© the mcgraw-hill companies, inc., 2008 mcgraw-hill/irwin 8-1 chapter 8 mathematics of pricing...

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© The McGraw-Hill Companies, Inc., 2008McGraw-Hill/Irwin

Chapter 8

Mathematics of Pricing

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Chapter Outline

8.1Markup and Markdown

8.2Profit Margin

8.3Series and Trade Discounts

8.4Depreciation

Chapter Summary

Chapter Exercises

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8.1 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.

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• 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.

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FORMULA 8.1.1Markup Based on Cost

P = C(1 + r)where

P represents the SELLING PRICEC represents the COST

and r represents the PERCENT MARKUP

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Example 8.1.1

• 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?

• SolutionP = C(1 + r)

P = $14.95(1 + 40%) = $20.93

Markup = $20.93 -- $14.95 = $5.98

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Example 8.1.2• Problem

– Hegel’s Bagels and Vienna Coffeehouse 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.

• SolutionP = C(1 + r)P = $7.95(1 + 65%) = $4.82Markup = $7.95 -- $4.82 = $3.13

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– 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)

r = 0.4285714 = 42.86%

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• 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.

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FORMULA 8.1.2

Markdown

MP = OP(1 – d)

where

MP represents the MARKED-DOWN PRICE

OP represents the ORIGINAL PRICE

d represents the PERCENT MARKDOWN

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– 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

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– Hal’s Hardware Haven 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? How much of a dollar savings is this versus the original price?

• SolutionMP = OP(1 – d)$29.97 = OP(1 – 40%)OP = $49.95

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Example 8.1.6

• 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?

• SolutionMP = OP(1 – d)

$450 = $599.95(1 – d)

d = 0.2499374 = 24.99%

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– Gemma’s Gemstone Gewelry bought a necklace for $375. In the store, Gemma 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

– MarkdownMP = OP(1 – d)MP = $450(1 – 20%) = $360

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8.1 Markup and MarkdownExample 8.1.8• 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 = $135MP = OP(1 – d)$100 = $135(1 – d)d = 25.93%

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Section 8.1 Exercises

Problem 1:

Markup Based on Cost

Problem 2:

Markdown

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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

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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

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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

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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

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8.2 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.

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8.2 Profit Margin


– 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 8.22

• 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

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8.2 Profit Margin


– 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%

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8.2 Profit Margin


– 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%

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8.2 Profit Margin


– 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%

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8.2 Profit Margin


– 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%– 0.02961% x $63,073 = $18.67

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8.2 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!

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8.2 Profit Margin

FORMULA 8.2.1Markup Based on Selling Price

C = SP(1 – r)

where C represents the ITEM’S COST

SP represents the SELLING PRICEand

r represents the GROSS PROFIT MARGIN

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8.2 Profit Margin


– 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

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8.2 Profit Margin


– 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.

– Lynne 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

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Problem 1:

Gross Profit Margin

Problem 2:

Net Profit Margin

Problem 3:

Markup Based on Selling Price

Problem 4:

Grab Bag

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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

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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

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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

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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 = 15.88%

BACK TO GAME BOARD

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Problem 3

• Determine the selling price of an item costing $395.72 in order to have a 40% gross profit margin.

CHECK YOUR ANSWER

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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

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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

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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

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8.3 Series and Trade Discounts

• Merchants are normally free to set prices as they see fit, basing their pricing decisions on costs, profit targets, and competition.

• Still, many manufacturers do set suggested prices for their products. The suggested price for an item is known as a list price or manufacturer’s suggested retail price (MSRP).

• When a product has a list price, it is not uncommon for the item to be sold to a merchant on the basis of a discount to the list price. This is known as a trade discount.

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– Ampersand Computers bought 12 computers from the manufacturer. The list price is $895.00 and the manufacturer offered a 25% trade discount. How much did Ampersand pay for the computers?

• Solution$895.00 x 25% = $671.2512 x $671.25 = $8,055.00

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– Samir’s House of Gadgets placed an order for 500 thingmies (list price $4.95), 350 jimmamathings (list price $8.95), and 800 hoozamawhatzits (list price $17.99). The manufacturer offers a 27 ½% trade discount and includes shipping in its prices. Find the total due on the invoice for this order.

