Chapter 5 | Mathematics of Merchandising
27. A distributor purchased 500 golf sets at $450 each. The markup is 40% of the cost and overhead expense is 20% of
the cost. It sold 30% of the sets at the regular selling price, 50% of the remaining sets at a discount of 25%, and the
remaining sets at the cost price. Find the overall profit or loss on the sale of the golf sets.
28. Maggie purchased 200 designer bags at $180 each. The markup is 60% on cost and the overhead expense is 15% on cost. She
sold 25% of the bags at the regular selling price, 40% of the remaining bags at a discount of 70%, and the remaining bags
at the cost price. Find the overall profit or loss on the sale of the bags.
29. High Tech Heaven purchased 500 electronic items for $280 each and sold 425 items at a markup of 80% on cost.
Two months later, it sold 50 items at cost. Three months later, it sold the remaining items at 15% below cost. The
overhead expenses are 20% on cost.
a. What was the total amount of markup realized?
b. What was the total amount of profit realized?
30. A retailer purchased 750 shirts for $45 each. She sold 650 shirts at a markup of 110% on cost. A few months later,
she sold 25 shirts at cost. When the design of the shirts were no more in style, she sold the remaining shirts at 25%
below cost. Their overhead expenses are 30% on cost.
a. What was the total amount of markup realized?
b. What was the total amount of profit realized?
5.7 |
Effective Markup and Effective
Rate of Markup
In Sections 5.4 to 5.6, you learned that in business, goods are usually sold at a higher price than
their cost (C) and the amount added to the cost in determining the selling price (S) of an item is
the amount of markup (M), which is necessary to cover the overhead expenses (E) and the desired
operating profit (P) of the business.
You also learned both the table method (vertical analysis) and formula method (horizontal analysis)
for solving problems involving cost, expense, profit, markup, selling price, rate of markup on cost,
rate of markup on selling price, markdown (D), rate of markdown, and calculating the reduced
profit or loss (PRed) when goods are sold at a reduced selling price or sale price (SRed).
In this section, you will learn to perform calculations involving effective markup and effective
rate of markup.
Effective Markup
Businesses sell goods on discounts by a percent reduction of the selling price and often sell goods
at different prices at different points of time, for various reasons. When goods are sold at different
selling prices, the original markup (M) on the item will be reduced, because the cost of the item
remains the same. This reduced markup is referred to as the effective markup.
Example 5.7(a)
Effective Markup Calculations, Given the Rate of Markup on Cost and the Rate of Markdown
The cost of an item is $400. The rate of markup based on cost is 30%. During a sale, the item was
marked down by 20%. Calculate the following:
(i) Amount of markup.
(ii) Selling price.
(iii)Amount of markdown.
(iv)Sale price.
(v) Amount of effective markup.
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Solution
Enter the known quantities for the variables and
identify those that are to be calculated.
Amount
Rate
M
$120.00
0.30C
+C
$400.00
S
$520.00
(iii) D = 0.20S = 0.20 × 520.00 = $104.00
-D
$104.00
(iv) SRed = S - D = 520.00 - 104.00 = $416.00
SRed
$416.00
(i) M = 0.30 C = 0.30 × 400.00 = $120.00
(ii) S = C + M = 400.00 + 120.00 = $520.00
0.20S
(v) Amount of effective markup = SRed - C
= 416.00 - 400.00
= $16.00
Effective
ExampleMarkup
5.7(b) Calculations, Given the Rate of Markup on Selling Price and the Rate of Markdown
The cost of an item is $280. The rate of markup based on selling price is 20%. During a sale, the
item was marked down by 15%. Calculate the following:
(i) Selling price.
(ii) Amount of markup.
(iii)Amount of markdown.
(iv)Sale price.
(v) Amount of effective markup.
Solution
Enter the known quantities for the variables and
identify those that are to be calculated.
(i) S=C+M
S = 280.00 + 0.20S
0.80S = 280.00
280.00
0.80
S=
S = $350.00
(ii) M = 0.20S = 0.20 × 350.00 = $70.00
Amount
Rate
M
$70.00
0.20S
+C
$280.00
0.80S
S
$350.00
S
-D
$52.50
0.15S
SRed
$297.50
(iii) D = 0.15S = 0.15 × 350 = $52.50
(iv) SRed = S - D = 350.00 - 52.50 = $297.50
(v) Amount of effective markup = SRed - C = 297.50 - 280.00 = $17.50
Effective Rate of Markup
If all items are sold at the same price, then the amount of markup per unit would be the difference
between the unit selling price and the unit cost. However, this is not the case in business most of
the time because the selling price differs after each markdown.
