Mathematics of Merchandising Chapter 4 McGraw-Hill Ryerson©

Learning Objectives Calculate After completing this chapter, you will be able to: Calculate LO 1. … the net price of an item after single or multiple trade discounts LO 2. … a single discount rate that is equivalent to a series of multiple discounts LO 3. … the amount of the cash discount for which a payment qualifies

Learning Objectives Understand Solve LO 4. …the ordinary dating notation for the terms of payment of an invoice Solve LO 5. …merchandise pricing problems involving mark ups and markdowns

The Distribution Chain Receive varying levels of ‘trade discounts’ Middlemen Middlemen Manufacturer Distributor Receive varying levels of ‘trade discounts’ Wholesaler Retailer Consumer

Trade Discount Calculating D Discount Rate List Price L LO 1. Calculating Formula Amount of discount = dL D Discount Rate List Price L Formula Net Price = L(1 – d) i.e. Net Price = List Price – Amount of Discount Q

Trade Discount Q Net Price = L(1 – d) 30% = 3000(1 – .3) = 3000(.7) The price of office equipment is $3000. The manufacturer offers a 30% trade discount. Find the net price and the trade discount amount. Formula Net Price = L(1 – d) 30% = 3000(1 – .3) = 3000(.7) = $2100 Formula Amount of discount = dL = .3* $3000 = $900 More…

/(1 – .3) Trade Discount = $3000 Q Net Price = L(1 – d) N/(1 – d) L = An order for power tools has a $2100 net price after a 30% trade discount. What is the list price? Formula Net Price = L(1 – d) N/(1 – d) L = /(1 – .3) = 2100 = 2100/(.7) = $3000

Trade Discount Note Series Discounts Middlemen Distributor Wholesaler LO 2. Series Discounts This refers to the giving of further discounts as incentives for more sales. Middlemen Distributor Wholesaler For example 15% off first … then 10% off next … then a further 5% off next Note This does not mean a TOTAL of 30% Discount!

Trade Discount Q N = L(1 – d) L Formula (1-d1) (1-d2) (1-d3) N = The price of office furniture is $20000. The series discounts are 20%,10%, 5%. What is the net price? Formula N = L(1 – d) L (1-d1) (1-d2) (1-d3) N = = 20000(1-.2)(1-.10)(1-.05) = 20000(.8)(.9)(.95) = 20000(.6840) = $13680

Trade Discount Q N = L(1 – d) 27.33% Find the single discount rate that is equivalent to the series 15%, 10% and 5%. N = L(1 – d) Apply the multiple discounts to a List price of $100 Step 1 N = 100 (1-d1) (1-d2) (1-d3) discounts 15% 10% 5% .90* = 100 (.85* .95) Step 2 Calculate the dollar amount of the discount = 100 (.7268) = 72.68 = 100 – 72.67 = $27.33 27.33%

Trade Discount Q = 100(.8)(.92)(.98) = $72.13 Calculator The price of car parts is $20,000. The series discounts are 20%, 8%, 2%. What is the single equivalent discount rate? = 100(.8)(.92)(.98) Apply the multiple discounts to a List price of $100 Step 1 = $72.13 discount = 100 – 72.13 Step 2 Calculate the dollar amount of the discount = 27.87 = 27.87 % Calculator

= 100 (.8)(.92)(.98) Step 1 Step 2 100 72.13 27.87 72.13 .8 100 .92 27.87 .98 27.87 %

Cash Discount

A discount given for the prompt payment of an account. Cash Discount LO 3. A discount given for the prompt payment of an account. Invoice Returned Goods Freight Sales Tax & Trade Discounts No Cash Discount

May Cash Discount Discount & Credit Periods Discount period Within 10 Days Period for buyer to take advantage of Discount Terms Within 30 Days Credit period Period for buyers to pay invoices Terms

IF Not …then full amount payable in 30 days Cash Discount LO 4. Terms Invoice Terms 2/10, n/30 Dated May 3 2% discount IF paid in 10 days Terms 2/10, n/30 IF Not …then full amount payable in 30 days Paid on May 10th $500 Therefore, discount can be claimed! Net payment

Cash Discount N = 500(1-.02) = 500(.98) = $490 N = L(1 – d) $500 Formula N = L(1 – d) Invoice $500 Terms 2/10, n/30 N = 500(1-.02) = 500(.98) = $490

Partial Payments Q You owe $400. Your terms were 3/10, n/30. Within 10 days you sent in a payment of $100. How much is your new balance? Amount credited L = Amount paid /(1-d) Step 1 - or - Amount credited = Payment /(1-d) = $100/.97 100 - .03 Amount credited = $103.09 Step 2 Old Balance =$400 - $103.09 = $296.91 New Balance

Mark Up & Mark Down

Selling Price Cost Terminology Marketing Manufacturer Distributor The price charged to Consumers by Retailers Cost The price charged to middlemen in ‘The Distribution Chain’ Wholesaler Retailer Consumer

Terminology Marketing The X Co. Inc Gross Sales $ X Less: Cost of Good Sold X Gross Profit X (or Margin/MarkUp) Less: Operating Expenses X Net Profit (Income) $ X Operating Expenses are the expenses the company incurs in operating the business, e.g. rent, wages and utilities