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8.3 Series and Trade DiscountsExample 8.3.2 Cont.• Solution

Quantity Product # Description MSRP Total

500 Thingmies $4.95 $2,475.00

350 Jimmamathings $8.95 $3,132.50

800 Hoozamawhatzits $17.99 $14,392.00

Subtotal $19,999.50

LESS: 27.5% discount ($5,499.86)

Net $14,499.64

PLUS: Freight $00.00

Total due $14,499.64

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FORMULA 8.3.1Trade Discounts

NP = LP(1 – d)

where

NP represents the NET (DISCOUNTED) PRICELP represents the LIST PRICE

d represents the PERCENT DISCOUNT

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– What is the net cost for each jimmamathing in the previous example?

• SolutionNP = LP(1 – d)NP = $8.95(1 – 27.5%)NP = $6.49

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– Samir realized that he forgot to order 400 doohickeys. He called the manufacturer and was given a price of $2,652 for them. He did not ask for the list price but realizes that he needs to know it now. What is the list price for a doohickey?

• Solution

$2,652/400 = $6.63

NP = LP(1 – d)$6.63 = LP(1 – 27.5%)LP = $9.14

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– A manufacturer offers a 30% trade discount. If the merchant sells items at a 10% discount to list, what is the gross profit margin? What is the markup based on cost?

• Solution– We will use $100 for convenience.– The cost would be 70% x $100 = $70– The selling price would be 90% x $100 = $90– Gross Profit Margin

C = SP(1 – r)$70 = $90(1 – r)r = 22.22%

– Markup Based on Cost$90 = $70(1 + r)r = 28.57%

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• Series discounts are multiple discounts to a price in succession.

• Sometimes, a manufacturer may offer multiple trade discounts.

• For example, a company might normally offer a 25% trade discount but during a special promotion or to match a competitor’s pricing, might offer an additional 15% discount.

• Despite appearances, it’s incorrect to conclude that success discounts of 25% and 15% are equivalent to a single discount of 40%.

• The single discount equivalent to a series of discounts is referred to as the single equivalent discount.

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– The list price for a herbal weight loss supplement is $39.95. The manufacturer normally offers a 25% trade discount, but during a special promotion it offers an additional 15% discount. Find the net price for this item.

• Solution75% x $39.95 = $29.9685% x $29.96 = $25.47

This could also be calculated more simply as (75%)(85%)($29.96) = $25.47

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– Find the single equivalent discount for successive 25% and 15% discounts.

• Solution– We will work from an assumed price of $100.

These discounts will reduce the price to 75% x 85% x $100 = $63.75

This is a total discount of $100 -- $63.75 = $36.25

As a percent of the list price, it’s $36.25/$100 = 36.25%

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– You work for a company that manufactures photovoltaic (solar) panels. Your company’s 70-watt panel lists for $295 and you offer an 18% trade discount.

– A competing company lists its 70-watt panel for $305 and offers a 25% trade discount.

– Ingraham Solar Systems, one of your main customers, tells you that it is considering switching to your competitor’s panels because of their lower cost.

– What additional discount do you need to offer to match your competitor’s price?

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Example 8.3.9 Cont.• Solution

– You are selling your panels for 82% x $295 = $241.90

– Your competitor is selling for 75% x $305 = $228.75

– You would need to drop your current net price by $241.90 -- $228.75 = $13.15

– As a percent of $241.90, it works out to $13.15/$241.90 = 5.44%

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• A merchant may require customers to pay for their orders in advance, before the merchandise is shipped.

• It is not unusual, though, for a seller to sell items on credit, especially to customers with whom the seller has (or hopes to build) a good relationship.

• Even when credit is extended, the seller still wants to be paid promptly and late payments may incur interest charges.

• A cash discount is a discount offered for prompt payment.

• The period of time during which the cash discount is available is called the discount period.

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Dating MethodDiscount Period

Begins:Abbreviation Example

Ordinary On the invoice dateNone. Assumed if

not otherwise indicated.

