Business Math Chapter 9 Markup and Markdown 1

Business Math Chapter 9: Markup and Markdown 1

Markup and Markdown § Find the cost, markup or selling price when any two of the three are known. § Find the percent of markup based on the cost when the cost and selling price are known. § Find the selling price when the cost and percent of markup based on the cost are known. (continued) Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 2

Markup and Markdown (continued) § Find the cost when the amount of markup and the percent of markup based on the cost are known. § Find the cost when the selling price and the percent of markup based on the cost are known. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3

Markup = Selling price – Cost Selling price - Markup = Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 4

Try these examples. If an item sells for $20 and has a markup of $12, what is the cost of the item? Answer: $8 If an item costs $16 and is sold for $20, what is the markup of that item? Answer: $4 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 5

Find the percent of markup based on the cost when the cost and selling price are known. When the markup is based on cost The rate of cost is always 100% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 6

n A retailer can buy a shirt from a wholesaler at $10. 00. The retailer will add $5. 00 to the cost. n The retailer then sells it for $15. 00. n Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 7

P=Rx. B Using the formula Markup = rate of markup x cost Change the equation so the rate of markup is equal to markup divided by the cost. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 8

Rate of markup based on cost The shirt Cost $10 Rate of cost 100% +Markup $5 + Rate of markup ? =Selling price $15 = Rate of Selling price ? Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 9

Five Step Solution Plan 1. What you know… Rate of cost always equals 100%; MU and C values. 2. What you are looking for? Rate of markup and rate of selling price 3. Solution plan Rate of markup = MU divided by cost 4. Solution Carry out operation 5. Conclusion Add rate of MU to C to find rate of SP. Does it make sense? Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 10

Substitute the known values n n A shirt that costs $10 and sells for $15 has a markup rate of 50% $5 divided by $10 is equal to. 5 or 50% Rate of markup [based on cost] is equal to 50% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 11

Try these examples 1. Duke’s photography pays $9 for a 5 x 7 photograph. If the photograph is sold for $15, what is the percent of markup based on cost? Answer: 66. 67% 2. Lilly buys tea from England for $4 a box and sells it in “The Tea Party” for $12 a box. Find the percent of markup based on cost. Answer: 200% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 12

Find the selling price when the cost and percent of markup based on the cost are known A boutique pays $5 a pair for handmade earrings and sells them at a 50% markup based on cost. Find the selling price of the earrings. Cost +Mark-up =Selling price $5 Rate of Cost 100% ? Rate of markup +50% ? Rate of SP =150% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 13

Find the selling price n The rate of the selling price is found by adding the rate of cost (100%) to the rate of markup. n Selling price = Rate of selling price (based on cost) x cost. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 14

Do these examples. n What is the selling price for a CD which costs the retailer $8. 00 and is marked up 60% based on cost? Answer: $12. 80 n What is the selling price for a set of hairbrushes which cost the salon $12. 00 and is marked up 150% based on cost? Answer: $30 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 15

Find the cost when the amount and the percent of markup are known. A DVD movie is marked up $6. 50 which represents a 40% markup based on cost. What is the cost of the DVD? Cost ? RC +MU 6. 50 +RMU = SP ? 100% 40% = RSP 140% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 16

Find the cost by dividing the markup amount by the markup rate n Cost = Markup rate n Cost = $6. 50 40% [or 0. 4] n Cost = $16. 25 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 17

Try these two examples n Find the cost of a box of ballpoint pens which has been marked up $4 and has a markup rate of 30%. Answer: $13. 33 n Find the cost of a pair of shoes that has been marked up $25 and has a markup rate of 50%. Answer: $50 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 18

Find the cost when the selling price and the percent of markup based on cost are known. A camera sells for $20. The markup rate is 50% of the cost. Find the cost of the camera and the markup. Cost ? RC 100% +Markup ? +RMU 50% = Selling price $20 = RSP 150% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 19

Find the cost by dividing the selling price by the rate of the selling price n Cost = Selling price Rate of the selling price n Cost = $ 20 150% (or 1. 5) n Cost = $13. 33 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 20

Try these examples. n Find the cost and markup of a bicycle tire which sells for $18 and is marked up 50% of the cost. Answer: $12 and $6 n Find the cost and markup of a moisturizing cream which sells for $30 and is marked up 150% of the cost. Answer: $12 and $18 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 21

9. 2 Markup based on selling price and markup comparisons n Find the amount of markup and the percent of markup based on selling price when the cost and selling price are known. n Find the selling price when the amount of markup and the percent of markup based on selling price are known. (continued) Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 22

9. 2 Markup based on selling price and markup comparisons (continued) n Find the selling price when the cost and the percent of markup based on the selling price are known. n Find the cost when the selling price and the percent of markup based on the selling price are known. n Compare the markup based on cost with the markup based on selling price. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 23

Take note! n In the previous section, the markup based on cost, the rate of cost was always 100%. n In this section, the markup based on selling price, the rate of selling price is always 100%. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 24

Find the amount of markup and the percent of markup. A calculator costs $5 and sells for $10. Find the rate of markup based on the selling price. Cost $5 Rate of Cost ? +Markup ? +Rate of Markup = Rate of Selling price ? = Selling price $10 100% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 25

