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Chapter 9

Chapter 9. Mathematics of Pricing. START. EXIT. Chapter Outline. 9.1 Markup and Markdown 9.2 Profit Margin Chapter Summary Chapter Exercises. 9.1 Markup and Markdown.

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Chapter 9

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  1. Chapter 9 Mathematics of Pricing START EXIT

  2. Chapter Outline 9.1 Markup and Markdown 9.2 Profit Margin Chapter Summary Chapter Exercises

  3. 9.1 Markup and Markdown • A very large part of the business conducted in this world is a matter of buying things and then turning around and selling them to someone else at a profit. • The price a business pays for an item is called the wholesale price or cost. • The price a business sells the item for is known as a retail price.

  4. 9.1 Markup and Markdown • One common method used for setting the selling price for an item is markup based on cost. • To determine a price with this method, we simply take the cost of the item and add on a pre-determined percent of the item’s cost.

  5. 9.1 Markup and Markdown FORMULA 9.1.1 Markup Based on Cost P = C(1 + r) where P represents the SELLING PRICE C represents the COST and r represents the PERCENT MARKUP

  6. 9.1 Markup and Markdown Example 9.1.1 • Problem • An auto mechanic charges a 40% markup based on cost for parts. What would the price be for an air filter that cost him $14.95? What is the dollar amount of his markup on this item? • Solution P = C(1 + r) P = $14.95(1 + 40%) = $20.93 Markup = $20.93 -- $14.95 = $5.98

  7. 9.1 Markup and Markdown Example 9.1.2 • Problem • Starbucks sells souvenir coffee mugs for $7.95. The markup based on cost is 65%. Find (a) the cost of each mug and (b) the dollar amount of the markup. • Solution P = C(1 + r) $7.95 = C(1 + 65%), So C = $4.82 Markup = $7.95 -- $4.82 = $3.13

  8. 9.1 Markup and Markdown Example 9.1.3 • Problem • An electronics retailer offers a computer for sale for $1,000. The retailer’s cost is $700. What is the markup percent? • Solution P = C(1 + r) $1,000 = $700(1 + r) 1.428571429 = 1 + r r = 0.428571429 = 42.86%

  9. 9.1 Markup and Markdown • We are all familiar with the idea of prices being marked down as part of a sale or some other promotion, for example. • To calculate a marked-down price, we simply apply the percent the price is to be marked down to the original price, and then subtract.

  10. 9.1 Markup and Markdown FORMULA 9.1.2 Markdown MP = OP(1 – d) where MP represents the MARKED-DOWN PRICE OP represents the ORIGINAL PRICE d represents the PERCENT MARKDOWN

  11. 9.1 Markup and Markdown Example 9.1.4 • Problem • At its Presidents’ Day Sale, a furniture store is offering 15% off everything in the store. What would the sale price be for a sofa that normally sells for $1,279.95? What is the dollar amount of the markdown? • Solution MP = OP(1 – d) MP = $1,279.95(1 – 15%) = $1,087.96 Dollar amount markdown = $1,279.95 - $1,087.96 = 191.99

  12. 9.1 Markup and Markdown Example 9.1.5 • Problem • Hal’s Hardware is having a going-out-of-business sale. According to its ad, everything in the store is marked down 40%. If a set of patio lights is offered at a marked-down price of $29.97, what was the original price? • Solution MP = OP(1 – d) $29.97 = OP(1 – 40%) OP = $49.95

  13. 9.1 Markup and Markdown Example 9.1.6 • Problem • At the end of the summer, a backyard play set that usually sells for $599.95 is marked down to $450. What is the markdown percent? • Solution MP = OP(1 – d) $450 = $599.95(1 – d) 0.7500625 = 1 - d d = 0.2499374 = 24.99%

  14. 9.1 Markup and Markdown Example 9.1.7 BE CAREFUL!!! • Problem • Jenna’s Gemstones store bought a necklace for $375. In the store, Jenna marked up this price by 20%. Several months later, when the necklace still had not sold, she decided to mark down the price by 20%. What was the marked down price? • Solution • Markup P = C(1 + r) P = $375(1 + 20%) = $450 • Markdown MP = OP(1 – d) MP = $450(1 – 20%) = $360

  15. 9.1 Markup and Markdown Example 9.1.7 (cont) Question: Why didn’t things work out here as “common sense” would have suggested? The markup is a percent of the cost, the markdown is a percent of the marked-up selling price. Since those two 20%’s are NOT 20% of the same thing, they are not really the same at all. It is really important to not make assumptions off the bat when comparing markup and markdown percents. Be careful and work things through!

