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    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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    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 ...

    Solution Summary

    The following problem addresses purchases and pricing. Step by step answers are provided for each.

    $2.49

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