Three Schedules for One Machine: Straight Line, Declining Balance, Units of Production

Three inputs decide everything, and the tax code overrides one of them

Every depreciation schedule starts from three numbers: what the asset cost, what it will be worth when you are done with it, and how long that will take. Cost less salvage is the depreciable base — the amount that will pass through the profit and loss account over the asset's life. On our machine that base is $50,000 minus $5,000, so $45,000. Notice that only the base and the life are shared across methods; nothing about the base tells you the shape of the schedule, and nothing about the shape changes the base. That separation is the whole reason there can be three answers to one question.

Then the tax code arrives and deletes the salvage value. MACRS computes depreciation on the full unadjusted basis; the property is depreciated to zero regardless of what it will actually fetch, which is why the total tax deduction over the schedule is $50,000 and not $45,000. The same is true, for the same reason, of every accelerated regime in continental Europe: the schedule runs the full cost down to nothing. This is the first and largest divergence between the books and the return, and it is $5,000 on this machine — bigger than any difference the choice of method will ever make.

Straight line answers how long, not how fast

Straight line divides the depreciable base by the number of years: $45,000 over five gives $9,000 a year, or 18 percent of cost annually. Its virtue is that it makes one assertion and only one — that the asset gives up its usefulness at a constant rate — and it is honest about being an assertion. Its weakness is the same thing. A machine that runs three shifts in its first year and sits under a tarpaulin in its fourth is charged identically in both, and the accounts say nothing about that. When a business asks why its margin collapsed in a quiet year, straight-line depreciation is often part of the answer, because the cost stayed while the output left.

There is a second, quieter property worth knowing. Because the charge never varies, straight line makes the book value fall in a straight line too, and after two years our machine stands at $32,000. Nothing about a real market for used machines behaves that way — the resale value of most equipment falls fastest early and then flattens — so a straight-line book value systematically overstates what the asset would fetch in the first half of its life. If you are using book value as a proxy for what you could sell for, you are using the wrong number, and the size of the error is largest exactly when it matters most.

Declining balance is an asymptote with a stopping rule bolted on

Double declining balance takes twice the straight-line rate — here 2 divided by 5, so 40 percent — and applies it to the book value rather than to the base. Year one is $50,000 × 40 percent = $20,000. Year two is $30,000 × 40 percent = $12,000. Then $7,200, then $4,320. After four years you have deducted $43,520 and the book value is $6,480. Left alone, the fifth year would take $2,592 and drop the book value to $3,888, which is below the $5,000 salvage. So the rule is that you stop: year five takes only $1,480, the amount that brings book value exactly to salvage. The schedule totals $45,000, the same as straight line.

The stopping rule is not a detail; it is what makes the method usable at all. A percentage of a shrinking balance is a geometric sequence, and a geometric sequence with a positive ratio never reaches zero. Whether the untruncated schedule ends above or below the salvage value is an accident of the rate: at 40 percent over five years the book value would land at $50,000 × 0.6⁵ = $3,888, below salvage; at 20 percent over ten years it would land at $50,000 × 0.8¹⁰ = $5,368.71, above it. Declining balance therefore always needs an external instruction to finish — either stop at salvage, or switch to straight line on the remaining book value. Every tax system that uses the method builds that switch in, and the tax authority, not you, decides when it happens.

Units of production is the only method that can report a zero year

Units of production abandons the calendar. Divide the $45,000 base by the total output the asset is expected to deliver — say 90,000 units — and you get a rate of $0.50 per unit. A year of 24,000 units charges $12,000; a year of 9,000 units charges $4,500; a year in which the machine is out of service charges nothing at all. The method turns a fixed cost into a variable one on the face of the accounts, which is exactly what a production manager means when they say the machine costs fifty cents a piece. No other method can say that sentence truthfully.

The cost of that realism is that you have to forecast total output, and the forecast is doing all the work. Halve the expected lifetime output and you double the charge per unit; the annual figure then moves for a reason that has nothing to do with the year being reported. IAS 16 permits the method and also requires the estimate to be reviewed at least at each financial year end, which is a polite way of saying that the number is a judgement you will have to defend. In practice units of production is used where output really is the wearing agent and really is measured — mining, oil and gas, aircraft engines by cycle, presses by stroke — and almost nowhere else.

What the tax code actually lets you do

In the United States the answer is MACRS, and MACRS is not a choice — it is a prescribed schedule. Our machine falls into 5-year property. The general depreciation system applies 200 percent declining balance, switches to straight line the moment straight line on the remaining basis is larger, ignores salvage value entirely, and applies the half-year convention, which treats every asset as placed in service at the midpoint of the year no matter when you actually bought it. That last rule is why a five-year schedule takes six tax years. The published percentages are 20.00, 32.00, 19.20, 11.52, 11.52 and 5.76, and you can rebuild them from those four rules alone: 40 percent of 100 halved is 20; 40 percent of the remaining 80 is 32; 40 percent of 48 is 19.20; in year four, 40 percent of 28.80 is 11.52 and straight line over the remaining 2.5 years is also 11.52, so the switch happens; and the last half year takes what is left, 5.76.

