Pricing approaches · M02 · Sunflower Intelligence

Before you start

You will be able to

Classify costs as fixed or variable and calculate the contribution margin per unit and as a ratio of price.
Convert between a markup on cost and a margin on price, and set the price that achieves a target margin.
Calculate the break-even volume, the break-even revenue and the volume needed for a target profit.
Apply cost-plus, target-return, value-based and competition-based pricing, and explain what each one leaves out.
Identify a product’s price floor and price ceiling and use them, with competitors’ prices, to judge a proposed price.

Review first

The product life cycle — Lantern Cold Brew is being priced for its launch, an introduction-stage decision; the life cycle explains why launch costs are high and volumes uncertain.
Percentages: finding a percentage of an amount and expressing one amount as a percentage of another.

Fictional case A fictional coffee business founded by Ana Lim. It starts as a catering and barista-training service, opens its own cafés and an online shop for beans, and plans a canned cold brew.

The idea

Fictional case

Lantern Coffee Co. is ready to launch Lantern Cold Brew, a 250 ml can of cold brew, in Harbour City. The product is settled: one flavour, made from an Ethiopian single-origin coffee that costs $0.74 a can to brew, can and deliver to the distributor. The plan puts the can in supermarkets, in natural and specialty grocers, and in Lantern’s own cafés and online shop. One decision is still open on Ana Lim’s desk: the price. On the supermarket shelf the can will sit next to Summit Brew at $3.79, Arcadia Coffee at $2.89 and Daily Grind RTD at $2.29. The working plan says $3.49. Is that a good number, and how would anyone know?

Of the four elements of the marketing mix, price is the only one that brings money in. Developing the product, getting it onto shelves and promoting it all cost money; price is how the business recovers some of the value it creates. Price is also the element that can be changed fastest, the one competitors notice first, and a message in itself: a can at $3.49 claims to be better than one at $2.29. This lesson builds the tools for setting a price from three directions: what the product costs, what customers would pay for it, and what competitors charge.

Fixed and variable costs

Costs behave in two different ways as volume changes. A variable cost is incurred for each unit made or sold, so its total rises in proportion to volume: for Lantern, the liquid, the can, the co-packer’s fee and freight to the distributor come to $0.74 for every single-origin can. A fixed cost stays the same in total over a period, whatever the volume, within the range of activity the business is planning for: the yearly fee a supermarket charges to stock a product, the salaries of the launch team, a promotion budget once it is committed. Selling twice as many cans doubles the variable costs and leaves the fixed costs where they were.

Lantern Cold Brew’s launch costs in the default plan (fictional)
Cost	Amount	Behaviour
Liquid, can, co-packer fee and freight (single-origin)	$0.74 per can	Variable
Packing and delivery of café and online orders	$0.45 per can sold direct	Variable
Listing fee, supermarkets	$9,000 per flavour a year	Fixed
Listing fee, natural and specialty grocers	$2,000 per flavour a year	Fixed
Fixed cost of the café and online channel	$6,000 a year	Fixed
Promotion budget	$120,000 a year	Fixed once committed
Launch team and brand work (overhead)	$60,000 a year	Fixed
Fixed costs in total	$197,000 a year

Figures from the course market file. A one-flavour range carries no extra range cost. The share of the shelf price kept by retailers and the distributor is not a cost Lantern pays: it never reaches Lantern at all, so it is deducted from the price instead.

Total cost is the fixed costs plus the variable cost per unit times the number of units. Average cost, total cost divided by units, is what people usually mean by “what a can costs”, and it is slippery because it depends on volume. The plan’s $197,000 of fixed costs spread over 100,000 cans add $1.97 to each can’s $0.74 cost of goods, an average of $2.71. Spread over 200,000 cans they add $0.985, an average of about $1.73. Average cost cannot be known until you know how many cans you will sell, and how many you sell depends on the price. Keep that circle in mind: it is the main weakness of pricing from cost alone.

Contribution margin

What each unit adds after its own variable costs is its contribution margin: the price the seller receives minus the variable cost per unit. The name describes what it does. Each unit’s contribution goes first towards covering the fixed costs and then, once they are covered, becomes profit. The contribution margin ratio expresses the contribution as a share of the price.

\text{CM} = P - VC \qquad\qquad \text{CM ratio} = \dfrac{P - VC}{P}

Notice the words “the price the seller receives”. Lantern does not receive the shelf price. In supermarkets the distributor and the retailer together keep 32% of the shelf price, so of every $3.49 a shopper pays, Lantern receives $3.49 \times (1 - 0.32) = 2.3732$ , about $2.37. Its contribution per can is $2.3732 - 0.74 = 1.6332$ , about $1.63, and its contribution margin ratio is $1.6332 \div 2.3732 \approx 68.8\%$ . Tracing what each party keeps between the shelf price and the producer is called a price build-up; lesson 6 builds one for every channel.

