Lesson 3.2 35 min
Contribution margin
Contribution per unit and as a ratio, then product mix and testing a price change before you make it.
Contribution margin is what each sale leaves after its variable costs, available to cover fixed costs and then to produce profit. Gross margin, from lesson 1.2, is an accounting measure that follows the financial statements. Contribution margin is a decision measure that follows cost behaviour. They differ whenever cost of goods sold includes fixed costs or operating expenses include variable ones.
Per unit and as a ratio
Contribution margin per unit = Price − Variable cost per unit
Contribution margin ratio = Contribution margin per unit ÷ Price
The per-unit figure answers "how much does one more sale add?" The ratio answers "how much of each sales dollar is left?" The ratio is useful when units are hard to define, such as a plumbing company that sells hours, parts and permits on one invoice.
Finding the variable cost of a product
A careful variable cost includes everything that would not be spent if the sale didn't happen. For a cafe drink that means the ingredients, the cup, lid and sleeve, and the card processing fee, which is a percentage of the price. Wages for staff already scheduled, rent and the espresso machine are not variable with one drink.
Card fees are an easy item to leave out. Northside pays 2.5% of each sale to its processor in this case. On a latte that is 14 cents, about a tenth of the drink's variable cost.
Product mix
A business that sells several products has a weighted average contribution margin that depends on the mix. Selling more of a high-ratio product raises the average even if total sales stay the same. This is the logic behind putting the drip coffee by the till and the muffins behind the counter, and behind pricing a service call so the first hour carries a higher rate.
When a constraint limits output, the product to push is the one with the highest contribution per unit of the constraint, not per unit of product. A cafe with one espresso machine and a morning queue should look at contribution per minute of machine time.
Testing a price change
Before cutting or raising a price, compute the volume needed to keep total contribution where it is.
Break-even volume after a price change = Current total contribution ÷ New contribution per unit
If the volume you expect is above that figure, the change adds contribution. If it is below, it loses money even though sales may rise. The calculation is easy to do on a napkin and stops a price cut being judged by its effect on revenue alone.
Worked case
Northside's menu, and Hartley's hour
Northside's three biggest sellers, with variable costs built up from their parts. Card fees are 2.5% of the price, rounded to the cent.
| Item | Components | Total |
|---|---|---|
| Latte | espresso, double shot 0.42, milk 0.48, cup and lid 0.22, card fee 0.14 | 1.26 |
| Drip coffee | brewed coffee 0.24, cup and lid 0.22, card fee 0.08 | 0.54 |
| Muffin | muffin, wholesale 1.80, bag 0.05, card fee 0.10 | 1.95 |
| Item | Price | Variable cost | Contribution | Ratio |
|---|---|---|---|---|
| Latte | 5.50 | 1.26 | 4.24 | 77.1% |
| Drip coffee | 3.00 | 0.54 | 2.46 | 82.0% |
| Muffin | 4.00 | 1.95 | 2.05 | 51.2% |
The drip coffee has the highest ratio at 82.0% but leaves less per cup than the latte. The latte leaves $4.24 per cup and on a typical day earns more than half the total contribution. The figures below are for a single sample day, a Tuesday in March, and are not tied to the annual totals in module 1.
| Item | Units | Revenue | Contribution |
|---|---|---|---|
| Latte | 100 | 550.00 | 424.00 |
| Drip coffee | 90 | 270.00 | 221.40 |
| Muffin | 40 | 160.00 | 82.00 |
| Total | 980.00 | 727.40 |
The owners consider cutting the drip price from $3.00 to $2.50 to win morning commuters. At the new price, the card fee falls to $0.06 and contribution per cup is $1.98. To keep the current daily contribution of $221.40 from drip coffee, Northside would need to sell 111.8 cups a day, up from 90. They expect about 130, which would give $257.40, a gain of $36.00 a day. The decision then rests on whether 130 is realistic and whether the queue can handle it.
For Hartley, a billable hour brings in $177 ($125 of labour and $52 of materials) against variable costs of $47, for a contribution of $130 per hour and a ratio of 73.45%.
Template
Menu contribution and price test
Build up the variable cost of each product from its parts and a card fee rate, see contribution per unit, ratio and daily totals, and test a price change against the break-even volume. Northside's menu is loaded.
The full working file, 3-2-contribution-margin.xlsx, is in the Accounting and Finance Toolkit, Part 1. The lesson above teaches the method and shows the worked numbers, so you can build it yourself in any spreadsheet.
Exercises
Work these, then open the answers
A muffin supplier offers a 20-cent discount if Northside commits to a larger order. What is the new muffin contribution and ratio?
Answer
Variable cost falls from 1.95 to 1.75, so contribution rises from 2.05 to 2.25, and the ratio from 51.2% to 56.3% (2.25 ÷ 4.00).
Explain why Hartley's plumber wage is excluded from the contribution per hour.
Answer
The plumbers are salaried, so billing one more hour doesn't change total wages. Wages are part of fixed costs in this model.
Northside considers raising the latte price to $5.75. Card fee becomes $0.14 (2.5% of 5.75 = 0.14375, rounded). How many lattes a day keep contribution at today's level?
Answer
New contribution = 5.75 − (0.42 + 0.48 + 0.22 + 0.14) = 4.49. Today's latte contribution is 4.24 × 100 = 424. Break-even volume = 424 ÷ 4.49 = 94.4 lattes. If sales stay above about 95, the increase adds contribution.
Check
4 questions
Sources
Sources
- Principles of Accounting, Volume 2: Managerial Accounting, OpenStax, Rice University