calculate profit or loss for the year from changes in capital over time

Cambridge IGCSE Accounting 0452 – Topic 5.6: Incomplete Records

Learning objective

Calculate the profit or loss for the year when only the changes in capital are known, and understand how this technique fits into the wider “incomplete records” toolkit (statement‑of‑affairs method and ratio‑reconstruction).

Key concepts

• Capital – the owner’s equity in the business at a specific point in time.
• In an incomplete set of records the detailed income‑statement figures may be missing, but the movement in capital is still recorded.
• The profit or loss can be derived from the change in capital, together with any drawings and any capital introduced during the year.

Capital‑movement method (core calculation)

For a sole trader or a partnership the relationship is:

$$ \text{Opening Capital} \;+\; \text{Profit (or Loss)} \;-\; \text{Drawings} \;+\; \text{Capital introduced} \;=\; \text{Closing Capital} $$

Sign conventions – Drawings are subtracted (they reduce equity) and capital introduced is added (it increases equity). When a loss occurs the profit figure will be negative.

Re‑arranged to solve for profit (or loss):

$$ \text{Profit (or Loss)} \;=\; \text{Closing Capital} \;-\; \text{Opening Capital} \;+\; \text{Drawings} \;-\; \text{Capital introduced} $$

Step‑by‑step procedure

1. Read the opening capital at the start of the year.
2. Read the closing capital at the end of the year.
3. Identify the total drawings made by the owner(s) during the year.
   Checkpoint: Verify that all drawings recorded in the ledger (including cash withdrawals not explicitly labelled “drawings”) have been captured.
4. Identify any additional capital that has been introduced (capital introduced).
5. Substitute the figures into the formula above.
6. Interpret the sign of the answer:
   • Positive → profit.
   • Negative → loss.

Checklist before finalising the answer

• Have I added the drawings back to the profit/loss calculation?
• Have I deducted any capital introduced?
• Is the result expressed with the correct sign (profit = +, loss = –)?
• Have I written the answer in pounds (£) and to the nearest whole pound?
• Have I confirmed that any non‑operating equity movements (e.g., loan repayments, owner’s loan withdrawals) are **not** being treated as drawings?

Interpretation of the result

• A profit increases the owner’s equity; a loss reduces it.
• This method assumes that the only movements in equity are profit/loss, drawings and capital introduced. Other equity movements can distort the figure. Typical examples that may appear in exam questions are:
  • Partner’s loan repayments (treated as a reduction of a liability, not a drawing)
  • Owner’s loan withdrawals (recorded as “owner’s loan”, not as drawings)
  • Repayment of a capital loan from a bank
  • Re‑valuation of assets (rare in IGCSE)

Extension – Opening & Closing Statements of Affairs

When the full set of accounts is missing, an opening statement of affairs and a closing statement of affairs give a snapshot of the business’s financial position.

Opening statement of affairs	Closing statement of affairs
Assets (at start of year) – e.g., £20 000 Liabilities (at start of year) – e.g., £8 000 Capital = Assets – Liabilities – e.g., £12 000	Assets (at end of year) – e.g., £24 500 Liabilities (at end of year) – e.g., £9 200 Capital = Assets – Liabilities – e.g., £15 300

By comparing the two statements you can confirm the movement in capital calculated by the capital‑movement method.

Extension – Using Ratios when Records are Incomplete

When the profit figure is unknown, ratios such as markup, margin and inventory turnover can be used to reconstruct missing sales or cost figures, which then feed into the capital‑movement calculation.

• Mark‑up (on cost):
  $$\text{Mark‑up} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\%$$
• Margin (on selling price):
  $$\text{Margin} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Selling Price}} \times 100\%$$
• Inventory turnover:
  $$\text{Inventory turnover} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}$$

These formulas can be rearranged to find the missing cost, selling price, or COGS, which are then used in the capital‑movement method.

Worked examples

Example 1 – Limited company (core method)

Item	Amount (£)
Opening capital (1 January)	12,000
Closing capital (31 December)	15,500
Total drawings during the year	2,000
Capital introduced	0

Calculation:

$$ \text{Profit} = 15,500 - 12,000 + 2,000 - 0 = 5,500 $$

Result: £5,500 profit for the year.

Example 2 – Sole trader (core method – corrected)

Item	Amount (£)
Opening capital (1 January)	8,400
Closing capital (31 December)	7,600
Drawings	1,200
Capital introduced	300

Calculation:

$$ \begin{aligned} \text{Profit} &= 7,600 - 8,400 + 1,200 - 300 \\ &= -800 + 1,200 - 300 \\ &= 400 - 300 \\ &= 100 \end{aligned} $$

Result: £100 profit for the year.

Common mistakes to avoid

• Forgetting to add drawings back to the profit calculation.
• Omitting any capital introduced (or treating it as a reduction rather than an addition).
• Confusing the sign of the result – a negative figure indicates a loss.
• Including non‑operating equity movements as drawings.
• Mixing up mark‑up and margin when using the ratio extension.

Practice questions

1. Opening capital: £8,400
   Closing capital: £9,200
   Drawings: £1,100
   Capital introduced: £0
   Calculate the profit or loss.
2. Opening capital: £5,500
   Closing capital: £4,800
   Drawings: £600
   Capital introduced: £200
   Calculate the profit or loss.
3. Opening capital: £10,000
   Closing capital: £12,500
   Drawings: £1,500
   Capital introduced: £800
   Calculate the profit or loss.

Answers to practice questions

Question	Profit / Loss (£)
1	£1,300 profit (9,200 – 8,400 + 1,100 – 0 = 1,300)
2	£300 loss (4,800 – 5,500 + 600 – 200 = –300)
3	£2,800 profit (12,500 – 10,000 + 1,500 – 800 = 2,800)