Lantern Cold Brew in supermarkets: the cost floor, competitors’ prices and a ceiling that must be estimated (fictional market).

For Lantern in supermarkets the floor is easy to find. A can loses money if Lantern’s share of the shelf price is below its $0.74 cost, which happens when the shelf price is below $0.74 \div 0.68 \approx 1.09$ . The ceiling is harder: it depends on how much better Lantern tastes to its target market than Arcadia or Summit, and that is a question for market research, not for the cost sheet. The rest of this lesson works through the three families of pricing methods, which start from costs, from customers and from competitors.

In depth

Cost-plus pricing and the markup

Cost-plus pricing sets the price by adding a fixed percentage to the unit cost. That percentage is the markup, and its base is the cost:

\text{Markup} = \dfrac{P - C}{C} \qquad\qquad P = C \times (1 + \text{markup})

A hardware shop that buys a tape measure for $6.00 and applies a 50% markup prices it at $6.00 \times 1.5 = 9.00$ . Cost-plus pricing is common where products are many and similar and costs are clear: retailers with thousands of lines, builders and contractors quoting for materials and labour, and contracts in which the buyer agrees to pay the supplier’s costs plus a fee. It is quick, consistent and easy to explain to a customer.

Its weakness is that it looks only inwards. A markup says nothing about what customers would pay or what competitors charge, so it leaves money on the table when customers value the product highly and prices the product out of the market when they don’t. And if the “cost” includes a share of the fixed costs, it rests on a volume forecast that itself depends on the price, the circle described above.

Margin: the same profit measured on the price

A margin, or margin on price, divides the same profit per unit by the price instead of the cost:

\text{Margin} = \dfrac{P - C}{P}

Because the price is larger than the cost whenever there is a profit, a margin is always smaller than the markup it matches. The tape measure bought for $6.00 and sold for $9.00 has a markup of $3 \div 6 = 50\%$ and a margin of $3 \div 9 \approx 33.3\%$ : one profit, two percentages. To convert between them, express the same profit per unit on each base. With cost $C$ and markup $k$ , the price is $C(1 + k)$ and the profit per unit is $Ck$ , so the margin is $Ck \div C(1 + k) = k \div (1 + k)$ . Solving that for $k$ gives the markup that delivers a margin $m$ :

m = \dfrac{k}{1 + k} \qquad\qquad k = \dfrac{m}{1 - m} \qquad\qquad P = \dfrac{C}{1 - m}

Matching markups and margins
Markup on cost	Margin on price
25%	20%
50%	33.3%
100%	50%
150%	60%
300%	75%

A markup of 100% doubles the cost and gives a 50% margin. No markup, however large, gives a margin of 100%.

Usage varies between industries, so always ask “a percentage of what?”. Some business-mathematics texts call the margin the markup on selling price, and some retailers say “markup” when they mean a percentage of the retail price. Two kinds of margin appear in this course. Gross margin subtracts only the cost of goods; contribution margin subtracts every variable cost. For Lantern’s supermarket cans they are the same, $1.63, because the cost of goods is the only variable cost. A can sold through Lantern’s online shop also carries $0.45 of packing and delivery, which is variable too, so its contribution is $3.49 - 0.45 - 0.74 = 2.30$ . Whether that $0.45 also counts in gross margin is a convention. This course deducts it from the price, as it deducts the trade’s share, so the direct net price is $3.49 - 0.45 = 3.04$ and gross margin and contribution are both $2.30 (the simulator does the same). A business that recorded fulfilment as a selling expense below gross profit would report a gross margin of $3.49 - 0.74 = 2.75$ on the same can, with the same $2.30 contribution.

Break-even analysis

Pricing decisions are judged by profit, and profit appears only once the fixed costs are covered. Profit for a period is the contribution from every unit sold minus the fixed costs, $\pi = (P - VC) \times Q - FC$ . Setting profit to zero and solving for the volume $Q$ gives the break-even point, the volume at which total contribution exactly covers the fixed costs:

Q_{\text{BE}} = \dfrac{FC}{P - VC} \qquad\qquad R_{\text{BE}} = \dfrac{FC}{\text{CM ratio}} \qquad\qquad Q_{\text{target}} = \dfrac{FC + \pi^{*}}{P - VC}

Dividing the fixed costs by the contribution margin ratio instead gives the break-even revenue, the sales value needed. A business that wants a target profit $\pi^{*}$ must cover it as well as the fixed costs, which gives the target-profit volume. A sandwich bar that sells at $9.00, with a variable cost of $4.00 a sandwich and fixed costs of $15,000 a month, breaks even at $15{,}000 \div 5 = 3{,}000$ sandwiches a month, which is $27,000 of sales. To earn $5,000 a month it needs $20{,}000 \div 5 = 4{,}000$ sandwiches.

