ᎏᎏ X CA/U ⫻ X CO/EXCA/E/XCA/U
6.7 Depreciation and Depletion Methods
Depreciation is important in economic analysis because it is a tax-allowed deduction included in tax cal- culations. Depreciation is used in relation to tangible assets such as equipment, computers, machinery, buildings, and vehicles. Depletion, on the other hand, is used in relation to investments in natural resources such as minerals, ores, and timber. Almost everything depreciates as time proceeds; however, land is considered a nondepreciable asset. Depreciation can be defined as (Newnan et al., 2004):
● A decline in the MV of an asset (deterioration).
● A decline in the value of an asset to its owner (obsolescence).
● Allocation of the cost of an asset over its depreciable or useful life. Accountants usually use this definition, and it is employed in economic analysis for income-tax computation purposes.
Therefore, depreciation is a way to claim over time an already paid expense for a depreciable asset.
For an asset to be depreciated, it must satisfy these three requirements (Blank and Tarquin, 2002):
1. The asset must be used for business purposes to generate income.
2. The asset must have a useful life that can be determined and is longer than 1 year.
3. The asset must be one that decays, gets used up, wears out, becomes obsolete, or loses value to the owner over time as a result of natural causes.
Depreciation Notations Let
n⫽recovery period in years
B⫽first cost, unadjusted basis, or basis S⫽estimated salvage value
Dt⫽annual depreciable charge MV⫽market value
BVt⫽book value after period, t
d⫽depreciation rate⫽1/n t⫽year (t⫽1,2,3,…,n).
Depreciation Terminology
● Depreciation: The annual depreciation amount, Dt, is the decreasing value of the asset to the owner.
It does not represent an actual cash flow or actual usage pattern.
● Book depreciation: This is an internal description of depreciation. It is the reduction in the asset investment due to its usage pattern and expected useful life.
● Tax depreciation: This is used for after-tax economic analysis. In the United States and many other countries, the annual tax depreciation is tax deductible using the approved method of computation.
● First cost or unadjusted basis: This is the cost of preparing the asset for economic use and is also called the “basis.” This term is used when an asset is new. Adjusted basis is used after some depre- ciation has been charged.
● Book value: This represents the remaining undepreciated capital investment after the total amount of depreciation charges to date have been subtracted from the basis. It is usually calculated at the end of each year.
● Salvage value: Estimated trade-in or MV at the end of the asset’s useful life. It may be positive, neg- ative, or zero. It can be expressed as a dollar amount or as a percentage of the first cost.
● Market value: This is the estimated amount realizable if the asset were sold in an open market. This amount may be different from the BV.
● Recovery period: This is the depreciable life of an asset in years. There are often different n values for book and tax depreciations. Both values may be different from the asset’s estimated productive life.
● Depreciation or recovery rate: This is the fraction of the first cost removed by depreciation each year.
Depending on the method of depreciation, this rate may be different for each recovery period.
● Half-year convention: This is used with the modified accelerated cost recovery system (MACRS) depreciation method. It assumes that assets are placed in service or disposed of midyear, regard- less of when these placements actually occur during the year. There are also midquarter and mid- month conventions.
6.7.1 Depreciation Methods There are five principal depreciation methods:
● Classical (historical) depreciation methods
Sraight line (SL)
Declining balance (DB)
Sum-of-years’-digits (SOYD).
● MACRS.
6.7.1.1 Straight-Line Method
This is the simplest and the best-known method of depreciation. It assumes that a constant amount is depreciated each year over the depreciable (useful) life of the asset; hence, the BV decreases linearly with time. The SL method is considered the standard against which other depreciation models are compared.
It offers an excellent representation of an asset used regularly over an estimated period, especially for book depreciation purposes. The annual depreciation charge is given as
Dt⫽ ⫽(B⫺S)d (6.41)
The BV after t year(s) is given as
BVt⫽B⫺ t (B⫺S)⫽B⫺tDt (6.42)
ᎏn B⫺S ᎏn
6.7.1.2 Declining Balance Method
This method is commonly applied as the book depreciation method in the industry because it accelerates the write-off of asset value. It is also called fixed (uniform) percentage method; therefore, a constant depreciation rate is applied to the BV of the asset. According to the Tax Reform Act of 1986, two rates are applied to the SL rate; these are 150 and 200%. If 150% is used, it is called the DB method, and if 200%
is used, it is called the double declining balance (DDB) method. The DB annual depreciation charge is
Dt⫽ 冢1⫺ 冣t⫺1 (6.43)
Total DB depreciation at the end of t years is
B冤1⫺冢1⫺ 冣t冥⫽B[1⫺(1⫺d )t] (6.44)
Book value at the end of t years is
B冢1⫺ 冣t⫽B(1⫺d )t (6.45)
For DDB (200% depreciation) method, substitute 2.0 for 1.5 in Equations (6.43)–(6.45).
