Retail Merchandising Mathematics and Formulas

Comprehensive vocabulary flashcards covering formulas and terminology for retail merchandising math, including inventory accounting, markup, markdown, profit, turnover, and open-to-buy planning.

Billed Cost

The gross cost of merchandise before deducting cash discounts, calculated as: $\text{Billed cost} = \text{List price} - \text{Trade discount(s)}$ or $\text{Billed cost} = \text{\# Units purchased} \times \text{Invoice cost}$

Total Cost of Goods Sold

The total cost associated with acquiring and preparing goods for sale, calculated as: \text{Total cost of goods sold \} = \text{Billed cost \} + \text{Inward freight charges \} + \text{Workroom costs \} - \text{Cash discount \$}

Cost of Goods Sold %

The relationship of the cost of goods sold expressed as a percentage of net sales: \text{Cost of goods sold \%} = \frac{\text{Cost of goods sold \}}{\text{Net sales \}} \times 100

Customer Returns and Allowances

The total monetary value of credits or refunds granted to customers for returned or damaged merchandise, calculated as: \text{Customer returns and allowances \} = \text{Total of all refunds or credits to the customer on individual items \} \times \text{Number of units actually returned} or \text{Customer returns and allowances \} = \text{Gross sales \} \times \text{Customer returns and allowances \%}

Customer Returns and Allowances %

The percentage relationship of total returns and allowances compared to gross sales, calculated as: \text{Customer returns and allowances \%} = \frac{\text{Customer returns and allowances \}}{\text{Gross sales \}} \times 100

Gross Sales

The total initial revenue from all merchandise transactions before accounting for customer returns and allowances: $\text{Gross sales} = \text{Total of all the prices charged to consumers on individual items} \times \text{Number of units actually sold}$ or \text{Gross sales \} = \frac{\text{Net sales \}}{100\% - \text{Customer returns and allowance \%}}

Net Sales

The actual sales revenue retained by the retailer after deducting customer returns and allowances: \text{Net sales \} = \text{Gross sales \} - \text{Customer returns and allowances \$}

Build / Percentage Change / Trend

The percentage rate of change comparing current sales against a prior period or planned figure: $\text{Build/percentage change/trend} = \frac{\text{This year sales} - \text{Last year sales}}{\text{Last year sales}} \times 100$ or $\text{Build/percentage change/trend} = \frac{\text{This year sales} - \text{Planned sales}}{\text{Planned sales}} \times 100$

Gross Margin

The remaining profit after deducting the total cost of goods sold from net sales: $\text{Gross margin} = \text{Net sales} - \text{Total cost of goods sold}$ or \text{Gross margin \} = \text{Gross margin \%} \times \text{Net sales \}

Gross Margin %

Gross margin expressed as a percentage of net sales, determined by: \text{Gross margin \%} = \frac{\text{Gross margin \}}{\text{Net sales \}} \times 100 or $\text{Gross margin \%} = \frac{\text{Maintained markup} + \text{Cash discounts} - \text{Alteration costs}}{\text{Net sales}} \times 100$

Operating Expenses

The combined total of all non-merchandise costs required to operate a retail business: $\text{Operating expenses} = \text{Direct expenses} + \text{Indirect expenses}$ or \text{Operating expenses \} = \text{Operating expenses \%} \times \text{Net sales \}

Net Profit

The final bottom-line profit remaining after all cost of goods sold and operating expenses have been paid: $\text{Net profit} = \text{Net sales} - \text{Cost of goods sold} - \text{Operating expenses}$ or $\text{Net operating profit} = \text{Gross margin} - \text{All operating expenses}$

Markup % on Retail

The percentage of the retail price that represents markup: \text{Markup \% on retail} = \frac{\text{Markup \}}{\text{Retail \}} \times 100 = \frac{\text{Retail \} - \text{Cost \}}{\text{Retail \$}} \times 100

Markup % on Cost

The percentage markup based directly on the cost of the goods: \text{Markup \% on cost} = \frac{\text{Markup \}}{\text{Cost \}} \times 100 = \frac{\text{Retail \} - \text{Cost \}}{\text{Cost \$}} \times 100

Initial Markup %

The markup originally placed on merchandise to cover planned expenses, reductions, and profits: $\text{Initial markup \%} = \frac{\text{Gross margin \%} + \text{Retail reductions \%}}{100\% + \text{Retail reductions \%}}$ or \text{Initial markup \%} = \frac{\text{Gross margin \} + \text{Retail reductions \}}{\text{Sales \} + \text{Retail reductions \}} \times 100

Cumulative Markup %

The average markup percentage achieved across all merchandise available for sale during an accounting period: \text{Cumulative markup \%} = \frac{\text{Cumulative markup \}}{\text{Cumulative retail \}} \times 100

Maintained Markup %

The actual markup percentage achieved on net sales after accounting for markdowns and discounts: $\text{Maintained markup \%} = \frac{\text{Net sales} - \text{Gross cost of goods sold}}{\text{Net sales}} \times 100$ or $\text{Maintained markup \%} = \text{Initial markup \%} - \text{Retail reduction \%} \times (100\% - \text{Initial markup \%})$

Retail Reduction %

The percentage difference between initial markup and maintained markup relative to retail sales: $\text{Retail reduction \%} = \frac{\text{Initial markup \%} - \text{Maintained markup \%}}{\text{Sales (100\%)} - \text{Initial markup \%}}$ or $\text{Retail reduction \%} = \frac{\text{Initial markup \%} - \text{Maintained markup \%}}{100\% - \text{Initial markup \%}}$