Find the rate of markup by dividing the markup by the selling price and multiplying it by 100% n The markup amount is the difference between the selling price and the cost. n Divide the markup by the selling price to get the difference and then multiply it by 100%, to get the rate of markup. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 26

Find the amount of markup and the percent of markup (based on SP ) for the following items: n A dog collar which costs $4 and sells for $10. Answer: $6 and 60% n A notebook which costs $1. 25 and sells for $2. Answer: $. 75 and 37. 5% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 27

Find the selling price when the amount of markup and the percent of markup based on the selling price are known. n Subtract the percent of markup from 100% to obtain the rate of cost. n Divide the markup by the rate of markup based on SP Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 28

Find the cost and selling price if a handbag is marked up $5 with a 20% markup rate based on selling price. Cost ? RC ? + MU $5 +RMU 20% = SP ? = RSP 100 % Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 29

Find the selling price and the amount of the markup n SP = Markup Rate of Markup based on selling price n SP = $5 20% or [0. 2] n SP = $ 25 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 30

Find the selling price and amount of markup based on selling price for the following items: n A cell phone which has been marked up $50 and with a markup rate of 33% based on selling price. Answer: $150 n A pair of socks which has been marked up $3 and with a markup rate of 60% based on selling price. Answer: $5 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 31

Find the selling price when the cost and the percent of markup based on selling price are known. n Subtract the rate of markup from 100% to determine the rate of cost. n Selling price = Cost [divided by] Rate of Cost based on SP Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 32

Find the selling price and markup for a pair of jeans which costs the retailer $28. What is the selling price? Cost $28 RC ? + MU ? + RMU 30% = SP ? = RSP 100% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 33

To find the selling price, divide the cost by the rate of cost n SP = Cost Rate of cost n SP = $28 70% [ = 0. 7] n SP = $40 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 34

Find the selling price and markup (based on selling price) for the following items: A handheld calculator that costs the retailer $2 and is marked up 60%. Answer: $5 and $3 A box of gourmet chocolates that costs $8 a box and is marked up 75%. Answer: $32 and $24 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 35

Find the cost when the selling price and percent of markup based on selling price are known. Subtract the rate of markup from the rate of selling price to determine the rate of cost. Cost = Rate of Cost x Selling Price Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 36

Find the markup and cost of a box of pencils that sells for $2. 99 and is marked up 25% of the selling price. First, find the rate of cost. Cost ? RC ? + MU ? +RMU 25% = SP $2. 99 = RSP 100% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 37

Compare the markup based on cost with markup based on selling price Find the markup based on cost and the markup based on selling of a computer that costs $1, 500 and sells for $2, 000. Cost 1500 +MU 500 RC +R MU = SP 2000 =RSP 100% Cost 1500 ? +MU ? =SP RC ? 500 +R ? MU 2000 =RSP 100% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 38

What is the difference? n The percentage of markup based on cost is 33. 33%. n The percentage of markup based on selling price is 25%. n What accounts for the difference? Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 39

Converting a markup based on selling price to a markup based on cost. The markup rate based on cost is equal to the markup rate based on selling price divided by 100% minus the markup rate based on selling price. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 40

Converting a markup based on cost to a markup based on selling price. The markup rate based on selling price is equal to the markup rate based on cost divided by the markup rate based on cost plus 100%. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 41

9. 3 Markdown, Series of Markdowns and Perishables n Find the amount of markdown, the reduced (new) price, and the percent of the markdown. n Find the final selling price for a series of markup and markdowns. n Find the selling price for a desired profit on perishable and seasonal goods. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 42

Find the amount of markdown, the reduced (new) price and the percent of the markdown. The original selling price is always 100% Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 43

Find the markdown and rate of markdown n The markdown is found by subtracting the new price from the original price. n The markdown rate is found by dividing the markdown by the original price and multiplying that figure by 100%. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 44

A lamp originally sold for $36 and is marked down to sell for $30. Find the markdown and rate of markdown. $ % Original Selling Price (S) $36 100% -Markdown = New Price $6 $30 ? ? Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 45

Find the final selling price for a series of markup and markdowns. n Each new price becomes the base. n For markups based on cost, multiply the base by 1 + the rate of markup. n For markdowns, multiply the base by the complement of the rate of markdown. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 46

Find the final selling price Find the final price for an item that cost $18, marked up by 20% and then, was marked down 33%, and subsequently marked up 10% and finally marked down by 50% for clearance. Answer: $7. 91 Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 47

Find the selling price for a desired profit on perishable and seasonal goods. n Determine the cost by multiplying the unit price by the quantity. n Determine the markup rate and amount and add to the cost. n Establish the expected to sell amount. n Divide the total selling price by the expected to sell amount. Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 48

Find the per pound selling price n n n Mr. Green buys 100 pounds of tomatoes at $. 15 lb. and establishes a markup rate of 120% based on cost. What is the total cost? TC = $15 + MU=$18 =Total SP =$33 He expects to sell 90%. How many pounds is he expected to sell? Expected to sell = 90 Divide the TSP by “expected to sell” number. SP = $0. 37 lb. (rounded) Cleaves/Hobbs: Business Math, 7 e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 49