Break-even analysis rests on assumptions worth stating aloud. Price and variable cost per unit are the same at every volume: no volume discounts, no overtime rates. Fixed costs stay fixed over the range considered; a second production line or an extra listing would add a step. When several products or channels are involved, their mix stays constant, so an average contribution per unit can be used. Above all, break-even volume is not a forecast. It tells you how many units a price needs, not how many it will sell, and its value lies in comparing the two.

Target-return pricing

Target-return pricing runs break-even analysis the other way round. Instead of asking what volume a price needs, it asks what price earns a chosen return on the capital invested, at a forecast volume:

P = \text{unit cost} + \dfrac{r \times I}{Q}

Here the unit cost is the full cost per unit at the forecast volume $Q$ , that is, the variable cost plus the fixed costs spread over $Q$ ; $I$ is the capital invested and $r$ the target rate of return. Capital-intensive businesses use it to make sure an investment pays its way. A fictional maker of electric bikes invests $2,400,000 in tooling and wants a 15% return a year. It forecasts 6,000 bikes a year, with a variable cost of $850 a bike and fixed costs of $1,800,000 a year, so its unit cost at the forecast is $850 + 1{,}800{,}000 \div 6{,}000 = 1{,}150$ . The target-return price is $1{,}150 + 0.15 \times 2{,}400{,}000 \div 6{,}000 = 1{,}210$ .

The method shares cost-plus pricing’s blind spot and adds a trap: the return arrives only if the forecast volume is sold. If the bikes sell 4,000 a year at $1,210, their contribution is $(1{,}210 - 850) \times 4{,}000 = 1{,}440{,}000$ , which does not cover the $1,800,000 of fixed costs: a loss of $360,000 instead of the planned $360,000 profit. The price was set as if demand did not depend on it. OpenStax’s marketing text makes the same point: a target-return price is only as good as the sales estimate behind it.

Value-based pricing

Value-based pricing starts from the customer instead of the cost. Its central idea is economic value, the value of a product relative to the customer’s next-best alternative. In the formulation that goes back to Thomas Nagle’s pricing books, economic value has two parts. The reference value is the price of the best alternative the customer would otherwise buy. The differentiation value is the value, positive or negative, of everything that makes your offer different from that alternative: lower running costs, less downtime, a better taste, but also a less familiar name or the cost of switching.

\text{Economic value} = \text{reference value} + \text{differentiation value}

Economic value is the price ceiling for a customer who fully understands the difference. Customers who don’t understand it will value the product less, which is why value-based pricing goes hand in hand with showing customers the value. Pricing a little below economic value leaves the customer part of the gain, and that share is their reason to switch. Cost plays no part except to set the floor, which is why value-based prices can sit far above cost. Software is the extreme case: another licence costs the seller almost nothing, yet if it saves a customer thousands of dollars of staff time a year more than the alternative does, a price of thousands of dollars can still be a good deal for the customer.

For a supermarket shopper choosing a cold brew, the reference value depends on which alternative that shopper would buy. A shopper who would otherwise take Arcadia at $2.89 is weighing a quality gap: Lantern scores 7.5 out of 10 on the taste panel against Arcadia’s 6. At $3.49, Lantern is betting that the better taste and the single-origin story are worth at least $0.60 a can to that shopper. A shopper who would otherwise take Summit at $3.79 is weighing a different trade: slightly lower quality (7.5 against 8) and a less familiar brand, for $0.30 less. Neither number can be read from costs. Both are questions for research, and different shoppers will answer them differently.

Competition-based pricing

Competition-based pricing takes competitors’ prices as the main input. In going-rate pricing a firm charges about what others charge. It is the norm where products are hard to tell apart and buyers compare prices instantly, such as fuel along a busy road or a standard grade of steel: price above the going rate and customers leave; price below it and rivals follow, so everyone earns less. The going rate also has a practical appeal, because it sums up what the whole market has learned about demand and costs.

Sealed-bid pricing is used when a buyer invites confidential bids and awards the contract to one bidder, usually the lowest acceptable one. Each bidder weighs a higher price, which earns more if it wins, against a lower chance of winning. A fictional installer bidding to fit battery storage for a city council estimates that the job will cost it $1,000,000. It judges that a bid of $1,200,000 has a 40% chance of winning, $1,100,000 a 70% chance and $1,050,000 a 90% chance. The expected contributions are $0.4 \times 200{,}000 = 80{,}000$ , $0.7 \times 100{,}000 = 70{,}000$ and $0.9 \times 50{,}000 = 45{,}000$ , so on these estimates, and if it can live with a 60% chance of winning nothing, the highest bid is the best bet. The arithmetic is easy; the probabilities are judgements built from what the firm knows about its rivals’ costs and past bids.

