By Muhammad Shahid Iqbal Engineering Economics Module No. 12 Depreciation By Muhammad Shahid Iqbal

Introduction to Depreciation Any equipment purchased today will not work forever. This may be due to wear and tear of the equipment or obsolescence of technology. It is to be replaced at the proper time for continuance of any business. The replacement of the equipment at the end of its life involves money. This must be internally generated from the earnings of the equipment. Decrease in value of physical assets with passage of time and use Accounting concept establishing annual deduction to reflect effect of time and use on asset’s value in firm’s financial statements to match yearly fraction of value used by asset in production of income over asset’s economic life In economics, depreciation is the gradual and permanent decrease in the economic value of the capital stock of a firm, nation or other entity, either through physical depreciation, obsolescence or changes in the demand for the services of the capital in question.

Property is Depreciable if it Must be used in business or held to produce income have a determinable useful life, longer than one year wear out, decay, get used up, become obsolete, or lose value from natural causes not be inventory, stock in trade, or investment property DEPRECIABLE PROPERTY TANGIBLE - can be seen or touched Personal property - such as machinery,vehicles,equipment, furniture Real property - anything erected on, growing on, or attached to land (Since land does not have determinable life itself, it is not depreciable) INTANGIBLE - personal property, such as copyright, patent or franchise

Depreciation Methods Straight Line Depreciation Method: This method assumes a constant depreciation value per year. In this method of depreciation, a fixed sum is charged as the depreciation amount throughout the life time of an asset such that the accumulated sum at the end of the life of the asset is exactly equal to the purchase value of the asset. Annual Depreciation = Dt = P = price of a depreciating asset Dt = Depreciation amount for the period t. S = Salvage value of the asset. N = Life of the Asset Bt = P – t x [(P-S)/n] Bt = Book value of the asset at the end of the period t.

Straight Line Depreciation Method A company has purchased an equipment whose first cost is 1,00,000 with an estimated life of eight years. The estimated salvage value of the equipment at the end of its life time is Rs. 20,000. Determine the depreciation charge and book value at the end of various years using the straight line method of depreciation. Compute the depreciation and book value for period 5

Depreciation Methods Declining Balance Depreciation Method Depreciation methods that provide for a higher depreciation charge in the first year of an asset's life and gradually decreasing charges in subsequent years are called accelerated depreciation methods. This may be a more realistic reflection of an asset's actual expected benefit from the use of the asset: many assets are most useful when they are new. One popular accelerated method is the declining-balance method. Under this method the book value is multiplied by a fixed rate.

Depreciation Methods Depreciation = Book value x Depreciation rate Dt =  K x Bt-1      Book value = Cost - Accumulated depreciation Bt = Bt-1 - Dt = Bt-1– K x Bt-1 = (1 - K) x Bt-1 The formula for depreciation and book value in terms of P is as follows: Dt =  K (1 - K)t-1 x P Bt = (1 - K)t x P The most common rate used is double the straight-line rate. For this reason, this technique is referred to as the double-declining-balance method. Depreciation rate for double declining balance method            = Straight line depreciation rate x 200%

Sum-of-years' digits method Depreciation Methods Sum-of-years' digits method Sum-of-years' digits is a depreciation method that results in a more accelerated write-off than straight line, but less than declining-balance method. Under this method annual depreciation is determined by multiplying the Depreciable Cost by a schedule of fractions. depreciation = (original cost − salvage value) x Rate First, determine sum of years' digits. if the asset has useful life of 5 years, the years' digits are: 5, 4, 3, 2, and 1. The sum of the digits is: 5+4+3+2+1=15 Formula = n(n+1) / 2 Rate = n – t + 1/ [n(n+1)/2]

Units-of-production depreciation method Under the units-of-production method, useful life of the asset is expressed in terms of the total number of units expected to be produced: Suppose, an asset has original cost $70,000, salvage value $10,000, and is expected to produce 6,000 units. Depreciation per unit = ($70,000−10,000) / 6,000 = $10 10 x actual production will give you the depreciation cost of the current year. The table below illustrates the units-of-production depreciation schedule of the asset.