BM - C6 - Chapter 6 PDF

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Chapter 6...

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MGMT 1001 – Business Mathematics Course: Textbook

MGMT 1001 Hummelbrunner/Halliday/Hassanlou/Coombs:

Contemporary

Business

Mathematics with Canadian Applications 12th Edition Plus MyMathLab with Pearson

CHAPTER 6 Objectives 1. Solve problems involving trade discounts. 2. Calculate single rates of discount for a discount series. 3. Apply methods of cash discount. 4. Solve problems involving markup based on either cost or selling price. 5. Solve problems involving markdown. 6. Solve integrated problems involving discounts, markup, and markdown.

Trade Discounts, Cash Discounts, Markup, and Markdown Determining a suitable selling price for each product or service is crucial for long-term sustainability. Some firms use a cost plus methodology, marking up the cost of each product or service by a certain percentage that is large enough to cover expenses and still leave a respectable profit. Other organizations select their desired profit percentages first, and then work backwards to set their prices.

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MGMT 1001 – Business Mathematics Supply Chain •

The supply chain defines the channels or stages that a product passes through as it is converted from a raw material to a finished product purchased by the consumer.

•

In some supply chains, the distributor and wholesaler are separated.

•

In other supply chains, the manufacturer also serves as the wholesaler.

•

Within the supply chain, all of the channels must make a profit on the product to remain in business.

•

Each channel applies a markup above its cost to buy the merchandise.

•

A manufacturer or supplier can set a list price and then offers a trade discount or a series of trade discounts.

•

Any of the channels within the supply chain may offer a cash discount to encourage prompt payment for the product.

•

When the product is sold to the consumer, the regular selling price may be marked down or discounted to a sale price.

Page 2 of 18

MGMT 1001 – Business Mathematics Supply Chain Terminology

Determining Cost with Trade Discounts •

A trade discount is a reduction of a list price or manufacturer’s suggested retail price (MSRP). –

•

Usually stated as a percent of the list price or MSRP.

Trade discounts are used by manufacturers, distributors, and wholesalers as pricing tools to; –

determine different prices for different levels of the supply chain.

–

communicate changes in prices.

–

enable changes in prices.

Page 3 of 18

MGMT 1001 – Business Mathematics Trade Discount Formulas Trade Discount Abbreviations

Amount of Discount=

List Price=

Rate of × List Discount Price

A=dL

Amount of Discount Rate of Discount

L=

Trade Discount Abbreviations

Rate of Discount=

A d

Blank

Amount of Discount List Price

Net Price=List Price−Amount of Discount

d=

A L

N=L−A

POINTERS AND PITFALLS This diagram is a useful aid in remembering the various forms of the amount of discount formula A = dL. Variables on the same line are multiplied together. Variables on different lines are divided. For example, in solving for d, note that A is above the L. Therefore, d = A/L. Similarly, L = A/d.

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MGMT 1001 – Business Mathematics Using Trade Discount Formulas •

A product is listed at a price of $95.00 and is subject to a trade discount of 30%.

•

Amount of discount = 0.3 x $95 = $28.5

•

Net Price = $95 – $28.5 = $66.5

•

Using Trade Discount Formulas (2 of 3)

•

The value of a 20% discount is $25.00. Find the list price.

•

List Price=¿

•

L=

25 0.2

= $125

A d

•

Using Trade Discount Formulas (3 of 3)

•

Find a rate of discount for a TV set listed at $880 less a discount of $150.

•

Rate of discount

–

d=

d=

150 880

= 17,04%

A L

Net Price Factor •

Instead of computing the amount of discount and then deducting this amount from the list price, the net price can be found by using the more efficient net factor approach.

Net Price Factor Formulas Formulas

Net Price=List Price ×

Net Price Factor (NPF)

Net Price Factor ( NPF )=1−d

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MGMT 1001 – Business Mathematics

N=L ( 1−d )

Computing Net Price Using the Net Factor •

Find the net price if the list price is $56 less 18%. Net price = $56 x (1 - 0.18) = 45.92

N=L ( 1−d )

Discount Series •

A manufacturer may offer two or more discounts to different members of the supply chain; –

If a list price is subject to two or more discounts, these discounts are called a discount series.

–

Additional discounts offered to encourage large volume orders and early orders for seasonal items.

–

Additional discounts may be offered to different members of the merchandising chain.