Choosing an approach

Three starting points for a price
Approach	Starts from	Answers	Blind spot
Cost-plus and target-return	Unit cost, plus a markup or a target return	Will this price cover our costs at the volume we expect?	What customers would pay, and how volume depends on price
Value-based	The customer’s next-best alternative and the value of the difference	What is the most this customer would pay, and why?	Needs research; customers may not see the value without help
Competition-based	Competitors’ prices or their expected bids	Where will customers and rivals accept our price?	Our own costs, and how our product differs

In practice the three are used together. Costs show where the floor is and what volume each price needs; customer value shows where the ceiling is; competitors’ prices show how customers will read your price. Setting a price is choosing a position in the space between floor and ceiling, and break-even analysis tells you whether that position can pay. How customers respond to a price within that space, measured by elasticity, is the subject of the next lesson.

Formulas

Contribution margin per unit

\text{CM} = P - VC

$P$: Price the seller receives per unit, after any trade margin, commission or fulfilment cost deducted from it$ per unit
$VC$: Variable cost per unit$ per unit

Assumes. Variable cost per unit is the same at every volume.

What each unit contributes towards fixed costs and then profit.

Contribution margin ratio

\text{CM ratio} = \dfrac{P - VC}{P}

$\text{CM ratio}$: Share of each dollar of price left after variable costs%
$P$: Price the seller receives per unit$ per unit
$VC$: Variable cost per unit$ per unit

Multiply revenue by the ratio to get total contribution.

Markup on cost and the cost-plus price

k = \dfrac{P - C}{C} \qquad P = C\,(1 + k)

$k$: Markup: profit per unit as a share of the cost%
$C$: Unit cost the markup is applied to$ per unit
$P$: Selling price$ per unit

Say which cost the markup is applied to: purchase cost, variable cost or full cost.

Margin on price

m = \dfrac{P - C}{P}

$m$: Margin: profit per unit as a share of the price%
$P$: Selling price$ per unit
$C$: Unit cost$ per unit

Also called the markup on selling price in some texts.

Converting between markup and margin

m = \dfrac{k}{1 + k} \qquad k = \dfrac{m}{1 - m}

$k$: Markup on costdecimal
$m$: Margin on pricedecimal

Assumes. Both are measured on the same cost and price.

Price that gives a target margin

P = \dfrac{C}{1 - m}

$C$: Unit cost$ per unit
$m$: Target margin on pricedecimal
$P$: Price that gives the target margin$ per unit

Not C × (1 + m): that is a markup of m, which gives a smaller margin.

Break-even volume

Q_{\text{BE}} = \dfrac{FC}{P - VC}

$Q_{\text{BE}}$: Units that must be sold in the period for total contribution to equal fixed costsunits
$FC$: Fixed costs for the period$
$P - VC$: Contribution margin per unit$ per unit

Assumes. Price, variable cost per unit and fixed costs are constant over the range considered; with several products or channels, the mix is constant.

Round up to a whole unit: one unit fewer leaves a loss.

Break-even revenue

R_{\text{BE}} = \dfrac{FC}{\text{CM ratio}}

$R_{\text{BE}}$: Sales value at which total contribution equals fixed costs$

Volume for a target profit

Q_{\text{target}} = \dfrac{FC + \pi^{*}}{P - VC}

$Q_{\text{target}}$: Units that must be sold in the period to earn the target profitunits
$FC$: Fixed costs for the period$
$\pi^{*}$: Target profit for the period$
$P$: Price the seller receives per unit$ per unit
$VC$: Variable cost per unit$ per unit

Target-return price

P = \text{unit cost} + \dfrac{r \times I}{Q}

$P$: Target-return price$ per unit
$\text{unit cost}$: Full cost per unit at the forecast volume: variable cost plus fixed costs ÷ Q$ per unit
$r$: Target rate of return on the capital invested, per period%
$I$: Capital invested$
$Q$: Forecast unit sales for the periodunits

Assumes. The forecast volume is achieved at this price.

If sales fall short, unit cost rises and the return is not earned.

Economic value to the customer

\text{EV} = \text{reference value} + \text{differentiation value}

$\text{reference value}$: Price of the customer’s next-best alternative$
$\text{differentiation value}$: Value to the customer of every difference from that alternative, positive or negative$

The ceiling for a fully informed customer; a value-based price usually sits below it.

Worked examples

A first example: Lantern’s supermarket price build-up

Fictional figures

Lantern Cold Brew is planned at $3.49 a can on the supermarket shelf. Supermarkets and their distributor together keep 32% of the shelf price. The three liquids Lantern could use cost $0.58 (classic blend), $0.74 (single-origin) and $0.88 (organic single-origin) per can. How much does Lantern receive per can, and what are its gross margin per can, its margin on price and its markup on cost with each liquid?

