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Price minus variable cost: what one more sale is worth, why it is not profit per unit, and the decisions it settles.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will work out what one sale contributes, total that across a month, and take the fixed costs off once at the end to get profit. You will also use contribution to settle the decisions it settles — whether an extra order is worth taking, and which of two products to push when something is scarce — and name what the arithmetic leaves out.
Dilla sells soup from a market stall. A cup goes for 6 dollars, and the soup, cup and lid in it cost her 2 dollars 40.
The pitch, the license and the insurance come to 1,080 dollars a month whatever she sells.
A depot has offered to take 200 cups a month at 4 dollars each, collected at closing time.
The pan holds them and the order costs her no market hours.
Her brother says 4 dollars is under what a cup costs once the pitch is counted in, so she should refuse.
March has 24 trading days, and Dilla needs 1,440 dollars of takings in the month to come out even.
Nine days in, the tin holds 460 dollars.
Two of those nine were the wettest days of the year and the market was half empty.
Her market pitch costs 1,080 dollars a month and sold 900 cups in a good month.
A pitch outside the station costs 1,400 a month, and last year's trader there sold about 1,200 cups.
Nobody has counted this year.
You can split costs into fixed and variable, cost a unit, and state a price as a markup or a margin. This lesson puts the variable half of the costs against the price and gets the most useful number in the course: what one sale is worth to the business. Every decision in the rest of the course — break-even, targets, whether to take an order, which product to push — is made with it.
| Term | What it means |
|---|---|
| Contribution | Price minus variable cost: what one sale gives the business toward its fixed costs. |
| Total contribution | Contribution per sale times the number of sales in the period. |
| Contribution margin | Contribution as a percentage of the price. |
| Profit | Total contribution minus the fixed costs, taken off once for the period. |
| Spare capacity | Time, space or equipment that would otherwise sit idle this period. |
| Constraint | The scarce thing that limits how much the business can do: bench hours, oven space, stock. |
| Contribution per unit of constraint | Contribution divided by how much of the scarce thing one sale uses. |
Read the offer. Two people are looking at the same stall and reaching opposite answers, and neither is being careless.
Her brother is right that 4 dollars is below what a cup costs once the pitch is counted in. Sell every cup at 4 dollars and the stall closes. And the order still puts money on the table, because the pitch is paid for whether the pan is full or half full.
Something is at stake either way. Refusing hands back money the stall needs. Accepting starts a habit of pricing under cost, and the depot will ask again in June for 300.
The number that settles it is below. The one they were arguing about — cost per unit — does not.
$$\text{contribution} = \text{price} - \text{variable cost}$$
It is not profit on one unit, and the difference is the whole point. Profit needs the fixed costs, and those belong to the month rather than to any sale — so they are taken off once, from the total, at the end:
$$\text{profit} = (\text{contribution} \times \text{units sold}) - \text{fixed costs}$$
Contribution is the number that answers decisions. What does one more sale do for me? It adds its contribution. Which of these two products should I push? The one contributing more per unit of whatever is scarce. Is this order worth taking? If it contributes anything and costs no capacity you had a better use for, yes.
Allocated fixed cost answers none of those, because it moves when you change the allocation method and again when the volume changes. Contribution does neither.
Another way: steps
Another way: table
One lunch box at 8 dollars, 5 of it variable, against 1800 of fixed cost.
| Boxes sold | Contribution | Fixed cost | Profit |
|---|---|---|---|
| 300 | 900 | 1800 | −900 |
| 600 | 1800 | 1800 | 0 |
| 900 | 2700 | 1800 | 900 |
The contribution column rises in a straight line, the fixed column never moves, and the profit column crosses zero exactly once. That crossing is break-even, and the next lesson goes and finds it.
List what the sale causes. Materials used, the payment fee, packaging, delivery, and the owner's hours in the unit if they are being costed as a costing input. These are the variable costs of one sale. Leave out anything that is paid for the month whether or not this sale happens.
Subtract from the price. Contribution per sale is price minus that variable cost. If it is negative, the sale loses money on its own terms and no volume will help.
Total over the period. Contribution per sale times the sales. If several products are sold, total each and add.
Take the fixed costs off once. Total contribution minus the period's fixed costs is the profit.
Use it for the decision in front of you. For an extra order, the change in profit is the order's total contribution, provided it uses capacity that would otherwise sit idle and displaces no full-price sale. For a choice between products competing for the same scarce resource, divide each contribution by how much of the resource one sale uses.
Two checks. Revenue minus all variable costs minus fixed costs must give the same profit as the contribution route; if not, a cost is in the wrong group. And the per-sale contribution should not change when volume changes: if it does, a fixed cost has crept into it.
The arithmetic of an extra order is simple: if the price is above the variable cost and the capacity is spare, the month is better off by the order's total contribution. That is why hotels sell last-minute rooms cheaply, why airlines sell standby seats, and why a bakery sells the day's leftovers at half price at closing time. The room, the seat and the oven are already paid for.
