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Calculation and understanding of accounting ratios

Paper 1 – Multiple ChoicePaper 2 – Structured Written Paper

This section is examined in Paper 1 and Paper 2.

Why Calculate Ratios?

Financial statements (like the Statement of Profit or Loss and Statement of Financial Position) provide raw numbers, but they are hard to interpret in isolation. Ratios convert these numbers into relationships that allow us to assess a business's performance.

We categorize ratios into two main groups:

  1. Profitability Ratios: How well is the business making money? (Related to: Statement of Profit or Loss)
  2. Liquidity and Efficiency Ratios: Can the business pay its debts, and how efficiently does it manage stock and credit? (Related to: Statement of Financial Position)
Profitability Ratios

1. Gross Profit Margin
Measures the profit made on each dollar of sales after covering the direct cost of goods sold.

\text{Gross Profit Margin} = \frac{\text{Gross Profit}}{\text{Revenue}} \times 100

  • Gross Profit: Revenue minus Cost of Sales.
  • Revenue: Total sales value.
  • Result: Expressed as a percentage (%).

2. Mark-up
Measures the profit added to the cost price. It is often used in retail pricing.

\text{Mark-up} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \times 100

  • Note: Mark-up is based on cost, whereas Gross Margin is based on revenue. Therefore, Mark-up will always be a higher percentage than Gross Margin for the same business.

3. Profit Margin (Net Profit Margin)
Measures the final profit after ALL expenses (operating costs, interest, tax) have been paid.

\text{Profit Margin} = \frac{\text{Net Profit}}{\text{Revenue}} \times 100

  • Net Profit: The bottom line of the Statement of Profit or Loss.

4. Return on Capital Employed (ROCE)
Measures how efficiently the business uses its long-term capital to generate profit. This is a key measure of overall efficiency.

\text{ROCE} = \frac{\text{Operating Profit}}{\text{Capital Employed}} \times 100

  • Operating Profit: Profit before interest and tax (often called EBIT).
  • Capital Employed: Total Assets minus Non-Current Liabilities. Alternatively, Equity plus Non-Current Liabilities.
  • Result: Expressed as a percentage (%).
Liquidity Ratios

5. Current (Working Capital) Ratio
Measures the ability to pay short-term debts with all current assets.

\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}

  • Result: Expressed as a ratio, e.g., 2:1.
  • Interpretation: A ratio of 1.5:1 to 2:1 is generally considered healthy. Below 1:1 suggests liquidity problems.

6. Acid Test (Liquid) Ratio
A stricter test of liquidity. It removes inventory because stock is not always easy to convert into cash quickly.

\text{Acid Test Ratio} = \frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}}

  • Numerator: Sometimes called 'Liquid Assets' or 'Quick Assets'.
  • Result: Expressed as a ratio, e.g., 0.8:1.
  • Interpretation: A ratio of 1:1 is often considered the benchmark for adequacy.
Efficiency Ratios (Turnover)
Important Note on Credit vs. Cash: In Cambridge exams, if a question gives 'Revenue' or 'Purchases' without specifying cash/credit splits for turnover ratios, you must assume all sales are on credit and all purchases are on credit unless told otherwise.

7. Rate of Inventory Turnover (Times)
Measures how many times inventory is sold and replaced over a period.

\text{Inventory Turnover (Times)} = \frac{\text{Cost of Sales}}{\text{Average Inventory}}

  • Average Inventory: (\text{Opening Inventory} + \text{Closing Inventory}) / 2.
  • Result: Expressed in 'times'.

8. Inventory Turnover (Days)
Measures the average number of days inventory is held before being sold.

\text{Inventory Holding Period (Days)} = \frac{\text{Average Inventory}}{\text{Cost of Sales}} \times 365

  • Result: Expressed in 'days'.

9. Trade Receivables Turnover (Days)
Measures the average number of days it takes to collect cash from customers.

\text{Receivables Collection Period (Days)} = \frac{\text{Trade Receivables}}{\text{Credit Sales}} \times 365

  • Note: Use Credit Sales only. If only 'Revenue' is given, assume it is all credit.
  • Result: Expressed in 'days'.

10. Trade Payables Turnover (Days)
Measures the average number of days the business takes to pay its suppliers.

\text{Payables Payment Period (Days)} = \frac{\text{Trade Payables}}{\text{Credit Purchases}} \times 365

  • Note: Use Credit Purchases. If 'Purchases' is given without a cash/credit split, assume it is all credit.
  • Result: Expressed in 'days'.

Trade Payables Turnover (Times)
Sometimes asked as the inverse of the days ratio:

\text{Payables Turnover (Times)} = \frac{\text{Credit Purchases}}{\text{Average Trade Payables}}

Worked Example: Profitability Ratios

Scenario: A business has Revenue of 200,000 and Cost of Sales of120,000. Operating Profit is 40,000. Capital Employed is150,000.

1. Calculate Gross Profit Margin

  • First, find Gross Profit: \text{Revenue} - \text{Cost of Sales} = 200,000 - 120,000 = 80,000.
  • Formula: (80,000 / 200,000) \times 100.
  • Answer: 40%.

2. Calculate Mark-up

  • Formula: (\text{Gross Profit} / \text{Cost of Sales}) \times 100.
  • Calculation: (80,000 / 120,000) \times 100.
  • Answer: 66.67% (to two decimal places).

3. Calculate Profit Margin

  • Formula: (\text{Net Profit} / \text{Revenue}) \times 100. Here, Net Profit is Operating Profit (40,000).
  • Calculation: (40,000 / 200,000) \times 100.
  • Answer: 20%.

