Pricing Waterfall

Pricing Waterfall

Pocket Price Waterfall, Pocket Price Band, Profit Levers and the Price-Volume-Mix Bridge

Transaction price management

Marn and Rosiello (1992) distinguish three levels of price management: industry supply and demand, the product's market positioning, and the transaction, where the exact price of each deal is set by the base price, terms, discounts, allowances, rebates and bonuses. Most companies report invoice price, but between the invoice and the money that actually stays with the company lie payment-terms discounts, annual volume rebates, cooperative advertising, promotional allowances and freight, none of them visible on the invoice and most of them buried in company-wide expense accounts. Two pictures make the leaks visible: the pocket price waterfall for one transaction and the pocket price band across transactions. Money in this tool is a plain number in one currency; nothing is converted.

The pocket price waterfall

Starting from the list (base) price, the on-invoice elements (standard dealer or distributor discount, order-size discount, competitive or exception discount, promotional discounts printed on the invoice) are deducted to the invoice price; the off-invoice elements (cash or payment-terms discount, the carrying cost of extended terms, annual volume bonus or rebate, co-op advertising, merchandising allowances, product-line rebates, marketing allowances, freight paid by the seller, and where they apply returns, slotting and warranty costs) are deducted to the pocket price. The drop from list to pocket is the pocket discount. Each element is entered as an amount per unit or as a percent of a basis: the list price, the invoice price (a 2 % payment-terms discount is 2 % of the invoice), the pocket price (a rebate paid on realised revenue; the tool solves the implied equation) or the running price before the element (a chain of successive discounts: 10 % then 10 % of the remainder leaves 81 %). Subtracting the cost of goods and the variable cost of sales from the pocket price gives the pocket margin.

The article's examples, reproduced by the test script of the tool: a linoleum flooring manufacturer at a dealer list price of 6.00 per square yard loses 0.10 (order size) and 0.12 (competitive discount) to an invoice price of 5.78, then 0.30 (payment terms), 0.37 (annual volume bonus), 0.35 (off-invoice promotions), 0.20 (co-op advertising) and 0.09 (freight) to a pocket price of 4.47, 22.7 % below invoice; the Castle Battery Company's Power-Lite battery, the tool's default, goes from a base price of 28.40 through a standard dealer discount of 4.26, an order-size discount of 0.71 and an exception discount of 2.27 to an invoice price of 21.16, then through a cash discount of 1.2 % (0.25), receivables carrying cost 0.22, co-op advertising 0.85, a merchandising allowance 0.60, an annual volume rebate 0.74 and freight 0.32 to a pocket price of 18.18, a pocket discount of 10.22 or 36 % and 14 % below invoice; Tech-Craft's waterfall in percent of dealer list drops 16.7 points on the invoice to 83.3 and 22.4 more off the invoice to 60.9, a 39.1 % pocket discount. The authors found off-invoice drops of 16.7 % to 22.7 % of invoice across consumer goods, chemicals, computers and footwear companies.

Profit levers

Exhibit 1 of the article compares the operating-profit gain from a 1 % improvement in each lever for the average economics of 2,463 companies in the Compustat aggregate: price 11.1 %, variable cost 7.8 %, volume 3.3 %, fixed cost 2.3 %. The arithmetic is a contribution income statement: a 1 % higher price at the same volume adds 1 % of revenue to profit, a 1 % lower variable cost adds 1 % of the variable costs, 1 % more volume adds 1 % of the contribution (revenue less variable costs) and a 1 % lower fixed cost adds 1 % of the fixed costs, so each lever is that line divided by the operating profit. An income statement of 70.3 % variable cost, 20.7 % fixed cost and 9.0 % operating profit reproduces the four published figures, and the tool prints them beside the levers of the entered economics (revenue at the pocket price times volume, the entered cost of goods and variable cost of sales, the fixed costs). Castle, with a return on sales near 7 %, gains about 14 % of operating profit per 1 % of price. The levers work in reverse too: a 1 % price concession not matched by volume destroys the same percentage of profit. Marn, Roegner and Zawada (2004) repeat the comparison for a later sample of companies; Nagle, Hogan and Zale's break-even sales change is the complementary question: with a contribution margin of CM % of price, a price change of ΔP % leaves the total contribution unchanged only if the volume changes by −ΔP/(CM + ΔP), so a 10 % cut at a 30 % margin needs 50 % more volume and a 10 % rise can lose 25 % of the volume before it hurts. The tool tabulates that change for cuts and rises of 2 % to 15 %.

The pocket price band

No product sells at a single pocket price. Across accounts the realised pocket price spreads over a band that the article draws as the percent of volume sold at each pocket price: the flooring maker's band ran from 3.80 to 5.80 per square yard, a 35 % difference between the highest and lowest priced transactions; Castle's Power-Lite sold from 14 to 25 around an average of 20, more than ± 25 %, and the authors saw bands of 60 % (lighting fixtures), 70 % (computer peripherals), 200 % (specialty chemicals) and 500 % (fasteners). The band's width is the opportunity, and the identity of the accounts at its low end is the diagnosis: at Castle they were small, old-favourite accounts that knew whom to call for an extra exception discount or another point of co-op money, while some large accounts bought at the high end, the reverse of the company's declared policy of rewarding volume. Castle fixed it by capping exception discounts at 5 %, giving the sales force nine months to lift or drop the outliers, and tracking pocket price by transaction; average pocket prices rose 3 % and operating profit 42 %.