2/10, n/30

End of MonthAt the end of the month following the invoice date

EOM 2/10, n/30, EOM

ProximoAt the end of the month following the invoice date

PROX 2/10, n/30, PROX

Receipt of GoodsWhen the buyer receives the merchandise

ROG 2/10, n/30, ROG

PostdatedAs of date indicated on the invoice

AS OF2/10, n/30, AS OF

3/7/08

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– Ned’s Furniture Galaxy ordered a shipment of dining room sets. The invoice was dated March 14, 2007, and the order arrived on March 28, 2007. The manufacturer offers a 2 ½% cash discount for payment within 10 days.

– To take advantage of this discount, when must Ned make payment if the dating method is (a) ordinary dating, (b) end of month, (c) receipt of goods, or (d) postdated as of May 1, 2007?

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Example 8.3.10 Cont.• Solution

– With ordinary dating, the clock starts ticking on the invoice date, March 14, so Ned must make the payment by March 24.

– With EOM dating, the clock starts ticking at the end of March, so Ned must pay by April 10.

– The furniture arrived on March 28 so Ned must pay by April 7.

– The discount period begins on May 1 so Ned must pay by May 11.

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Problem 1:

Trade Discounts

Problem 2:

Series Discounts

Problem 3:

Cash Discounts

Problem 4:

Grab Bag

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Problem 1

• Book-a-Nook bought 100 copies of a popular novel. The list price for each book is $14.99 and the publisher offered a 20% trade discount. How much did Book-a-Nook pay for the novels?

CHECK YOUR ANSWER

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Solution 1

• Book-a-Nook bought 100 copies of a popular novel. The list price for each book is $14.99 and the publisher offered a 20% trade discount. How much did Book-a-Nook pay for the novels?

• $14.99 x 80% = $11.99• $11.99 x 100 = $1,199.00

BACK TO GAME BOARD

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Problem 2

• Your favorite department store is having a 25% off sale. If you pay with your store credit card, you will get an additional 10% off. You found a suit for $99. What is a sale price of this suit if you take an advantage of both discounts?

CHECK YOUR ANSWER

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Solution 2• Your favorite department store is having a 25% off

sale. If you pay with your store credit card, you will get an additional 10% off. You found a suit for $99. What is a sale price of this suit if you take an advantage of both discounts?

• 75% x 90% x $99 = $66.83

BACK TO GAME BOARD

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Problem 3

• Alexa’s Antiques Boutique ordered several pieces from the dealer. The invoice was dated May 18, 2007. The dealer also offered a 2% cash discount for payment within 10 days.

• If Alexa wants to take an advantage of this offer, when and how much should she pay?

CHECK YOUR ANSWER

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Solution 3• Alexa’s Antiques Boutique ordered several pieces from the dealer

for a total of $25,467.89. The invoice was dated May 18, 2007, terms 2/10, n/30.

• If Alexa wants to take an advantage of this offer, when and how much should she pay?

• If not otherwise indicated, we assume that the dating method is ordinary, so discount period begins on the invoice date.

• The discount is 2% so Alexa would pay only 98% x $25,467.89 = $24,958.53.

• The last day to pay is 10 days after the invoice date, so it’s May 28, 2007.

BACK TO GAME BOARD

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Problem 4• It’s time to replenish the office supplies so Donna, the secretary, placed

an order below. How much will Donna’s company pay if they take an advantage of the cash discount?

CHECK YOUR ANSWER

Quantity Description Unit Price Total

10 boxes Pencils $4.95 $40.95

10 boxes Pens, Black Ink $7.43 $70.43

5 packages Notepads $10.40 $52.00

Subtotal

LESS: 15% trade discount

Net Price

LESS: 2% cash discount (2/10, n30)

Subtotal

Sales Tax (7%)

Total Due

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Solution 4

BACK TO GAME BOARD

Quantity Description Unit Price Total

10 boxes Pencils $4.95 $40.95

10 boxes Pens, Black Ink $7.43 $70.43

5 packages Notepads $10.40 $52.00

Subtotal $163.38

LESS: 15% trade discount ($24.51)

Net Price $138.87

LESS: 2% cash discount (2/10, n30) ($2.78)

Subtotal $136.09

Sales Tax (7%) $9.53

Total Due $145.62

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8.4 Depreciation

• The dollar value of any thing that can be owned will change as time goes by. Some things, like real estate and collectibles, are expected to go up in value over time.