The rest of the world reaches the same destination by different roads, and the spread is wider than most people expect. On the same $50,000 machine with a five-year life, the first-year tax deduction is $10,000 under MACRS, but the equivalent French dégressif regime would give 35 percent, the German degressive AfA 30 percent, and the Spanish and Portuguese constant-percentage methods 40 percent — while Italy, which has no declining-balance option at all and halves the first year, would give 10 percent. Same machine, same life, and a first-year deduction that varies by a factor of four across six tax systems. If you are modelling a purchase in more than one country, this is the line of the model that will surprise you.

What the choice is actually worth, in money

Here is the calculation almost nobody does. Accelerating a deduction does not create a deduction; it moves it earlier, and the value of moving it earlier is the interest you earn on the tax you did not pay yet. So price it. Take the $50,000 machine, a 25 percent tax rate and a 6 percent discount rate. Straight line over five years produces a tax shield with a present value of $10,530.91. The MACRS schedule produces $10,657.80. The whole advantage of the accelerated method, on this asset with these assumptions, is $126.89 — one quarter of one percent of the purchase price.

That number should recalibrate the conversation. Accelerated depreciation matters when the amounts are large, when the discount rate is high, when the tax rate is high, or when the business genuinely needs cash now rather than later — and in those cases it can matter a great deal, because the effect scales with all four. It does not matter much on a single mid-sized machine in a stable business at ordinary rates. What does matter, in every case, is getting the useful life and the classification right, because those determine the whole shape of the schedule and are the things a tax inspector actually looks at. Spend the effort there, not on the method.

Frequently asked questions

Do the three methods give a different total deduction over the asset's life?

No. On our machine all three total exactly $45,000, which is cost less salvage, and they must — the depreciable base does not depend on how you spread it. What changes is the year in which each slice is recognised. Straight line puts $9,000 in each of five years; double declining balance puts $32,000 in the first two years and $13,000 in the last three; units of production puts whatever the output puts there. The only way a method changes the total is if it changes an input, and there is exactly one place that happens: the tax code deletes the salvage value, so every accelerated tax schedule totals the full $50,000 rather than $45,000. That $5,000 difference is not a timing effect at all — it is a genuine difference in the amount deducted, and it is larger than any timing advantage the method can produce.

Can I use one method in the accounts and a different one on the tax return?

In most systems yes, and in the United States it is the normal state of affairs rather than an exception. The accounts are governed by an accounting framework that asks you to reflect the pattern in which the asset's economic benefits are consumed; the tax return is governed by a statute that prescribes a schedule. The two rarely coincide, and the difference between them is a temporary difference that produces deferred tax. The practical consequence is that you will maintain two registers for the same asset, and that the book value in the accounts and the tax written-down value will diverge for the whole life of the asset before converging to the same place at disposal. Several continental systems are less permissive and tie the tax deduction to the amount actually booked, which means the accounting entry has to be made before the deduction can be claimed. Check which regime you are in before you assume you have a free choice.

What salvage value should I use, and does the tax authority care?

For the accounts, the residual value is your best estimate of what you would get for the asset today if it were already the age and in the condition it will be at the end of its useful life, net of disposal costs. It is an estimate, it must be reviewed at least annually, and if it rises above book value the depreciation charge falls to zero rather than going negative. For tax, the answer in most accelerated regimes is that nobody cares: MACRS explicitly computes depreciation on the full unadjusted basis and depreciates to zero, and the continental declining-balance regimes do the same. That asymmetry is deliberate. The tax system recovers any over-depreciation at disposal instead, by taxing the excess of the sale price over the written-down value — which is why an asset sold for more than its tax value produces a taxable gain even when it produced no economic profit.

Why does a five-year schedule take six tax years?

Because of the convention that decides when the asset is treated as entering service. MACRS applies the half-year convention to most personal property: whatever date you actually placed the asset in service, the tax code treats it as the midpoint of the year, so the first year gets half a year of depreciation and the leftover half year lands in an extra year at the end. That is why 5-year property runs 20.00, 32.00, 19.20, 11.52, 11.52 and 5.76 percent across six tax years rather than five. There is also a mid-quarter convention that replaces it when more than 40 percent of the year's additions were placed in service in the last quarter, and a mid-month convention for real property. Other systems reach the same place differently — Italy simply halves the first year's coefficient, and France prorates the first dégressif annuity from the first day of the month of acquisition. In every case the effect is the same: the schedule is one period longer than the useful life.

What happens if I sell the asset before the schedule ends?

The schedule stops and the difference between the sale price and the written-down value is settled in one go. If you sell our machine after three years, the book value under straight line is $23,000 and under double declining balance it is $10,800 — a gap of $12,200 on the very same asset. Sell it for $15,000 and the straight-line books show a loss of $8,000 while the declining-balance books show a profit of $4,200. Neither is wrong; they are the arithmetic consequence of two different assertions about how the machine wore out, and the total profit over the whole holding period is identical because the earlier depreciation charges differ by exactly the same $12,200. For tax the same reversal happens with a sharper edge, because the excess of proceeds over the tax written-down value is generally taxed as ordinary income up to the amount of depreciation previously claimed rather than as a capital gain. Accelerating a deduction, then, does not only move the deduction forward — it also moves the recapture forward if you sell early.