4. Calculate ROCE

  • Formula: (\text{Operating Profit} / \text{Capital Employed}) \times 100.
  • Calculation: (40,000 / 150,000) \times 100.
  • Answer: 26.67% (to two decimal places).
Worked Example: Liquidity and Efficiency Ratios

Scenario:

  • Current Assets: 50,000 (including Inventory of10,000)
  • Current Liabilities: 25,000</li> <li>Cost of Sales:120,000
  • Average Inventory: 15,000</li> <li>Credit Sales:180,000
  • Trade Receivables: 15,000</li> <li>Credit Purchases:90,000
  • Trade Payables: 7,500</li> </ul> <p><strong>1. Calculate Current Ratio</strong></p> <ul> <li>Formula:\text{Current Assets} / \text{Current Liabilities}.</li> <li>Calculation:50,000 / 25,000.</li> <li>Answer: <strong>2:1</strong>.</li> </ul> <p><strong>2. Calculate Acid Test Ratio</strong></p> <ul> <li>Formula:(\text{Current Assets} - \text{Inventory}) / \text{Current Liabilities}.</li> <li>Calculation:(50,000 - 10,000) / 25,000 = 40,000 / 25,000.</li> <li>Answer: <strong>1.6:1</strong> (or 1.6).</li> </ul> <p><strong>3. Calculate Inventory Turnover (Days)</strong></p> <ul> <li>Formula:(\text{Average Inventory} / \text{Cost of Sales}) \times 365.</li> <li>Calculation:(15,000 / 120,000) \times 365.</li> <li>Answer: <strong>45.6 days</strong> (or 46 days if rounding to whole number).</li> </ul> <p><strong>4. Calculate Trade Receivables Turnover (Days)</strong></p> <ul> <li>Formula:(\text{Trade Receivables} / \text{Credit Sales}) \times 365.</li> <li>Calculation:(15,000 / 180,000) \times 365.</li> <li>Answer: <strong>30.4 days</strong> (or 30 days).</li> </ul> <p><strong>5. Calculate Trade Payables Turnover (Days)</strong></p> <ul> <li>Formula:(\text{Trade Payables} / \text{Credit Purchases}) \times 365.</li> <li>Calculation:(7,500 / 90,000) \times 365$.
  • Answer: 30.4 days (or 30 days).
⚠︎ Confusing Gross Profit Margin and Mark-up
The Error: Students often use the same formula for both, or swap the denominators.

The Correction:

  • Gross Profit Margin uses Revenue (Sales) as the denominator. It tells you how much of every dollar of sales is profit.
  • Mark-up uses Cost of Sales as the denominator. It tells you how much profit was added to the cost.

Memory Aid: 'Margin' relates to the top line (Revenue). 'Mark-up' relates to the base cost.

⚠︎ Incorrect Numerator for Acid Test Ratio
The Error: Including Inventory in the numerator, or deducting Trade Payables from Current Assets.

The Correction: The Acid Test Ratio measures liquid assets. Inventory is not liquid enough. Therefore, you must subtract Inventory from Current Assets. Do NOT subtract Current Liabilities from the numerator; that is a different calculation entirely.

Correct Formula: (\text{Current Assets} - \text{Inventory}) / \text{Current Liabilities}.

⚠︎ Using Total Sales for Receivables Ratio
The Error: Using 'Total Revenue' or 'Cash Sales + Credit Sales' in the denominator for Trade Receivables Turnover.

The Correction: Trade Receivables only arise from Credit Sales. Cash sales do not create receivables. If the question does not specify cash vs credit, assume all sales are credit. If it specifies cash sales, you must subtract them from total revenue to find Credit Sales.

Showing Workings for Calculation Questions
When to use: Always, in Paper 2 structured questions where marks are awarded for calculations.

Why examiners accept this: Cambridge mark schemes award method marks (M) separately from accuracy marks (A). If you write the correct formula with the correct numbers substituted, you get the method mark even if your final arithmetic is wrong. Without showing workings, you only get the accuracy mark if the answer is correct, and zero if it is not.

Example: Instead of writing 'Answer: 40%', write:
'Gross Profit Margin = (80,000 / 200,000) \times 100 = 40%.'
This shows the examiner you know the formula and how to apply it.

Rounding and Units in Ratio Answers
When to use: When presenting final answers for profitability and efficiency ratios.

Why examiners accept this: Precision matters. Profitability ratios are typically required to two decimal places. Efficiency ratios (days) are often accepted as whole numbers or one decimal place, but check the question. Liquidity ratios should be shown as X:1 or a decimal.

Example: For Gross Profit Margin, '40%' is correct, but '40.00%' is safer if two decimal places are implied. For Inventory Days, '45.6 days' is better than '45.6'. Always include the unit (% or days) to avoid ambiguity.

Past Paper Style Questions
Q:
A company has Revenue of 500,000 and Cost of Sales of300,000. Calculate the Gross Profit Margin.
A:
Gross Profit = 500,000 -300,000 = 200,000.<br>Gross Profit Margin = (200,000 / $500,000) × 100 = 40%.
Q:
Calculate the Acid Test Ratio for a business with Current Assets of 80,000 (Inventory20,000) and Current Liabilities of $50,000.
A:
Liquid Assets = 80,000 -20,000 = 60,000.<br>Acid Test Ratio =60,000 / $50,000 = 1.2:1.
Q:
Credit Sales are 120,000 and Trade Receivables are10,000. Calculate the Trade Receivables Turnover in days.
A:
(Trade Receivables / Credit Sales) × 365
= (10,000 /120,000) × 365
= 30.4 days.
Q:
Operating Profit is 50,000 and Capital Employed is250,000. Calculate ROCE.
A:
(Operating Profit / Capital Employed) × 100
= (50,000 /250,000) × 100
= 20%.
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