Markup, markdown and pricing

Every business that sells goods has to decide what to charge. The price has to cover what the goods cost, contribute to the costs of running the business, and leave a profit, while still being a price customers will pay. Retailers, wholesalers and manufacturers express these decisions through markup, the amount added to cost to reach a selling price, and markdown, the reduction from a regular price to a sale price. This lesson develops the arithmetic of both, shows why the same markup can be quoted as two different percentages, and works through a full buying and selling cycle.

The pricing equation

The selling price of an item can be split into three parts: the cost of the item to the seller, a share of the seller's operating expenses (rent, wages, utilities, advertising and so on, sometimes called overhead), and the operating profit.

Here S is the selling price, C the cost, E the operating expenses per unit, P the operating profit per unit and M the markup (also called gross profit or the dollar markup). The markup must cover expenses before any profit is made. A sale at a price above cost but below cost plus expenses still loses money.

Markup on cost and markup on selling price

A dollar markup can be expressed as a percentage of two different bases. Markup on cost uses cost as the base; markup on selling price, which is the same as the gross margin, uses the selling price as the base. Manufacturers and many small businesses think in terms of markup on cost; retailers and accountants usually think in terms of margin on selling price, because financial statements express everything as a percentage of sales.

Because cost is always smaller than selling price, the markup on cost is always the larger of the two percentages. When someone quotes a markup percentage, always ask which base they mean. The two convert into each other with simple formulas, where \( m_c \) is the markup on cost and \( m_s \) the markup on selling price, both as decimals.

Markdowns

A markdown is a reduction from the regular selling price. Stores mark goods down to clear seasonal stock, to meet competitors, to move damaged or slow-selling goods, or as promotions to bring customers in. The markdown rate is always based on the regular selling price.

A markdown hits profit hard, because the full reduction comes out of the markup. The item still cost the same, and the expenses of running the store do not shrink because a price was cut. A useful benchmark is the break-even price, the price at which the sale covers cost and expenses exactly, with no profit or loss.

Successive markdowns work like chain discounts: multiply the complements. A coat marked down 20 % and then a further 15 % is selling at 0.80 × 0.85 = 0.68 of its regular price, a total markdown of 32 %, not 35 %.

A complete buying and selling cycle

Real products rarely all sell at one price. Some sell at the regular price, some at a markdown, and the last few may be cleared at or below cost. The margin a business actually earns, the realized margin, is therefore lower than the margin built into the regular price. Buyers plan for this by setting an initial markup high enough to absorb expected markdowns.

The calculation can be reversed to set the initial markup. If a buyer expects to sell 60 % of a line at the regular price and the rest at an average of 30 % off, and needs a realized margin of 35 %, the regular price must be high enough that the blended revenue still leaves 35 %. Spreadsheet models of this kind, sometimes called open-to-buy plans, are a core tool for retail buyers.

Pricing in practice

The arithmetic gives a starting price, but pricing decisions also depend on customers and competitors. Cost-plus pricing (cost plus a standard markup) is simple and common in wholesale and contracting. Competitive pricing matches or undercuts rivals. Value-based pricing sets a price by what customers believe the product is worth, which can be far above cost for a strong brand or a specialized service. Psychological pricing uses prices ending in 99 or 95, which shoppers tend to read as noticeably cheaper than the next round number. Price elasticity, the sensitivity of the quantity sold to the price, decides whether a price cut raises or lowers total revenue; lesson 11 returns to this with break-even analysis.

# Markup conversions and a markdown check
def margin_from_cost(mc): return mc / (1 + mc)
def cost_from_margin(ms): return ms / (1 - ms)
for mc in (0.25, 0.50, 0.60, 1.00):
    print(f"markup on cost {mc:.0%} = margin {margin_from_cost(mc):.1%}")
C, e_rate, p_rate = 84, 0.20, 0.10
S = C / (1 - e_rate - p_rate)
E = e_rate * S
print(f"price {S:.2f}, break-even {C + E:.2f}, max markdown {(S - C - E) / S:.0%}")
units = [(120, 112.00), (60, 84.00), (20, 70.00)]
revenue = sum(n * p for n, p in units)
print(f"revenue {revenue:,.0f}, realized margin {(revenue - 200 * 70) / revenue:.1%}")

markup on cost 25% = margin 20.0%
markup on cost 50% = margin 33.3%
markup on cost 60% = margin 37.5%
markup on cost 100% = margin 50.0%
price 120.00, break-even 108.00, max markdown 10%
revenue 19,880, realized margin 29.6%