Background

Annual depreciation allowances in practice

Methodological issues

Estimates of value decline and effect of general inflation

Physical assets that decline in value over their lives (usually after starting to produce net receipts) make up a very large proportion of tangible investment (business) assets. Such assets include plant and equipment, horticultural plants/trees, mineral and petroleum deposits, many infrastructure projects, etc. Where there is a long period of delay in the production of net receipts from such an asset (common with agricultural, mining and infrastructure assets), the asset's value is likely to increase more and more the closer access to net receipts becomes. Beyond that period, however, value commonly declines as net receipts decline either from declining gross receipts or increasing annual costs or both.

Any income tax law that is serious about incorporating sound estimates of annual change in value of assets and liabilities needs to deal well with the declining values of depreciating tangible assets. The large numbers of depreciating tangible assets usually involved in a business venture makes it is very difficult to attribute the contribution of each depreciating asset to the venture's annual net receipts. This precludes the general use of the change in value methodology illustrated in Figure 4. Nevertheless, tax laws commonly seek to estimate annual change in value specific to each of hundreds or even thousands types of certain categories of depreciating tangible assets - like plant and equipment and horticultural plants - from 'effective life' determination or from market value data specific to each type of asset.

From time to time some countries flirt with fixed statutory write-off rates across a wide range of depreciating tangible assets with very different effective lives and rates of value decline. These statutory write-off rates therefore bear no relation with the lives of the assets involved and usually provide write-off that is considerably accelerated compared to actual reduction in value. Specific tangible depreciating assets also often attract accelerated write-off for particular policy purposes.

• Accelerated depreciation for specific assets (eg forestry) might achieve a desired increase in activity in those assets at the expense of others but with consequential price/cost increases as after-tax returns initially bloated by accelerated write-off revert to normal levels (mirroring the effects of increasing property values illustrated in the discussion on negative gearing) and with the inevitable attention of financial entrepreneurs.

• Accelerated depreciation across a wide range of assets (eg plant and equipment) has less chance of achieving a desired increase in activity across those assets relative to others given associated price increases, potential tax rate increases to cover transitional tax revenue losses and potential interest rate and exchange rate increases. What will be achieved, however, are distortions in decision-making favouring longer-lived assets over shorter-lived assets (and over regular maintenance expenditure) - see Mayo (1984).

• Accelerated depreciation aimed at offsetting the effects of inflation on write-off arrangements under nominal income taxation arrangements miss the mark widely - given the annual adjustments required to all assets and liabilities in addition to annual nominal economic depreciation to adjust for the effects of inflation.

In seeking to achieve the important aim of obtaining sound estimates of annual reduction in (nominal) value of depreciating tangible assets, 'effective lives' of assets are often used to obtain rates of write-off as are direct estimates of annual rate of decline in asset value. Thus, estimates of the annual reduction in value of depreciating tangible assets typically derive from schedules of effective lives or write-off rates to apply to different types of these 'depreciable' assets.

Academic studies, such as Hulten and Wykoff (1981), have concluded that depreciable assets like plant and equipment often deteriorate at a constant rate peculiar to the type of asset involved. This means, in turn, that with broadly constant inflation, the value of a depreciable asset and the net receipts (gross sales revenue less annual expenditure like repairs and maintenance) produced by it would also often decline year by year at a particular constant rate. With a constant rate of decline in net receipts, the decline may be due to declining gross receipts, rising repair and maintenance costs or both. The effects of obsolescence, where ongoing innovation results in improved versions of the asset type - say producing gross receipts more efficiently with less maintenance required - would also be reflected in the particular rate of decline applicable to a specific type of depreciable asset.

Under conditions of broadly constant inflation, direct estimates of the changing value of depreciable assets offer one way of providing the declining (or reducing) balance depreciation rates to apply to the assets. With say a 30% declining write-off percentage, the 30% is applied to tax (depreciated) value at the start of the year to obtain the annual depreciation allowanced for tax purposes. Tax value of $1000 at start Year 1 declines to $700 at end Year 1 (start Year 2) with $300 depreciation allowed in Year 1, declines a further 30% to $490 at end Year 2 with $210 depreciation allowed in Year 2, and so on until disposal of the asset (when difference between disposal price and tax value is usually included in tax assessments). If the asset's value is actually declining at 30% per year the declining balance allowances will match annual economic depreciation. Direct estimation seeks to obtain that 30% figure from market data on asset values.