Lantern Cold Brew at $3.49 in supermarkets (fictional)
Liquid	Cost per can	Gross margin per can	Margin on net price	Markup on cost
Classic blend	$0.58	$1.79	75.6%	309%
Single-origin	$0.74	$1.63	68.8%	221%
Organic single-origin	$0.88	$1.49	62.9%	170%

Trade share: the distributor and retailer keep $3.49 \times 0.32 = 1.1168$ , about $1.12 of each can.
Lantern’s net price: $3.49 \times (1 - 0.32) = 2.3732$ , about $2.37. This, not $3.49, is the price in all of Lantern’s calculations.
Gross margin per can is net price minus cost of goods: classic $2.3732 - 0.58 = 1.7932$ ; single-origin $2.3732 - 0.74 = 1.6332$ ; organic $2.3732 - 0.88 = 1.4932$ .
Margin on price divides by the net price: $1.7932 \div 2.3732 \approx 75.6\%$ , $1.6332 \div 2.3732 \approx 68.8\%$ and $1.4932 \div 2.3732 \approx 62.9\%$ .
Markup on cost divides by the cost: $1.7932 \div 0.58 \approx 309\%$ , $1.6332 \div 0.74 \approx 221\%$ and $1.4932 \div 0.88 \approx 170\%$ . Check one with the conversion formula: $2.207 \div (1 + 2.207) \approx 0.688$ , the single-origin margin.

Answer. Lantern receives $2.37 a can. Its gross margin per can is $1.79 (classic), $1.63 (single-origin) or $1.49 (organic): margins on price of 75.6%, 68.8% and 62.9%, or markups on cost of 309%, 221% and 170%.

What it means. The $0.30 difference in cost between the cheapest and the dearest liquid moves the margin by about 13 percentage points, yet every option leaves well over half of the net price to cover fixed costs. See how different the two percentages look for the same can: a markup of 221% sounds greedy and a margin of 68.8% less so, yet both describe the same $1.63. With $197,000 of fixed launch costs to cover, a high contribution per can is not yet profit, as the next example shows.

A harder example: Can Lantern’s launch plan break even?

Fictional figures

Lantern’s default plan sells single-origin cans in one flavour at $3.49 through supermarkets, natural and specialty grocers, and its own cafés and online shop, with a $120,000 promotion budget. Using the course market file, find the plan’s fixed costs, its contribution per can in each channel, its break-even volume and the volume needed for a $50,000 profit. To keep the hand calculation simple, make two assumptions: Lantern’s cans sell across the three channels in proportion to each channel’s share of category volume (45%, 15% and 10%), and the whole promotion budget is a fixed cost. The last step compares the answer with the simulator, which makes neither assumption.

Fixed costs for the year: supermarket listing $9{,}000 \times 1 = 9{,}000$ (one flavour); natural grocers’ listing $2{,}000 \times 1 = 2{,}000$ ; the direct channel’s fixed cost, 6,000; range cost for one flavour, 0; promotion $50{,}000 + 40{,}000 + 20{,}000 + 10{,}000 = 120{,}000$ ; launch overhead, 60,000. In total $FC = 197{,}000$ . The whole promotion budget is treated as fixed here, including the $20,000 for trade promotions, although trade deals really behave more like a discount on each promoted can.
Contribution per can in each channel: supermarkets keep 32%, so $3.49 \times 0.68 - 0.74 = 1.6332$ ; natural grocers keep 38%, so $3.49 \times 0.62 - 0.74 = 1.4238$ ; direct sales carry no trade margin but $0.45 of packing and delivery, so $3.49 - 0.45 - 0.74 = 2.30$ .
Average contribution per can, weighting each channel by its share (the three shares add up to $0.45 + 0.15 + 0.10 = 0.70$ ): $(0.45 \times 1.6332 + 0.15 \times 1.4238 + 0.10 \times 2.30) \div 0.70 = 1.17851 \div 0.70 \approx 1.6836$ .
Break-even volume: $197{,}000 \div 1.6836 \approx 117{,}012.2$ . Round up: Lantern needs 117,013 cans, because 117,012 would leave a small loss.
Target profit of $50,000: $(197{,}000 + 50{,}000) \div 1.6836 \approx 146{,}710.7$ , so 146,711 cans.
Context: Harbour City buys 4.8 million cans a year, 70% of them, or 3,360,000 cans, through Lantern’s three channels. Break-even needs $117{,}013 \div 3{,}360{,}000 \approx 3.5\%$ of those cans, and the $50,000 profit $146{,}711 \div 3{,}360{,}000 \approx 4.4\%$ .
Compare with the simulator. The Marketing Mix Simulator’s default plan breaks even at about 117,425 cans, at $1.51 contribution per can: close to 117,013 but not the same, because it drops both assumptions. First, its shoppers don’t buy in the proportions 45 : 15 : 10. It predicts about 92,139 cans in supermarkets, 87,075 in natural grocers and 19,781 direct, because quality-minded natural-grocer shoppers take to a single-origin can far more readily (Lantern wins about 12.1% of that channel’s cans against 4.3% of supermarkets’). With so many cans at the lower natural-grocer margin, its average gross margin is about $1.61 a can, not $1.68. Second, it charges the $20,000 of trade promotions to the promoted cans, about $0.10 a can averaged over all cans, so its fixed costs are $177,000. The two differences pull in opposite directions and nearly cancel: $177{,}000 \div (1.60785 - 0.10050) = 177{,}000 \div 1.50735 \approx 117{,}425$ .