Margin available to meet Expenses and make a Profit Terminology Marketing Formula Selling Price (S) = Cost (C) + Markup (M) $1200 $900 $300 This side up Computer = + Margin available to meet Expenses and make a Profit

+ = Up Mark 133% If the MarkUp is to be 33% on Cost then… Selling Price (S) = Cost (C) + Markup (M) 100% 33.33% + = 133% % MarkUp is The Rate Cost is 100% The Base $ MarkUp is The Portion

Mark Up Q You buy Sunday newspapers for $1.00. You plan to sell them for $1.50. (A) What is your $ markup? (B) …and your percent markup on cost? (A) Selling Price $1.50 Less: Cost 1.00 MarkUp $ .50 Percent markup on cost… (B) = Dollar Markup = $ .50 = 50% Cost $ 1.00

Calculating the Selling Price when … Mark Up Calculating the Selling Price when … you know Cost & Percent Mark Up on Cost

Mark Up Q Ray’s Appliances bought a sewing machine for $150. To make the desired profit, he needs a 60% markup on Cost. (A) What is Ray’s $ markup? (B) What is his Selling price? $ %/100 240 2? ? 1.60 Example Selling Price 150 Less: Cost 1.00 MarkUp .60 90 ? S = C + M = $150 + .60($150) = $150 + $90 = $240

Calculating the $MarkUp and Percent on Cost

Up Mark Q S = C + M (A) 35 1.40 $35 = C + .40(C) 25 1.00 1.40C 1.40 Jane’s flower business sells floral arrangements for $35. To make her desired profit, Jane needs a 40% markup on cost. (A) What do the flower arrangements cost Jane? (B) What is the dollar markup? $ %/100 S = C + M (A) Selling Price 35 1.40 ? $35 = C + .40(C) Less: Cost 25 ? 1.00 1.40C 1.40 $35 1.40 = MarkUp 10 .40 ? C = $25 (B) M = S - C M = $35 - $25 M = $10

Calculating the MarkUp and Percent on Selling Price

Up Mark Reminder Becomes …on Selling Price Formula Formula …on Cost Selling Price (S) = Cost (C) + Markup (M) % MarkUp is The Rate $ MarkUp is The Portion Cost is 100% The Base Selling Price Selling Price is 100% The Base Cost

Up Mark Q (A) Selling Price 2.50 1.00 Less: Cost 2.00 .80 MarkUp .50 You buy Sunday newspapers for $2.00. You plan to sell them for $2.50. (A) What is your $ markup? (B) …and your percent markup on Selling Price? $ %/100 (A) Selling Price 2.50 1.00 Less: Cost 2.00 .80 MarkUp .50 .20 % markup on Selling Price (B) = 20% Dollar Markup Selling Price $ .50 $ 2.50 =

Mark Up Q Ray’s Appliances bought a sewing machine for $150. To make the desired profit, a 60% markup on Selling Price is needed. (A) What is the Selling price? (B) What is the $ markup? $ %/100 1.00 .60 .40 (A) 375 2? 1.00 Selling Price 150 .40 Less: Cost MarkUp 225 .60 ? S = C + M (B) M = S - C M = $375 - $150 M = $225 = $150 + .60(S) .40S = $150 S = $150/.40 = $375

Up Mark Q S = C + M (A) 35 1.00 $35 = C + .40($35) 21 .60 Jane’s flower business sells floral arrangements for $35. To make her desired profit, Jane needs a 40% markup on Selling Price. (A) What do the flower arrangements cost Jane? (B) What is the dollar markup? $ %/100 S = C + M (A) Selling Price 35 1.00 $35 = C + .40($35) Less: Cost 21 ? .60 ? $35 = C + $14 MarkUp 14 .40 ? $35 - $14 = C (B) M = S - C M = $35 - $21 M = $14 $21 = C

Mark Up Converting

% Markup on Selling Price to % Markup on Selling Price Converting 50% MU on Cost = ? % MU on S 33% MU on SP = ? % MU on Cost % Markup on Selling Price to % Markup on Cost % Markup on Cost to % Markup on Selling Price Formula Formula % markup on S % markup on C 1 - % markup on S 1 + % markup on C .33 = .33 .50 = .50 = .50 = .33 1 - .33 .67 1+ .50 1 .50

Mark Down

Mark Down $Markdown %Markdown = Q Formula Selling Price (original) Sears marked down a $50 tool set to $36. What is (a) the $markdown and (b) the %markdown? $Markdown = Old S – New S = $50 - $36 = $14 Markdown %Markdown = Markdown $14 $50 = 28% = Old S

Mark Down Q S = Cost/(1 - .45) S = $57.75 / .55 = $105.00 $105.00 1.00 Ski bindings bought for $57.75 were marked up 45% of the Selling Price. When the bindings were discontinued, they were marked down 40%. What was the Sale Price after the 40% markdown? $ %/100 S = Cost/(1 - .45) S = $57.75 / .55 = $105.00 1.00 .45 = .55 $105.00 1.00 Selling Price ? Less: Cost 57.75 .55 ? MarkUp $ 47.25 .45 ? Selling Price $105.00 1.00 S(R) = S * (1-d) = 105.00* .60 = $63.00 1.00 .40 = .60 Less: Discount 42.00 ? .40 $ 63.00 .60 *S(R) ? * Reduced S

This completes Chapter 4