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C H A PT E R -III
METHODS OF DEPRECIATION
Depreciation is a allowable expenses in general accounting purposes and income tax accounting purposes. But it differ categorically from other conventional expenses because depreciation charge does not occur any outflow of business fund. This chapter deals with the different methods of depreciation with their merits and demerits so that a firm is in a position to choose the best method.
The periodical amount of depreciation is affected by the following factors^
the cost of the asset;
the life of the asset;
the expected residual value of the asset;
and, by the method of depreciation selected for amortisation of the asset which must be systematic and rational. Cost of asset means the basic acquisition cost of the asset plus all incidental expenses which are required to the asset into use. The incidental expenses like freight, import duty, Brokerage, legal expenses and installation charges are also form a part of cost of asset. There are some controversies regarding repairs and maintenance cost. In general, heavy repairs and maintenance cost which increases the life of the asset or keep the asset in its usable state^ are also to be capitalised. The useful life of an asset is the period of time during which the firm expects to use the asset for earning revenue^ It is not an easy task to estimate an accurate life of the asset. The useful service life of an asset may come to an end whether as a result of physical causes or as a result of changing economic significance or both''. Ronald Ma observed that “the life of the asset is the shorter of the life determined by (a) physical wear and tear, taking the maintenance policy of the firm into account, (b) obsolescence, and (c) where a machine has been installed to exploit a wasting asset.
the period of exploitation or in the case of a machine with a specialised function the period determined by the effective and sufficient demand for its products.”^ The physical, engineering life of the asset can be determined with a fair degree of accuracy, but technological obsolescence and demand for a product cannot be determined easily. So, instead of exact working life only the probable useful period may be assumed through rational approach like, past experience, quality of asset, expert’s opinion, consulting asset’s manual, statistical tools for forecasting etc. Salvage value of an asset refers to the amount that can be expected to realise from disposal of the asset at the ends of its useful life. That means it is the difference between the cost of the asset and the total depreciation during its life. Expecting a few cases, salvage values of retired assets are not of any great significance. Still an incorrect estimate of the salvage value, however small it may be cannot but result incorrect measure of the periodical depreciation^. Once the cost of the asset, useful lives and the salvage value are determined the problem of depreciation is reduced to one of finding a suitable basis of allocation of the cost of the asset less salvage value over the periods that use services of the asset. In general accounting practice, the choice of method of allocating the cost of a tangible fixed asset over its effective life i.e. depreciation should depend upon the patterns of expected benefits obtainable in each period from its use. The main problem of this approach is that there is no dependable way to measure the quantum of service that can be received from the asset over its expected service life. In actual practice what happen is that the accountant selects a method to be used as the basis for allocating the depreciable cost. Sometimes, accountant are guided by a management’s policy relating to the allocation of cost of fixed asset. In all the cases, however, the problem boils dovm to the question of selecting a method which has to be systematic and rational’. An interim report on an AICPA accounting research study on depreciation by Charles W. Lamden*, reported that the focus of much of the dissatisfaction is on the variety of cost allocation methods admissible under generally accepted accounting
the investment of the amount charged for depreciation for ensuring cash flow to meet the replacement cost of the asset. Another assumption under this method is the maintenance of capital. Annuity method, sinking fund method are included under this group. v) Miscellaneous Method This method comprises those which do not fall within the ambit of the above stated categories. It depends on arbitrary methods of allocation or any combination of time or use basis. Group or composite method, replacement method, revaluation method are included in this group. Charles W. Lamden’^ indicated that the systematic and rational criteria might have allowed a wide variety of methods. In practice, however, four basic approaches have been follow ed: i) Straight - line apportionment overtime, that is a uniform amount of amortised cost for each period in the estimated life of the property unit. ii) Reducing charge methods which produce decreasing amount of amortised cost over the life of the property unit. iii) Production and revenue methods which amounts of amortised cost that vary directly with the volume of production or the amount of revenue. iv) Compound interest methods which produce increasing amounts of amortised cost over the life of the property unit. Accountants’ Encyclopaedia''* classified depreciation method under the following categories :
- Methods producing a uniform charge in each final year a) Straight line method b) Annuity method
- Methods producing a decreasing charge in each fiscal year (accelerated methods)
a) Fixed percentage on declining balance - scientific methods
b) Fixed percentage on declining balance - unscientific method (Income tax method) c) Sum-of-years’-digits method or Reducing fraction method
- Methods producing a fluctuating charge in each fiscal year viz.