Answer. On the example’s two assumptions, fixed costs are $197,000 and the average contribution is about $1.68 a can, so the plan breaks even at 117,013 cans a year and needs 146,711 cans for a $50,000 profit: about 3.5% and 4.4% of the cans sold through Lantern’s channels. The simulator, which models the channel mix and the trade deals, puts break-even at about 117,425 cans.

What it means. The calculation turns a price into a sales target that someone can judge. A new brand that only 12% of category buyers have heard of needs roughly one can in every 29 sold in its channels just to break even. The average contribution also depends on the channel mix: if more cans sell through Lantern’s own shop ($2.30 a can), break-even falls; if more sell through natural grocers ($1.42), it rises, which is what happens in the simulator. That two different routes land within about 400 cans of each other is partly luck, so state your assumptions whenever you quote a break-even figure. Break-even volume is a target to test against evidence of demand, not a forecast.

Applied: a business decision: A value-based price for a battery system

Fictional figures

Voltwise Storage, a fictional battery-storage installer, is quoting for a cold-storage warehouse that wants a battery system to cut its peak electricity charges. The warehouse’s best alternative is a rival’s system quoted at $180,000. Voltwise’s system installs in two fewer days, and each day of installation forces the warehouse to rent refrigerated trailers at $6,000 a day. Voltwise includes a ten-year warranty; extending the rival’s seven-year warranty to ten years would cost the warehouse $15,000. Against that, Voltwise is a new name to the warehouse, whose engineers would need $4,000 of extra training on its control software. Voltwise’s variable cost for the job (equipment, labour, commissioning) is $140,000, and its usual practice is to quote cost plus 25%. What price range makes sense, and what would cost-plus leave on the table?

Reference value: the price of the next-best alternative, $180,000.
Differentiation value: the shorter installation saves $2 \times 6{,}000 = 12{,}000$ ; the longer warranty saves 15,000; the extra training costs 4,000. Net: $12{,}000 + 15{,}000 - 4{,}000 = 23{,}000$ .
Economic value: $180{,}000 + 23{,}000 = 203{,}000$ , the ceiling for a well-informed buyer. The floor is Voltwise’s $140,000 variable cost.
Cost-plus quote: $140{,}000 \times 1.25 = 175{,}000$ , which is $5,000 below the rival’s quote and $28,000 below economic value.
A value-based quote shares the $23,000 of differentiation value. At $192,000 the warehouse is $203{,}000 - 192{,}000 = 11{,}000$ better off than with the rival, and Voltwise’s contribution is $192{,}000 - 140{,}000 = 52{,}000$ instead of $175{,}000 - 140{,}000 = 35{,}000$ , a margin of $52{,}000 \div 192{,}000 \approx 27.1\%$ .

Answer. Any price between the $140,000 floor and the $203,000 economic value can win a profitable sale. A quote of about $192,000 gives the warehouse an $11,000 reason to switch and earns Voltwise $17,000 more contribution than the $175,000 cost-plus quote.

What it means. Cost-plus pricing would have undercut the rival for no reason: the warehouse would rationally pay more than the rival’s price for a system that saves it money. The value calculation also tells Voltwise what to say. The quote should show the trailer rental avoided and the warranty saving, because a buyer who doesn’t see the $23,000 will compare $192,000 with $180,000 and choose the rival.

Explore

The Marketing Mix Simulator with every decision fixed at the default plan except the price. Move the price between $1.99 and $4.99 and watch units, revenue, gross margin and contribution. The simulator’s revenue is what Lantern receives after trade margins and direct fulfilment; its contribution is what remains after cost of goods, the discounts Lantern funds on promoted cans, the other $100,000 of promotion, listing fees and the online shop’s $6,000 fixed cost, before the $60,000 launch overhead. Its break-even cans cover the overhead too; at $3.49 it shows about 117,425 rather than the challenging example’s 117,013, and the last step of that example explains the difference. Its demand comes from a model of shoppers choosing between brands, so it answers a question break-even analysis can’t: how many cans the model predicts at each price.