Purchase Balance

The remaining uncommitted procurement budget available to a buyer: $\text{Purchase balance} = \text{Total planned (pieces, retail, cost, or markup \%)} - \text{Purchases to date}$

Book Inventory at Retail

The accounting record of stock on hand at retail value, calculated as: $\text{Book inventory at retail} = \text{Opening book/physical inventory} + \text{Net retail purchases} + \text{Other stock additions} - \text{Net sales} - \text{Markdown differences} - \text{Other deductions from stock}$

Book Inventory at Cost

The cost valuation of book inventory, calculated using the complement of the cumulative markup percentage: $\text{Book inventory at cost} = \text{Opening retail book inventory} \times (100\% - \text{Cumulative markup \% achieved on stock} + \text{Purchases})$

Shortage (or Overage) $

The dollar difference between the closing book inventory value and the actual physical count: \text{Shortage (or overage) \} = \text{Closing book inventory at retail \} - \text{Physical inventory count at retail \$}

Shortage %

The percentage of inventory shrinkage relative to annual net sales: \text{Shortage \%} = \frac{\text{Shortage \}}{\text{Annual net sales \}} \times 100

Planned Dollar Shortage

The budgeted dollar allowance allocated for inventory shortage: $\text{Planned dollar shortage} = \text{Planned shortage percentage} \times \text{Planned net sales \$}$

Turnover

The velocity at which average stock is sold and replenished within a specific timeframe: $\text{Turnover} = \frac{\text{Net sales for period}}{\text{Average retail stock for the same period}}$ or $\text{Turnover rate} = \frac{\text{Planned sales for period}}{\text{Average retail stock/inventory}}$

Average Retail Stock / Inventory

The average level of inventory carried during a specific operational period: $\text{Average retail stock/inventory} = \frac{\text{Planned sales for period}}{\text{Turnover rate}}$ or $\text{Average retail stock/inventory} = \frac{\text{Sum of beginning inventories} + \text{Ending inventory for given period}}{\text{Number of inventories}}$

GMROI

Gross Margin Return on Investment, a productivity metric evaluating inventory profitability relative to its cost: $\text{GMROI} = \frac{\text{Gross margin \%} \times \text{Turnover}}{100\% - \text{Markup \%}}$ or \text{GMROI} = \frac{\text{Gross margin \}}{\text{Average inventory at cost \}}

Weeks of Supply (WOS)

The projected duration that current stock levels will satisfy customer demand based on turnover rate: $\text{Weeks of Supply} = \frac{\text{\# Weeks in time period}}{\text{Turnover for the time period}}$ or $\text{Number of weeks of supply} = \frac{\text{\# Weeks in time period}}{\text{Turnover for the time period}}$

Stock-to-Sales Ratio

The proportion of beginning inventory to planned sales for a specified month: $\text{Stock-to-sales ratio} = \frac{\text{Retail stock at given time in the period}}{\text{Sales for the period}}$ or $\text{BOM stock} = \text{Planned monthly sales} \times \text{Stock-to-sales ratio}$

Basic Stock

The baseline minimum reserve inventory needed to protect against stockouts under the basic stock method: $\text{Basic Stock} = \text{Average Inventory} - \text{Average Monthly Sales}$

BOM Stock

Beginning-of-month stock level, calculated via the basic stock, weeks of supply, or stock-to-sales methods: $\text{BOM stock} = \text{Basic Stock} + \text{Planned Sales for Month}$ or $\text{BOM stock} = \text{Average weekly sales} \times \text{Number of weeks of supply}$

Open-to-Buy (OTB)

The dollar amount of uncommitted planned purchases available for a specific month: $\text{OTB} = \text{Planned purchases for the month} - \text{Outstanding orders to be delivered that month}$

OTB for Balance of Month

The remaining purchasing power left in a buying budget for the rest of an active month: $\text{OTB for balance of month} = \text{Planned purchases for month} - \text{Merchandise received to date} - \text{Merchandise on order}$ or $\text{OTB for balance of month} = \text{Planned EOM stock} + \text{Planned sales for balance of month} + \text{Planned markdowns for balance of month} - \text{Actual stock-on-hand} - \text{On order}$

Planned Monthly Purchases at Retail

The planned retail value of merchandise that should be ordered for delivery during a specific month: $\text{Planned monthly purchases at retail} = \text{Planned EOM stock} + \text{Planned sales for month} + \text{Planned markdowns for month} - \text{Planned BOM stock}$

Planned Monthly Purchase at Cost

The cost value equivalent of planned monthly retail purchases: $\text{Planned monthly purchase at cost} = \text{Planned retail purchases} \times (100\% - \text{Planned markup \%})$

Markdown Cancellation

An upward price adjustment that restores the retail price of merchandise after an earlier markdown: \text{Markdown cancellation} = \text{Higher retail \} - \text{Markdown price \}

Net Markdown $

The net retail reduction realized after subtracting markdown cancellations from gross markdowns: \text{Net markdown \} = \text{Gross markdown \} - \text{Markdown cancellation \$}

Total Seasonal Markdown %

The percentage relationship between total seasonal markdowns and total seasonal net sales: $\text{Total seasonal markdown \%} = \frac{\text{Total dollar seasonal markdowns}}{\text{Total seasonal sales \$}} \times 100$

Net Cost

The actual cost paid for an item after deducting all applicable discounts from billed or list cost: \text{Net cost \} = \text{Billed cost \} - \text{Cash discount \$} or \text{Net cost \} = \text{Billed cost \} - \text{Quantity discount \} - \text{Cash discount \}