220 + 0.25(220) + 0.20(220) = RM319
(b) Gross profit = NP + OE = 0.25(220) + 0.20(220) = RM99
(c) Net profit = 0.25(220) = RM55
(d) Breakeven price = C + OE = 220 + 0.20(220) = RM264
(e) Maximum reduction in price
= retail price – breakeven price = RM319 – RM264
= RM55
(f) Net profit = RM280 – RM264 = RM16
Example 9
A dealer bought a hi-fi set for RM2,000 less 10% and
5%. He sold it at a discount of 20%. If the gross
profit earned by the dealer is 20% on the net retail
price, find the list price of the hi-fi set.
Solution
Cost price of the hi-fi set = RM2,000 (1 – 10%)(1 – 5%) = RM1,710
The dealer wanted a 20% mark-up on net retail price.
Let the net retail price be x. Thus,
net retail price = cost + mark-up
x
RM1,710
0.2x
x = RM1,710 + 0.2x
0.8x = 1,710
x = RM2,137.50
Let the list price of the hi-fi set be L. From
NP = L(1 – r), we get
RM2,137.50 = L(1 – 0.2)
L = 2,137.50/0.8
= RM2,671.88
Hence, the list price is RM2,671.88.
Example 10
An item costing RM200 was listed in a catalogue at
RM400 with a trade discount of 20%. After some
time, the cost of the item decreased to RM180. If
the dealer wants to maintain the same mark-up per
cent as before the cost reduction, find the extra trade
discount that may be given to a customer.
Solution
• Method 1
When the cost was RM200, the selling price was
= RM400(1 – 20%) = RM320.
Hence, if the cost is RM180, the selling price should be
= (320/200) × 180 = RM288,
using the principle of proportionality.
From
NP = L(1 – r1)(1 – r2)
288 = 400(1 – 20%)(1 – r2)
with r2 = the extra discount
r2 = 10%
Hence, the extra trade discount to be given is 10%.
Continue
• Method 2
Reduction in selling price = RM320 – RM288 = RM32
Additional discount = Reduction in price/Original price
= (32/320) × 100
= 10%
• The lower new selling price may help the dealer to be
more competitive and to increase sales.
SUMMARY
1. Cost price is the amount paid for an item when it is acquired.
2. Retail price is the amount received when the item is sold.
3. Mark-up is the difference between retail and cost prices.
4. List price is the price that is listed or displayed.
5. Markdown is the difference between the old retail price
and the new retail price.
6. Operating expenses are the expenses incurred in the running of a
business like wages, rent and insurance.
7. Net profit is the amount left after deducting operating expenses from
the mark-up.
8. Breakeven price is the retail price in which there is no gain or loss.
9. R etail price = Cost price + mark-up