What each skier-day contributes toward fixed costs

Twenty-one dollars a skier

Northlake Nordic Centre Inc. sells a skier-day for 30. Serving it costs 9 of variable cost — fuel, café supplies, rental wear, card fees (L9.3). The other 21 is what that skier-day contributes toward the season's fixed costs, and once the fixed costs are covered, toward operating income:

$$\text{CM per unit}=\text{Price}-\text{Variable cost per unit}=30-9=21$$

Every skier-day adds 21 — no more, no less, inside the relevant range. That is why the owner's question in L9.1 ("what if 20,000 ski instead of 15,000?") has a one-line answer: 5,000 more skier-days contribute 5,000 × 21 = 105,000 more.

In total, and as a ratio

At 20,000 skier-days the season's sales are 600,000, variable costs 180,000, and total contribution margin 420,000:

Sales                    20,000 × 30   600,000
Less: variable costs     20,000 × 9    180,000
Contribution margin      20,000 × 21   420,000

The contribution margin ratio is CM as a share of sales. It comes out the same per unit and in total, because both are the same 21-in-30:

$$\text{CM ratio}=\frac{21}{30}=\frac{420,000}{600,000}=0.70$$

and since variable costs take the other 30 cents of every sales dollar, the variable-cost ratio is 9 ÷ 30 = 0.30 and the CM ratio is 1 − 0.30. The ratio is the tool for a business without a single unit — Bramble Lane Outfitters Ltd. cannot say what a "unit" of headlamps-and-canoes contributes, but it can say that 31 cents of every sales dollar does — and it is the tool for break-even in dollars (L10.2). The denominator is always sales: CM ÷ variable cost (21 ÷ 9 = 2.33) is a number, but it is not a ratio anyone uses.

Contribution margin is not gross margin

Bramble Lane's gross margin was 35 % (L8.1): net sales 75,000 less cost of goods sold 48,750. Its contribution margin ratio is lower. Gross margin is cut by function — sales less the cost of the goods, and nothing else. But the store also pays card fees of 1,500 and delivery of 1,500 in that quarter, both of which rise with sales and sit below gross profit among operating expenses on the functional statement. Contribution margin is cut by behaviour — sales less every variable cost, wherever the functional statement files it:

Net sales                          75,000
Variable costs  48,750 + 1,500 + 1,500   51,750
Contribution margin                23,250     ratio 0.31

Gross margin 35 %, CM ratio 31 %. For a service business like Northlake there is no cost of goods sold and no gross margin at all — only a CM. The two are different cuts of the same statement and a case that gives you both is checking that you know which costs each one subtracts.

Cedar Ridge Golf Club Ltd.

Green fee 55; variable cost 3.00 a round; 30,000 rounds. CM per round 52; total CM 30,000 × 52 = 1,560,000; CM ratio 52 ÷ 55 = 0.9455. A golf club is nearly all fixed cost, so almost every dollar of a green fee is contribution — which is why a rained-out weekend hurts a club far more than it hurts a retailer.