  16. 9.1 Markup and Markdown Example 9.1.8 • Problem • If prices are calculated with a 35% markup based on cost, what is the percent that those prices should be marked down to get back to their original cost? • Solution • We don’t know what sort of things we are pricing here, much less the dollar amounts of those things. However, since we are working with percents, the actual dollar amounts don’t really matter. We choose a convenient cost of $100. P = C(1 + r) P = $100(1 + 35%) P = $135 MP = OP(1 – d) $100 = $135(1 – d) d = 25.93%

  17. Section 9.1 Exercises

  18. Problem 1 • Wal-Mart charges $2.35 for a carton of eggs. If the price is based on a 45% markup based on cost, how much did they pay the chicken farmer? CHECK YOUR ANSWER

  19. Solution 1 • Wal-Mart charges $2.35 for a carton of eggs. If the price is based on a 45% markup based on cost, how much did they pay the chicken farmer? • P = C(1 + r) $2.35 = C(1 + 45%) $2.35 = C x 1.45 C = $1.62 BACK TO GAME BOARD

  20. Problem 2 • You bought an evening gown for $35, what a deal! If the markdown percent was 70%, what was the original price? CHECK YOUR ANSWER

  21. Solution 2 • You bought an evening gown for $35, what a deal! If the markdown percent was 70%, what was the original price? • $35 = OP(1 – 70%) $35 = OP x 0.30 OP = $116.67 BACK TO GAME BOARD

  22. 9.2 Profit Margin • The gross profit on an item is the difference between what the item cost and what it sold for. • Of course, the business of buying and selling is not that simple. Every store has to take on plenty of other overhead expenses such as rent, utilities, salaries, finance costs, advertising expenses, etc. Gross profit does not account for those. • The net profit, on the other hand, is the profit made after taking into account all of the expenses of doing business. • The profit margin is the profit expressed as a percent of the selling price.

  23. 9.2 Profit Margin Example 9.2.1 • Problem • Sally’s Fashion Paradise sells a dress that cost $45 for $65. Find the gross profit margin from this sale. • Solution • Gross Profit = $65 -- $45 = $20 • Gross Profit Margin = $20/$65 = 0.3077 = 30.77% Example 9.2.2 • Problem • Sally’s Fashion Paradise sells women’s purses, pricing them with a 35% gross profit margin. If a purse is priced at $72, what is the gross profit in that price? • Solution • Gross Profit = 35% x $72 = $25.20

  24. 9.2 Profit Margin Example 9.2.3 • Problem • Last year, sales at Sally’s Fashion Paradise totaled $219,540. The cost of the items sold was $147,470. What was the overall gross profit margin for the year? • Solution • Total Gross Profit = $219,540 -- $147,470 = $72,070 • Gross Profit Margin = $72,070/$219,540 = 32.83%

  25. 9.2 Profit Margin Example 9.2.4 • Problem • Last year, Sally’s Fashion Paradise had overhead expenses totaling $63,073. Find (a) expenses as a percent of sales and (b) the net profit margin. • Solution • $63,073/$219,540 = 28.73% • Net Profit = $72,070 -- $63,073 = $8,997 • Net Profit Margin = $8,997/$219,540 = 4.10%

  26. 9.2 Profit Margin Example 9.2.5 • Problem • Two years ago, Sally’s shop had sales totaling $153,670. The cost of the goods sold was $118,945, and her expenses totaled $57,950. Find her overall (a) gross profit margin and (b) net profit margin for that year. • Solution • Gross Profit = $153,670 -- $118,945 = $34,725 • Gross Profit Margin = $34,725/$153,670 = 22.60% • Net Profit = $34,725 -- $57,950 = -$23,225 • Net Profit Margin = -$23,225/$153,670 = -15.11%

  27. 9.2 Profit Margin Example 9.2.6 • Problem • In the year in which the dress sold for $65, the total sales were $219,540 and expenses were $63,073. If expenses are allocated in proportion to sales, how much of the store’s expenses is attributable to that dress? • Solution • $65/$219,540 = 0.02961% • 0.0002961 x $63,073 = $18.67

  28. 9.2 Profit Margin • Determining a price by using a target gross margin is called markup based on selling price, in contrast to markup based on cost. • If we know the item’s cost, and if we know our markup percent based on cost, calculating the selling price is fairly straightforward. • Profit margin, though, is a percent of the selling price. • Obviously, we don’t know the selling price before we know the selling price!

