Calculate opening inventory using COGS and turnover ratio

Steps:

• Gross profit = 40% of sales = 0.4 × $1,500,000 =$600,000; thus, COGS = $1,500,000 -$600,000 = $900,000.
• Inventory turnover = COGS / average inventory = 12; average inventory = $900,000 / 12 =$75,000.
• Average inventory = (opening inventory + closing inventory) / 2; so, ($opening +$50,000) / 2 = $75,000.
• Opening inventory = ($75,000 × 2) -$50,000 = $100,000.

Why A is correct:

• Matches the formula for inventory turnover: COGS divided by average inventory, where average is (opening + closing)/2.

Why the others are wrong:

• B: Likely miscalculates average inventory without halving the sum correctly.
• C: Possibly errs by using gross purchases directly in COGS without gross margin adjustment.
• D: Assumes turnover based on purchases instead of COGS, ignoring gross profit.

Final answer: A