Retail Math for Merchandise Planners

What retail math is

Retail math is the arithmetic that connects a merchandise plan's sales, margin, inventory and receipts so that a change in one is visible in the others. The equations themselves are simple — most are one division — and the skill is not in remembering them. The skill is knowing which decision each number supports, what it cannot see, and how to keep every term on one basis, one period and one grain so that two correct figures stop contradicting each other. This guide is the working reference, grouped by decision rather than alphabetically, with each formula's own page in the retail planning formulas library carrying the calculator.

Every number below is an illustrative worked example built to show a mechanism. None of the figures is a benchmark, an industry average or a market statistic, and none should be read as a target. Where a real target belongs — a stock-to-sales ratio, a markdown rate, a turns goal — it comes from the brand's own history, its channel mix and its cost base, not from a table.

The four families, and the decision each supports

The families are sequential in a season and circular across seasons. Margin math sets the ticket, productivity sets the stock the ticket has to be earned on, sell-down measures what the season actually did to that margin, and flow converts all of it into the receipts that start the next one. A plan where the four families are computed in different systems, at different grains, is a plan whose four answers will not reconcile — which is the structural argument in what is merchandise planning.

Family one: margin math

Initial markup (IMU)

IMU = (ticket retail − landed cost) ÷ ticket retail.

A style ticketed at 120 with a landed cost of 48 carries an IMU of (120 − 48) ÷ 120 = 60.0 per cent. Its cost complement — the share of the ticket the cost consumes — is 40.0 per cent, which is also the cost-to-ticket ratio. The two always sum to one, and the cost complement is the number that does the work later: it is what converts a retail plan into a cost buy.

Landed cost is the full delivered cost, not the ex-factory price. Freight, duty, inbound handling and, where the business carries it, the agent commission all belong in it; see landed cost. A cost complement built on an ex-factory price overstates IMU by the freight line, and the error only surfaces when the season's margin lands short. The initial markup entry defines the term; the initial markup formula and target costing pages carry the reverse calculation — solving for the cost a target IMU allows at a given ticket, which is the version a developer actually uses.

What IMU cannot tell you: whether the ticket is realistic. IMU is arithmetic on an intended price. A ticket set to hit a 60 per cent IMU on a cost that came back high produces a price the market may not pay, and the first markdown will say so. Keystone markup — doubling cost to set retail — is a pricing convention, not an IMU target; where freight and duty are heavy, keystone stops delivering the IMU it implies.

Where it gets misread: as margin. IMU is the margin before reductions. It is the ceiling, and no season lands on it.

Maintained markup and gross margin

MMU = (net sales − COGS) ÷ net sales, which for a season with no other adjustments is the same figure as gross margin per cent.

Take the same style through a season. A thousand units are bought at a 48 landed cost and ticketed at 120. Six hundred sell at full price. Four hundred sell at 84, a 30 per cent reduction off the ticket.

• →Original retail value: 1,000 x 120 = 120,000
• →Markdown dollars: 400 x (120 − 84) = 400 x 36 = 14,400
• →Net sales: 120,000 − 14,400 = 105,600
• →COGS: 1,000 x 48 = 48,000
• →Gross margin dollars: 105,600 − 48,000 = 57,600
• →Gross margin per cent: 57,600 ÷ 105,600 = 54.5 per cent

So a 60.0 per cent IMU delivered a 54.5 per cent maintained markup; the maintained markup entry sets out what sits between the two. The markdown was 12.0 per cent of original retail (14,400 ÷ 120,000) and it cost 5.5 margin points, not 12. The mechanism is visible in the identity: the realised cost complement is the original cost complement divided by the share of ticket retail actually realised — 0.40 ÷ (1 − 0.12) = 0.4545, so gross margin is 54.5 per cent. Markdown points and margin points are not interchangeable, and the exchange rate between them is set by the IMU. At a lower IMU the same markdown costs more margin, because the same reduction is being taken out of a thinner spread.

Two further lines separate the ticket from the money. Gross-to-net sales removes returns, cancellations and chargebacks; allowances removes the wholesale deductions — co-op, damages, compliance — that never appear on an order. A margin read that stops at gross sales is reading a number the business never collected.

