Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ...

Business Math, Eighth EditionCleaves/Hobbs

© 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

8.1 Single Trade Discounts

Find the trade discount using a single trade discount rate; find the net price using the trade discount.

Find the net price using the complement of the single trade discount rate.



Key Terms Suggested retail price, catalog price, list

price: three common terms for the price which the manufacturer suggests an item be sold to the consumer.

Trade discount: the amount of discount that the wholesaler or retailer receives off the list price or the difference between the list price and the net price



Net price: the price the manufacturer or retailer pays or the list price minus the trade discount.

Discount rate: a percent of the list price.

Key Terms



Manufacturer Wholesaler Retailer Consumer

Product flow



Consumer Retailer Wholesaler Manufacturer

List Price Net Price Net Price Cost

$80 $56 $40 $20 30% 50%

off list off list

Price flow



How to find the trade discount

Using a single trade discount rate:1. Identify the single discount rate and the

list price.

2. Multiply the list price by the single discount rate.

Trade discount = rate x list price



Look at this example Trade discount = rate x list price

Find the trade discount for a cd player that retails at $120 and has a trade discount rate of 35%.

Trade discount = 0.35 x $120 Trade discount = $42 What does the $42 mean? That the wholesaler or retailer will not pay $42

of the $120 list price.



Try these examples

Find the trade discount for a rug that lists for $290 and has a trade discount of 30%.

$87

Find the trade discount for styling gel that lists for $18 and has a trade discount of 15%.

$2.70



Find the net price

Using the trade discount:

1. Identify the list price and the trade discount.

2. Subtract the trade discount from the list price.

Trade discount = Rate x List Price

Net Price = List Price – Trade discount



Look at this example

Find the net price of a desk that lists for $320 and has a trade discount of 30%.

Trade discount = 0.30 x $320 = $96

Net price = List price – Trade discount

Net price = $320 - $96 = $224



Try these examples

Find the net price of a camera that lists for $240 and has a trade discount of 45%.

$132

Find the net price of a patio table that lists for $460 and has a trade discount of 20%.

$368



Find the net price Using the complement of the single trade

discount rate.

Complement of percent: the difference between 100% and the given percent.

Examples: The complement of 30% is 70%. The complement of 55% is 45% The complement of 5% is 95%.



How to find the net price1. Find the complement: subtract the single trade

discount from 100%.

2. Multiply the list price by the complement of the single trade discount.

Example:

Find the net price of a coffee maker that lists for $20 and has a trade discount rate of 20%.

80% is the complement of 20%

NP = $20 x 0.80 = $16



Try these examples

Find the net price of a set of golf clubs that lists for $1,500 and has a trade discount of 15%.

$1275

Find the net price of a bicycle that lists for $102 and has a trade discount of 30%.

$71.40



8.2 Trade Discount Series

Find the net price, applying a trade discount and using the net decimal equivalent.

Find the trade discount, applying a trade discount series and using the single discount equivalent.



Trade discount series Trade discount series or chain discount:

additional discounts that are deducted one after another from the list price.

Reasons to use discount series include:

To encourage volume purchases

To promote special or seasonal items

To entice a new client



Trade discount series step by step An item lists for $400 and has a discount of

20%. $400 x 0.2 = $80; $400 - $80 = $320

An additional discount of 10% is taken on the previous price. $320 x 0.1 = $32; $320 - $32 = $288

An additional discount of 5% is taken on the previous price.$288 x 0.05 = $14.40; $288 - $14.40 = $273.60

$273.60 is the final price



Can you add the discounts together and apply it as one?

If the item has three discounts of 20%, 10% and 5%, can you add them together and apply a 35% discount?

No, because each time you apply the additional discount, the base becomes smaller. Directly applying a 35% discount would result in a final price of $260.

$260 ≠ $273.60



The net decimal equivalent

To find the net decimal equivalent of a trade discount series:

1. Find the net decimal equivalent: multiply the decimal form of the complement of each trade discount rate in a series.

2. Multiply the list price by the net decimal equivalent.



Look at this example Find the net price of an order with a list price of

$800 and a trade discount series of 20/10/5. Find the complement of each of the trade

discount rates. They are 0.80, 0.90 and 0.95.

Multiply them together. The net decimal equivalent is 0.684 Apply the net decimal equivalent to the list

price. NP = 0.684 x $800 = $547.20



Try these examples

A tool set lists for $325 and has a trade discount series of 20/10/10. Find the net price.

$210.60

A dress shirt lists for $125 and has a trade discount series of 15/10/7.5. Find the net price.

$88.45



8.2.2 Find the Trade Discount

To find the trade discount by applying a trade discount series and using the single discount equivalent:

1. Find the single discount equivalent by subtracting the net decimal equivalent from “1.”

2. Multiply the list price by the single discount equivalent.

TD = single discount equivalent x list price



Key Terms

Single discount equivalent: the complement of the net decimal equivalent. It is the decimal equivalent of a single discount rate that is equal to the series of discount rates.

Total amount of a series of discounts = single discount equivalent x list price

Net amount you pay = net decimal equivalent x list price




Use the single discount equivalent to calculate the trade discount on a $3,200 lawn tractor with a discount series of 30/20/10.

Find the net decimal equivalent by multiplying the complements of each discount rate. 0.70 x 0.80 x 0.90 = 0.504

To find the single discount equivalent, subtract the net decimal equivalent from “1.”



Subtract the net decimal equivalent (0.504) from “1” to find the single discount equivalent.

The result is 0.496 (or 49.6%).

The single discount equivalent is 0.496; apply it to the price of $3,200.

TD = $3,200 x 0.496 = $1,587.20

The trade discount on the tractor is $1,587.20.That is the amount that you do not pay.

