DuPont Analysis and Ratio Based Problems for CA Inter

Understand DuPont Analysis and Ratio Based Problems

Key rules to remember

Three-factor DuPont (ROE)

ROE = Net profit margin × Total asset turnover × Equity multiplier

Net profit margin = PAT ÷ Sales; asset turnover = Sales ÷ Total assets; equity multiplier = Total assets ÷ Shareholders' equity.

Return on Assets (ROA)

ROA = PAT ÷ Total assets = Net profit margin × Total asset turnover

ROE = ROA × Equity multiplier.

Equity multiplier

Equity multiplier = Total assets ÷ Equity = 1 + (Debt ÷ Equity)

Here debt means all outside liabilities, if total assets = equity + outside liabilities.

Gross profit ratio

Gross profit ÷ Sales × 100

Use it to get cost of goods sold: COGS = Sales − Gross profit.

Stock turnover

COGS ÷ Average (or closing) stock

Use the base the question states. If it is silent, use closing stock.

Debtors collection period

Debtors ÷ Credit sales × 365 (or 360, as stated)

Inverse: Debtors = Credit sales × Days ÷ 365.

Current ratio

Current assets ÷ Current liabilities

Quick ratio = (Current assets − Stock) ÷ Current liabilities, where prepaid expenses are also excluded if stated.

Fixed asset turnover

Sales ÷ Net fixed assets

Gives fixed assets when sales are known.

How to solve DuPont Analysis and Ratio Based Problems questions

1. 1List every ratio and absolute figure given. Write what each ratio links, for example stock turnover links COGS and stock.
2. 2Find the starting point. It is usually one absolute figure such as sales, net worth, share capital or fixed assets.
3. 3Move to the P&L items first: sales, gross profit, COGS, then net profit using the margin ratios.
4. 4Derive balance sheet items one at a time using turnover, collection period and current ratio. Note whether the question uses sales or COGS as the base.
5. 5Get totals from relationships such as equity multiplier, debt-equity or proportion of fixed assets to net worth. Balancing figures such as cash or reserves come last.
6. 6Check that total assets equal total equity and liabilities. If not, recheck the base used for each ratio.
7. 7For DuPont, compute the three factors separately, multiply them, and confirm that the product equals PAT ÷ Equity.
8. 8Write one line of interpretation: which driver is strong or weak and what it means for risk.

Quickest way: Anchor and chain with a working grid

Common mistakes in DuPont Analysis and Ratio Based Problems

• Using sales as the base for stock turnover when the question uses cost of goods sold.

  Students remember turnover as sales ÷ something and apply it everywhere.

  Fix: Check the definition each time. Stock turnover uses COGS. Debtor ratios use credit sales. Creditor ratios use credit purchases.

• Mixing up net profit margin and gross profit margin in the DuPont chain.

  Both are called margin in the question.

  Fix: DuPont uses PAT ÷ Sales. If only gross margin is given, bring down expenses and tax first.

• Taking equity multiplier as Debt ÷ Equity.

  The two sound similar.

  Fix: Equity multiplier is Total assets ÷ Equity. It equals 1 plus debt-to-equity only when all outside liabilities are counted as debt.

• Using 365 days when the question says 360, or the reverse.

  Students apply the habit and skip the note at the end of the question.

  Fix: Underline the day-count instruction before starting the working.

• Forcing every Balance Sheet item from a ratio and ending with a mismatch.

  Students do not realise one item should be the balancing figure.

  Fix: Derive all but one item from ratios. Take the last one by difference, then cross-check with any unused ratio.

• Giving a ROE figure with no comment.

  Students treat DuPont as pure calculation.

  Fix: Add a line saying which driver (margin, turnover or leverage) explains ROE and whether the leverage adds risk.

Worked examples