Sales Math Formulas

Gross Profit

$$ \text{Gross Profit} = \text{Sales Price} - \text{Cost of Goods Sold} $$

Gross profit is the financial gain obtained when the selling price exceeds the cost. It represents the amount of money earned after cost.

Example:

Selling Price = $150, Cost = $100 → Gross Profit = $50

\[\text{Gross Profit} = 150 - 100 = 50\]

Sales Price given Cost and Margin

$$ \text{Sales Price} = \frac{\text{Cost}}{1 - \text{Margin}} $$

Margin is expressed as a decimal (e.g., 30% → 0.30). This formula grosses up cost to the selling price, ensuring the margin is preserved.

Example:

Cost = $70, Margin = 0.30 → Sales Price = $100

\[\text{Sales Price} = \frac{70}{1 - 0.30} = \frac{70}{0.70} = 100\]

Cost given Price and Margin

$$ \text{Cost} = \text{Sales Price} \times (1 - \text{Margin}) $$

Rearranging the price formula allows cost to be derived from price and margin.

Example:

Price = $100, Margin = 0.30 → Cost = $70

\[\text{Cost} = 100 \times (1 - 0.30) = 100 \times 0.70 = 70\]

Margin given Price and Cost

$$ \text{Margin} = \frac{\text{Sales Price} - \text{Cost of Goods Sold}}{\text{Sales Price}} \times 100\% $$

Calculates the profit margin based on the selling price and cost of goods sold. Margin is expressed as a percentage.

Example:
  • List Price = $100
  • Distributor Discount = 40% → Distributor Price = $60
  • Customer Discount = 20% → Customer Price = $80
\[\text{Distributor Margin} = \frac{80 - 60}{80} = 0.25 \; (25\%)\]