What maintained markup cannot tell you: where the margin went. It is a net of full-price sales, markdowns, discounts and shrink. Decomposing a plan miss is the method for splitting it back out, and until it is split, a margin miss has no owner.

Family two: inventory productivity

Turns

Inventory turns = COGS ÷ average inventory at cost.

A department with 4,800,000 of annual COGS and 1,200,000 of average inventory at cost turns 4.0 times. The inventory turns formula page carries the period variants and the inventory turns entry the definition; the two rules that matter are that both terms sit on the same basis — cost with cost, retail with retail, never mixed — and that "average inventory" means an average of enough points to survive seasonality. A twelve-point monthly average and a two-point opening-and-closing average will not produce the same turns on a seasonal business, and the two-point version flatters a department that peaks mid-year.

What turns cannot tell you: whether the speed was worth having. Turns is blind to margin. It rewards a department that moves cheap goods quickly exactly as much as one that moves profitable goods quickly.

GMROI

GMROI = gross margin dollars ÷ average inventory at cost.

The same department earns 5,760,000 of gross margin on 10,560,000 of net sales, against 1,200,000 of average inventory at cost:

• →GMROI = 5,760,000 ÷ 1,200,000 = 4.8
• →Cross-check: gross margin per cent x sales-to-stock = 0.5455 x 8.8 = 4.8
• →And in terms of turns: GMROI = turns x (gross margin dollars ÷ COGS) = 4.0 x (5,760,000 ÷ 4,800,000) = 4.0 x 1.2 = 4.8

That last identity is the one to keep. It says GMROI is turns scaled by the markup ratio, so two departments can turn identically and return very different margin per inventory dollar. A second department turning the same 4.0 times at a 30 per cent gross margin returns 4.0 x (0.30 ÷ 0.70) = 1.7, because at that margin every dollar of cost of goods carries 30 cents of margin against 70 cents of cost. Same speed, roughly a third of the return. A turns target alone will call both departments healthy; see GMROI and the GMROI formula.

What GMROI cannot tell you: whether the inventory was available where demand was. It is a whole-period, whole-category average, so it nets a store sitting on dead stock against one that was out of stock, and the lost sales never enter the numerator. It also says nothing about the working capital cycle — payment terms can make a strong GMROI cash-hungry, which is what working capital tied in inventory measures.

Weeks of supply and forward weeks of supply

Weeks of supply = units on hand ÷ average weekly unit sales.

With 6,400 units on hand and a trailing average of 800 units a week, weeks of supply is 8.0 weeks. Now run the same 6,400 units down through a forward plan that climbs into a peak — 1,200, 1,400, 1,600, 1,800, then 1,000. The first four weeks consume 6,000 units, leaving 400 against a fifth week planned at 1,000, so forward weeks of supply is 4 + (400 ÷ 1,000) = 4.4 weeks.

The same stock is 8.0 weeks of cover and 4.4 weeks of cover at the same moment. The trailing figure divides by where demand has been; the forward figure runs it against where the plan says demand is going. Ahead of a peak, a floor set or a promotion, the trailing figure is the one that gets a business caught short — and it is the easier of the two to produce, because it needs no forward plan behind it.

Stock-to-sales ratio

Stock-to-sales = beginning-of-month stock ÷ that month's planned sales.

A month opening with 600,000 of stock against a 200,000 sales plan runs a 3.0 stock-to-sales ratio; the stock-to-sales ratio entry covers what the ratio is holding. Where the sales rate is flat inside the period, stock-to-sales multiplied by the weeks in the period approximates weeks of supply: 3.0 x 4 = 12 weeks. Where the month is phased steeply that approximation fails, because the ratio uses one opening stock against a whole month's sales while weeks of supply walks the weeks. How to set a stock-to-sales ratio covers deriving the target rather than inheriting it, and how to phase a sales plan covers the phasing the ratio depends on.

Family three: sell-down

Sell-through rate

Sell-through = units sold ÷ a denominator that has to be named. The two defensible denominators are units available — beginning stock plus receipts — and units received alone.

