IGCSE Accounting 0452 - 5.6 Incomplete Records

Objective

Apply the techniques of mark-up, margin and inventory turnover to arrive at missing figures.

1. Mark-Up Method

The mark-up method is used to calculate the cost of goods sold (COGS) when the closing stock is known, but the opening stock and purchases are missing. It works by assuming a standard mark-up percentage is applied to the cost of goods sold to arrive at the selling price. This allows us to work backwards to find the COGS.

Formula:

$$COGS = Selling \ Price - Mark-up$$

Where:
Selling Price = Selling price of the goods
Mark-up = Percentage mark-up x COGS

Example:

A business has a closing stock of £2,000 and a mark-up of 40% on COGS. The selling price of all goods sold is £6,000.

Calculation:

1. Calculate the COGS: $$COGS = Selling \ Price - (40\% \times COGS)$$ $$COGS + 0.40 \times COGS = Selling \ Price$$ $$1.40 \times COGS = £6,000$$ $$COGS = \frac{£6,000}{1.40} = £4,285.71$$

Therefore, the cost of goods sold is £4,285.71.

2. Margin Method

The margin method is used to calculate the cost of goods sold when the closing stock and the selling price are known, but the opening stock and purchases are missing. It relies on the concept of gross profit (margin) being a percentage of the COGS.

Formula:

$$COGS = Closing \ Stock - (Opening \ Stock - Purchases)$$

Alternatively, if the margin is given:

$$COGS = \frac{Closing \ Stock \times (1 - Margin)}{1 - Margin}$$

Where:
Closing Stock = Closing stock value
Opening Stock = Opening stock value
Purchases = Value of goods purchased
Margin = Gross profit as a percentage of COGS

Example:

A business has a closing stock of £3,000, an opening stock of £1,000 and a margin of 30% on COGS.

Calculation:

1. Calculate the COGS: $$COGS = \frac{£3,000 \times (1 - 0.30)}{1 - 0.30}$$ $$COGS = \frac{£3,000 \times 0.70}{0.70}$$ $$COGS = £3,000$$

Therefore, the cost of goods sold is £3,000.

3. Inventory Turnover Method

The inventory turnover method is used to calculate the cost of goods sold when the closing stock, purchases, and opening stock are known. It uses the concept of inventory turnover ratio, which is a measure of how many times a business sells and replaces its inventory during a period.

Formula:

$$COGS = Opening \ Stock + Purchases - Closing \ Stock$$

Alternatively, if the inventory turnover ratio is given:

$$COGS = Closing \ Stock \div Inventory \ Turnover \ Ratio$$

Where:
Opening Stock = Opening stock value
Purchases = Value of goods purchased
Closing Stock = Closing stock value
Inventory Turnover Ratio = COGS / Average Inventory

Example:

A business has an opening stock of £500, purchases of £8,000 and a closing stock of £1,500. The inventory turnover ratio is 16.

Calculation:

1. Calculate the COGS: $$COGS = £500 + £8,000 - £1,500$$ $$COGS = £6,000$$

Alternatively, using the inventory turnover ratio:

$$COGS = £1,500 \div 16 = £93.75$$

Therefore, the cost of goods sold is £6,000.

Method	Formula	Information Required
Mark-Up	$$COGS = Selling \ Price - Mark-up$$	Selling Price, Mark-up
Margin	$$COGS = \frac{Closing \ Stock \times (1 - Margin)}{1 - Margin}$$	Closing Stock, Margin
Inventory Turnover	$$COGS = Opening \ Stock + Purchases - Closing \ Stock$$	Opening Stock, Purchases, Closing Stock