But three things sit outside the arithmetic, and each can outweigh it. Displacement: if the cheap order uses time that a full-price customer would have booked, its real cost includes the contribution lost on that customer. Reference prices: a customer who pays 4 once expects 4 again, and so may others who hear of it. Capacity that is not really spare: an owner who takes every marginal job can fill the week with work that barely contributes, leaving no room for the work that pays the rent.
So the rule is: contribution tells you what an order is worth on its own; judgment about customers and capacity tells you whether on its own is the right way to look at it.
A practical habit follows. Before quoting a low price, write down three things beside the contribution: which customer or hour it might displace, what the customer will be told the price is for, and how much of the month's capacity the order uses. If all three are comfortable, the contribution is the answer. If any one of them is not, the order needs a better price, a smaller size or a different day before it is worth taking.
Most small businesses are limited by one thing at a time: the owner's hours, the bench, the oven, the stall's display space, the cash to buy stock. When one thing is the limit, the right comparison between products is contribution per unit of that thing, not contribution per sale.
A kitchen whose oven is full every morning should compare dishes by contribution per oven-hour. A stall with a small table should compare lines by contribution per shelf-meter. A repair shop with one bench should compare jobs by contribution per bench-hour. The product that earns most per sale is often not the one that earns most per hour of the constraint, and a business that pushes the wrong one is busy and short at the same time.
When the constraint changes — a second oven, an extra helper — the ranking can change too, so the calculation is worth repeating whenever the limit moves.
The same reasoning works for money as a constraint. A stall owner with 300 dollars to spend on stock before market day should compare lines by contribution per dollar of stock: a crate of mangoes costing 20 that contributes 10 returns half its cost, while a box of herbs costing 6 that contributes 5 returns more than four-fifths. When the cash runs out before the table does, the herbs are the better use of it, even though each crate of mangoes contributes twice as much. Name the constraint first; the right ranking follows from it.
A small theater has 180 seats and puts on a play five nights a week. Its fixed costs for a week — the cast, the crew, the hall, the lighting — come to 9,000 dollars whether the house is full or empty. The variable cost of one more audience member is tiny: about 2 dollars for the ticket fee, a program and extra cleaning. Full-price tickets are 30 dollars, so each contributes 28.
Tuesdays usually sell only 80 seats. The theater starts selling unsold Tuesday seats at 12 dollars through a same-day app. Each of those contributes 12 − 2 = 10 dollars. If 60 extra people come, the week gains 600 dollars of contribution that would otherwise not exist — and the fixed costs are exactly what they were.
The theater's managers watch for the risks outside the arithmetic. They keep the cheap seats to the day of the performance, so people who would have paid 30 in advance do not simply wait; they do not offer them on Fridays and Saturdays, when the house fills anyway; and they check each month whether full-price Tuesday sales have fallen since the app began. The number that starts the conversation is contribution; the conditions around it are what keep it honest.
Retailers call contribution per unit of shelf space space productivity and rearrange shelves by it. A slow-selling item with a high margin can earn less per meter of shelf than a fast-selling one with a low margin, and the shelf, not the margin, is what the shop is short of.
Subtracting a share of the rent as well. That gives profit per unit, not contribution, and profit per unit changes when volume changes without anything real having happened.
Refusing any price below full cost. With the rent already paid and the capacity idle, a sale above variable cost leaves the business better off. The real risks — displacing full-price work, resetting what a customer expects to pay — are worth weighing, and neither is the arithmetic.
Pushing the highest-margin line. Highest contribution per unit of the scarce thing. If the bench is the constraint, a 9 dollar contribution taking an hour beats a 20 dollar one taking three.
Taking fixed costs off every sale. They come off once, from the total. Subtracting them per unit makes every quiet month look catastrophic and every busy one look impossible.
Find the contribution of a 50-dollar repair using 18 of parts and fees.
$50 - 18 = 32$
Price minus what the sale causes.
Total it over seventy repairs in the month.
$70 \times 32 = 2240$
The month's pot of contribution.
Take the fixed costs of 1600 off once.
$2240 - 1600 = 640$
Profit for the month.
Find what one more repair adds.
$+32$
The fixed costs do not move with one more repair.
Compare with the average profit per repair.
$640 \div 70 \approx 9.14 \ne 32$
An average does not tell you what the next one does.
Write the two jobs: a screen contributes 32 in 45 minutes; a board repair contributes 50 in two hours.
$\text{screen } 32; \quad \text{board } 50$
Per sale, the board repair looks better.
Find the screen's contribution per bench hour.
$32 \div 0.75 \approx 42.67$
The bench is what is scarce.
Find the board's contribution per bench hour.
$50 \div 2 = 25$
The bigger job earns less from each hour.
Fill a 30-hour week with screens.
$30 \times 42.67 \approx 1280$
The better rate on every hour.
Fill the same week with boards.
$30 \times 25 = 750$
The same bench, far less contribution.