A season opens with 1,000 units, receives 4,000 and sells 3,250:

• →Against total available (5,000): 3,250 ÷ 5,000 = 65.0 per cent
• →Against receipts alone (4,000): 3,250 ÷ 4,000 = 81.25 per cent

Both are correct arithmetic on the same season, just over sixteen points apart, and which one appears in a deck decides whether the buy reads as sound or as long. The available-units convention answers "how much of what we could have sold did we sell"; the receipts convention answers "how did this specific buy perform". Fix one convention, name it in the report header, and never compare two periods across the two. The sell-through rate formula page and the sell-through rate entry use the receipts base — units sold ÷ units received, where "received" is the original buy for a finite-life style or beginning-of-period stock for a replenishment read — so a figure quoted from those pages is the 81.25 per cent read, not the 65.0 per cent one.

What sell-through cannot tell you: at what price. A 65 per cent sell-through reached at full price and one reached on a half-price promotion are the same number and different seasons, which is why sell-through is read alongside markdown per cent rather than on its own. It also hides size and colour composition — a style at 65 per cent whose core sizes are gone cannot reach 80 per cent at any price, because there is nothing left that fits the customer standing in front of it.

Markdown per cent

Markdown per cent = markdown dollars ÷ net sales where the plan is read against the money collected, or markdown dollars ÷ original retail where it is read against the ticket the goods were set at.

The season above: 14,400 ÷ 105,600 = 13.6 per cent of net sales, or 14,400 ÷ 120,000 = 12.0 per cent of original retail. One season, two figures, 1.6 points apart, and the gap widens as the markdown rate rises. The margin identity earlier uses the original-retail base; a weekly trading report built off net sales uses the other. Markdown rate and the markdown per cent formula both use the net-sales base, so a figure taken from either is the 13.6 per cent read. The EBITDA markdown impact page carries the flow-through to the bottom line.

One accounting rule is worth stating because it moves the receipt plan: keep the markdown line gross. Markdown money recovered from a vendor reduces the cost of the vendor's goods; it does not restore the retail value the markdown removed, so netting it against planned markdowns understates reductions and under-plans receipts.

Aging

Aging splits on-hand units by time since receipt. Of the 6,400 units on hand, 2,560 were received more than twelve weeks ago — 40.0 per cent of the stock is over twelve weeks old. Aging is the only line in this family that does not need a sale to have happened, which makes it the earliest of the three signals: it flags stock that is not moving before sell-through has had enough denominators to show it. Aging inventory and end-of-season exit strategies cover the action; the return rate belongs beside it, because a returned unit should re-enter the aging buckets on its original receipt date rather than the return date — where the system is configured the other way, a returns spike resets the aging profile of stock that has not moved.

Family four: flow

Flow is where the other three families become a buy. The identity is one line, and open-to-buy by vertical treats it in full.

Receipt need = planned EOP + planned sales + planned reductions − BOP Open-to-buy = receipt need − on order

A month for the department in the stock-to-sales example above — 600,000 of opening stock against a 200,000 sales plan — with the ticket and landed cost from the style example at the top of this guide:

The receipt plan is the first four lines; subtracting on order leaves what is still open. Converting to a cost buy uses the cost complement: 50,000 x (1 − 0.60) = 20,000 at cost, which at a 120 ticket and a 48 cost buys roughly 416 units.

Now move the cost. If landed cost has risen to 52.80 — a 44 per cent cost-to-ticket ratio and a 56 per cent IMU — but the plan still converts at last season's 40 per cent complement, the buyer is told that 20,000 buys 416 units. At 52.80 it buys 20,000 ÷ 52.80 = 378 units. A stale cost complement removes 38 units from the buy without appearing anywhere in the plan at the time it is written, because every retail line still reconciles. The shortfall lands later: 378 units at a 120 ticket is 45,360 of retail receipts against a 50,000 retail receipt need, so the month closes 4,640 short on receipts and under target on EOP. Planning margin on a moving cost base covers holding the plan where the movement is visible.