Nevertheless, as well a declining balance depreciation, typically, straight line (or prime cost) depreciation is allowed as an alternative to declining balance depreciation with the relationship between prime cost and declining balance specified as:

Declining balance rate = Multiplicative factor x prime cost rate                          (1)

With a multiplicative factor of 1.5, the above 30% declining balance percentage would translate into a 20% prime cost percentage. The asset with a tax value of $1000 at the start of Year 1 would attract $200 prime cost depreciation allowances in Year 1 and the ensuing 4 years (after which the asset's tax value would be zero). For such a depreciation schedule to match annual economic depreciation, the asset's actual value would have to have the unlikely profile of decreasing by $200 year by year until complete collapse at the end of Year 5. This value profile is very different from a constantly declining profile. Despite this difference, reasons for allowing prime cost write-off as an option might include simplicity and getting depreciation of assets ‘off taxpayers’ books’ after a set number of years.

The method of directly estimating value decline of depreciable assets from market data is show as Method 1 in Figure 46. For some assets, estimation is possible from deep secondary (used asset) markets where prices of used assets are available year by year. For other assets, sufficient information might be available on residual values relative to purchase price after a particular number of years - a rate of decay can be computed that is consistent with particular initial and residual values over a set number of years.

The more traditional method of determining write-off rates for depreciable assets is shown as Method 2 in Figure 46. This method starts with the determination of the 'effective life' of an asset. The general idea behind effective life is that, absent obsolescence, each type of depreciable asset becomes incapable of providing the required level of service from a technical or engineering point of view after a particular number of years. The presence of technical advancement, however, means that a depreciable asset may become obsolete and need to be replaced by an improved asset before it is used for its full effective life even when the asset is maintained in good order and condition. The wide range of factors potentially relevant to the estimation of effective life include: engineering information relevant to physical asset life; industry- or asset-relevant considerations included in manufacturers’ specifications; the particular circumstances of use of the asset; and the level of repairs and maintenance required for the type of asset involved as it ages. Ongoing technical advancement typical of a particular type of depreciable asset may well be captured in that asset type's effective life determination. The traditional estimate of effective life then provides the basis for determination of the prime cost and declining balance rate of write-off of depreciable assets.

The prime cost rate is obtained from the effective life measure by:

prime cost rate = 1/effective life                                             (2)

Determination of rates of write-off for depreciable assets might be left solely to the taxation authorities or some scope might be allowed for self-assessment by taxpayers. For example:

• Taxpayers may be able to self-assess the write-off rates of their assets up front based on their own particular use of the assets.

• Taxpayers may able to adjust the rate of write-off during the period of use of assets by re-assessing write-off rates against changed circumstances, with that changed write-off applying to an unchanged tax (depreciated) value.

• Taxpayers may even be permitted to use a change in secondary market values of the taxpayer’s asset to invoke a balancing adjustment - or a 'marking to market' - in the absence of disposal, which would change the depreciated (tax) value of the asset (and increase assessable income or allowable deductions depending on the direction of the change).

The selection of a suitable multiplicative factor in equation (1) may be helped by the observation that in practice, effective lives estimated directly from technical factors via Method 2 in Figure 46 may closely match effective lives estimated indirectly from market value data via Method 1 in Figure 46. Take a depreciable asset declining in value at say 15 per cent per year (with net receipts produced by the asset also declining at 15 per cent). Say the 15 per cent decline in net receipts (gross sales revenue less annual expenditure like repairs and maintenance) is due solely to rising repairs and maintenance costs - with gross receipts remaining constant at $250 (the net receipts of Year 1). This situation would see maintenance costs increasing year by year to keep producing $250 of product but with net receipts declining at 15%:

Year	Asset Value $	Gross receipts $	Net receipts $	Annual costs $
Year 1	850.0	250	250	0
Year 2	722.5	250	212.5	37.5
Year 3	614.1	250	180.6	69.4
Year 4	522.0	250	153.5	96.5
Year 5	443.7	250	130.5	119.5
Year 6	377.2	250	110.9	139.1
Year 7	320.6	250	94.3	155.7
Year 8	272.5	250	80.1	169.9
Year 9	231.6	250	68.1	181.9
Year 10	196.9	250	57.9	192.1
Year 11	167.3	250	49.2	200.8
Year 12	142.2	250	41.8	208.2
Year 13	120.9	250	35.6	214.4

