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Difficulty: Very hardProfit and Loss

A retailer buys a wholesale lot of 100100 tablets for $4,000\$4,000. They pay an additional $1,000\$1,000 for shipping, software updates, and packaging before the tablets are ready for sale. The retailer sells 4040 of these tablets at a 10%10\% loss on their true unit cost. In order to achieve an overall profit of 20%20\% on the entire initial investment, what must be the selling price for each of the remaining tablets?

  1. A
    $56\$56
  2. B
    $60\$60
  3. $70\$70Answer
  4. D
    $75\$75

Answer

The remaining tablets must be sold for $70\$70 each.
To achieve a 20% overall profit, the retailer must make a total of 6,000ona6,000 on a 5,000 total investment. Since the first 40 tablets were sold at a loss for 1,800total,theremaining1,800 total, the remaining 4,200 must be made up entirely by the remaining 60 tablets. Dividing 4,200by60yields4,200 by 60 yields 70 per tablet.

Step-by-Step Solution

1
Calculate the total investment and the target revenue.
Total Investment = $4,000\$4,000 + $1,000\$1,000 = $5,000\$5,000. Target Revenue = $5,000\$5,000 + (0.200.20 × $5,000\$5,000) = $6,000\$6,000.
To find how much money must be made in total, you must first account for all costs (purchase + overhead) and then add the desired 20% overall profit.
2
Determine the true unit cost per tablet.
Unit Cost = $5,000\$5,000 ÷ 100100 = $50\$50 per tablet.
The unit cost must reflect the total investment spread across all items, not just the original purchase price.
3
Calculate the revenue generated from the first 40 tablets.
Selling price = $50\$50 - (0.100.10 × $50\$50) = $45\$45. Revenue = 4040 × $45\$45 = $1,800\$1,800.
These tablets were sold at a 10% loss on their true unit cost.
4
Find the remaining revenue needed from the unsold tablets.
Remaining Revenue Needed = $6,000\$6,000 (Target) - $1,800\$1,800 (Collected) = $4,200\$4,200.
This is the exact dollar amount the remaining stock must generate to hit the overall profit goal.
5
Calculate the required selling price per remaining tablet.
Remaining tablets = 100100 - 4040 = 6060. Selling Price = $4,200\$4,200 ÷ 6060 = $70\$70.
Dividing the remaining revenue goal by the remaining inventory gives the required per-unit price.

Key Concept

Multi-stage Profit and Loss with Overhead Allocation
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Topics

Profit and Loss

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