The leverage in the flow identity

Cut the sales plan by 10 per cent, from 200,000 to 180,000, and hold the EOP target flat:

• →Receipt need = 560,000 + 180,000 + 40,000 − 600,000 = 180,000
• →Open-to-buy = 180,000 − 150,000 = 30,000

A 10 per cent cut to the sales plan removed 40 per cent of the open dollars. The open-to-buy is a residual, so it absorbs the whole of any change the other four lines do not.

Now let the stock target move with the sales plan, which is what a stock-to-sales ratio does. If next month's plan also falls 10 per cent, the EOP target falls with it, from 560,000 to 504,000:

• →Receipt need = 504,000 + 180,000 + 40,000 − 600,000 = 124,000
• →Open-to-buy = 124,000 − 150,000 = −26,000

The month is 26,000 overbought on commitments already placed. Nothing was miscalculated at any step. A modest forecast change can move a balance from comfortably open to closed, and the sign flips before anyone raises it in a trade meeting, which is the case for the cadence argued in how often to reforecast and read weekly at the weekly trade meeting.

Downstream of the balance sit the unit-level formulas that turn dollars into a purchase order: buy quantity, style-colour depth, size curve allocation, safety stock and the replenishment trigger. At the store end, fair share allocation and door-level demand decide where the units land, and fill rate measures whether wholesale got what it ordered.

How the same formula reads by vertical

The equations do not change. What changes is the grain the number is meaningful at, the period it is held for, and which reductions exist at all.

Apparel. The flagship framing. Sell-through is read at style-colour and checked against the size curve, because a total-level rate hides a broken size run: once the middle sizes are gone, the remaining sizes read as slow demand when they are really unsellable residue. Turns are seasonal, not annual, and markdown cadence is planned against the season exit.

Footwear. The unit is a pair and the plan is a size run within a model-colour. A model at a strong sell-through with the core run exhausted is finished regardless of the headline figure, so weeks of supply is held per size band rather than per model. Odd pairs and try-on damage are real reduction lines. Assortment planning for footwear brands covers the depth arithmetic.

Accessories and bags. Core and seasonal pools behave differently and should not be averaged: carryover core turns slowly with almost no markdown exposure, so turns understate it and GMROI is the fair read. Attach rate links the category's sales plan to the anchor category it sells alongside, which means its sales line moves when apparel's does. Planning accessories lines covers the split.

Home and furniture. Container economics dominate. Cost is landed and moves with freight, so the cost complement has to be refreshed per booking cycle. Lead times measured in months make forward weeks of supply the only useful cover read, and the forward calculation must include on-water stock. Turns are structurally low, and cube constrains a receipt plan as tightly as dollars do: open dollars against a full container buy nothing. See OTB planning for home goods.

Outdoor. Planning runs on the model year, not the fiscal season, and quantity is largely fixed at the dealer prebook close, before the year opens. Sell-through is measured against the model-year changeover date, because carryover into the next model year is a different product story than carryover within a season. See planning a model year changeover.

Health and beauty. The grain is the shade, not the SKU. A foundation range averaged across its shade ladder looks balanced while the mid-depth shades are out of stock and the tails are aging, so sell-through by shade is the only read that supports a rebuy. Period after opening (PAO) and batch dating create reductions no apparel plan carries: testers consumed at counter, and stock written off at a dating cut-off whether or not it sold. Dating rules and weeks of supply covers holding cover against an expiry rather than a season.

Sporting goods. Dealer prebooks close before the model year, so the buy is largely fixed and in-season open-to-buy funds little beyond an at-once layer bought preseason. The meaningful productivity read is against prebook coverage rather than trailing weeks of supply, and closeout timing sits on the model-year calendar. See merchandise planning for sporting goods brands.

Toys and games. A single Q4 peak makes annual turns close to meaningless as an in-season signal: the same stock is a shortage in week 40 and dead in week 52. Forward weeks of supply against the peak phasing is the working number, and licensed windows add a reduction line with a fixed end date. See planning a licensed product window.

