Mathematics of Merchandising

Transcription

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2 4-2 Mathematics of Merchandising Chapter 4

3 4-3 Learning Objectives After completing this chapter, you will be able to: > Calculate the net price of an item after single or multiple trade discounts > Calculate a single discount rate that is equivalent to a series of multiple discounts > Understand the ordinary dating notation for the terms of payment of an invoice > Calculate the amount of the cash discount for which a payment qualifies > Solve merchandise pricing problems involving markup and markdown

4 4-4 The Distribution Chain Manufacturer Distributor Wholesaler Retailer Consumer

5 4-5 Trade Discount Amount & Net Price Formulas N = L(1 - d) Trade discount amount = List price * discount rate Net Price = List price - Trade discount amount

6 4-6 The price of office equipment is $3,000. The manufacturer offers a 30% trade discount. What are the trade discount amount and the net price? N = L(1 - d) 30% N = 3000(1 -.3) = 3000(.7) = $2100 Trade discount = $3,000 x.30 = $900 Net Price = $3,000 - $900 = $2,100

7 4-7 The price of office equipment has a $2,100 net price and a 30% trade discount. What is the list price? N = L(1 - d) Re-organize to solve for L L = N / (1 - d) = 0.70 L = $2,100 /.70 = $3,000

8 4-8 Chain Discounts Two or more discounts: 15/10/5 To calculate discount = 30% Find the single equivalent discount rate: 1 - (1-d 1 )(1-d 2 )(1-d 3 ) = 1 - (.85 *.90 *.95) = =.2733 = 27.33%

9 4-9 The price of a office furniture is $20,000. The chain discount is 20/10/5. What is the net price? N = L(1-d 1 )(1-d 2 )(1-d 3 ).8 *.9 *.95 sto * rcl = $6 320

10 The price of a office furniture is $20,000. The chain discount is 20/10/5. What is the single equivalent discount rate? D = 1 - (1-d 1 )(1-d 2 )(1-d 3 ) rcl = If you used storage in the last question, now you just need Other wise 31.6%.8 *.9 *.95 = - 1 =

11 4-11 Cash Discounts Discount for prompt payment. Not taken on freight, returned goods, sales tax, & trade discounts. Mar. 1 Mar. 10 Discount Period Time period buyer has to take advantage of cash discount Credit Period Mar. 1 Mar. 31 Time period sellers gives buyers to pay invoices

12 4-12 Ordinary Dating Method Two ten, net thirty N = L(1 - d) $500 invoice dated May 3; terms 2/10, n/30; paid on May 10. N = 500(1-.02) = 500(.98) = $ May 3 May 13 April2 Discount Period (10 days) Credit Period (30 DAYS)

13 4-13 Partial Payment Sara owes $400. Sara s terms were 3/10, n/30. Within 10 days Sara sent in a payment of $100. How much is her new balance? Amount credited, L = Amount paid, N / (1-d) Amount credited = payment / (1 - d) or 100 /.97 = Amount credited = +/- $ New balance

14 4-14 Terminology Cost - The price retailers pay to a manufacturer Selling Price - The price retailers charge customers Markup, margin, or gross profit - The difference between the cost of bringing the goods into the store and the selling price Operating expenses or overhead - The regular expenses of doing business such as rent, wages, utilities, etc. Net profit or net income - The profit remaining after subtracting the cost of bringing the goods into the store and the operating expenses

15 4-15 Basic Selling Price Formula Selling price (S) = Cost (C) + Markup (M) $1,200 Computer $900 - Price paid to bring computer into store $300 - Dollars to cover expenses and profit

16 4-16 Markup Based on Cost Dollar markup is the portion Cost + Markup = Selling Price 100% 33% 133% Cost is 100% - the Base Percent markup on cost is the rate

17 Johnny buys Sunday s newspaper for $1.00. He plans to sell them for $1.50. What is Johnny s markup? What is his percent markup on cost? 4-17 $ Selling Price - $ Cost $ Markup $ $1.00 $.50 Percent Markup based on Cost = Dollar Markup Cost = $.50 = 50% $1.00

18 Calculating Selling Price When You Know Cost and Percent Markup on Cost Ray s Appliances bought a sewing machine for $150. To make desired profit, he needs a 60% markup on cost. What is Ray s dollar markup? What is his selling price? 4-18 SP - Cost MU $ _ % (/100) 240? 1.6? ?.60 S = C + M S = $ ($150) S = $150 + $90 S = $240 Dollar Markup

19 Calculating Dollar Markup and Percent on Cost Jane s imported flower business sells floral arrangements for $35. To make her desired profit, Jane needs a 40% markup on cost. What do the flower arrangements cost Jane? What is the dollar markup? SP - Cost MU $ _ % (/100) 35? 1.40 _? ?.40 S = C + M $35 = C +.40(C) $35 = 1.40C $25 = C M = S - C M = $35 - $25 M = $

20 4-20 Markup Based on Selling Price Dollar markup is the portion Cost + Markup = Selling Price 75% 25% 100% Selling Price is 100% - the Base Percent markup on selling price is the rate

21 Johnny buys Sunday s newspaper for $1.00. He plans to sell them for $1.50. What is Johnny s markup? What is his percent markup on selling price? 4-21 Dollar Markup = Selling Price - Cost $.50 = $ $1.00 SP - Cost MU _SP % (/100) ?.50?? Percent Markup on Selling Price = Dollar Markup Selling Price $.50 = 33% $1.50

22 Calculating Selling Price When You Know Cost and Percent Markup on Selling Price Ray s Appliances bought a sewing machine for $150. To make desired profit, he needs a 60% markup on selling price. What is Ray s dollar markup? What is his selling price? 4-22 SP - Cost MU $ _ % (/100) 375? ? 225?.60 M = SP - C M = $375 - $150 M = $225 SP = C + M SP = $ (SP) 0.4SP = $150 SP = $150/.4 = $375

23 Calculating Dollar Markup and Percent on Cost Jane s imported flower business sells floral arrangements for $35. To make her desired profit, Jane needs a 40% markup on selling price. What do the flower arrangements cost Jane? What is the dollar markup? 4-23 SP - Cost MU $ _ % (/100) _? 21 -? 14?.40 M = S - C M = $35 - $21 M = $14 SP = C + M $35 = C +.40($35) $35 = C + 14 $21 = C Dollar Markup

24 4-24 Conversion Formula for Converting Percent Markup on Selling Price to Percent Markup on Cost % markup on SP 1 - % markup on SP Formula for Converting Percent Markup on Cost to Percent Markup on Selling Price % markup on C 1 + % markup on C.33 =.33 = =.50 =

25 4-25 Markdowns Markdown percent = Dollar markdown Selling price (original) Sears marked down a $50 tool set to $36. What are the dollar markdown and the markdown percent? $14 $50 = 28% $50-$36 Markdown

26 4-26 Ski bindings bought for $57.75 were marked up 45% of the selling price. When the binding was discontinued, it was marked down 40%. What was the sale price of the binding? MU +Cost SP - D RSP $ _ % (/100) ? $63.00??.60 SP = /.55 = $ RSP =.6 * = $63.00 You could alternatively have found MU, then added to get SP, and then found the discount and subtracted from SP

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