10.5 Depreciation of fixed assets
10.5.1 Methods of depreciation
The amount of depreciation of a fixed asset is determined by taking into account the original cost of the asset, the recoverable cost at the time of the retirement of the asset and the expected useful life. Out of these factors, only the original cost is known with certainty and the other two factors can only be estimated. The total amount to be depreciated is the difference between the original cost of the asset and the recoverable amount at the time of its retirement and this difference is to be charged over the useful life of the asset. There are four frequently used methods of computing depreciation.
(i) Straight line method;
(ii) Units of production method;
(iii) Diminishing balance method; and (iv) Sum-of-the-years-digit method.
(i) Straight line method (SL Method)
This method is based on the assumption that the asset provides the same level of service throughout its useful life and hence equal amount should be charged as the expense over the estimated life of the asset. Consider the following example.
Example 4: The original cost of a machine is Rs. 15,000. After being used for 5 years, the machine is expected to fetch Rs. 5,000. Calculate the depreciation charged per annum by the straight- line method.
Sol: The annual depreciation can be calculated as follows
Original cost - Salvage value Annual depreciation =
Useful life 15, 000 5, 000
5 Rs. 2, 000
= −
=
The annual depreciation can also be calculated as a percentage on the net cost. The annual percentage is the 100 divided by the number of years of useful life, i.e. 100/5 = 20 in this case. Then the annual depreciation is given by
( )
( )
Annual depreciation = Original cost - Salvage value 20 100 15, 000 5, 000 20
100 Rs. 2, 000
×
= − ×
=
This method is a simple method of computing depreciation and it provides a uniform allocation of costs to periodic revenues. Hence this is a widely used method.
(ii) Units of the production method (UP Method)
In this method, depreciation is charged on the basis of estimated productive capacity of the asset under consideration. In this method, first of all the depreciation is calculated in an appropriate unit of production such as hour, kilometer or the number of operations. Then annual depreciation is calculated by multiplying the unit depreciation by the number of units in one year.
In our case, let the estimated life of the machine in hours is 10,000 hours. Then depreciation per hour (if the number of units in a year is 3,000) is given by
Original cost - Salvage value Unit depreciation =
Useful life in units 15, 000 5, 000
10, 000 Re. 1.00 per hour Annual depreciation
= −
=
= Unit depreciation units per year Re. 1.00 per hour 3000 hours Rs. 3, 000
×
= ×
=
(iii) Diminishing balance method (written-down value method) (DB Method)
This method results in a diminishing periodic depreciation charge over the estimated life of the asset.
In this method, each year, depreciation is charged by applying a rate to the net cost of the asset as at the beginning of that year. Next book value at a particular point of time is the original cost minus total depreciation accumulated up to that point of time. The rate to be applied is usually the double the straight-line depreciation rate.
In our example, the straight-line depreciation rate is 20% and, therefore, the diminishing balance rate would be 40%. This rate would be applied to the original cost of the asset for the first year and thereafter to the net book value over the estimated life of the asset. The asset's residual value is not taken into consideration for calculation of net book value. However, the asset is not to be depreciated below its residual value in the last year. We have the following table to calculate the depreciated value of the asset over different years:
Table 10.21
Year Net cost (Rs.) Rate (%) Depreciation for the year (Rs.)
1 10,000 5/15 3,333
2 10,000 4/15 2,667
3 10,000 3/15 2,000
4 10,000 2/15 1,333
5 10,000 1/15 667
Both diminishing balance method and the sum-of-the-year-digits method provide for a higher depreciation charge in the first year of the use of the asset and a gradually declining periodic charge thereafter. Hence they are referred to as accelerated methods of depreciation.
Comparison of different methods of depreciation Depending upon the different methods of computing depreciation, the annual depreciation may be different and hence difference in the annual profit. But overall depreciation charged and the overall profit will be same at the end of the project.
For our case, let the annual profits before depreciation be Rs. 30,000. The following table shows the impact of different methods of depreciation on this annual profit and the overall profit of the project:
Table 10.22
Depreciation (Rs.) Profit after depreciation (Rs.) Year Profit before
depreciation (Rs.)
Straight- line method
Diminishing balance method
Sum- of-the-
year- digits method
Straight- line method
Diminishing balance method
Sum-of- the- year- digits method
1 30,000 2,000 6,000 3,333 28,000 24,000 26,667
2 30,000 2,000 3,600 2,667 28,000 26,400 27,333
3 30,000 2,000 400 2,000 28,000 29,600 28,000
4 30,000 2,000 - 1,333 28,000 30,000 28,667
5 30,000 2,000 - 667 28,000 30,000 29,333
Total (Rs.) 1,50,000 10,000 10,000 10,000 1,40,000 1,40,000 1,40,000
Rs. (‘000)
5000
.
4000
.
2000
.
1000
.
3000
.
0
. .
1
.
2
.
3
.
4
.
5
Sum- of- the- years -digit - method Straight-line method Diminishing balance method
6000
.
Time Fig. 10.5
Example 5: A firm is interested in assessing the cash flows associated with the replacement of old equipment by a new one. The book value of the old equipment is Rs. 90,000 and it can be sold for the same price. The remaining useful life of the equipment is 5 years after which it will have no salvage value.