Look at this example (continued)



8.3 Cash Discount and Sales Terms

Find the cash discount and the net amount using ordinary dating terms

Interpret and apply EOM terms

Interpret and apply ROG terms

Find the amount credited and the outstanding balance from partial payments

Interpret freight terms



8.3.1 Find the Cash Discount and the Net Amount

Bills are often due within thirty days from the date of the invoice.

To encourage prompt payment, companies offer an incentive of a cash discount if the invoice is paid within a specified period.

“2/10 n/30” means “take a 2% cash discount if paid within 10 days; pay the net price if covered within 30 days.”




Find the cash discount for an invoice dated December 1 for $1,500 with terms of 2/10 n/30.

If the invoice is paid on December 9th, for example, the payment would include the discount and the amount would be $1,470.

If the invoice is paid on or after December 11th, the amount to pay would be $1,500.



Try these examples Annie’s Plants has received an invoice for

$450.00 for potting soil dated November 3 with terms of 5/10 n/30. If the invoice is paid on November 12, how much would Annie’s pay?

$427.50

What if the bill is paid on November 30?

They would not be able to take the discount and would have to pay the full amount of $450.



“Thirty days has September…”

To calculate the exact number of days for a cash discount, you must know how many days are in each month, so if you are not sure…learn them.

There are two tips in the text to help you; using a chart is usually the most reliable.



Use the complement to find the net amount of an invoice

An invoice of $500 which reads 2/10 n/30 tells you that a discount of 2% is available if the payment is made within 10 days.

To calculate the net amount directly, use the complement of the discount (in this case, 0.98) and multiply it by the total amount.

$500 x 0.98 = $490 = net amount to be paid



Try this example Sycamore Enterprises received a $1,248 bill for

computer supplies dated September 2 with sales terms of 2/10, 1/15, n/30. A 5% penalty is charged after 30 days. Find the amount due for the following dates: September 12, September 15, October 1, October 3.

September 12 (2% discount) = $1,223.04

September 15 (1% discount) = $1,235.52

October 1 (no discount) = $1,248.00

October 3 (5% penalty) = $1,310.40



8.3.2 Interpret and Apply EOM (end-of-month) Terms

Another type of sales term are EOM terms.

For example, an invoice might be 2/10 EOM, meaning that a 2% discount is allowed if the bill is paid during the first month or up until 10 days of the month after the month on the date of the invoice.

If the invoice is dated November 19, then the 2% discount is allowed up to and including December 10.



Look at these examples An invoice dated March 4 with terms of 3/15

EOM would mean that a 3% discount would be applicable until April 15.

An invoice dated August 25 with terms of 5/10 EOM would mean that a 5% discount would be applicable until September 10.

An invoice dated December 2 with terms of 2/20 EOM would mean that a 2% discount would be applicable until January 20.



An EOM exception!

An exception occurs when the invoice is dated on or after the 26th of the month.

The discount would be applicable until the specified day of the month following the month of the invoice.

Example: An invoice dated April 27 with terms of 3/10 EOM would be eligible for the discount if the bill is paid on or before June 10.



8.3.3 Apply Receipt of Goods (ROG) Terms

A cash discount is allowed when the bill is paid within the specified number of days from the receipt of goods, not from the date of the invoice.

Multiply the invoice amount times the complement of the discount rate.

Sales terms stating 1/10 ROG mean that a 1% discount is applicable 10 days after the goods are received; not when the invoice is dated.



Try this example

Judy’s Fine Jewelry received an invoice for 50 silver charm bracelets for a total of $550. The invoice is dated April 1. She received the bracelets on April 6. If the terms are 3/10 ROG and the invoice is paid on April 11, how much will she pay?

$533.50



8.3.4 Find the Amount Credited and the Outstanding Balance

Partial payment: a payment that does not equal the full amount of the invoice less any cash discount.

Partial discount: a cash discount applied only to the amount of the partial payment.

Amount credited: the sum of the partial payment and the partial discount.

Outstanding balance: the invoice amount minus the amount credited.



Applying the percentage formula In applying the percentage formula to find the

amount credited, the rate is the complement of the discount rate; the percentage is the partial payment; and the amount credited is the base.

B = P/R

Sometimes a customer cannot pay the entire amount of an invoice, but takes advantage of a discount period to apply that discount to a part of the total due.



Look at this example If the Semmes Corporation received a $875 invoice with

terms of 3/10 n/30 and could not pay the full amount within 10 days, but chose to send in a $500 partial payment on Day 5, what amount was credited to their account?

B (amount credited) = P (partial payment) divided by R (complement of the discount rate)

B = 500/0.97= $515.46 = amount credited

The balance would be the difference.

$875 - $515.46 = $359.54 = balance



8.3.5 Interpret Freight Terms

Bill of lading: shipping document that includes a description of the merchandise, the number of pieces, weight, name of the consignee (sender), destination, and method of payment of freight charges.

FOB shipping point: “free on board” buyer pays for shipping when shipment is received.

Freight collect: The buyer pays the shipping when the shipping is received.



More key terms

FOB destination: “free on board” at the destination point. The seller pays the shipping when the merchandise is shipped.

Freight paid: The seller pays the shipping when the merchandise is shipped.

Prepay and add: The seller pays the shipping when the merchandise is shipped; but, the shipping costs are added to the invoice for the buyer to pay.



Remember that cash discounts do not apply to shipping costs

Example: The Home Doctor received a shipment of hand tools with an invoice total of $800 (including shipping) and sales terms of 3/10 n/30. The invoice is dated June 2 and the shipping costs are $125. Calculate the payment of the invoice if it is paid on June 10.

Subtract the shipping charges: $800 – 125 = $675

Apply the discount: $675 x 0.97 = $654.75

Add the shipping charges back in:

$654.75 + 125 = $779.75= amount to be paid

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