Math Problem Statement

Wooster Company imports and sells a product produced in Canada. In the summer of 2021, a natural disaster disrupted production, affecting its supply of product. On January 1, 2021, Wooster’s inventory records were as follows: | Year purchased | Quantity (units) | Cost per unit | Total cost | |----------------|------------------|---------------|------------| | 2019 | 5,000 | $150 | $750,000 | | 2020 | 10,000 | $200 | $2,000,000 | | Total | 15,000 | | $2,750,000 | Through mid-December of 2021, purchases were limited to 14,000 units, because the cost had increased to $300 per unit. Wooster sold 18,000 units during 2021 at a price of $400 per unit, which significantly depleted its inventory. Assume that Wooster makes no further purchases during 2021. Wooster uses the LIFO inventory method. Compute Wooster’s gross profit for 2021.

Solution

To calculate Wooster's gross profit for 2021, let's go through the steps systematically.

  1. Total Revenue from Sales in 2021:

    • Wooster sold 18,000 units at $400 per unit. Total Revenue=18,000×400=7,200,000\text{Total Revenue} = 18,000 \times 400 = 7,200,000
  2. Cost of Goods Sold (COGS) Using LIFO (Last-In, First-Out):

    • Under the LIFO method, the most recent inventory is sold first.
    • Wooster had an inventory of 15,000 units on January 1, 2021:
      • 10,000 units from 2020 at $200 per unit.
      • 5,000 units from 2019 at $150 per unit.
    • Wooster sold 18,000 units in 2021, so we need to consider all of these units plus 3,000 additional units.

    Step-by-Step COGS Calculation:

    • First 10,000 units (from 2020) at $200 per unit: 10,000×200=2,000,00010,000 \times 200 = 2,000,000
    • Next 5,000 units (from 2019) at $150 per unit: 5,000×150=750,0005,000 \times 150 = 750,000
    • Remaining 3,000 units (new purchases in 2021) at $300 per unit: 3,000×300=900,0003,000 \times 300 = 900,000

    Total COGS: 2,000,000+750,000+900,000=3,650,0002,000,000 + 750,000 + 900,000 = 3,650,000

  3. Gross Profit Calculation:

    • Gross Profit = Total Revenue - COGS Gross Profit=7,200,0003,650,000=3,550,000\text{Gross Profit} = 7,200,000 - 3,650,000 = 3,550,000

Answer: The correct answer is $3,550,000.


Would you like a deeper explanation on any part of the solution?

Related Questions

  1. How would the gross profit change if Wooster used FIFO instead of LIFO?
  2. What would the gross profit be if Wooster only sold 15,000 units?
  3. How does the increase in purchase cost ($300) affect the overall gross profit?
  4. Why might a company choose LIFO over FIFO for inventory accounting?
  5. How would Wooster's profit margin be impacted if the selling price per unit decreased?

Tip

In inventory management, LIFO tends to increase COGS and decrease gross profit when costs are rising, which can lead to tax benefits in inflationary periods.

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Math Problem Analysis

Mathematical Concepts

Inventory Accounting
Cost of Goods Sold (COGS)
Gross Profit Calculation

Formulas

Total Revenue = Units Sold * Price per Unit
COGS (LIFO) = Sum of Cost of Last Units Purchased
Gross Profit = Total Revenue - COGS

Theorems

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Suitable Grade Level

College/University - Accounting and Finance