It should be noted that salvage value is not used in equations for DB and DDB methods; therefore, these methods are independent of the salvage value of the asset. The implication of this is that the depreciation schedule may be below an implied salvage value, above an implied salvage value, or just at the level of the implied salvage value. Any of these three situations is possible in the real world. However, the U.S. Internal Revenue Service (IRS) does not permit the deduction of depreciation charges below the salvage value, while companies will not like to deduct depreciation charges that would keep the BV above the salvage value. The solution to this problem is to use a composite depreciation method. The IRS provides that a taxpayer may change from DB or DDB to SL at any time during the life of an asset. However, the question is when to switch. The criterion used to answer this question is to maximize the PW of the total depreciation.
6.7.1.3 Sum-Of-Years’-Digits Method
This method results in larger depreciation charges during the early years of an asset (than SL) and smaller charges at the latter part of the estimated useful life; however, write-off is not as rapid as for DDB or MACRS. Similar to the SL method, this method uses the salvage value in computing the annual depreci- ation charge. The annual depreciation charge is
Dt⫽ (B⫺S)⫽dt(B⫺S)
SUM⫽
(6.46)
The BV at the end of t years is
BVt⫽B⫺ (B⫺S) (6.47)
6.7.1.4 Modified Accelerated Cost Recovery System Method
This is the only approved tax depreciation method in the United States. It is a composite method that automatically switches from DB or DDB to SL depreciation. The switch usually takes place whenever the SL depreciation results in larger depreciation charges, that is, a more rapid reduction in the BV of the asset. One advantage of the MACRS method is that it assumes that the salvage value is 0; therefore, it always depreciates to 0. Another outstanding advantage of this method is that it uses property classes,
t(n ⫺(t/2)⫹0.5) ᎏᎏᎏᎏSUM n(n⫹1)
ᎏᎏ2 n ⫺t⫹1 ᎏᎏSUM
ᎏ1.5n ᎏ1.5n
ᎏ1.5Bn ᎏ1.5Bn
which specify the recovery periods, n. The method adopts the half-year convention, which makes the actual recovery period to be 1 year longer than the specified period. The half-year convention means that the IRS assumes that the assets are placed in service halfway through the year, no matter when the assets were actually placed in service. This convention is also applicable when the asset is disposed of before the end of the depreciation period. The MACRS method consists of two systems for computing depreciation deductions: general depreciation systems (GDS) and alternative depreciation systems (ADS). Alternative depreciation systems are used for properties placed in any tax-exempt use as well as properties used pre- dominantly outside the United States. The system provides a longer recovery period and uses only SL method of depreciation. Therefore, this system is generally not considered an option for economic analy- sis. However, any property that qualifies for GDS can be depreciated under ADS, if preferred.
The following information is required to depreciate an asset using the MACRS method:
● The cost basis
● The date the property was placed in service
● The property class and recovery period
● The MACRS depreciation system to be used (GDS or ADS)
● The time convention that applies (e.g., half or quarter-year convention).
The steps involved in using the MACRS depreciation method are:
1. Determine the property class of the asset being depreciated using published tables. Any asset not in any of the stated classes is automatically assigned a 7-year recovery period under the GDS system.
2. After the property class is known, read off the appropriate published depreciation rates.
3. The last step is to multiply the asset’s cost basis by the depreciation rate for each year to get the annual depreciation charge.
The MACRS annual depreciation amount is
Dt⫽(first cost)(tabulated depreciation rate)⫽dtB (6.48) The annual BV is
BVt⫽first cost⫺sum of accumulated depreciation
⫽B⫺冱j⫽1t Dj (6.49)
6.7.2 Depletion Methods
Depletion is applicable to natural resources from places such as mines, wells, and forests. It recovers investment in natural resources; therefore, it is the exhaustion of natural resources as a result of their removal. There are two methods of calculating depletion: cost (factor) depletion and percentage depletion (Park, 2001; Newnan et al., 2004). In the United States, except for standing timber and most oil and gas wells, depletion is calculated by both methods and the larger value is taken as the depletion for the year.
6.7.2.1 Cost Depletion
This is based on the level of activities; however, the total cost of depletion cannot exceed the first cost of the resource. The annual depletion charge is
(year’s usage or volume) (6.50)
6.7.2.2 Percentage Depletion
This is a special consideration for natural resources. It is an annual allowance of a percentage of the gross income from the property. Since it is based on income rather than the cost of the property, the total depletion
first cost ᎏᎏresource capacity
on a property may exceed the cost of the property. The percentage depletion allowance in any year is limited to not more than 50% of the taxable income from the property. The percentage depletion amount is
percentage⫻gross income from property (6.51)
The percentages are usually published and they change from time to time.