Depreciation Methods Explained: SL, SYD, DB
Straight line, sum-of-the-years-digits and declining balance on the same £48,000 asset. What each schedule does to book value, to tax, and to the DEPR worksheet.
The short answer
Straight line spreads the depreciable base evenly, sum-of-the-years-digits weights it by remaining life, and declining balance applies a fixed percentage to a falling book value. All three write off the same total — only the timing differs. On a £48,000 asset falling to £6,000 over six years, year one is £7,000 by straight line, £12,000 by SYD and £16,000 by 200% declining balance. Earlier deductions are worth more in present value, so the choice is a cash flow decision dressed as an accounting one.
Depreciation methods argue about one thing only: which years get the deduction. Every method in the DEPR worksheet writes off exactly the same total, so nothing about the asset changes when you switch between them. What changes is when the tax relief arrives — and money arriving sooner is worth more.
That makes the choice a cash flow question rather than a bookkeeping one. Here is what each method does to the same machine, and what the differences are worth.
What every method has in common
-
Depreciable base = Cost − Salvage
On the BA II Plus this is RDV at the start: remaining depreciable value. RBV, the remaining book value, includes the salvage and therefore never falls below it.
A commercial oven costs £48,000, has a six-year useful life and an expected residual value of £6,000.
The depreciable base is £42,000. Every method below writes off £42,000 and leaves book value at
£6,000. The distinction between RBV and RDV is worth fixing early: at the end of year one under
straight line, RBV is £41,000 and RDV is £35,000, because £6,000 of the book value is salvage that will
never be depreciated.
Straight line: the same charge every year
-
Annual charge = (Cost − Salvage) ÷ Life = 42,000 ÷ 6 = 7,000
£7,000 a year, six times. That is 16.67% of the base annually, and by the end of year three exactly half the base has gone. Straight line is the default for financial reporting in most jurisdictions because it matches the way most assets are actually used — evenly — and because it is impossible to get wrong.
Sum-of-the-years-digits: front-loaded, but bounded
SYD weights each year by the life remaining at its start, over the sum of all the digits.
-
Year k charge = (Life − k + 1) ÷ (1 + 2 + … + Life) × Base
For a six-year life the denominator is 21, so the fractions run 6/21, 5/21, 4/21, 3/21, 2/21, 1/21.
| Year | Fraction | Charge | Accumulated | Book value |
|---|---|---|---|---|
| 1 | 6/21 | £12,000.00 | £12,000.00 | £36,000.00 |
| 2 | 5/21 | £10,000.00 | £22,000.00 | £26,000.00 |
| 3 | 4/21 | £8,000.00 | £30,000.00 | £18,000.00 |
| 4 | 3/21 | £6,000.00 | £36,000.00 | £12,000.00 |
| 5 | 2/21 | £4,000.00 | £40,000.00 | £8,000.00 |
| 6 | 1/21 | £2,000.00 | £42,000.00 | £6,000.00 |
Year one takes 28.57% of the base and the first three years take 71.43%. SYD needs no adjustment at the end — the fractions sum to exactly 1, so the schedule lands on salvage by construction.
Declining balance: a percentage of a shrinking number
Declining balance ignores salvage while computing the charge. It applies a fixed rate — a stated multiple of the straight line rate — to the opening book value.
-
Rate = Factor ÷ Life = 200% ÷ 6 = 33.3333% of opening book value
| Year | Opening book value | Charge at 33.3333% | Book value |
|---|---|---|---|
| 1 | £48,000.00 | £16,000.00 | £32,000.00 |
| 2 | £32,000.00 | £10,666.67 | £21,333.33 |
| 3 | £21,333.33 | £7,111.11 | £14,222.22 |
| 4 | £14,222.22 | £4,740.74 | £9,481.48 |
| 5 | £9,481.48 | £3,160.49 | £6,320.99 |
| 6 | £6,320.99 | £320.99 | £6,000.00 |
Year one is £16,000 — 38.10% of the base, more than double straight line. But the schedule ends awkwardly. Pure declining balance would charge £2,107.00 in year six and leave book value at £4,213.99, below the £6,000 salvage. The worksheet therefore charges only what is left to write off: £320.99, a stub fifty times smaller than the first year’s charge.
DBX: declining balance with a crossover
DBX fixes the tail by switching to straight line as soon as straight line on the remaining depreciable
value would give a bigger charge. On this asset, it never does.
| Year | DB charge | Straight line alternative | Larger |
|---|---|---|---|
| 3 | £7,111.11 | £3,833.33 | DB |
| 4 | £4,740.74 | £2,740.74 | DB |
| 5 | £3,160.49 | £1,740.74 | DB |
The £6,000 salvage keeps the straight line alternative small, so declining balance stays ahead for the whole
life and DBX produces exactly the same schedule as DB. Drop the salvage to zero and the picture
changes:
| Year | DB | DBX |
|---|---|---|
| 1 | £16,000.00 | £16,000.00 |
| 2 | £10,666.67 | £10,666.67 |
| 3 | £7,111.11 | £7,111.11 |
| 4 | £4,740.74 | £4,740.74 |
| 5 | £3,160.49 | £4,740.74 |
| 6 | £6,320.99 | £4,740.74 |
Both write off £48,000. DB limps down to £3,160.49 and then mops up £6,320.99 in a single year; DBX
levels off at £4,740.74 for the last three. A 150% factor crosses over on the original asset too, in year
5, where the charge stops falling and settles at £4,593.75 for the final two years.
