Time-based versus use-based; the schedule

One machine, two patterns

On 1 January of its third year Northlake Nordic Centre Inc. buys a snowcat for 150,000. It expects to run it five winters, or about 9,000 engine hours, and then sell it for 15,000. The depreciable amount is 150,000 − 15,000 = 135,000 — that much, and no more, will be expensed over the snowcat’s life. The question every method answers differently is how much of it in each year.

Straight-line: the same charge every year

If the snowcat gives up its usefulness evenly with time, the charge is the same each year:

$$\text{Annual amortization}=\frac{\text{Cost}-\text{Residual}}{\text{Useful life}}=\frac{150,000-15,000}{5}=27,000$$

The schedule ends at the residual value, which is the check: five charges of 27,000 exhaust the 135,000 and leave the asset at exactly what Northlake expects to sell it for. The year-end entry is the one from Module 5 — Dr Amortization Expense 27,000 / Cr Accumulated Amortization – Equipment 27,000. The asset account itself is never credited; its cost stays at 150,000 until the machine leaves. In Excel, =SLN(150000,15000,5).

Units-of-production: a charge per hour

A snowcat’s wear follows its engine hours more than the calendar — a long snowy winter uses it up faster than a short one. Units-of-production charges by use. First a rate:

$$\text{Rate per hour}=\frac{\text{Cost}-\text{Residual}}{\text{Total expected hours}}=\frac{135,000}{9,000}=15.00\text{ per hour}$$

Then each year’s charge is the rate times that year’s hours: year 1 at 2,100 hours → 2,100 × 15 = 31,500; year 2 at 1,800 hours → 27,000; carrying amount after two years 150,000 − 58,500 = 91,500. The rate is on the depreciable amount, not on cost — 150,000 ÷ 9,000 = 16.67 an hour would expense the residual value too, and by the end the carrying amount would be 0 instead of 15,000.

The cap

Estimates are estimates. Suppose the snowcat actually runs 2,100, 1,800, 1,900 and 1,700 hours in years 1–4 — 7,500 hours, 112,500 of amortization — and then 1,900 hours in year 5. At 15 an hour that would be 28,500, taking total amortization to 141,000 and the carrying amount to 9,000, below the residual value. Amortization never goes past the depreciable amount: only 1,500 hours’ worth (135,000 − 112,500 = 22,500) remains, so year 5’s charge is 22,500, whatever the hours, and the carrying amount stops at 15,000. Conversely, if the machine runs fewer than 9,000 hours in five years, the unamortised balance simply waits — or the estimate is revised (L11.4).

Which one

Straight-line fits an asset that wears with time — a building, a lodge roof, office furniture. Units-of-production fits one whose wear tracks output — a vehicle by kilometres, a machine by hours, a gravel pit by tonnes — and it makes the expense variable, moving with the season, which is why Module 9 said an amortization charge can be either a fixed or a variable cost depending on the method chosen.