• We call that increase in something’s dollar value price appreciation.

• Other things, though, become less valuable with use and the passing of time. Computers and electronics become obsolete, used cars command lower prices, and business equipment becomes less valuable.

• The decline in something’s dollar value is called depreciation.

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8.4 Depreciation


– According to a wine expert, the market price for a very rare bottle of Chateau la Plonque wine is $3,650. In an interview in a wine trade publication, he states that he expects this particular bottle to appreciate at a 7% annual rate for the next 10 years.

– If his prediction turns out to be correct, what will the price be 10 years from now?

• SolutionFV = PV(1 + i)n

FV = $3,650(1.07)10

FV = $7,180.10

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8.4 Depreciation


– Todd just bought a new car for $23,407. According to an online used car pricing service, the value of this car will decline at a 15% annual rate. Assuming this is correct, what will the car’s value be in 5 years?

• SolutionFV = PV(1 + i)n

FV = $23,407(0.85)5

FV = $10,386

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8.4 Depreciation

• When we calculate depreciation by assuming that each year’s depreciation is a set percent of a decreasing value, the amount of annual depreciation decreases with each passing year. For this reason, this is often referred to as declining balance depreciation.

• There is another very commonly used method for calculating depreciation, though. With straight-line depreciation, we assume that the price declines by the same dollar amount each year.

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8.4 Depreciation


– The Cotswold Real Estate Agency purchased a computer for $2,000. The useful life of the computer is 5 years. The computer is assumed to have no salvage value.

– Find (a) the straight-line depreciation rate, (b) the depreciated value of the computer, and (c) the depreciated value after 7 years.

• Solution– The computer will lose its full $2,000 initial value in 5 years, and

since it loses the same amount each year, the depreciation rate is $2,000/5 = $400 per year.

– If the computer’s value drops by $400 per year for 3 years, that means it will be worth $2,000 – 3($400) = $800 at the end of the 3 years.

– Since the computer’s useful life is 5 years, from that time on it has a value of $0.

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8.4 Depreciation

FORMULA 8.4.1Straight-Line Depreciation Rate

where

D represents the ANNUAL DEPRECIATION AMOUNTIV represents the INITIAL VALUE OF THE ITEM

SV represents the SALVAGE (RESIDUAL) VALUEUL represents the USEFUL LIFE OF THE ITEM

UL

SVIVD

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8.4 Depreciation

FORMULA 8.4.2Straight-Line Depreciation

DV = IV – D(n) when n < ULDV = 0 when n ≥ UL

where

DV represents the DEPRECIATED VALUEn represents the NUMBER OF YEARS THAT HAVE

PASSED

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8.4 Depreciation


– Rework Example 8.4.3 using D and DV formulas.• Solution

– First, we find the annual depreciation amount.

– Then, we find the depreciated value after 3 years:

DV = IV – D(n) = $2,000 -- $400(3) = $800

– Since n = 7 and UL = 5, and 7 > 5, we conclude that the value after 7 years is $0.

400$5

0$000,2$

UL

SVIVD

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Problem 1:

Percent Depreciation

Problem 2:

Straight-Line Depreciation

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Problem 1

• Ardeth just bought a new copier for $3,700. According to the published index, the value of this copier will decline at a 10% annual rate. Assuming this is correct, what will the copier’s value be in 3 years?

CHECK YOUR ANSWER

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Solution 1• Ardeth just bought a new copier for $3,700.

According to the published index, the value of this copier will decline at a 10% annual rate. Assuming this is correct, what will the copier’s value be in 3 years?

• FV = PV(1 + i)n

FV = $3,700(0.90)3

FV = $2,697.30

BACK TO GAME BOARD

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Problem 2

• Jen’s Bakery bought a delivery van for $28,500. The useful life of the van is 10 years. The expected salvage value is $3,000. Find the straight-line depreciation rate.