Discount Series Formulas Formulas NET PRICE = L (1 − d1)(1 − d2)(1 − d3) … (1 − dn) For every discount series, a single equivalent rate of discount (SERD) exists;

Single Equilavent Rate of Discount for a =1−NPF for the Discount Series Discount Series SERD = 1− [(1 − d1)(1 − d2)(1 − d3)…(1 − dn)]

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MGMT 1001 – Business Mathematics

Discount Series •

An item listed at $160 is subject to the trade discount series 5%, 15%, and 20%. Net Price = $160 (1-0.05)(1-0.15)(1-0.2) = $103.36 NET PRICE = L (1 − d1)(1 − d2)(1 − d3) … (1 − dn)

•

Another approach List Price

$160.00

Less 5% Discount

95%

Net Price after First Discount

$152

Less 15% Discount

85%

Net Price after Second Discount

$136

Less 20% Discount

80%

Net Price after Third Discount

$128

Discount Series •

A manufacturer sells a LED TV for $998 less 30%, 10%, 20% Find; i.

The Net Price.

ii.

Amount of Discount.

iii.

The Single equivalent rate of discount.

i.Net Price = List Price × NPF Page 7 of 18

MGMT 1001 – Business Mathematics

NET PRICE= L ( 1−d 1) (1−d 2 )( 1−d 3 ) ⋯ ( 1−d n ) ii.

Net Price = $998(1-0.3)(1-0.1)(1-0.2) = $502.992

iii.

Discount = List Price – Net Price

= $998 - $502.992 = $495 iii.

Discounts are 30%, 10%, 20%

Single Equilavent Rate of Discount for a =1− [ ( 1−d 1 ) ( 1−d 2) ( 1−d 3 ) ⋯ ( 1−d n ) ] Discount Series

Single Equilavent Rate of Discount for a =1− [ ( 1−0.30 ) (1−0.10 )( 1− 0.20 ) ] Discount Series

Caution: In calculating the single equivalent discount, do not sum individual discounts

Payment Terms and Cash Discounts •

An invoice for the goods is sent, and the seller specifies payment terms on the invoice.

•

The business selling the goods can offer a cash discount to encourage prompt payment.

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MGMT 1001 – Business Mathematics Cash Discounts •

All payment terms have three things in common: 1. The rate of discount is stated as a percent of the net amount of the invoice (the amount after trade discounts are deducted). 2. The discount period is stated. –

indicating the time period when the cash discount can be applied

3. The credit period is stated. – •

indicating the time period when the invoice must be paid

Offered in a variety of ways; 1. Ordinary dating, whereby payment terms are based on the invoice date. 2. End-of-month dating, or E.O.M. dating. –

Shift the invoice date to the last day of the month.

3. Receipt-of-goods dating, or R.O.G. –

Used when the transportation of the goods takes a long time.

Sample Sales Invoice

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MGMT 1001 – Business Mathematics

Ordinary Dating •

Commonly used payment terms are 2/10, n/30 (read “two ten, net thirty”)

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MGMT 1001 – Business Mathematics

–

if payment is made within 10 days of the date of the invoice, a discount of 2% may be deducted from the net amount of the invoice.

–

•

otherwise, payment of the net amount of the invoice is due within 30 days.

Determine the payment needed to settle an invoice with a net amount of $950, dated September 22, terms 2/10, n/30, if the invoice is paid.

i.

On October 10.

ii.

On October 1.

•

Ten days after September 22 is October 2. The discount period ends October 2

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MGMT 1001 – Business Mathematics i.

October 10 is beyond the last day for taking the discount, the full amount of the invoice of $950 must be paid.

ii.

October 1 is within the discount period; the 2% discount can be taken. Amount paid = Net amount − 2% of the net amount = $950 – 0.02*$950 = $931

End-of-the-Month Dating •

Commonly the credit period (such as n/30) is not stated. –

In our example, “2/10, n/30 E.O.M.” would be written “2/10 E.O.M.

•

End-of-the-Month Dating (2 of 2)

•

An invoice for $1,233.95 dated July 16, terms 2/10, n/30 E.O.M., is paid on August 10. What is the amount paid: –

If the invoice is to be treated as if the invoice date were July 31? 25 July

–

If the last day for taking the discount is August 10? – 15 Aug

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MGMT 1001 – Business Mathematics Receipt-of-Goods Dating •

Hansa Import Distributors has received an invoice of $8465.00 dated May 10, terms 3/10, n/30 R.O.G., for a shipment of clocks that arrived on July 15.

