When the straight line holds; picking the driver
◈ 7 cardsRecognise mixed and step costs, state what the relevant range is and why extrapolating outside it fails, and choose the activity driver for a service business.
Two more shapes
Not every cost is purely fixed or purely variable. Two other shapes appear on every cost list, and a case will plant one of each.
A mixed cost has a fixed part and a variable part. Northlake Nordic Centre Inc.'s hydro bill is a 1,400 monthly connection charge — payable in a month with no snow at all — plus snowmaking and lighting power that rises with skier-days, about 0.90 per skier-day. At 12,000 skier-days the month costs 1,400 + 0.90 × 12,000 = 12,200. Neither the fixed nor the variable description fits the whole bill; the two parts have to be separated (L9.4) before the bill can be predicted.
A step cost is fixed over a band of activity and then jumps. Ski patrol runs one patroller per 1,500 skier-days a day; at 1,501 a second is rostered, and the cost doubles in one stride. Over a narrow range a step cost behaves as fixed; over a wide one it climbs like a staircase. Salaried staff who are added by the shift are steps too — which is why direct labour is always variable is a manufacturing rule that does not survive a ski hill.
The relevant range
The lodge lease is 96,000 — within the range the lodge can serve, roughly 10,000 to 30,000 skier-days a season. Beyond 30,000 Northlake would need a second lodge, and the "fixed" cost would step. Below 10,000 it might sublet half. The relevant range is the band of activity inside which the fixed/variable descriptions hold and the cost line is straight. Every cost equation in this module is a straight line drawn through that band, and extrapolating outside it is a guess: a variable cost may earn volume discounts at high volumes (curving down), a fixed cost may step, and the neat total = fixed + variable × units stops being true.
| Skier-days | Lease | Patrol | Hydro |
|---|---|---|---|
| 8,000 | ? — below the range | 6 patroller-days | 8,600 |
| 15,000 | 96,000 | 10 | 14,900 |
| 25,000 | 96,000 | 17 | 23,900 |
| 35,000 | ? — a second lodge | 24 | ? |
What is one unit of Northlake?
Everything above was measured per skier-day, and that choice is the first decision in any cost analysis. The activity driver (or cost driver) is the measure of volume that the variable costs actually follow. For Northlake it is the skier-day: grooming, café supplies, rental wear and card fees all rise with the number of people on the trails. It is not revenue dollars — a season pass and a day pass produce different dollars for the same trail wear — and not the number of passes sold, because a season-pass holder generates thirty skier-days and a day-pass holder one.
Other service businesses have their own: a golf club counts rounds played; a motel counts room-nights; a clinic counts patient visits; a trucking firm counts kilometres. A merchandiser such as Bramble Lane Outfitters Ltd. usually has to use sales dollars, because a headlamp and a canoe are not one unit of anything — which is why its analysis runs on ratios (L9.5) rather than per-unit figures.