CHECK YOUR ANSWER

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Solution 2• Jen’s Bakery bought a delivery van for $28,500.

The useful life of the van is 10 years. The expected salvage value is $3,000. Find the straight-line depreciation rate.

• Because the expected salvage value is only $3,000, the depreciation rate is ($28,500 -- $3,000)/10 = $2,550

BACK TO GAME BOARD

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Chapter 8 Summary

• Markup Based on Cost• Determining Markup

Percent• Markdown• Gross Profit Margin• Net Profit Margin• Markup Based on

Selling Price

• Trade Discounts• Series Discounts• Cash Discounts• Price Appreciation• Percent Depreciation• Straight-Line

Depreciation

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Chapter 8 Exercises

Section 8.1 Section 8.2 Section 8.3 Section 8.4

$100 $100 $100 $100

$200 $200 $200 $200

EXIT

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Section 8.1 -- $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

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Section 8.1 -- $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

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Section 8.1 -- $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

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Section 8.1 -- $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

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Section 8.2 -- $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

8-86

Section 8.2 -- $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%

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8-87

Section 8.2 -- $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

8-88

Section 8.2 -- $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

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8-89

Section 8.3 -- $100• Jasmine’s Hair Creations salon has placed an

order for some beauty products. The total list price for this order is $374.50 but the supplier is offering a 15% trade discount. What is the total cost of this order?

CHECK YOUR ANSWER

8-90

Section 8.3 -- $100

• Jasmine’s Hair Creations salon has placed an order for some beauty products. The total list price for this order is $374.50 but the supplier is offering a 15% trade discount. What is the total cost of this order?

• Trade Discount = $374.50 x 15% = $56.18• Total Cost = $374.50 -- $56.18 = $318.32

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8-91

Section 8.3 -- $200• Nancy’s Yarn Boutique is selling rolls of yarn for

$8.99 each. Nancy normally offers a 10% discount on any purchases over $100. However, during Mother’s Day sale, she is offering a 5% off all purchases.

• If Doris purchased 12 rolls of yarn, how much did she pay?

CHECK YOUR ANSWER

8-92

Section 8.3 -- $200• Nancy’s Yarn Boutique is selling rolls of yarn for

$8.99 each. Nancy normally offers a 10% discount on any purchases over $100. However, during Mother’s Day sale, she is offering a 5% off all purchases.

• If Doris purchased 12 rolls of yarn, how much did she pay?

• 12 x $8.99 = $107.88• 0.90 x 0.95 x $107.88 = $92.24

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8-93

Section 8.4 -- $100• The current fair market price of your house is

$89,200. According to the local Chamber of Commerce, the housing market in your area will appreciate at a 8% annual rate for the next 10 years. If the prediction is accurate, what will the price of your house be in 10 years?

CHECK YOUR ANSWER

8-94

Section 8.4 -- $100• The current fair market price of your house is

$89,200. According to the local Chamber of Commerce, the housing market in your area will appreciate at a 8% annual rate for the next 10 years. If the prediction is accurate, what will the price of your house be in 10 years?

• FV = PV(1 + i)n

FV = $89,200(1 + 8%)10 = $192,576.11

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8-95

Section 8.4 -- $200• You just bought a brand new car for $21,590.

According to an online new car pricing service, the value of this car will decline at a 5% annual rate. Assuming this is correct, what will the car’s value be in 5 years when you pay off the loan?

CHECK YOUR ANSWER

8-96

Section 8.4 -- $200• You just bought a brand new car for $21,590.

According to an online new car pricing service, the value of this car will decline at a 5% annual rate. Assuming this is correct, what will the car’s value be in 5 years when you pay off the loan?

• FV = PV(1 + i)n

FV = $21,590(1 + (-5%))5

FV = $16,705.93

BACK TO GAME BOARD

© the mcgraw-hill companies, inc., 2008 mcgraw-hill/irwin 8-1 chapter 8 mathematics of pricing...

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