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Business Math

Business Math. Chapter 8: Trade and Cash Discounts. 8.1 Trade Discount and Net Price. 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.

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Business Math

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  1. Business Math Chapter 8: Trade and Cash Discounts

  2. 8.1 Trade Discount and Net Price • 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.

  3. 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

  4. Key Terms • 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.

  5. Product flow ManufacturerWholesaler Retailer Consumer

  6. Price flow Consumer Retailer Wholesaler Manufacturer List Price Net Price Net Price Cost $80 $56 $40 $20 30% 50% off list off list

  7. How to find the trade discount • Using a single trade discount rate: • Identify the single discount rate and the list price. • Multiply the list price by the single discount rate. • Trade discount = rate x list price

  8. Look at this example. • Trade discount = rate x list price Find the trade discount for a lamp that retails at $140 and has a trade discount rate of 45%. • Trade discount = 0.45 x $140 • Trade discount = $63 • What does the $63 mean? • That the wholesaler or retailer will not pay $63 of the $140 list price.

  9. Try these examples. • Find the trade discount for a porcelain vase that lists for $90 and has a trade discount of 70%. • $63 • Find the trade discount for styling gel that lists for $13 and has a trade discount of 40%. • $5.20

  10. Find the net price • Using the trade discount: • Identify the list price and the trade discount. • Subtract the trade discount from the list price. Trade discount = Rate x List Price Net Price = List Price – Trade discount

  11. Look at this example. • Find the net price of a software program that lists for $220 and has a trade discount of 35%. • Trade discount = 0.35 x $220 = $77 • Net price = List price – Trade discount • Net price = $220 - $77 = $143

  12. Try these examples. • Find the net price of a camera that lists for $300 and has a trade discount of 42%. • $174 • Find the net price of a down jacket that lists for $150 and has a trade discount of 20%. • $120

  13. 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%.

  14. How to find the net price • Find the complement: subtract the single trade discount from 100%. • 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

  15. 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

  16. 8.2 Net price and 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.

  17. 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

  18. Trade discount series step by step • An item lists for $400 and has a discount of 20%. $400 x 0.2 = $80 $320 • An additional discount of 10% is taken on the previous price. $320 x 0.1 = $32 $288 • An additional discount of 5% is taken on the previous price.$288 x 0.05 = $14.40 $273.60 • $273.60 is the final price.

  19. 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

  20. The net decimal equivalent • To find the net decimal equivalent of a trade discount series: • Find the net decimal equivalent: multiply the decimal form of the complement of each trade discount rate in a series. • Multiply the list price by the net decimal equivalent.

  21. Look at this example. • Find the net price of an order with a list price of $600 and a trade discount series of 15/10/5. • Find the complement of each of the trade discount rates. • They are 0.85, 0.90 and 0.95. Multiply them together. • The net decimal equivalent is 0.72675 • Apply the net decimal equivalent to the list price. • NP = 0.72675 x $600 = $436.05

  22. Try these examples. • A tire lists for $85 and has a trade discount series of 10/10/5. Find the net price. • $65.41 • A silk tie lists for $125 and has a trade discount series of 20/10/5. Find the net price. • $85.50

  23. 8.2.2 Find the trade discount By applying a trade discount series and using the single discount equivalent • Find the single discount equivalent by subtracting the net decimal equivalent from “1.” • Multiply the list price by the single discount equivalent. TD = single discount equivalent x list price

  24. 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

  25. Look at this example • Use the single discount equivalent to calculate the trade discount on a $1,500 fax machine 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.”

  26. Look at this example(continued) • 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 $1,500. • TD = $1,500 x 0.496 = $744 • The trade discount on the fax machine is $744.[That is the amount that you do not pay.]

  27. 8.3 Net amount and the cash discount • 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

  28. 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.”

  29. Look at this example • Find the cash discount for an invoice dated December 1 for $750 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 $735. • If the invoice is paid on or after December 11th, the amount to pay would be $750.

  30. 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.

  31. “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.

  32. 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

  33. 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

  34. 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 10days of the month after the month in the date of the invoice. • If the invoice is dated November 19, then the 2% discount is allowed up to and including December 10.

  35. 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.

  36. An EOM exception! • An exception occurs when the invoice is dated onorafter the 26 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.

  37. 8.3.3 Apply ROG (receipt of goods) 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.

  38. 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

  39. 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.

  40. 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.

  41. 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

  42. 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.

  43. 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.

  44. 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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