Baby and juvenile. Long-lived items sell for years, so a low sell-through in a season is a normal reading rather than a problem, and productivity is read over the life of a certified configuration. Registry demand is a forward read of intent created at item level ahead of purchase, which makes it usable in the forward cover calculation. Bulky goods are cube-constrained like furniture. See planning with registry demand.

Jewelry and watches. The plan is piece-level at low velocity, so turns are structurally low and the governing measures are margin per piece and GMROI. Metal cost moves the cost base between commitment and sale, so the plan is held at cost. Memo stock placed with a retailer stays on the brand's books, which means it sits in on-hand inventory and drags turns while producing no sale until the retailer sells or buys it. See merchandise planning for jewelry and watch brands.

The defect to avoid is applying one vertical's convention to another. A furniture plan read on apparel's trailing weeks of supply will chronically under-order against its lead time. A beauty plan read at SKU rather than shade will rebuy a balanced-looking range that is out of stock where it sells.

Where the numbers disagree, and which one to trust

Two correct numbers that contradict each other are not an error to reconcile away. The gap is the finding.

• →Units versus dollars. A department plans 1,000 units at a 120 average unit retail, for 120,000. It sells 1,100 units at a 102 AUR, for 112,200. Units are 10 per cent ahead; dollars are 6.5 per cent behind, because AUR fell 15 per cent. The dollar plan is the one the business is funded against; the unit beat explains where the dollars went. Average unit retail and plan versus actual variance carry the split.
• →Sell-through versus sell-through. 65 per cent and 81.25 per cent, one season. Trust the denominator that matches the question being asked, and never mix the two in a trend.
• →Trailing versus forward cover. 8.0 weeks and 4.4 weeks, one stock position. Before a peak, trust forward.
• →Turns versus GMROI. 4.0 and 4.0, returning 4.8 and 1.7. Trust GMROI for investment decisions and turns for cash-cycle ones.
• →Retail method versus cost method. A retail-method plan carries markdowns as a reduction because a price cut lowers the stock's retail value; a plan held at cost does not, because a markdown changes margin, not cost. Where the cost base moves — landed cost, metal — trust the cost view, because a stale cost complement hides the movement until the goods land.
• →Total versus grain. A category at plan can be two styles far ahead and six behind. Every formula in this guide is true at total and actionable only at the grain the decision is made at.

Two habits keep the disagreements honest. Reconcile the season in units and dollars side by side, which is the discipline of how to hindsight a season. And state the calendar: a 4-5-4 month and a calendar month are different denominators, and a comparison across the two carries a week of noise before any trading happened. See the 4-5-4 calendar and retail calendar: 4-5-4 versus 4-4-5.

How RetailNorthstar handles the arithmetic

RetailNorthstar holds the merchandise financial plan, assortment planning, buy planning, open-to-buy and allocation on one shared data model, so the four families compute from the same sales, cost, stock and on-order lines rather than from four exports. Margin, cover and open-to-buy move together when a plan line changes, and balances are held by channel, category and period rather than only at total. In-season sell-through informs buy-depth and allocation recommendations — AI-assisted planning working from the brand's own data — while deep statistical forecasting runs through integrations.

The same model plans for apparel, footwear, accessories, home and furniture, outdoor, sporting goods, health and beauty, toys and games, baby and juvenile, and jewelry and watch brands, with apparel as the flagship vertical.

Related resources

• →Retail Planning Formulas — every formula on this page, with calculators
• →What Is Merchandise Planning? — the plan these numbers describe
• →Open-to-Buy by Vertical — the flow identity in full, category by category
• →How to Hindsight a Season — reconciling units and dollars after the fact
• →Decomposing a Plan Miss — splitting a margin miss into owners
• →How to Set a Stock-to-Sales Ratio — deriving the target rather than inheriting it
• →Planning Margin on a Moving Cost Base — what to do when landed cost will not sit still
• →GMROI — the measure, and its two drivers
• →Merchandise Financial Plan — where the four families live together
• →Retail Math Cheatsheet — the same formulas on one printable page
• →Formulas by Role — the subset each planning role uses day to day
• →Open-to-Buy Template — a working spreadsheet version of the flow identity