# Retail Math Definitions and Formulas: Sell Through Rate, AUC, and More

Stitch Labs helps brands manage their biggest asset – inventory – with the best inventory management software for high-growth brands.

Retailers rely on a variety of metrics to gauge the health and productivity of their businesses. Every week, they examine GM%, AUR, Inventory BOP, Sell Through %, and more in order to understand patterns, identify potential risks, and benchmark against industry trends. Inventory planners, specifically, are seen as the gatekeepers of these metrics. They are responsible for managing (and planning) these key metrics in their financial plans and inventory accounting, evaluating potential risks and opportunities, and offering solutions to drive improvements.

In order to effectively do this, planners should be well-versed in retail math, specifically the inputs driving retail metrics and the interdependencies between these metrics. In this guide, we provide you with formulas, definitions, and examples of some of the most important metrics used in retail companies to gain inventory control.

# Term and Equations

## Average Initial Retail

This is the price a retailer sets to sell its merchandise. AIR can sometimes align with MSRP, which is the Manufacturer’s Suggested Retail Price. AIR is the original ticket price and is not impacted by promotions or markdowns.

#### (AIR)= AUC/ (100%- IMU%) , Inventory at Retail / Units of Hand

Example: You decide to implement a diverse pricing scheme for your dress assortment. The AIR of maxi dresses will be \$200, the AIR of short party dresses will be \$150, and the AIR of casual summer dresses will be \$75.

To get the AIR of inventory, you’ll need to calculate the total retail AIR, then divide by the total units of inventory.

• Maxi Dresses: \$200 x 15 units = \$3000
• Short Party Dresses: \$150 x 30 units = \$4500
• Casual Summer Dresses: \$75 x 40 units = \$3000
• (\$3000 + \$4500+ \$3000) / ( 15 units + 30 units + 40 units) = (\$10,500/85 units) = \$123.52 AIR of Inventory

This tells us that, on average, the ticket price of a unit of inventory is \$123. Though you have items retailing at \$200 and \$150, the majority of your inventory is at a lower ticket price. What would need to happen in order to show a higher AIR of Inventory? If you are selling through your lower AIR product at a fast rate, then your remaining inventory is the higher AIR inventory. Also, if your company decides to buy more inventory at an AIR higher than \$123.52, your inventory investment will skew towards the higher AIR, therefore showing a greater AIR of inventory.

## Average Unit Retail (AUR)

This is the average price paid by the consumer for merchandise sold during a given time period. AUR takes into account any discounting during the time period (promotions, markdowns), and is not to be confused with AIR (see definition above).

Of the two variables involved in this equation, one is within your control and the other is not.

• You have control over what sales prices you charge and the discounting that can impact the product—either by markdown or a promotion. You can then track performance over time to see which pricing and promotional decisions had the biggest impact on sales.
• You can’t control what a customer purchases or how much they buy. You can, however, track their purchases to determine when and how much they buy, studying how those choices impact the AUR. For example, if your customers buy more expensive items the AUR goes up and, conversely, will go down if they purchase less expensive items.

#### Average Unit Retail (AUR) = Total Retail Sales \$ / Total Unit Sold

Example: Let’s say you want to determine the AUR of tops sold during a given week. This is information that could be used during an in-season review meeting to discuss pricing and discount strategies. If you’re told that the number of tops units sold that week was 200 and the total sales from those tops were \$5,000.00, what would the AUR be? \$25. This tells you that, on average, a customer paid \$25 for a top from your company. But what if all your tops have ticket prices of \$30? That means some sort of promotion was at play last week, allowing your AUR to be lower than your AIR.

## Average Unit Costs (AUC)

This is the average price your company pays to obtain the merchandise sold during a given time period.

AUC is a large factor in determining your profitability. If your AUC is going up while your Average Unit of Retail (AUR) remains the same (or declines), your margins and profits will suffer. On the other hand, if you can lower your AUC while maintaining your AUR, you’ll increase your profitability.

