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Chapter 5 Mathematics of Merchandising Copyright © 2022 McGraw-Hill Education Limited. Microsoft® PowerPoint® Presentation by Hussam Jawad and Howard Umrah, Durham College. Previously updated by Julie Howse, St. Lawrence College Learning Objectives LO1 Calculate the net price of an item after single or multiple trade discounts. LO2 Calculate a single discount rate that is equivalent to a series of discounts. LO3 Understand the ordinary dating notation for the terms of payment of an invoice. LO4 Calculate the amount of the cash discount for which a payment qualifies. LO5 Solve merchandise pricing problems involving markup and markdown. 5-2 Introduction • Products for purchase by the consumer undergo the marketing chain. As products move from the manufacturer to the consumer, they are marked up, marked down and under go trade discounts. • This chapter explores calculations needed for product distribution and merchandising. 5-3 Trade Discounts • Goods move from a manufacturer to the ultimate consumer through a distribution chain or merchandising chain. • We need a way to determine the prices of goods along the chain. 5-4 Trade Discounts • Typically, the distributor will have a set of list prices for the goods (chosen to approximate the retail price). • The distributor will offer the wholesaler a trade discount off of the list prices. 5-5 Trade Discounts • The net price is the list price minus the trade discount. Net price = List price – Amount of trade discount Net price = List price – (Rate of trade discount x List price) Net price = List price(1– Rate of trade discount) Let N = Net price L = List price d = Rate of trade discount This shortens our equation to: 5-6 Trade Discounts Net price = List price – Amount of trade discount Net price = List price – (Rate of trade discount x List price) Net price = List price(1– Rate of trade discount) Let N = Net price L = List price d = Rate of trade discount 5-7 Example: 5.1A A wholesaler lists an item at $117 less 20%. What is the amount of the discount and the net price to a retailer? Given : 𝐿=$ 117, 𝑑=0.20 Amount of discount=𝑑𝐿=( 0.20 ) ( $ 117 )=$ 𝟐𝟑 . 𝟒𝟎 5-8 Example: 5.1B After a trade discount of 30%, a garage is able to purchase windshield wiper blades for a net price of $19.46. What is the list price of the blades? Given : 𝑑=0.30 , 𝑁=$ 19.46 Substituting these values in our formula , we have 5-9 Multiple Discounts • Sometimes, a seller/vendor may offer multiple discounts. • i.e. the usual trade discount plus a volume purchase discount and a promotional discount • In this case, the discounts are compounded (not added). • In a case with three discounts, we could calculate the net price as follows: 5-10 Equivalent Single Discount Rate • An equivalent discount rate is the single discount rate that gives the same net price as the combined effect of multiple discounts. • This rate will always be less than the simple sum of the multiple discount rates. 5-11 Example: Equivalent Discount Rate A wholesaler offers a trade discount of 20% and a promotional discount of 10%. How much would a retailer pay for $100 worth of goods? What is the equivalent discount rate? Given : 𝐿=$ 100 , 𝑑 1=0.20 , 𝑑 2=0.10 $ 100 − $ 72 Equivalent discount= × 100 %=𝟐𝟖 % $ 100 5-12 Example: Equivalent Discount Rate Spring Sale 50% OFF + 30% OFF + an additional 20% OFF (with our email) What is the single equivalent discount rate? 5-13 Skill Check i. ii. iii. Calculate the sale price of an item with cost of $36.90 after a 15% trade discount. A supplier bought merchandise from the manufacturer totaling $6050. The supplier was given a series of discounts, 8%, 5% and 3% respectively. What was the final cost of the merchandise? Determine the equivalent rate of discount of an $60 item that underwent discounts of 20% and 15%. 5-14 Cash Discounts & Terms of Payment • Transactions within the merchandising chain often involve trade credit. • Following a transaction, the vendor will send the buyer an invoice which includes: • Items purchased • Unit prices • Applicable trade discount rates • Shipping cost • Taxes • Amount due 5-15 Invoice Example Items purchased Unit price Discount rates Shipping cost, Taxes, Amount due 5-16 Terms of Payment An invoice normally states the terms of payment, including: • Credit period – the length of time until the invoice is due. • Cash discount rate – discount applied for early payment. • Cash discount period – the time period when the cash discount is available. • The date on which both the credit period and the discount period begin. 5-17 Dating Notation • With ordinary dating, both the credit period and the discount period are measured from the invoice date (day 0). • For example, if an invoice was dated July 3rd with a 30-day credit period, then July 4th would be considered day 1 and August 2nd would be day 30. • Payments made on August 3rd or later would be charged the overdue-account penalty. 