Twice the straight-line rate on carrying amount; the final-year plug; same total, different timing
◈ 10 cardsBuild a double-declining-balance schedule that ignores residual until the final-year plug and never goes below it, and compare the three methods’ totals and timing to say which a private company might choose and why.
A rate on what is left
Some assets give most of their usefulness early — a computer, a rental fleet, a machine that is at its most productive when new. Double-declining balance front-loads the charge to match. The rate is twice the straight-line rate: the snowcat’s straight-line rate is 1 ÷ 5 = 20 %, so DDB uses 40 %. And — the part that makes the method different — the rate is applied to the carrying amount at the start of the year, not to the depreciable amount. Residual value is ignored in the arithmetic until the last year.
| Year | Opening carrying amount | × 40 % | Expense | Accumulated | Closing carrying amount |
|---|---|---|---|---|---|
| 1 | 150,000 | 60,000 | 60,000 | 60,000 | 90,000 |
| 2 | 90,000 | 36,000 | 36,000 | 96,000 | 54,000 |
| 3 | 54,000 | 21,600 | 21,600 | 117,600 | 32,400 |
| 4 | 32,400 | 12,960 | 12,960 | 130,560 | 19,440 |
| 5 | 19,440 | (7,776) | 4,440 | 135,000 | 15,000 |
Year 1 is 150,000 × 40 % = 60,000 — on cost, because that is the opening carrying amount; 135,000 × 40 % = 54,000 is the wrong base. Each later year takes 40 % of a smaller figure, so the charge falls: 36,000, 21,600, 12,960. Year 5 by formula would be 19,440 × 40 % = 7,776, which would leave the carrying amount at 11,664 — below the 15,000 residual. So the final year is a plug: the expense is whatever brings the carrying amount exactly to residual, 19,440 − 15,000 = 4,440. Had the residual been lower — say 5,000 — the formula would have applied and the last year would have been 7,776, with a small balance left to plug in a sixth year or on disposal; the rule is simply that the carrying amount never drops below residual. In Excel, =DDB(150000,15000,5,1) gives 60,000 and the function stops at residual on its own — but check the last year by hand, because the paper marks the plug.
Same total, different timing
| Year | Straight-line | Units-of-production | Declining balance |
|---|---|---|---|
| 1 | 27,000 | 31,500 | 60,000 |
| 2 | 27,000 | 27,000 | 36,000 |
| 3 | 27,000 | 28,500 | 21,600 |
| 4 | 27,000 | 25,500 | 12,960 |
| 5 | 27,000 | 22,500 | 4,440 |
| Total | 135,000 | 135,000 | 135,000 |
All three expense exactly 135,000 over the life; none is “more accurate”. What differs is the pattern: straight-line is flat, units-of-production follows the hours, declining-balance is heavy early and light late. In year 2 DDB charges 36,000 against straight-line’s 27,000 — 9,000 more expense, 9,000 less net income, and a carrying amount 42,000 lower on the balance sheet — and the difference reverses in years 4 and 5.
Why a private company gets to choose
ASPE requires a method that is rational and systematic and reflects the pattern in which the asset’s benefits are used up; within that, the choice is an accounting policy, disclosed and applied consistently. So the answer to “which method” is an argument about the pattern: straight-line when usefulness is steady with time, or when simplicity and a predictable charge matter — most private companies, most assets; declining balance when the asset is most productive early, or when repairs will rise later so that a falling amortization charge keeps the total cost of using it level; units-of-production when use varies — a snowcat’s hours swing with the snow, and the charge should swing with them. An owner who wants DDB “because it is more accurate” has the wrong reason, and an examiner will ask you to say so and then recommend from the pattern.