What refers to the lessening of the value of an asset due to the decrease in the quantity available?

16.2 - 16.7 - Depreciation and Depletion

One definition of the word depreciation is to lessen in estimated value:  lower the worth of.  In general, the value of an asset decreases with time because of age, wear, or obsolescence.  A number of methods for systematically expressing the decreasing value of assets with time have been developed over the years.  These so-called depreciation models result in values which (1) affect income taxes, and (2) provide information to investors about the worth of the assets of public companies.

Depreciation affects income taxes because it is one of the deductions (from income) that businesses can take before calculating the amount of taxes they owe per the following equation:

Taxes = (income – deductions) (tax rate)

Since depreciation is a deduction (just as labor costs, rent, and other expenses are for businesses), the taxes owed are reduced by an amount equal to the depreciation times the tax rate (assuming income stays the same).  For example, a business that has a depreciation deduction of $5000 in a year when its tax rate is 40% would have its tax bill reduced by $2000 that year (i.e. $5000 * 0.40).  The depreciation calculated for this purpose is called tax depreciation and must be determined using only IRS-approved models.  Book depreciation refers to the depreciation procedures used by corporations to more accurately reflect to shareholders the value of their assets.  Two of the models used for depreciating assets are discussed below.

The modified accelerated cost recovery system (MACRS) is the only currently-approved depreciation model allowed for tax depreciation in the United States.  According to this model, the depreciation charge for a given year is calculated by multiplying the asset’s depreciable amount (known as its basis, B, which is usually its first cost) by a depreciation rate.  In equation form, MACRS depreciation is

            Dt = dtB

                        where:  dt = depreciation rate, %

                                    B = Asset’s basis, $

The depreciation rates, dt, are available in tables like Table 16-2 shown below for assets which have recovery periods (n) of 3 to 20 years.

Thus, the depreciation charge in year 3 for a $10,000 asset which has a 5-year recovery would be $1,920 (i.e. $10,000 * 0.1920)

The book value of an asset refers to its undepreciated amount and is represented as the difference between the first cost, B, and the sum of the depreciation that has been charged up to that time.   In equation form,

                        BVt = B - �D           (B - Sums of D's )

For example, an asset that costs $10,000 and has a 5-year recovery period would have a book value at the end of year 3 equal to:

            BV3 = 10,000 – 10,000 (0.20) – 10,000 (0.32) – 10,000 (0.1920)

                   = 10,000 – 10,000 (0.20 + 0.32 + 0.1920)

                   = $2,880

While the MACRS model is the only one approved for tax depreciation, a model frequently used by corporations for book depreciation is the straight line model.  Under this model, the depreciation charge is the same each year per the following equation:

            D = (B – SV) / n

            where:             B = Asset first cost

                               SV= Asset salvage value

                                  n = Asset life

Thus, an asset which has a first cost of $10,000 with an expected salvage value of $2000 after a 5-year useful life would have a depreciation charge of $1,600 each year

[i.e.(10,000–2000)/5].

The book value of an asset depreciated by the straight line method would be

            BVt = B – tD

            where t = no. of years asset has been depreciated

The depreciation models discussed up to this point apply to assets that can be replaced.  For assets that cannot be replaced, like natural resources, different procedures are used for tax accounting purposes.  There are two methods which can be used to account for this so-called depletion:   cost depletion and percentage depletion.

Cost depletion involves the multiplication of a cost factor, pt, by the amount of resource removed in a given year.  The factor, Pt, is equal to the first cost of the resource divided by the total amount of recoverable resource:

           Pt = (first cost)  / resource capacity

The annual depletion deduction is Pt times the amount of resource harvested in that year.  For example, if a gold mine which cost $1,000,000 had an estimated 4000 ounces of gold, the depletion factor would be $250 per ounce (i.e. 1,000,000/4000).   The depletion charge in a year when 1,000 ounces is removed would be $250,000 (i.e. 250 * 1000).

Percentage depletion is a procedure wherein a certain percentage of the income from harvesting the resource is taken as the deduction.  The percentage that is taken is a function of the type of resource involved as shown in the table below:

Thus, if 10,000 ounces of gold are harvested in a year when gold is selling for $270 per ounce, the depletion allowance deduction would be (0.15) (10,000) (270) = $405,000 (subject to certain tax law restrictions).

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