a) Unit or production method b) Working hours method c) Inventory or Revolution Method
- Method producing on increasing charge each fiscal year a) Sinking fund method Grant and Norton classified the depreciation accounting method other than straight line method in the following categories :
- Consistent methods based on time (a) Methods giving smaller writes-off than straight line in early years of life. (i) Sinking fund or present worth method (ii) Retirement method (iii) Replacement method (b) Methods giving larger write-off than straight line in early years of life. (i) Declining balance method (ii) Sum-of-years’ digits method (iii) Multiple straight-line method
- Consistent methods based on use (a) Production method (b) Combination of the production and straight line method
- Irregular methods (a) Retirement reserve method
STRAIGHT LINE METHOD
Under this method, an equal amount is provided each year for depreciation of each asset until the asset has been written down to nil or its scrap value at the end of the estimated life of the asset'’. The name of this method is derived from the fact if the successive annual depreciation over the life of the asset are plotted on a graph, the result will be a straight line with a slope equal to the armual depreciation. This method is also called ‘Fixed Installment Method’ because a uniform amount of depreciation is charge each year'*. The formula of the annual depreciation under the method is :
D = (^) n ^
Where, D = Annual depreciation. C = Cost of the asset S = Salvage or scrap value n = Estimated life of years. This method can be recommended only when the following conditions are satisfied. a) The asset is expected to render an uniform service through out its estimated useful hfe'^. b) Annual repairs and maintenance costs are assumed to remain constant over its life^°. c) The asset is expected to earn an equal amount of revenue each year throughout its life. d) The amount of depreciation is a function of time only.
Repair Cost^‘ To mulify, the higher shut down and repair costs in the later part of the asset’s Hfe, a partial rectification of this method is possible by estimating the total amount of repair cost over the life of the asset. The depreciation and repairs are accounted for as a unit. The annual cost would then be :
Cost - Estimated salvage value + Repair cost Estimated Life in Years. Merits There are several merits of the method a) This method is not only simple to understand but also easy to calculate. b) The book value of an asset can be fully written off c) The life of the certain assets sometimes depend on contracts like leasehold property, patents, trade marks etc. In such case this method is very much appropriate. d) Effective life of an assets, scrap value, repairs and maintenance cost, rate of interest etc. cannot be measured with certainty. So, no single method can weight all the factors at a time with equal importance for fixing the amount of depreciation. From this view point, this method appears most reasonable as some favourable impact of some factors are offset by unfavourable effects of others.
Demerits
As against the advantages enumerated above, the straight-line method has some disadvantages also. Some of the disadvantages are :
a) This method does not take into account the interest on capital invested on the assets^^. b) Under this method the amount of depreciation can never be equal to the value of services rendered from the asset. An asset is expected to render
d, = C .r .....................(1) V, = C - d , .....................(2) From (1) & (2) we get, V, = C - C. r or,V, = C ( l - r ) ......................(3) In the second year, d 2 = Vi .r .....................(4) From (3) & (4) we get, d 2 = C ( l - r ). r or,d 2 = C. r ( l - r ) ......................(5) A nd,V 2 = V , - d 2 .....................( 6 ) From (3), (5) and ( 6 ) we get, V 2 = C ( l - r ) - C r ( l - r ) or,V 2 = C ( l - r ) ( l - r )
or,V2 = C (l-r)^ ................... (7)
In the third year, d 3 = V 2. r ...................... ( 8 )
From (7) and ( 8 ) we get,
d 3 = C ( l - r ) ". r
or,d 3 = C r ( ( l - r f ..................... (9)
A nd,V 3 - V 2 - d 3 ................... (1 0 )
From (7), (9) and (10) we get,
Thus in the first year
V 3 = C ( 1 - r ) ' - d r ( l - r ) '
Or , V 3 = C ( l - r ) ' ( l - r )
Or,V3 = C ( l - r ) ^ .................... (11) If we follow the equation no. (1), (5) and (9) we can easily determine d 4 , ds and so on i.e. d] = C.r. d 2 = C r ( l - r ) dj = C r ( l - r ) ^ d 4 = C r ( l - r ) ’
d„ = C r ( l - r ) " - ‘ Similarly, if we follow the equation no.(3) (7) and (11) we can easily determine the value of V 4 , V 5 and soon i.e. V, = C ( l - r ) V 2 = C(l-r)' Vj = C ( l - r ) ’ V, = C ( l - r ) '
V. = C ( l - r ) " It appears from the above, both depreciation and the book value of the asset are reducing at a constant rate. d„ = C r ( l - r ) " ' andV , = C ( l - r ) " In general terms.
