Turnovers

This is the number of times the average stock held has been sold or replaced during a given period.

Given:

Opening Stock = Tshs 2,000 Closing Stock = Tshs 2,500 Purchases = Tshs 14,000 Sales = Tshs 25,000 Expenses = Tshs 4,000

i. Cost of Goods Sold (COGS)

$$\text{COGS} = \text{Opening Stock} + \text{Purchases} - \text{Closing Stock}$$ $$\text{COGS} = 2000 + 14000 - 2500 = 16000 - 2500 = 13500$$

ii. Average Stock

$$\text{Average Stock} = \frac{\text{Opening Stock} + \text{Closing Stock}}{2}$$ $$\text{Average Stock} = \frac{2000 + 2500}{2} = \frac{4500}{2} = 2250$$

iii. Gross Profit

$$\text{Gross Profit} = \text{Sales} - \text{COGS}$$ $$\text{Gross Profit} = 25000 - 13500 = 11500$$

iv. Net Profit

$$\text{Net Profit} = \text{Gross Profit} - \text{Expenses}$$ $$\text{Net Profit} = 11500 - 4000 = 7500$$

v. Rate of Stock Turnover

$$\text{Rate of Stock Turnover} = \frac{\text{COGS}}{\text{Average Stock}}$$ $$\text{Rate of Stock Turnover} = \frac{13500}{2250} = 6 \text{ times}$$

Mark-up is the profit expressed as a fraction or percentage of the cost price.

$$\text{Mark-up \%} = \frac{\text{Gross Profit}}{\text{Cost Price}} \times 100$$

Given:

Cost Price = 400 Selling Price = 500

i. Gross Profit

$$\text{Gross Profit} = \text{Selling Price} - \text{Cost Price}$$ $$= 500 - 400 = 100$$

ii. Mark-up Percentage

$$\text{Mark-up \%} = \frac{100}{400} \times 100 = 25\%$$

iii. Margin

Margin is the profit expressed as a percentage of the selling price.

$$\text{Margin \%} = \frac{\text{Gross Profit}}{\text{Selling Price}} \times 100$$ $$= \frac{100}{500} \times 100 = 20\%$$

They refer to the same profit but expressed as a fraction of different bases:

To convert Mark-up to Margin:

$$\text{Margin} = \frac{\text{Markup Numerator}}{\text{Markup Denominator} + \text{Markup Numerator}}$$

Example: Mark-up = $\frac{2}{11} \Rightarrow \frac{2}{13}$ Margin

To convert Margin to Mark-up:

$$\text{Mark-up} = \frac{\text{Margin Numerator}}{\text{Margin Denominator} - \text{Margin Numerator}}$$

Example: Margin = $\frac{3}{13} \Rightarrow \frac{3}{10}$ Mark-up

Given the following for 2005:

Opening Stock = 400 Closing Stock = 600 Purchases = 5,200 Mark-up Rate = 20%

i. Cost of Goods Sold (COGS)

$$\text{COGS} = \text{Opening Stock} + \text{Purchases} - \text{Closing Stock}$$ $$= 400 + 5200 - 600 = 5000$$

ii. Gross Profit

Mark-up is 20% on cost, so:

$$\text{Gross Profit} = 20\% \times 5000 = \frac{20}{100} \times 5000 = 1000$$

iii. Sales Figure

$$\text{Sales} = \text{COGS} + \text{Gross Profit}$$ $$= 5000 + 1000 = 6000$$