Common mistakes

“A 40% markup gives a 40% margin.”
A markup divides the profit by the cost; a margin divides it by the price. A 40% markup is a $0.40 \div 1.40 \approx 28.6\%$ margin, and a 40% margin needs a $0.40 \div 0.60 \approx 66.7\%$ markup. When the target is a margin, price = cost ÷ (1 − margin).
“Break-even uses the shelf price.”
Lantern never sees $3.49: supermarkets and the distributor keep 32%, so its price is $2.37. Using the shelf price gives a contribution of $2.75 a can instead of $1.63 and a break-even volume about 40% too low. Always use the price the seller receives, net of trade margins, commissions and fulfilment costs.
“Spread the fixed costs over the units and add a markup.”
Fixed costs per unit depend on volume, and volume depends on price, so a price built on average cost assumes the answer. If sales fall short, average cost rises, and a business that raises its price to cover the shortfall sells even less. Treat fixed costs as a total to be covered by contribution, which is what break-even analysis does.
“Value-based pricing means charging what the product is worth to the customer.”
Economic value is measured against the customer’s next-best alternative, not against doing without. A battery system may save a warehouse far more than its price over its life, but so would the rival’s system. The ceiling is the alternative’s price plus the value of the differences, not the whole saving.
“The break-even volume is how many we will sell.”
Break-even says how many units a price needs, not how many it will sell; the two meet only by coincidence. The useful step is the comparison. Lantern’s plan needs about 3.5% of the cans sold in its channels: is there evidence that shoppers will buy that many at $3.49?

Guided practice

Work through these with hints when you need them. Every hint and every worked solution is there to be used.

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On your own

No hints this time. Answer, check, and read the feedback; the solution appears once you have answered or if you ask for it. Your first answers count toward mastery.

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In practice

Lantern tests $3.49 from three directions

Ana’s team checks the $3.49 plan against all three starting points. Competitors first: $3.49 places Lantern between Arcadia ($2.89) and Summit ($3.79), nearer the premium brand, which matches its taste score of 7.5 against Summit’s 8 and Arcadia’s 6. Value next: the team designs a shelf test to see whether shoppers who usually buy Arcadia will pay $0.60 more for Lantern, and whether Summit buyers will trade down to it for $0.30 less. Costs last: the challenging example shows that at $3.49 the plan breaks even at about 117,000 cans, roughly 3.5% of the cans sold through the three channels it uses.

That last figure is the one a finance director will ask about. Is 3.5% of the channels’ volume plausible for a brand that only 12% of category buyers know? If the team doubts it, it has three levers: a price that earns more per can, accepting that it may sell fewer cans; lower fixed costs, such as fewer listings or a smaller promotion budget; or a channel mix that keeps more of each sale. Each is a trade-off, and the simulator in the Explore section lets you test them against a model of demand.

A hotel’s two floors

Hotel revenue managers work with the difference between the short-run and the long-run floor every day. At 6 p.m., a room unsold for tonight is worth nothing tomorrow, so any rate above the variable cost of an occupied room (cleaning, laundry, energy, amenities, booking fees) adds contribution towards fixed costs the hotel pays regardless. Over a season, though, rates must cover all the costs, and if guests learn that late rooms are cheap they stop booking early at full rates. Revenue managers therefore offer late discounts in ways that are hard for regular guests to plan around, and protect the published rate.

Value-based pricing in business markets

In business-to-business markets, value-based pricing is often done with a calculation the customer can see. A supplier documents the customer’s alternative, estimates what its offer saves or earns compared with it, and prices to share the difference, as Voltwise does in the applied example. Writing for the ICAEW, the professional body for chartered accountants in England and Wales, two pricing specialists describe a chemicals supplier that estimated its product’s differentiation value at 8% above the best alternative and, after competitive simulations and estimates of customers’ reactions, chose a price 5% above the alternative: inside the value ceiling, with a reason left for the customer to buy.

The lesson for any industry is the order of the questions. Costs answer “what is the lowest price we could accept?”, not “what should we charge?”. The price itself comes from customers’ alternatives and from competitors, and costs then tell you whether the volume that price can earn will pay.

Knowledge check

Six questions, one attempt each, no hints. Score 80% or more to complete the lesson; you can take it again at any time.