The term effective rate of markup refers to the average markup based on total cost or on the total
sales. This is calculated as follows:
(i) Calculate the total cost (i.e., cost of all the items purchased).
Chapter 5 | Mathematics of Merchandising
185
(ii) Calculate the total sales (i.e., revenue from the sales of items at different selling prices).
(iii)Calculate the total markup by subtracting the total cost from the total sales.
(iv)Effective rate of markup on total cost is calculated by finding the ratio of the total amount
of markup to the total cost and converting it to a percent.
(v) Effective rate of markup on total sales is calculated by finding the ratio of the total
amount of markup to the total sales and converting it to a percent.
Formula 5.7(a)
Effective Rate of Markup on Total Cost
Effective Rate of Markup on Total Cost =
Formula 5.7(b)
Effective Rate of Markup on Total Sales
Effective Rate of Markup on Total Sales =
Example 5.7(c)
Understanding the Relationship Among Total Cost, Total Sales, and Effective Rate of
Markup
A retailer purchased 100 printers at $150 each, marked them up at 40% of the cost, and sold 70
of them at the regular selling price. During a sale, it offered a markdown of 20% and sold the
remaining printers. Calculate the following:
(i) Total cost of the printers.
(ii) Total sales of the printers.
(iii)Amount of effective markup on the printers.
(iv)Effective rate of markup on total cost.
(v) Effective rate of markup on total sales.
Solution
Enter the known quantities for the variables and
identify those that are to be calculated.
M = 0.40C = 0.40 × 150.00 = $60.00
S = C + M = 150.00 + 60.00 = $210.00
Qty
Total Amount
$150.00
100
15,000.00
S
$210.00
70
14,700.00
-D
$42.00
SRed
$168.00
30
5040.00
Amount
Rate
M
$60.00
0.40C
+C
D = 0.20S = 0.20 × 210.00 = $42.00
SRed = S - D = 210.00 - 42.00 = $168.00
(i) Total cost = 100 × 150.00
0.20S
= $15,000.00
(ii) Total sales = (210.00 × 70) + (168.00 × 30)
= 14,700.00 + 5040.00
= $19,740.00
Amount
Rate
Effective Markup
$4740.00
31.60%C
24.01%S
+ Total Cost
$15,000.00
Total Sales
$19,040.00
(iii)Amount of Effective Markup = Total sales - Total cost
= 19,740.00 - 15,000.00
= $4740.00
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(iv)Effective rate of markup on total cost = Total Amount of Markup × 100%
Total Cost
= 4740.00 × 100%
15,000.00
= 31.60%
Example 5.7(d)
(v) Effective rate of markup on total sales =
Total Amount of Markup
× 100%
Total Sales
=
4740.00
× 100%
19,740.00
= 24.01%
Calculating the Effective Rate of Markup on Cost when Items are Sold at Different Prices
On Time Clock Shop purchased 250 units of a particular model of watches. The cost was $75 per watch
and the regular selling price was $120 per watch. The company sold 175 of them at the regular selling
price. During a sale, it offered a markdown of 25% and sold another 50 units. The remaining units were
sold after an additional markdown of 10%. Determine the effective rate of markup on total cost.
Solution
Total cost = 75 × 250 = $18,750.00
Total sales = (120 × 175) + (90 × 50) + (81 × 25)
= $27,525.00
Total markup = Total sales - Total cost
= 27,525.00 - 18,750.00
= $8775.00
Effective rate of markup on total cost
= 8775.00 × 100%
18,750.00
= 46.80%
Amount
Rate
M
+C
$75.00
250
18,750
S
$120.00
175
21,000
- D1
$30.00
SRed 1
$90.00
50
4500
- D2
$9.00
SRed 2
$81.00
25
2025
0.25S
0.10S
Alternative Method
Markup at which 175 watches were sold = 120 - 75
= $45.00
Markup at which 50 watches were sold = 90 - 75
= $15.00
Markup at which 25 watches were sold = 81 - 75
= $6.00
Total markup = (175 × 45) + (50 × 15) + (25 × 6)
= $8775.00
Total cost = 75 × 250
= $18,750.00
Qty Total Amount
Amount
Rate
Effective Markup
$8775
46.80%C
Total Cost
$18,750.00
Total Sales
$27,525.00
Therefore, the effective rate of markup on total cost = 8775.00 × 100% = 46.80%
18,750.00
Example 5.7(e)
Calculating the Effective Rate of Markup on Selling Price when Items are Sold at Different Prices
A store that sells cameras purchased 120 units at $180 each. It expects to sell 50% of them at
regular price of $275 each, 30% of them after a markdown of 20%, and the remaining at the cost
price. Calculate the effective rate of markup on total cost.