  29. 9.2 Profit Margin FORMULA 9.2.1 Markup Based on Selling Price C = SP(1 – r) where C represents the ITEM’S COST SP represents the SELLING PRICE and r represents the GROSS PROFIT MARGIN

  30. 9.2 Profit Margin Example 9.2.7 • Problem • Determine the selling price of an item costing $45 in order to have a 35% gross profit margin. • Solution • C = SP(1 – r) $45 = SP(1 – 35%) SP = $69.23

  31. 9.2 Profit Margin Example 9.2.8 • Problem • A cooperative market allows its members to place special orders for items they want to buy in bulk. The price the member pays is based on an 8% markup on selling price. • Liz ordered a case of protein bars, for which the market’s cost was $24.17. How much will she pay for this order? • C = SP(1 – r) $24.17 = SP(1 – 8%) SP = $26.27

  32. Section 9.2 Exercises

  33. Problem 1 • Harvey’s sells watermelons for $4.99 each, even though farmers sell them for $2.00 each. What is the gross profit margin? CHECK YOUR ANSWER

  34. Solution 1 • Harvey’s Supermarket sells watermelons for $4.99 each, even though farmers sell them for $2.00 each. What is the gross profit margin? • Gross Profit = $4.99 -- $2.00 = $2.99 • Gross Profit Margin = $2.99/$4.99 = 59.92% BACK TO GAME BOARD

  35. Problem 2 • Harvey’s Supermarket had overhead expenses totaling $49,265, the cost of items sold was $153,076, and total sales were $240,543. • What is the net profit margin? CHECK YOUR ANSWER

  36. Solution 2 • Harvey’s Supermarket had overhead expenses totaling $49,265, the cost of items sold was $153,076, and total sales were $240,543. • What is the net profit margin? • Net Profit = $240,543 -- $153,076 -- $49,265 = $38,202 • Net Profit Margin = $38,202/$240,543 = 15.84% BACK TO GAME BOARD

  37. Problem 3 • Determine the selling price of an item costing $395.72 in order to have a 40% gross profit margin. CHECK YOUR ANSWER

  38. Solution 3 • Determine the selling price of an item costing $395.72 in order to have a 40% gross profit margin. • C = SP(1 – r) $395.72 = SP(1 – 40%) $395.72 = SP x 0.60 SP = $659.53 BACK TO GAME BOARD

  39. Problem 4 • You purchased a set of dishes for $67.45. If the markup based on selling price is 41%, what was the item’s cost? CHECK YOUR ANSWER

  40. Solution 4 • You purchased a set of dishes for $67.45. If the markup based on selling price is 41%, what was the item’s cost? • C = SP(1 – r) C = $67.45(1 – 41%) C = $39.80 BACK TO GAME BOARD

  41. Markup Based on Cost Determining Markup Percent Markdown Gross Profit Margin Net Profit Margin Markup Based on Selling Price Chapter 9 Summary

  42. Chapter 9 Exercises EXIT

  43. Section 9.1 -- $100 • A beauty salon charges a 45% markup based on cost for the hair color system. What would its price if the cost is $5.99? What is the dollar amount of the markup on this item? CHECK YOUR ANSWER

  44. Section 9.1 -- $100 • A beauty salon charges a 45% markup based on cost for the hair color system. What would its price if the cost is $5.99? What is the dollar amount of the markup on this item? • P = C(1 + r) P = $5.99(1 + 45%) P = $8.69 Markup = $8.69 -- $5.99 = $2.70 BACK TO GAME BOARD

  45. Section 9.1 -- $200 • At its Memorial Day sale, a department store is offering 20% off everything in the store. What would be the price of item originally priced at $159.34? CHECK YOUR ANSWER

  46. Section 9.1 -- $200 • At its Memorial Day sale, a department store is offering 20% off everything in the store. What would be the price of item originally priced at $159.34? • MP = OP(1 – d) MP = $159.34(0.80) MP = $127.47 BACK TO GAME BOARD

  47. Section 9.2 -- $100 • Last quarter, Randy’s Pool Supplies had sales totaling $492,780, the cost of the goods sold was $204,500, and expenses totaled $97,231. Find the overall net profit margin. CHECK YOUR ANSWER

  48. Section 9.2 -- $100 • Last quarter, Randy’s Pool Supplies had sales totaling $492,780, the cost of the goods sold was $204,500, and expenses totaled $97,231. Find the overall net profit margin. • Net Profit = $492,780 – $204,500 -- $97,231 • Net Profit = $191,049 • Net Profit Margin = $191,049/$492,780 = 38.77% BACK TO GAME BOARD

  49. Section 9.2 -- $200 • Arlene’s Gifts Galore is selling gift baskets purchased from a wholesaler for $20 each. Determine the selling price of each basket in order to have a 40% gross profit margin. CHECK YOUR ANSWER

  50. Section 9.2 -- $200 • Arlene’s Gifts Galore is selling gift baskets purchased from a wholesaler for $20 each. Determine the selling price of each basket in order to have a 40% gross profit margin. • C = SP(1 – r) $20 = SP(1 – 40%) $20 = SP(0.60) SP = $33.33 BACK TO GAME BOARD

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