•

What is the last day for taking the cash discount and how much is to be paid if the discount is taken? – $8,211.05 = $8465x(1-0.03)

•

Last day for taking the discount is ten days after receipt of the shipment, that is, July 25

Partial Payment •

When a business pays part of an invoice within the discount period the purchaser is entitled to the cash discount on the partial amount paid.

Partial Payment •

Royal Roads University has received an invoice of $2780 dated August 28, terms 2/10

•

What payment must be made on September 5 to reduce the debt i.

by $1,000?

The amount paid: $1,000 x (1 – 0.02) = $980 The amount owing is: $2,780 - $1,000 = $ 1,780 i.

to $1,000?

The amount paid: ($2,780 - $1,000)x (1-0.02) = $1,780x0.98 The amount owing is: $1,000

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MGMT 1001 – Business Mathematics i.

Reduce debt by $1000. Reducing the debt by $1000 requires paying $1000 less the discount.

ii. Reducing the debt to $1000 requires separating the debt into two parts.

Markup 

The primary purpose of operating a business is to generate profits.



The amount of profit depends on many factors. The selling price must cover: 1. The cost of buying the goods; 2. the operating expenses (or overhead) of the business; 3. the profit required by the owner to stay in business.

•

Selling Price = Cost of Buying + Expenses + Profit

therefore

Page 14 of 18

MGMT 1001 – Business Mathematics Rate of Markup •

A markup may be stated in one of two ways: 1. As a percent of cost; or 2. As a percent of selling price.

•

Computing the rate of markup involves comparing the amount of markup to a base amount.

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Depending on the method used, the base amount is either the cost or the selling price.

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Since the two methods produce different results, great care must be taken to note whether the markup is based on the cost or on the selling price.

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RATEOF MARKUP = MARKUP = M ×100 C COST BASED ON COST

•

M MARKUP RATE OF MARKUP = ×100 = BASED ON SELLING PRICE SELLING PRICE S

Question •

A dealer bought personal computers for $1850.00 less 32%, and 17%. They were sold for $1575.00. a) What was the markup as a percent of cost? b) What was the markup as a percent of selling price?

Solution •

Cost = $1850(1-0.32)(1-0.17) = $1,044.14

•

M = $1,575 - $1,044.14 = $530.86 a)

50.8% = 530.86/ 1,044.14

b)

33,7% = 530.86/ 1,575 Page 15 of 18

MGMT 1001 – Business Mathematics Finding the Cost or the Selling Price

•

Find the selling price of an item costing $52 if the markup is 40% of cost. S = C + 0.4C = $52 + 0.4x$52 = $72.8

•

Find the selling price of an item costing $52 if the markup is 40% of the selling price. S = C + 0.4xS S – 0.4S = $52 0.6S = $52, S = 52/0.6 = $86.67

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MGMT 1001 – Business Mathematics Markdown •

Reduction in price of article sold to customer.

•

Stated as a percent of the price to be reduced.

•

Computed as if it were a discount.

•

The cost of buying an article plus the overhead represents the total cost of the article.

•

If an article is sold at a price that equals the total cost, the business makes no profit, nor does it suffer a loss.

•

Businesses prefer to sell at a price that is at least the break-even price.

•

If the price does not even cover the cost of buying the item, the business suffers an absolute loss. Cost of Buying + Expenses = Total Cost

Markdown Formulas •

Sale Price = Regular Selling Price × NPF SR = S – MD

MD MARKDOWN RATEOF = ×100 = S MARKDOWN REGULAR SELLING PRICE

•

Sale Price = Regular Selling Price − Markdown SR = S (1− MD)

Markdown Example •

A bicycle originally priced at $179 was sold for $129. a) What was the amount of discount? b) What is the markdown rate? Page 17 of 18

MGMT 1001 – Business Mathematics a) Amount of discount = $179 - $129 = $50 b) Markdown Rate = $50 / $179 = 27.9%

Summary Trade discounts facilitate the pricing of goods along the merchandising chain from the manufacturer to the consumer. Cash discounts are price reductions which encourage prompt payment of invoices and markups allow the retailer to set a price to cover cost, expenses, and profit.

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