It could be that after 10 years of use owners of this type of asset replace it because the $192.1 of maintenance required to earn $57.9 of net receipts is considered excessive – even though the cash flows and declining asset value strictly say there is a continuing profitable pre-tax return (10%) to be had the following year. A declining balance write-off rate is translated into the corresponding effective life by combining equations (1) and (2) to give:

declining balance rate = multiplicative factor/effective life.

With effective lives determined from Method 2 on the basis of technical or engineering considerations, unexpected obsolescence could be considered to require replacement of depreciable assets with improved assets after some selected proportion (eg two-thirds) of the assets' effective lives. The multiplicative factor could then be selected that resulted in a broad match between the written-down values (tax values) of assets under both depreciation systems around the selected (two-thirds) proportion of assets' effective lives. Table 8 shows the multiplicative factor that equates asset tax value under declining balance depreciation with that under prime cost depreciation at different proportions of associated effective lives. The rate of prime cost depreciation follows immediately from the effective life of a column in the table - as per equation (2) - and the multiplicative factor is varied and with it the rate of declining balance depreciation - as per equation (1) - until tax values are equated at the proportion of effective life specified for each row of that effective life column.

TABLE 8: Multiplicative factor equalising tax value of declining balance and prime cost depreciation after a proportion of effective life (a) (b)

Proportion of effective life	30 year effective life	20 year effective life	10 year effective life	6 year effective life	5 year effective life	4 year effective life	2 year effective life
1/2	1.35	1.34	1.29	1.24	1.3(c)	1.17	1.0(d)
2/3	1.60	1.55	1.58	1.44	1.3(c)	1.48(e)	1.0(d)
3/4	1.84	1.77	1.82	1.81(f)	1.66	1.48(e)	(g)
9/10	2.45	2.40	2.26	1.81(f)	(h)	(h)	(h)

Notes to table:

1. Given the effective life at the head of each column, prime cost rate equals 1/effective life and declining balance rate equals multiplicative factor/effective life.
2. The whole number of years corresponding to the proportion of effective life specified at left of each row is obtained by rounding up. The rounding to produce whole years necessarily means that the trend of factors in the table may not be smooth down columns or across rows.
3. Rounding results in 3 years for both the 1/2 and 2/3 proportions.
4. Rounding results in 1 year for both the 1/2 and 2/3 proportions.
5. Rounding results in 3 years for both the 2/3 and 3/4 proportions.
6. Rounding results in 6 years for both the 3/4 and 9/10 proportions.
7. Rounding produces 2 years (ie the full effective life) for the 3/4 proportion and after 2 years the asset is fully written off under prime cost depreciation while there is always a positive written-down value with declining balance depreciation.
8. Rounding produces the full effective life for the 9/10 proportion and the asset is fully written off under prime cost depreciation at that time.

Choice of the multiplicative factor could be focussed on getting a broad match between the present value of the stream of declining balance depreciation allowances and the stream of alternative prime cost allowances - regardless of whether Method 1 or Method 2 was being applied (though, again, with Method 2 there would be no ultimate check being made against market value data). Table 9 shows the multiplicative factor equalising the present value of the two streams for different declining balance rates and different discount rates for present value computation. The results in the table indicate that:

• selection of discount rate is not crucial; and

• the equalising multiplicative factor is around 1.5 for shorter-lived assets, falling from that level for longer-lived assets with values falling around 10% or less per year.

Notes to table:

1. Assets are held for 10 years under both declining balance and prime cost depreciation (even though for assets with high declining balance rates, under prime cost depreciation the asset will be written of in full before the 10 years is up).
2. It is assumed that decline in asset value matches the declining balance percentage given at the top of the table. Thus, on disposal of the asset after 10 years, there is no balancing adjustment under declining balance depreciation. Under prime cost depreciation, however, there will be balancing adjustments for the difference between tax (depreciated) value and asset value at disposal time.
3. The prime cost rate is computed from the declining balance rate on the basis that from equation (1):

   prime cost rate = declining balance rate/multiplicative factor.