Once again, you can’t control what the customer chooses to buy, which is the key variable in this equation. Therefore, if the customer buys items that are expensive to produce or purchase for your company, the average unit cost will go up. Yet, if the customer buys items that are less expensive to produce, the average unit cost will go down.

#### Average Unit Costs (AUC) = Total Cost of Sales \$ / Total Unit Sold

Example: You’re trying to determine the AUC for the Belts your brand sells. The Standard Brown Belt costs \$4 per belt and you sold 15 last week. You also have a Classic Black Belt that costs \$5 per belt of which you sold 20 last week.

To get the total AUC for belts, you’ll need to calculate the total costs for each of the belts, then add each together and divide by the total units sold.

• Standard Brown Belt Sales total costs: \$4 x 15 units = \$60
• Classic Black Belt total costs: \$5 x 20 units = \$100
• (\$60 + \$100) / (15 units + 20 units) = \$4.57 is the AUC for Belts

But what if the next week the Classic Black Belt sells at a faster rate while the Standard Brown Belt’s sales rate declines? Let’s say you sold 25 units of the Classic Black Belt and only 10 units of the Standard Brown Belt.

Even though the total number of units sold and the cost of producing both products remains the same, the AUC has gone up to \$4.71. This is a result of customer purchasing more of your more costly item.

## Retail Sales

Within your retail sales report, the retail sales should represent what your total sales were for a given time period: days, weeks, months, etc. This is also referred to as retail volume. Note that this doesn’t take into account returns.

## Net Sales

This is indicative of a “true top line” of a business for a given period: days, weeks, months, etc. Since your inventory accounting excludes returns, damages, etc., this is the metric often used in a company’s income statement. Comparing Net Sales to total Retail Sales (or Gross Sales) can provide insight into the impact of returns and damages to your business.

## Cost Sales

This should represent what your total sales costs were for a given time period: days, weeks, months, etc.

## Gross Margin (\$)

Your gross margin is the difference between your total retail sales and your total retail costs. Certain retailers can operate very profitably with thin margins as long as their sales volume remains high. Conversely, brands with large margins can maintain strong profits with lower sales volume, but will still need to maintain a certain sales volume in order to stay profitable.

Many medium-sized retail businesses operate with a gross margin in the range of 25 to 35 percent.

#### Gross Margin (%) (also referred to as Product Margin % (PM%))

The percent of total sales revenue the company retains after paying the direct costs associated with producing products (AUC).

## Initial Mark Up (IMU) %

Your initial markup, or IMU, is the difference between the price you paid and what you charge customers. Not only should your initial sales price cover the cost of the item but it should also cover a portion of your overhead expenses–rent, utilities, insurance, etc–while leaving room for profit. Yet, many factors can affect how much you need to markup an item in order to get best return on investment: competition, market saturation, anticipated markdowns, and perceived customer value. If you miscalculate any of these elements, you could end up overpricing your product and needing to mark it down at a later date in order to move it.

Marking down items is an effective and common way to move aging inventory stored in your aged inventory reports, but if your markdowns are more than you initially anticipated, you could end up trading your profits just to make a sale.
A common misconception is that IMU% is equal to GM% (PM%). IMU% will be equal to the GM% only if AIR = AUR. If AUR differs from AIR, through promotional activity or discounting, your IMU% will differ from your GM%.

#### Initial Mark Up (IMU) % = (AIR – AUC) / AIR

Example: You need to determine the AIR to assign a handbag in order to hit an IMU% goal of 80%. The cost of the handbag is \$7. How would you determine the AIR?

To get to the AIR, you would need to do the following calculations:

• IMU%= (AIR – AUC) / AIR
• 80% = (AIR – \$7) / AIR * Replaced AIR with the variable a *
• 80% * a = (a – \$7)
• .8a= a-\$7
• -.2a= -\$7
• a= \$7/.-2
• a= \$35

Therefore, you will need to set your ticket price to \$35 in order to generate an 80% IMU%. Should your AUR actualize at \$21 due to discounting, your GM% is now 67%. This is a -13ppt variance from the IMU% due to the AUR degradation.

