Profit Margin Calculations for Sales Walehouses
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18. A jewellery store purchased a diamond rig for $2500 less 40% and 5%. The store's average unit overhead expenses are 30% of cost. The "regular price" of the ring is established so that, if it is sold in a "20% off" sale, the unit operating profit at the reduced price will be 20% of cost.
a. What is the reduced price of the ring in a "20% off" sale?
C = N(1 - d1)(1 - d2) = $2500(0.6)(0.95) = $1425
E = 0.30C and P(reduced) = 0.20C
E = 0.30($1425) = $427.50
P(reduced) = 0.20($1425) = $285
S(reduced) = C + E + P = $1425 + $427.50 + $285 = $2137.50
b. What is the regular price of the ring?
S(regular) = 1
S(reduced) = S(regular) - D(discount)
D = 0.20S(regular)
$2137.50 = S - 0.20S
$2137.50 = 0.80S
S(regular) = $2137.50 ÷ .80 = $2671.88
c. What is the operating profit if the ring happens to sell at the "regular price?"
S(regular) = $2671.88
P = S(regular) - C - E = $2671.88 - $1425 - $427.50 = $819.38
20. Furniture Warehouse bought upright freezers for $1800 less 33 1/3% and 5%. The store's overhead works out to 30% of cost. The freezers are initially priced so that a profit of 16 2/3% of cost will be realized when a freezer is sold at a "15% off" price.
a. What is the initial full rate of markup on cost?
C = N(1 - d1)(1 - d2) = $1800(0.66667)(0.95) = $1134.30
E = 0.30C = 0.30($1134.30) = $340.29
P = 0.16667C = 0.16667($1134.30) = $189.05
S(reduced) = C + E + P = $1134.30 + $340.29 + $189.05 = $1663.64
S(reduced) = $1663.64 D = 0.15S(regular)
S(reduced) = S(regular) - 0.15S(regular) = 0.85S(regular)
0.85S(regular) = $1663.64
S(regular) = $1663.64 ÷ 0.85 = $1957.22
M = S(regular) - C = $1957.22 - $1134.30 = $822.92
b. During its Scratch-and-Save Sale, customers qualify for an extra discount of either 5%, 7%, or 10%. This extra discount appears when the customer scratches a ticket at the time of a purchase. It is added to the basic 15% discount, making the combined discount 20%, 22%, or 25%, respectively. What is the store's profit or loss per freezer at each of these discounts?
d1 = 20%, d2 = 22% and d3 = 25%
S(regular) = $1957.22
S1(reduced) = S(regular)(1 - d1) = $1957.22(0.80) = $1565.78
P1 = S1(reduced) - C - E = $1565.78 - $1134.30 - $340.29 = $91.19
S2(reduced) = S(regular)(1 - d2) = $1957.22(0.78) = $1526.63
P2 = S2(reduced) - C - E = $1526.63 - $1134.30 - $340.29 = $52.04
S3(reduced) = S(regular)(1 - d3) = $1957.22(0.75) = $1467.92
P3 = S3(reduced) - C - E = $1467.92 - $1134.30 - $340.29 = -$6.67
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The following problem addresses purchases and pricing. Step by step answers are provided for each.
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PROBLEM 1
18. A jewellery store purchased a diamond rig for $2500 less 40% and 5%. The store's average unit overhead expenses are 30% of cost. The "regular price" of the ring is established so that, if it is sold in a "20% off" sale, the unit operating profit at the reduced price will be 20% of cost.
a. What is the reduced price of the ring in a "20% off" sale?
Total purchase discount 0.57
Purchase price of ring $1,425
Overhead rate 30%
Total cost of ...
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- B. Sc., University of Nigeria
- M. Sc., London South Bank University
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