From a pasted transaction set (account, volume, list price, invoice price, then the off-invoice leakages per unit or as a percent of that invoice) the tool computes each account's pocket price, the simple and volume-weighted means, the standard deviation, the range and the band width (max − min)/max, the histogram of volume by pocket-price bin, the accounts below an entered floor (percent of list) with their volume share and the revenue a lift to the floor would add, and the pocket price (percent of list) against account volume with the Pearson correlation, its t test on n − 2 degrees of freedom, the Spearman rank correlation and the least-squares slope. A negative, significant correlation means larger accounts do pay less; an insignificant one, as in the default illustrative set, means the band is driven by something other than account size.

Price-volume-mix bridge

The second part explains the revenue change between two periods, product by product. With prices p and quantities q in periods 1 and 2, totals Q₁ = Σ q₁, Q₂ = Σ q₂, R₁ = Σ p₁ q₁ and R₂ = Σ p₂ q₂:

• Volume effect = (Q₂ − Q₁) × R₁/Q₁: the change in total units at the period-1 average price. Per product it is allocated by period-1 quantity share.
• Mix effect = Σ p₁ (q₂ − q₁ Q₂/Q₁): the period-2 quantities at period-1 prices less what the period-1 mix scaled to the new total would have given; positive when the mix shifted toward higher-priced products.
• Price effect (standard convention) = Σ (p₂ − p₁) q₂, at period-2 quantities, so that price + volume + mix = R₂ − R₁ exactly. In the sequential convention the price effect is taken at period-1 quantities, Σ (p₂ − p₁) q₁, and the interaction Σ (p₂ − p₁)(q₂ − q₁) is reported as its own cross term; the four again sum to the revenue change exactly.

Both are identities, so the tool prints the sum of the effects beside the revenue change and the residual, which is round-off only. The conventions differ in where they put the interaction of a price change with a quantity change on the same product; the standard form, which is the sales-variance analysis of cost accounting (Horngren, Datar and Rajan: sales-volume variance split into sales-mix and sales-quantity variances, with the price variance at actual quantities), is the usual management report. A product new in period 2 (q₁ = 0; its period-1 price may be left blank and is taken as its period-2 price) appears entirely in mix, a discontinued one (q₂ = 0) entirely in mix and volume. When unit costs are given the same decomposition is made on the gross margin with the unit margin in place of the price plus a unit-cost effect −Σ (c₂ − c₁) q₂ (or q₁ with its own cross term in the sequential convention). The 50-product random check of the test script confirms every identity to 10⁻⁹.

Reading the results

The waterfall section lists every element with its stage, the entered value, the amount per unit, its percent of list and of invoice, the running price and the cumulative leakage, then the invoice price, pocket price, pocket discount and off-invoice percent as equations, the pocket margin, and the waterfall chart (totals on the zero line, leakages falling from the running level, each bar labelled with its percent of list). The lever section gives the income statement at the pocket price and the four levers beside the article's averages, then the break-even volume table. The band section gives the statistics, the histogram, the transaction table sorted by pocket price with the accounts below the floor in red, the floor table and the price-against-volume scatter with the correlation verdict. The bridge section gives the per-product table, the effects as equations with the identity check, the bridge chart and, with costs, the gross-margin table, equations and chart.

Limits

The waterfall is one transaction at a time: a volume rebate that depends on the year's total purchases, or a co-op allowance that depends on the retailer's advertising, must be entered at the rate that applied to the transaction. Percents of the pocket price are solved by iteration and must sum to less than 100 %. The levers assume the volume is unchanged by the price move and the costs are linear in volume; the break-even sales change is the pure contribution test and ignores competitive reaction. The band statistics treat each pasted line as one account or transaction; the correlation test assumes roughly normal scatter and is only a screening test. The bridge has no currency, discount or returns adjustments: enter net prices per unit.

Default case

The Castle Battery Power-Lite waterfall of the article (base price 28.40, invoice 21.16, pocket price 18.18, pocket discount 10.22 = 36 %, 14 % off invoice; the cash discount is entered as the article's 1.2 % of invoice, which gives 0.254 against the 0.25 printed, so the page shows 18.176) with an illustrative cost of goods of 13.50 and variable cost of sales of 1.20, an illustrative 100,000 units and 220,000 of fixed costs (operating profit 128,000, a 7 % return on sales and a price lever of 14.2 %, both close to the article's figures for Castle), a −5 % price move, and an illustrative 24-account transaction set whose band runs from 14.95 to 23.07 (35 % wide) around a volume-weighted mean of 20.32. The bridge box holds an illustrative six-product battery line whose effects are checked against the closed-form identities and an independent numpy computation.