Sales Math Formulas
Gross Profit
$$
\text{Gross Profit} = \text{Sales Price} - \text{Cost of Goods Sold}
$$
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
\[\text{Distributor Margin} = \frac{80 - 60}{80} = 0.25 \; (25\%)\]
Gross profit is the financial gain obtained when the selling price exceeds the cost. It represents the amount of money earned after cost.