o r , r = l - ..................(15)
To find out the value of dj, d 2 , ds etc. directly, we have already shown in terms of general equation i.e. dt=Cr(l-ry-' Where t = Estimated life of the asset which is ranging from 0 to n It may be v/ritten either as dt = [ r (1 - r)‘~ ’].C Thus instead of applying a fixed rate on the diminishing balances of the asset, it is also possible to compute depreciation by applying fluctuating rates on the original cost of the asset.^^ Diminishing balance method is characterised generally by predetermined fixed rate say 20%, 15% or 10% on the diminishing balance to charged depreciation in each year. But the same result may be obtained under this method by charging depreciation on variable rate on the initial cost of asset. What is needed for the purpose is some mathematical adjustment. It is observed from the above that a negative acceleration^^ is achieved under diminishing balance method. M erits: The diminishing balance method of depreciation has some advantages. These are mentioned b elo w : a) Under this method, depreciation is calculated according to the service yielding capacity of the asset. As amount of depreciation decreases gradually with the decrease in service potential of asset. b) This method can be proved very helpful in adopting the better matching of revenue and expenses as in the first few years depreciation being heavy and repairs light and in the last few years repairs being heavy and depreciation light. The combination of depreciation with the cost of
repairs and maintenance is resulted more or less even charge against revenue over the whole life time of the asset. c) There is no danger that asset will be over-depreciated since no matter how high the rate of depreciation is taken (less than 100%) there is always something left in the relative ledger account to which the rate would be applied in the next year.^^ d) This method is consistent with the principle that book value of an asset should be considered equal to the present value of its remaining service potentials because asset value decrease at higher rate in the earlier parts than in the later parts of the life.
Demerits :
There are certain objections to the use of this method. The main objections are as follow s: a) There is no certainty that the service yielding ability of depreciable assets will always reduce by a constant rate. b) This method puts too much emphasis on the historical cost. Proper emphasis is not given on the recovery of capital invested on the asset. Similarly interest on capital invested is also ignored here. c) The use of this method mitigates against accurate costing. It has been observed in practice that sometimes the assets can earn more or less the same amount of revenue for a long period o f time. In that case, different amount are charged for the use of same assets in different periods cannot be justified. d) This method does not give acceptable depreciation charges in either practice or theory where disposal costs of an asset are taken into account for purposes of determining the periodic rate.^*
The formula for measuring depreciation for a particular year is :
D, = ( C - S ) x ^ ^ /= 1
M erits:
The merits of the method are as follows : a) In this method, the quantum of depreciation is greater in the earlier years in comparison with the later years because the benefits received from the use of the asset are greater in the early years than in the later years. b) In the earlier year repairs are light but depreciation is heavy but in the later year, as the asset gets older the repairs are heavy but depreciation is light. So depreciation plus repairs will more or less constant every year and the charge to Profit and Loss Account should be uniform. c) If the asset is retired earlier than anticipated as result of unforeseen obsolescence, the loss upon retirement will be less than if straight line depreciation were used, because, asset are recovered at a higher rate in the earlier years where as only a small fraction remains left for recovering them in the later years. d) For tax accounting purposes, these methods have a clear advantage over the straight line method. The larger deductions in the early years mean that at the very least tax payments are postponed for a considerable period. On the other hand, this method gives a tax postponement with the greatest present value. e) In this method nearly three-fourth of total depreciation is charged within half of its life. That means three-fourth of blocked investment recovered within short span. f) This method is very simple to understand and simple to calculate.
g) This method is preferable for assets with services Uves of eight years or more.