The new equipment will cost Rs. 4,00,000. It can be sold for Rs. 2,50,000 after 5 years when it will not be needed. The new equipment will save Rs. 1,00,000 annually. If the depreciation is at a rate of 10%
by written down method and applicable tax rate is 50%, determine the cash flows resulting from the replacement project.
Sol:
Table 10.23: Cash flows from the replacement project (Rs.)
Year 0 1 2 3 4 5
A. Net investment (3,10,000)
B. Savings in operations 1,00,000 1,00,000 1,00,000 1,00,000 1,00,000
C. Depreciation on old equipment
9,000 8,100 7,290 6,561 5,905
D. Depreciation on new equipment
40,000 36,000 32,400 29,160 26,244
E. Incremental depreciation on new equipment (D-C)
31,000 27,900 25,110 22,599 20,339
F. Incremental taxable profit (B-E)
69,000 72,100 74,890 77,401 79,661
G. Incremental tax 34,500 36,050 37,445 38,700 39,830
H. Incremental profit after tax
34,500 36,050 37,445 38,700 39,830
I. Incremental net salvage 2,16,526*
J. Initial flow (A) (3,10,000)
K Operating flow (H+E) 65,500 63,950 62,555 61,299 60,169
L. Terminal flow (I) 2,16,526
M. Net cash flow (J+K+L) (3,10,000) 65,500 63,950 62,555 61,299 2,76,695
* Table 10.24: Table to calculate salvage value
Particulars Value (Rs.)
Salvage value of the new equipment after 5 years 2,50,000 Book value of the new equipment after 5 years 2,36,196
Profit on sale 13,804
Tax on profit 6,902
Salvage value of the old equipment after 5 years 0 Book value of the old equipment after 5 years 53,144
Loss on sale 53,144
Tax shield on loss 26,572
Incremental tax payable after 5 years if new equipment is bought 33,474
Net incremental salvage value 2,16,526
Example 6: The following information is available for a capital project:
Table 10.25
Particulars Value
Life of the project (years) 15
Initial outlay (Rs. in lacs) Plant and machinery Working capital
180 120 Financing (Rs. in lacs)
Equity
Long-term loans Trade credit Commercial banks
100 104 36 60 Expected annual sale (Rs. in lacs)
(Including depreciation but excluding interest)
350
Cost of sales (Rs. in lacs)
(Including depreciation but excluding interest)
190
Tax rate (%) 60
Salvage value (Rs. in lacs) Plant and machinery Working capital
180 120
Depreciation (written down method) 15%
Further, working capital will be fully recovered at the end of the project. The long-term debt carries an interest rate of 14% and is payable in eight equal annual installments. Short-term advance from the commercial banks will be maintained at Rs. 60 lakh and will have an interest rate of 8% per annum. It will be fully liquidated at the end of the project. The level of trade credit will remain at Rs. 36 lacs and will be fully paid at the end of the project. Calculate the cash flow stream associated with the following measures of investment.
(a) Total funds; (b) Long-term funds; and (c) Equity.
Sol: Table 10.26: Net cash flows relative to equity Years
Particulars
1 2 3 4 5 6 7
A Sales 350 350 350 350 350 350 350
A' Depreciation 27 22.95 19.51 16.58 14.09 11.98 10.18 B Operating cost
(Including depreciation but excluding interest)
190 190 190 190 190 190 190
C Interest on short-term bank borrowings
2.88 2.88 2.88 2.88 2.88 2.88 2.88
D Interest on term-loans 14.56 14.56 14.56 12.74 10.92 9.1 7.28 E Profit before tax 142.56 142.56 142.56 144.38 146.21 147.02 149.84
F Tax 85.536 85.536 85.536 86.628 87.72 88.81 89.9
G Profit after tax 57.024 57.024 57.024 57.752 58.48 59.39 59.97 H Net salvage value of fixed
assets
I Net salvage value of current assets
J Repayment of long-term loans 13 13 13 13 13 13 K Repayment of short-term loans
L Repayment of trade credit
M Net cash flows related to equity investors (G+H+I-J-K-L+ A')
84.024 66.974 63.534 61.332 59.57 58.37 57.15
N Net cash flows related to long- term funds
(G+A'+D (1-.60)+H+I-K-L)
84.024 79.974 63.534 61.332 59.57 58.37 57.55
O Net cash flows related to total funds
(G+A'+C(1-.6)+1.6D+H+I)
90.976 86.926 83.51 80.58 78.09 76.162 74.834
8 9 10 11 12 13 14 15
350 350 350 350 350 350 350 350 8.65 7.36 6.25 5.32 4.52 3.84 3.26 2.77
190 190 190 190 190 190 190 190
2.88 2.88 2.88 2.88 2.88 2.88 2.88 2.88
5.46 3.64 1.82 - 14.56 14.56 14.56 14.56
151.66 153.48 155.3 157.12 157.12 157.12 157.12 157.12
91 92.09 93.18 93.18 93.18 93.18 93.18 93.18
60.66 61.39 62.12 63.94 63.94 63.94 63.94 63.94
13.10
120.00
13 13 - - -
60 36 56.31 55.75 68.37 69.26 68.46 67.78 67.2 103.81 39.01 55.75 55.37 69.26 68.46 67.78 67.7 103.81 72.646 71.358 70.25 70.412 69.612 68.932 68.352 200.96