State the rule.
$\text{rank by contribution per unit of the constraint}$
Per sale is the wrong measure when one thing is scarce.
Write the stall's numbers from the reading: cups sell at 6, the soup, cup and lid cost 2.40, and the pitch, license and insurance are 1080 a month.
$6 - 2.40 = 3.60 \text{ contribution}$
Per normal sale.
The depot offers 4 a cup for 200 cups. Find the order's contribution per cup.
$4 - 2.40 = 1.60$
Only the variable cost is caused by the order.
Total it over the order.
$200 \times 1.60 = 320$
Money the month would not otherwise have.
Find the full cost her brother used, if she sells 400 cups a month.
$2.40 + 1080 \div 400 = 2.40 + 2.70 = 5.10$
Above the offer, which is why he said no.
Check the capacity.
$\text{the pan holds them; no market hours used}$
No full-price customer is turned away, so nothing is displaced.
Weigh the reference-price risk.
$\text{a bulk price for collection at closing, stated as such}$
Naming it as a bulk price keeps the stall's normal price intact.
Decide on the numbers and the judgment together.
$+320 \text{ a month, with the bulk terms written down}$
Contribution settles the arithmetic; the terms handle the risk outside it.
Find what one crate contributes.
$25 - 20 = 5$
Price less variable cost.
Total the contribution for the month.
$180 \times 5 = 900$
Per sale times the sales.
Take the fixed costs off once.
Maya's Ceramics has met its fixed costs for the month and has spare capacity. A customer offers $16$ dollars each for $40$ mugs — below the usual $25$, and below what the mugs cost once a share of the fixed costs is added in. Variable cost is $13$. What do the numbers say?
Complete the worked solution: a unit sells for $11$ dollars with a variable cost of $6$. The business sold $215$ this month and its fixed costs were $1016$. What was the month's profit?
Find the contribution per sale.
$11 - 6 =$ m
Price minus the costs the sale itself causes.
Total the contribution for the month.
$(\text{contribution}) \times 215 =$ t
Every sale adds its contribution to the pot.
Take the fixed costs off once.
$(\text{total}) - 1016 =$ p
Fixed costs belong to the month, not to any sale.
Find what one more sale would add.
$\text{one more sale} \Rightarrow + (\text{contribution})$
The fixed costs do not move, so the next sale adds exactly its contribution.
Check against the total revenue and total cost.
$215 \times 11 - 215 \times 6 - 1016 = (\text{profit})$
Revenue minus all costs gives the same profit.
A crate of mangoes at Monica's Market Stall sells for $25$ dollars and costs $20$ in materials, labor and fees that only happen when it is sold. The month's fixed costs are $750$, spread over the $200$ sold that works out at $3.75$ a unit. What does one sale contribute, in dollars?
Answer:
Maya's Ceramics sold $120$ mugs at $25$ dollars with a variable cost of $13$, against fixed costs of $1200$ for the month. What was the month's profit, in dollars?
Answer:
A repair bench is open $32$ hours a week and is always busy. A screen job contributes $31$ dollars and takes 1 hour; a board job contributes $58$ dollars and takes 2 hours. If the week is filled with the job that contributes more per bench hour, what is the week's total contribution, in dollars?
Answer:
Maya's Ceramics sells a mug for $25$ dollars, of which $13$ is variable cost, and sold $120$ of them last month. Its fixed costs were $1200$. Fill in what the sales contributed.
| Amount | |
|---|---|
| Price of one mug, dollars | 25 |
| Variable cost of one, dollars | 13 |
| Contribution per sale, dollars | |
| Contribution margin, percent of price | |
| mugs sold in the month | 120 |
| Total contribution for the month, dollars |
A stationery shop sells pens at $5$ dollars costing $3$, and desk lamps at 34 dollars costing 25. Last week it sold $161$ pens and $2$ lamps. How many dollars more did the pens contribute than the lamps?
| Amount | |
|---|---|
| Pens' contribution for the week, dollars | |
| Lamps' contribution for the week, dollars | |
| How much more the pens contributed, dollars |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Bright Home Cleaning sells a standard clean for $64$ dollars, of which $34$ is variable cost, and sold $45$ of them last month. Its fixed costs were $900$. Fill in what the sales contributed.
| Amount | |
|---|---|
| Price of one standard clean, dollars | 64 |
| Variable cost of one, dollars | 34 |
| Contribution per sale, dollars | |
| Contribution margin, percent of price | |
| standard cleans sold in the month | 45 |
| Total contribution for the month, dollars |
You can find contribution per sale, total it, get a month's profit from it, and rank products by contribution per unit of what is scarce. Tell someone why contribution is not profit on one unit, and why that difference matters when a customer offers you a low price. Next: the volume at which the total contribution exactly meets the fixed costs.
16. Your turn: a crate at 25, variable cost 20, 180 sold, fixed 750, step 3
$900 - 750 = 150$
The month's profit.