D em erits:
Although this method is considered to be a great imiovation in the field of depreciation accounting but it has some disadvantages which are given below :
a) This method also ignored the cost of capital on invested fund. b) In the earlier year greater depreciation is charged at a result less profit is available for declaring dividend in the earlier year. This may created serious problem for organisation to attract new investor. As dividend is one of the motivating factors for investment. Again more depreciation in the earlier year may resultant the high cost of production in the competitive market. DOUBLE DECLINING BALANCE METHOD In the USA the Internal Revenue Code of 1954^' permitted the tax payers who were using a declining balance method to charge depreciation for tax purpose a maximum of double the rate allowed under straight line method. This method of calculating depreciation was called double declining balance method. This method may be identified as a combination of straight line and diminishing balance method. Like diminishing balance method here the depreciation is charged on the opening written down value of the fixed asset. Like straight line method a fixed rate of depreciation is charged in this method. But the rate used is twice the straight line rate. It is important to mention here that under this method an over depreciated cost of the asset at the end of the life of asset than its anticipated salvage value. In that case there may be two options to deal with the problem. Depreciation charge for the last year may be adjusted to make salvage value equal to its anticipated salvage value. Alternatively, in the last year the firm may opt out for straight line depreciation for written off the over depreciated salvage value. Again, under most circumstances, the entire depreciation would not be allocated during the life of the asset i.e. the amount
d) Under this method the asset value can never be reduced to zero. SINKING FUND METHOD Under this method, depreciation is a provision by charging out of revenue for replacement of an asset and a means of maintaining capital. This method is based on the assumption that a fund is to be built up and that the amount of this fund should equal the total amount of the depreciation at the end of the useful life of the depreciable asset. An equal amount by way of depreciation is set aside by charging to the profit and Loss Account at the end of every accounting period, so that, all such equal installments if allowed to accumulate at a compound interest^^ would equal to the depreciable cost of the asset at the expiry of its useful life. Under all other methods of depreciation liquid cash may not be available to the firm at the time of replacement of asset because in those cases the amount of depreciation is retained in the business. In this method armual equal installment set off as depreciation is regularly invested outside the business in interest bearing easily marketable securities. Interest yielded on such securities is compounded or reinvested in each year. When the life o f the asset expires, investments are disposed off and the proceeds are utilised for replacing the old asset. This method is also known as ‘Depreciation Fund Method’ or ‘Redemption Fund Method’.^'* Form ula: Let, d = Sinking Fund Depreciation. C = Cost o f the asset. S = Salvage value i = Rate of interest in decimal term n = Years
Let it be assumed that the salvage value equal to zero. The accumulated amounts should then be equal to the cost of the existing asset. The accumulated amount can be obtained from the following :
C = d (l+i)"-' + d (1+i)"'^ + d (1+i)"-^ + ............ + d (l+ if^"'') + d ( 1 + if " or, C = d ( 1 + i f ' + d ( l+ if ^ + d (1+ if^ + ........ + d (1+i) + d .................. (1) Multiplying both side of the equation by (1+i) C (1+i) = d (1+i)" + d (1+i)"-' + d (1+i)"-' + ......... + d (1+i)' + d (1 + i) .................. (2) Subtracting equation (1) from equation (2), we get, C.i = d ( l+ i ) " - d or, C.i = d [ ( l + i ) " - l ]
or, d = — —— ................... (3) (1 + 0 " - 1 M erits: The main advantages of this method are as follows : a) Under this method, at the end of the specified time, a definite sum is available in cash to replace the old asset. b) Since the amount is invested outside the business there is no need to drawn money from the business for replacement purpose at the end of the life of the asset. This helps to avoid pressure on working capital. Demerits There are some weaknesses of this method and these are as follows : a) From the management view point the method is inefficient. Generally the internal rate of return of the firm is higher than the return on investment. As a result this causes substantial loss to the firm. b) There is always a risk factor about the loss on realisation of investments. That means if the market price of the investment in which depreciation is