Chapter 5 | Mathematics of Merchandising
Solution
= 21,600.00
+C
$180.00
S
$275.00
S
- D1
$55.00
0.20S
SRed 1
$220.00
Effective rate of markup on total cost
- D2
7140
× 100%
21,600
=
= 33.06%
Rate
Qty
Total Amount
120
21,600
60
16,500
36
7920
24
4320
M
Total sales = (60 × 275) + (36 × 220) + (24 × 180)
= 28,740
Effective markup = 28,740 - 21,600
= $7140
Therefore, the effective rate of markup on
total cost is 33.06%.
5.7 |
Amount
Total cost = 180 × 120
SRed 2
$180.00
C
187
Amount
Rate
Effective Markup
$7140
33.06%C
Total Cost
$21,600.00
Total Sales
$28,740.00
Exercises Answers to the odd-numbered problems are available at the end of the textbook
For the following problems, express the answers rounded to two decimal places, wherever applicable.
1. The cost of an oven is $65.00. The rate of markup based on cost is 45%. During a sale, the oven was marked down
by 30%. Calculate the following:
a. Amount of markup.
b. Selling price.
c. Amount of markdown.
d. Sale price.
e. Amount of effective markup.
2. The cost of a frying pan set is $15.50. The rate of markup based on cost is 25%. During a sale, the set was marked
down by 10%. Calculate the following:
a. Amount of markup.
b. Selling price.
c. Amount of markdown.
d. Sale price.
e. Amount of effective markup.
3. The cost of stereo equipment is $72.50 each. The rate of markup based on selling price is 60%. During a sale, the
equipment was marked down by 25%. Calculate the following:
a. Selling price.
b. Amount of markup.
c. Amount of markdown.
d. Sale price.
e. Amount of effective markup.
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Chapter 5 | Mathematics of Merchandising
4. The cost of a new cell phone case is $35.00. The rate of markup based on selling price is 50%. During a sale, the
item was marked down by 25%. Calculate the following:
a. Selling price.
b. Amount of markup.
c. Amount of markdown.
d. Sale price.
e. Amount of effective markup.
5. Steve's Cash n' Carry purchased 80 pencil cases at $6.50 each and marked them up at 25% of the cost and sold
75% of them at the regular selling price. During a sale, it sold the remaining pencil cases after a markdown of
10%. Calculate the following:
a. Total cost of the pencil cases.
b. Total sales of the pencil cases at the two different prices.
c. Amount of effective markup.
d. Effective rate of markup on total cost.
e. Effective rate of markup on total sales.
6. Circuit World purchased 175 monitors at $125 each and marked them up at 35% of the cost and sold 90 of them at
the regular selling price. During a sale, the store sold the remaining monitors after a markdown of 25%. Calculate
the following:
a. Total cost of the monitors.
b. Total sales of the monitors at the two different prices.
c. Amount of effective markup.
d. Effective rate of markup on total cost.
e. Effective rate of markup on total sales.
7. Nail & Hammer Shack purchased 225 table fans of a particular make. The unit cost was $25.50 and the regular
selling price was $49 each. The store sold 120 of them at the regular selling price. During a sale, it sold another
60 of them at markdown of 20%. The remaining units were sold at an additional markdown of 10%. Determine the
effective rate of markup on total cost.
8. Ace of Diamonds purchased 70 diamond bracelets at $225 each and the regular selling price was $300. The store
sold 50% of them at the regular selling price. During a sale, it sold another 25 of them at a markdown of 15%. The
remaining units were sold at an additional markdown of 10%. Determine the effective rate of markup on total cost.
9. A store purchased 500 DVDs at $3.60 each. The store expects to sell 300 DVDs at the regular selling price of $6,
another 150 DVDs after markdown of 20%, and the remaining DVDs at cost price. Calculate the effective rate of
markup on total cost.
10. Book World purchased 150 financial calculators at $22.50. The store expects to sell 70 units at the regular price
of $40, another 35 units after a markdown of 15%, and the remaining units at cost price. Calculate the effective
rate of markup on total cost.