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Difficulty: MediumProfit, Loss, and Markup

A specialty audio equipment distributor purchased a batch of 4040 high-fidelity headphones for a total cost of $10,000\$10,000. The distributor marked up the wholesale cost price of each unit by 60%60\% to establish its list price. During a seasonal promotion, 3030 of the headphones were sold at a 20%20\% discount off the list price. The remaining 1010 headphones were sold during an end-of-season clearance at a 40%40\% discount off the list price. What was the distributor's net profit percentage on the total purchase of all 4040 headphones?

  1. A
    12%12\%
  2. B
    1623%16\frac{2}{3}\%
  3. 20%20\%Answer
  4. D
    28%28\%
  5. E
    35%35\%

Answer

The distributor's net profit percentage on the total purchase is 20%20\%.
To find the overall net profit percentage, calculate total revenue across all sales and compare it to total cost. The cost per unit is $10,00040=$250\frac{\$10,000}{40} = \$250. Marking up by 60%60\% yields a list price of $250×1.60=$400\$250 \times 1.60 = \$400. The 3030 units sold at a 20%20\% discount generated 30×($400×0.80)=$9,60030 \times (\$400 \times 0.80) = \$9,600. The remaining 1010 units sold at a 40%40\% discount generated 10×($400×0.60)=$2,40010 \times (\$400 \times 0.60) = \$2,400. Total revenue was $9,600+$2,400=$12,000\$9,600 + \$2,400 = \$12,000. Net profit is $12,000−$10,000=$2,000\$12,000 - \$10,000 = \$2,000. Expressed as a percentage of total cost, $2,000$10,000×100%=20%\frac{\$2,000}{\$10,000} \times 100\% = 20\%.

Step-by-Step Solution

1
Calculate the wholesale cost price per unit and the list price per unit.
Wholesale cost per unit = $10,00040=$250\frac{\$10,000}{40} = \$250. List price per unit = $250×(1+0.60)=$400\$250 \times (1 + 0.60) = \$400.
Establishing the individual cost and marked-up retail base price is necessary to calculate discount prices.
2
Calculate the selling price and revenue for the two sales batches.
Promotional price = $400×(1−0.20)=$320\$400 \times (1 - 0.20) = \$320. Revenue from first batch = 30×$320=$9,60030 \times \$320 = \$9,600. Clearance price = $400×(1−0.40)=$240\$400 \times (1 - 0.40) = \$240. Revenue from second batch = 10×$240=$2,40010 \times \$240 = \$2,400.
Determining total revenue requires evaluating each portion of inventory sold at its respective discounted price.
3
Sum total revenue and compute total net profit.
Total Revenue = $9,600+$2,400=$12,000\$9,600 + \$2,400 = \$12,000. Total Net Profit = $12,000−$10,000=$2,000\$12,000 - \$10,000 = \$2,000.
Net profit is the absolute difference between total revenue generated and total wholesale cost incurred.
4
Compute the net profit percentage.
Net Profit Percentage = ($2,000$10,000)×100%=20%\left(\frac{\$2,000}{\$10,000}\right) \times 100\% = 20\%.
Profit percentage must always use the total original cost price as its base.

Key Concept

Calculating overall profit percentage across multi-tiered pricing by finding total revenue relative to original cost base.
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Topics

Profit, Loss, and Markup

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