The four schedules side by side
| Year | Straight line | SYD | DB 200% | DB 150% |
|---|---|---|---|---|
| 1 | £7,000.00 | £12,000.00 | £16,000.00 | £12,000.00 |
| 2 | £7,000.00 | £10,000.00 | £10,666.67 | £9,000.00 |
| 3 | £7,000.00 | £8,000.00 | £7,111.11 | £6,750.00 |
| 4 | £7,000.00 | £6,000.00 | £4,740.74 | £5,062.50 |
| 5 | £7,000.00 | £4,000.00 | £3,160.49 | £3,796.88 |
| 6 | £7,000.00 | £2,000.00 | £320.99 | £5,390.63 |
| Total | £42,000.00 | £42,000.00 | £42,000.00 | £42,000.00 |
| Method | Year 1 share | Through year 2 | Through year 3 |
|---|---|---|---|
| Straight line | 16.67% | 33.33% | 50.00% |
| SYD | 28.57% | 52.38% | 71.43% |
| DB 200% | 38.10% | 63.49% | 80.42% |
By the end of year three, declining balance has claimed 80.42% of the deduction against straight line’s 50%. That 30-point gap is the entire substance of the choice.
What the timing is actually worth
Tax relief is worth its present value, not its face value. At a 25% tax rate the total shield is £10,500 under every method — £42,000 × 25%. Discount it at 9%:
| Method | Total shield | PV of shield | Advantage over straight line |
|---|---|---|---|
| Straight line | £10,500.00 | £7,850.36 | — |
| SYD | £10,500.00 | £8,411.56 | £561.20 |
| DB 200% | £10,500.00 | £8,687.97 | £837.61 |
£837.61 on a £48,000 asset — about 1.7% of the purchase price, free, for choosing a different schedule. That figure is why accelerated depreciation exists as a policy lever and why capital allowance regimes are written the way they are. It also belongs in any cash flow analysis of an equipment purchase: the shield is a real cash inflow even though depreciation itself is not a cash outflow.
Book value, and the tax on selling early
The other consequence of method choice appears when an asset is sold before the end of its life, because the gain or loss is measured against book value.
| Method | Book value | Sale at £30,000 | Result |
|---|---|---|---|
| Straight line | £34,000.00 | −£4,000.00 | Deductible loss |
| SYD | £26,000.00 | £4,000.00 | Taxable gain |
| DB 200% | £21,333.33 | £8,666.67 | Taxable gain |
The same asset, the same price, the same date — and a £12,666.67 swing in taxable income, entirely from the depreciation method. Accelerated methods pull relief forward and then claw some of it back on disposal, which is worth remembering before treating the £837.61 above as pure gain.
M01: when the asset does not arrive in January
M01 prorates the first year by (13 − M01) ÷ 12 and pushes the remainder onto an extra calendar year. An
oven commissioned in July has M01 = 7, giving half a first year.
| Calendar year | Straight line | SYD |
|---|---|---|
| 1 | £3,500.00 | £6,000.00 |
| 2 | £7,000.00 | £11,000.00 |
| 3 | £7,000.00 | £9,000.00 |
| 4 | £7,000.00 | £7,000.00 |
| 5 | £7,000.00 | £5,000.00 |
| 6 | £7,000.00 | £3,000.00 |
| 7 | £3,500.00 | £1,000.00 |
Both still total £42,000. The straight line version simply splits the first and last rows; the SYD version blends two adjacent fractions in every row, which is why its year 2 charge of £11,000 sits between the £12,000 and £10,000 of the unprorated schedule.
Doing it on the calculator
Year 1 under 200% declining balance.
-
2ND -
DEPR -
2ND -
CLR WORK -
METH -
2ND -
SET ×2 → DB -
DB 200 -
ENTER -
↓ -
LIF 6 -
ENTER -
↓ -
M01 1 -
ENTER -
↓ -
YR 1 -
ENTER -
↓ -
CST 48000 -
ENTER -
↓ -
SAL 6000 -
ENTER -
↓ -
DEP -
↓ -
RBV -
↓ -
RDV
METH is a SET field, so you press 2ND SET to cycle rather than typing a value: once for SYD, twice for DB, three times for DBX.
DEP = 16,000.00, RBV = 32,000.00, RDV = 26,000.00. For any other year, arrow back to YR, type the
year, and read the three computed fields again — nothing else needs re-entering.
Four mistakes worth avoiding
- Subtracting salvage before applying a declining balance rate.
DBworks on the full book value, starting at cost. Only the floor involves salvage. Netting salvage off first understates every charge and the schedule will not total £42,000. - Expecting
DBXto differ fromDB. When salvage is a large fraction of cost, the crossover never triggers and the two are identical. Assuming otherwise leads people to hunt for a fault in the calculator. - Reading
RBVas the amount left to depreciate. That isRDV.RBVincludes the salvage, so it stops at £6,000 whileRDVreaches zero. - Leaving
M01at a stale value. LikeLIF, it survives between problems. A leftoverM01of 7 halves the first year of the next asset you enter and adds a phantom seventh row.
Depreciation is the one worksheet with no sign convention and no compounding, which makes it the easiest on the calculator and the easiest to misuse in an appraisal. Where it matters is the tax shield: put those figures into a cash flow analysis and the method choice moves the NPV, while the depreciation calculator prints every method’s schedule side by side so the comparison takes one entry rather than four.