5-18 Terms of Payment • Read as “two ten, net thirty”. • A 2% discount will be applied to payments made within 10 days. 2/10, n/30 Cash discount Discount period Credit period (2%) (10 days) (30 days) 5-19 Common Practices With Dating • If the last day of the discount period or the credit period falls on a non-business day, the period is extended to the next business day. • If no cash discount is offered, only the “net” figure for the credit period is given (for example, n/15 or n/30). • If a net figure for the credit period is not stated, it is understood that the credit period ends 20 days after the end of the discount period. For example, “2/10” by itself implies “2/10, n/30.” 5-20 Calculating Cash Discounts • We can use the formula we have already learned to help with cash discounts. • Substitute the invoice amount for L and the cash discount rate for d. • N will be the full payment that will settle the invoice within the discount period. 5-21 Example: Early Payment Discount An invoice for $1,000 with terms 2/10, n/30 is dated June 3rd. What payment will settle the invoice on June 7th? Given : 𝐿=$ 1,000 , 𝑑=0.02 5-22 Skill Check i. An invoice for $6,000 with terms 3/10, n/30 is dated August 5th. What payment will settle the invoice on August 10th? ii. An invoice for $2,000 with terms 2/10, n/30 is dated May 3rd. What payment will settle the invoice on May 31st? iii. An invoice for $3,000 with terms 2/10, 1/20, n/30 is dated May 3rd. What payment will settle the invoice on May 21st? 5-23 Markup • The markup or gross profit is the amount added to the cost of an item to arrive at its selling price. 𝑆 = 𝐶+ 𝑀 • The markup must be large enough to cover a portion of overall operating expenses and contribute toward the overall operating profit. 𝑀=𝐸 + 𝑃 5-24 Markup Let us define the following symbols: S C M E P = Selling price (per unit) = Cost (per unit) = Markup (per unit) = Overhead or operating expenses (per unit) = Operating profit (per unit) Given that Then, we end up with: 5-25 Markup Diagram • The two ways of expressing selling price (either as C+M or C+E+P) are shown below. 𝑆 = 𝐶+ 𝑀 𝑆 = 𝐶+ 𝐸 + 𝑃 5-26 Markup • Merchandisers prefer to think of markup in terms of percentages, using either: or (Also known as gross profit margin) 4-27 Example: Markup Coastal Marine is importing a new line of inflatable boats at a unit cost of $1860. Coastal estimates that operating expenses per unit will be 30% of cost. a) What should the markup and selling price be if Coastal’s desired operating profit per unit is 25% of cost? b) What are Coastal’s rate of markup on cost and rate of markup on selling price for the boats? 5-28 Example: Markup Product “Z” has a unit cost of $245. If the retailer wants 30% rate of markup on selling price, what is dollar amount of markup and what is selling price? therefore M=0.30 S 5-29 Markdown • A markdown is a reduction in the selling price of an item. • Markdowns may be used for a variety of reasons including: • to reduce excess inventory • to increase sales volume during sales • to attract additional customers 4-30 Markdown Substituting D for the amount of markdown, S for the regular selling price and S(reduced) for the reduced selling price gives: The rate of markdown is the markdown expressed as a percentage of the regular selling price: 5-31 Markdown We can also calculate the reduced selling price (or sale price) using our original discounting formula restated as: 5-32 Example 5.4A: Markdown Toby’s Cycle Shop advertises a 20% markdown on an Alpine mountain bike regularly priced at $445. Cycle City’s regular selling price for the same model of bike is $429. a) What is the reduced price at Toby’s? b) What rate of markdown would Cycle City have to offer to match Toby’s reduced price? 4-33 Example 5.4C: Markdown K&M Clearance Centre sells premium coffee makers for 60% off the regular selling price, which represents a discount of $95.40. What are the regular and reduced selling prices? We are given : 𝑅𝑎𝑡𝑒𝑜𝑓 𝑚𝑎𝑟𝑘𝑑𝑜𝑤𝑛=60 % 𝑎𝑛𝑑 𝐷=$ 95.40 5-34 Skill Check Noble furniture store is importing a new line of sofas at a unit cost of $750. Noble estimates that operating expenses per unit will be 25% of cost. a) What should the markup and selling price be if Noble’s desired operating profit per unit is 10% of cost? b) What are Noble’s rate of markup on cost and rate of markup on selling price for the sofas? 5-35 Skill Check Noble’s furniture store advertises a 20% sectionals regularly priced at $1550. Lennon’s regular selling price for the same sectional is $1300. a) What is the reduced price at Noble’s? b) What rate of markdown would Lennon have to offer to match Noble’s reduced price? 5-36 Skill Check Noble’s furniture store advertises a 20% sectionals regularly priced at $1750. Lennon’s regular selling price for the same sectional is $1300. a) What is the reduced price at Noble’s? b) What rate of markdown would Noble have to offer to match Lennon’s reduced price? 5-37 Chapter 5 End of Chapter Copyright © 2022 McGraw-Hill Education Limited. Microsoft® PowerPoint® Presentation by Hussam Jawad and Howard Umrah, Durham College. Previously updated by Julie Howse, St. Lawrence College