In conclusion, value or values for the multiplicative factor of equation (1) are required so long as either prime cost write-off is allowed or direct, technical estimates of effective life are used as a basis for depreciation write-off rates. Prime cost depreciation is likely to remain an option because of its practical appeal. Were Method 1, with its direct estimation of rate of declining balance, the sole method used for determining depreciation write-off rates, equating the present value of declining balance allowances with that of prime cost allowances determined according to equation (1) might be a reasonable basis for setting the multiplicative factor. Nevertheless, Method 2, with its estimation of effective life and immediate rate of prime cost write-off, is likely to remain a well-acceptable and practical method of determining depreciation write-off rates - a workable alternative to Method 1 when no suitable market data are available. Thus, the two methods will continue to co-exist despite the basic inconsistency between, on the one hand, constant rate of asset value decline and declining balance depreciation derived directly from Method 1 and, on the other, effective lives and prime cost depreciation derived directly from Method 2. Moreover, practicalities dictate that the two methods will continue to share a common multiplicative factor for converting prime cost rates to declining balance rates.

Broadly-based research may be able to shed light on how well declining balance write-off rates derived indirectly from effective lives of Method 2 match the rates of decline of actual market data for the same asset types. In the absence of such research, however, the selection of an across-the-board multiplicative factor linking prime cost and declining balance depreciation must necessarily remain arbitrary. In Australia, the traditional generally-applicable 1.5 multiplicative factor was increased to 2.0 in the 2006 budget.

Declining nominal value of a depreciating asset may be viewed as a function of the non-inflationary rate of decline in value of the asset (affected not only by physical wear and tear but influences such as obsolescence and market demand effects) and the effect of general inflation on its value. - see 1985 draft White Paper, Chapter 18, and Mayo (1984). Figure 47 illustrates the difference between non-inflationary decline in value and the effect of inflation on that for an asset with a 25% non-inflationary rate of decline and inflation at 2 1/2%.

Non-inflationary rate of decline

Beyond general inflation, influences that can impact on the rate of decline in value of a particular depreciable asset include:

• general market effects driven by changes in preferences, tastes, etc;

• obsolescence driven by technological advances in this particular asset type or related asset types;

• changes in the level of maintenance with this asset type relative to other assets; and

• changes in the proportion of ongoing capital expenditure typically undertaken with this class of asset that is incorrectly classed as recurrent expenditure for income tax purposes.
  • Capital improvements typically made to a class of asset would ideally be added to tax value and depreciated or depreciated in their own right as a separate asset. Only annual costs (such as maintenance or selling costs) would attract immediate write-off commensurate with being fully ‘used up’ in the year of expenditure.
  • In practice, it is often difficult to separate annual expenditure from capital improvements and inevitably some capital improvements would be treated as annual expenditure. There are two potentially offsetting effects of that treatment in relation to estimated rates of decline in value. On the one hand, the capital improvements would ‘hold up’ the value of the original asset, reducing both the estimated rate of decline in value (and increasing effective life estimated directly) and annual depreciation allowances. On the other hand, the taxpayer would attract immediate write-off for the capital improvements, increasing annual income tax deductions. At one hypothetical extreme, the two influences may completely offset each other if annual capital improvements typically made to a particular asset type just match the decline in value of the asset that otherwise would have occurred.

Direct estimates of rate of decline in asset value under Method 1 of Figure 46 are made inclusive of the effects of inflation. That would not present difficulties if the local central bank is operating monetary policy to keep inflation relatively steady. Problems would arise, however, if inflation were not broadly constant over the period of estimation and did not stay broadly at that constant level for the time that the estimated rate of decay is to be translated directly into declining balance depreciation rates.

Estimates incorporating an early period of relatively high inflation, for example, followed by a period of low and stable inflation, could result in very low estimated rates of decay in nominal value, which would not be representative of rates of decay in the future if low and stable inflation were expected to continue. Nevertheless, the estimating process can be adjusted for such circumstances – and more generally for other effects of inflation, including significant one-off effects on price levels.

Version 1.0 © Copyright Wayne Mayo 2009