Variable, fixed, and the per-unit trap
◈ 8 cardsDefine variable and fixed costs by what happens in total and per unit as activity changes, and say why the contribution-margin statement is internal and never part of the ASPE set.
The same costs, sorted a different way
Every statement so far sorted costs by what they are for — cost of goods sold, salaries, rent, amortization: the function of the spending. That is what a lender and the CRA need. It is useless for the question Northlake Nordic Centre Inc.'s owner asks every autumn: if 20,000 people ski this season instead of 15,000, what happens to our costs? To answer that, the same costs must be sorted by how they behave when activity changes. Northlake's activity is measured in skier-days — one person on the trails for one day.
Variable costs
A variable cost changes in total in direct proportion to activity, and is constant per unit. Groomer fuel is about $3 per skier-day — more skiers, more grooming passes, more diesel:
| Skier-days | Fuel, total | Fuel per skier-day |
|---|---|---|
| 15,000 | 45,000 | 3.00 |
| 20,000 | 60,000 | 3.00 |
The total moves; the per-unit figure sits still. Café supplies, rental-ski maintenance and the card fees on each trail pass behave the same way.
Fixed costs
A fixed cost is constant in total across the season whatever the activity, and therefore falls per unit as activity rises. The lodge lease is 96,000 a season whether 15,000 or 20,000 people ski:
| Skier-days | Lease, total | Lease per skier-day |
|---|---|---|
| 15,000 | 96,000 | 6.40 |
| 20,000 | 96,000 | 4.80 |
The total sits still; the per-unit figure moves. Salaried staff, insurance, the straight-line amortization of the groomer and the loan interest behave the same way: they are the cost of being open, not of any particular skier.
The per-unit trap
Northlake's owner reads the second table and says: "Our lease cost per skier-day fell from 6.40 to 4.80 — we are running the lodge more efficiently." Nothing of the kind happened. The lease is the same 96,000; it was simply spread over 5,000 more skiers. A fixed cost per unit is a fraction whose denominator is the volume, and it means nothing without that volume attached. The same trap runs the other way: a bad-snow year with 12,000 skier-days puts the lease at 8.00 per skier-day, and a manager who thinks that is a cost overrun will go looking for one that does not exist.
The rule for every decision in Modules 9 and 10: think of variable costs per unit and fixed costs in total. Never quote a fixed cost per unit without stating the volume it was computed at, and never multiply a fixed-cost-per-unit figure by a different volume.
Where this statement lives
Sorting costs by behaviour produces the contribution-margin (CM) format income statement (L9.6): sales, less variable costs, gives contribution margin; less fixed costs, gives operating income. It is a managerial statement — prepared for the owner, the manager, the pricing decision — and it is never part of the ASPE statement set. The external income statement classifies by function; the bank, the CRA and the family investors get that one. The CM statement is what Northlake uses to decide, and its figures are the same dollars re-sorted, so the bottom line agrees.