## Inventory BOP

This metric refers to how much inventory you have going into a week, month, quarter, etc. This can be expressed in terms of cost inventory or unit inventory. Inventory BOP is the same as inventory EOP for the previous week. Understanding your inventory BOP allows you to assess sales potential, and call out any sales risks due to inventory shortages. Your actual inventory BOP can diverge from your inventory BOP forecast for a variety of reasons including unexpected receipts received in the previous week or a miss or beat to the previous week’s sales forecast.

## Inventory EOP

This metric refers to how much inventory you have at the end of a week, month, quarter, etc. This can be expressed in terms of cost inventory or unit inventory.

## Inventory on Hand =

The amount of stock physically present in your warehouse or storage location. It’s important to remember with this metric that even if a product is sold, it is not subtracted from inventory on hand until it physically leaves the warehouse, so this number will usually be higher than your available inventory. (This definition is based on industry standards, though some customers do measure it differently.)

## Weeks on Hand

A ratio that estimates the number of weeks it will take a business to sell through its inventory. This metric takes into account current inventory levels, sales velocity, and future receipts. Weeks on hand is an estimation and should be used in conjunction with other inventory metrics to assess risk/opportunity. Also, the optimal weeks on hand number will vary depending on sector, maturity of business, and industry.

## Inventory Turnover (or Turn)

This metric tracks how quickly a retailer is selling and replacing inventory, ultimately providing insight into business efficiency and return on inventory investment. The higher the turnover, the less time your inventory spends collecting dust on your shelves (and the less money it costs you by doing so).

The average inventory turnover ratio will vary depending on your industry.

#### Inventory Turnover (or Turn) = Sales / Average Inventory On Hand (\$), Cost of Goods Sold / Average Inventory

Example: Your company reported 2016 net sales of \$10 million. Cost of goods sold came in at \$4 million. Your average inventory during the year was \$2 million. What is your inventory turn for the year?

• Turn = Sales / Average Inventory on Hand
• Turn = \$10 million / \$2 million
• Inventory Turn for the year = 5
• Days Inventory =
• (1 / 5) * 365 = 73
• This means that the entire inventory is sold in 73 days

How can you analyze this information? You can compare this inventory turn rate with turn rates from previous years to see if there are any shifts. You can also compare this to industry turn rates to gauge whether your company’s performance is on par or divergent from total industry.

## Sell Through % (Available)

The percentage of units sold during a period. It is calculated by dividing the number of units sold by the beginning on-hand inventory (for that same time period). This metric is useful for comparing products against each other as well as comparing how a specific product does week over week, month over month, etc. Sell through is a healthy way to assess if your investment is returning well for you. A high sell through % could indicate inventory opportunity while a low sell through % could indicate overinvestment. Remember that sell through % alone does not convey the full story. It is important to take into consideration factors such as time on offer, season code, and receipt cadence in conjunction with your sell through %.

## Inventory AUC

The average unit cost of your inventory at the beginning of a period (week, month, year, etc). The inventory AUC is an indicator of your product composition: high cost items, low cost items- and can be compared with the sales AUC to determine if there is alignment between what  you own and what you sell.

#### AUC = Inventory BOP (Cost) / Inventory BOP (Units)

Example: You determine that your inventory AUC is \$18.45 while your sales AUC is \$13.45. This misalignment indicates that you are selling the cheaper goods while your current inventory holding is skewing towards more expensive items. Achieving inventory AUC and sales AUC alignment is an important goal, and in-season levers can be pulled to achieve this.

# Conclusion

Inventory planning requires a keen balance of both quantitative and qualitative skills. A strong, foundational knowledge of retail math in addition to critical analysis and creative problem solving skills are key to ensuring the smart management of business. A high level of data interpretation amidst ambiguity is required to be successful in this role. The most successful inventory planners have tools that help them optimize inventory and accelerate growth with centralized data and flexible forecasts.

To learn more about the inventory planning function, the intricacies of this role, and the systems that support it, check out A Guide to Inventory Planning.