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Summary

Price is the only element of the marketing mix that earns revenue. Costs set its floor, customers’ alternatives set its ceiling, and competitors’ prices shape where in between customers will accept it.
Variable costs rise with every unit; fixed costs stay the same in total over the period. Contribution margin = price received − variable cost per unit, and the contribution margin ratio divides it by the price.
Markup is profit ÷ cost; margin is profit ÷ price. Margin = markup ÷ (1 + markup) and markup = margin ÷ (1 − margin). For a target margin, price = cost ÷ (1 − margin).
Break-even volume = fixed costs ÷ contribution per unit; add a target profit to the fixed costs for the target-profit volume. Use the price the seller actually receives.
Cost-plus and target-return prices ignore demand, so the return they promise depends on a volume forecast that the price itself affects.
Economic value = price of the next-best alternative + value of the differences. Value-based prices share that value with the customer and can sit far above cost.
At $3.49, Lantern receives $2.37 a supermarket can. If its cans sold in proportion to channel volume, it would earn about $1.68 a can across its channels and need about 117,000 cans, 3.5% of its channels’ volume, to cover $197,000 of fixed costs; the simulator, with its own channel mix and trade deals charged per can, also gives about 117,000.

Terms introduced

Fixed cost: A cost whose total stays the same over a period whatever the volume, within the range of activity planned: rent, salaries, listing fees, a committed promotion budget.
Variable cost: A cost incurred for each unit made or sold, so its total rises in proportion to volume: materials, packaging, per-unit fees, delivery.
Contribution margin: Price received minus variable cost per unit: what each unit contributes towards fixed costs and then profit. As a share of price it is the contribution margin ratio.
Break-even point: The volume (or revenue) at which total contribution equals fixed costs, so profit is zero: fixed costs ÷ contribution margin per unit.
Cost-plus pricing: Setting a price by adding a markup, a fixed percentage of the unit cost, to that cost.
Markup: Profit per unit as a percentage of cost: (price − cost) ÷ cost.
Margin: Profit per unit as a percentage of price: (price − cost) ÷ price. Also called margin on price or, in some texts, markup on selling price.
Target-return pricing: Setting the price that earns a chosen rate of return on the capital invested, at a forecast volume: unit cost + (target return × capital invested) ÷ forecast units.
Value-based pricing: Setting a price from the customer’s economic value: the price of the next-best alternative plus the value, positive or negative, of the differences from it.
Competition-based pricing: Setting a price mainly from competitors’ prices: charging the going rate in markets for similar products, or bidding against expected rival bids in sealed-bid contracts.
Price floor: The lowest price worth accepting, set by costs: in the short run the variable cost per unit; in the long run a price that covers all costs at a realistic volume.
Price ceiling: The highest price customers would pay, set by the value they place on the product compared with their alternatives.

Sources

Gomez Albrecht, M., Green, M. & Hoffman, L. (2023). Principles of Marketing, section 12.3, “The Five-Step Procedure for Establishing Pricing Policy”. OpenStax. openstax.org/books/principles-marketing/pages/12-3-the-five-…
Gomez Albrecht, M., Green, M. & Hoffman, L. (2023). Principles of Marketing, section 12.4, “Pricing Strategies for New Products” (includes break-even pricing). OpenStax. openstax.org/books/principles-marketing/pages/12-4-pricing-s…
Olivier, J.-P. Business Math: A Step-by-Step Handbook, section 6.2, “Markup: Setting the Regular Price”. LibreTexts (open textbook, CC BY-NC-SA 4.0). math.libretexts.org/Bookshelves/Applied_Mathematics/Business…
Hinterhuber, A. & Pollono, E. (2014). Financial strategy: value-based pricing, the driver to increased short-term profits. ICAEW Finance and Management Faculty, May 2014. icaew.com/technical/business-and-management/boards-and-commi…
Nagle, T. T. & Müller, G. (2018). The Strategy and Tactics of Pricing: A Guide to Growing More Profitably (6th ed.). Routledge. Chapter summaries as published by Deloitte. deloitte.com/content/dam/Deloitte/us/Documents/strategy/us-c…

Before you start

You will be able to

Review first

The idea

Fixed and variable costs

Contribution margin

In depth

Cost-plus pricing and the markup

Margin: the same profit measured on the price

Break-even analysis

Target-return pricing

Value-based pricing

Competition-based pricing

Choosing an approach

Formulas

Contribution margin per unit

Contribution margin ratio

Markup on cost and the cost-plus price

Margin on price

Converting between markup and margin

Price that gives a target margin

Break-even volume

Break-even revenue

Volume for a target profit

Target-return price

Economic value to the customer

Worked examples

Explore

Common mistakes

“A 40% markup gives a 40% margin.”

“Break-even uses the shelf price.”

“Spread the fixed costs over the units and add a markup.”

“Value-based pricing means charging what the product is worth to the customer.”

“The break-even volume is how many we will sell.”

Guided practice

On your own

In practice

Lantern tests $3.49 from three directions

A hotel’s two floors

Value-based pricing in business markets

Knowledge check

Summary

Key formulas

Terms introduced

Sources