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Depreciation Methods

Chapter 16

04/19/23 1

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Basic Idea

The capital investments of a corporation in tangible assets (equipment, computers, vehicles, buildings and machinery) are commonly recovered on the books of the corporation through depreciation.

Although the depreciation amount is not an actual cash flow, the process of depreciating an asset, also referred to as capital recovery, accounts for the decrease in an asset’s value because of age, wear and obsolescence.

Even though an asset may be in excellent working condition, the fact that it is worth less (has less value), is taken into account.

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Depreciation

An income tax system generally does not allow a deduction for the cost of an asset in the year that it is purchased. Instead, it spreads out the deduction over a period roughly consistent with the asset's useful economic life.

The amount allowed as an annual deduction roughly reflects the reduction in the value of the capital asset as it ages, and is called depreciation.

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Why Do Capital Assets Depreciate?

A capital asset might depreciate -- fall in value as it ages over its useful life -- for several reasons.

One reason is that as it ages it gets closer to the end of its useful life. The value of an asset is the present discounted value of the net cash flow it can produce.

Older assets have fewer years left to produce income, and therefore are worth less than otherwise similar, yet newer, assets that will produce an income flow over a longer life span.

Another reason is that capital assets wear out as they age, and so are less productive, or require more maintenance, than do newer capital assets.

Certain types of quality improvements in similar new assets will also reduce the value of older assets due to obsolescence.

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Significance of Depreciation

Economic depreciation measures the expected decline in the real market value of the asset in each period.

Depreciation lowers income taxes via the relation:

Taxes = (income - deductions)(tax rate)

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Depreciation Amounts

Federal tax law states that: Any productive asset with a finite life (greater than one year) must be depreciated for tax purposes rather than “expensed” in the year of purchase.

Depreciation amounts represent a prorated amount per year that can be treated as an “expense” (deduction) but is not a real cash flow.

Depreciation amounts represent a form of tax savings to the profitable firm.

Assume a tax rate of 30% of taxable income. For every $1 of eligible deductions the resultant tax savings

is: (0.30)($1.00) = $0.30. $1 of additional deductions saves the firm $0.30.

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Depreciation

Depreciation is the reduction in value of an asset. The method used to depreciate an asset is a way to

account for the decreasing value of the asset to the owner and to represent the diminishing value of the capital funds invested in it.

The annual depreciation amount Dt does not represent an actual cash flow, nor does it necessarily reflect the actual usage pattern of the asset during ownership.

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Terminology

Book value represents the remaining, capital investment (not yet depreciated) on the books after the total amount of depreciation charges (to date) have been subtracted from the basis. The book value (BV) is usually determined at the end of each year.

Market Value (MV) is the amount realized from sale on the open market.

Salvage Value (S) is the estimated trade-in value or market value at the end the asset’s useful life.

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Important Terms First Cost or Unadjusted Basis (B)

Initial purchase price + all costs incurred in placing the asset in service

Recovery Period (n) Depreciable life of the asset in question – often set by law

Depreciation Rate (dt) The fraction of the first cost removed by depreciation each year

Personal Property All property except real estate used in the pursuit of profit or

gain Real Property

Real estate and improvements, buildings and certain structures

Land is Real Property, but by law is NOT depreciable for tax purposes

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Book vs Tax Depreciation Depreciation may be performed for two reasons:

1. Use by a corporation or business for internal financial accounting (book depreciation).

2. Use in tax calculations per government regulations (tax depreciation). The methods applied for these two purposes may or may not utilize the same formulas. Book depreciation indicates the reduced investment in an asset based upon the usage

pattern and expected useful life of the asset. There are classical, internationally accepted depreciation methods used to determine book depreciation: straight line, declining balance, and the infrequently used sum-of-year digits method.

Tax depreciation is important because it is tax deductible; it can be subtracted from income when calculating the amount of taxes due each year. However, the tax depreciation amount must be calculated using a government approved method.

Tax depreciation must be calculated using MACRS; book depreciation may be calculated using any classical method or MACRS.

MACRS has the DB and SL methods, in slightly different forms, embedded in it, but these two methods cannot be used directly if the annual depreciation is to be tax deductible.

Many U.S. companies still apply the classical methods for keeping their own books, because these methods are more representative of how the usage patterns of the asset reflect the remaining capital invested in it. Additionally, most other countries still recognize the classical methods of straight line and declining balance.

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Depreciation Models

There are several models for depreciating assets. The straight line (SL) model is used historically.

Accelerated models, such as the declining balance (DB) model, decrease the book value to zero (or to the salvage value) more rapidly than the straight line method.

For the classical methods, straight line, declining balance, and sum-of-year digits (SYD), there are Excel functions available to determine annual depreciation.

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Depreciation Models (2)Straight Line (SL) It writes off capital investment linearly over n years.The estimated salvage value is always considered.This is the classical, nonaccelerated depreciation model.

Declining Balance (DB) (also known as fixed percentage or uniform percentage method)The model accelerates depreciation compared to straight line.The book value is reduced each year by a fixed percentage.The most used rate is twice the SL rate; called double declining balance (DDB). It has an implied salvage that may be lower than the estimated salvage. It is not an approved tax depreciation method in the United States. It is frequently used for book

depreciation purposes.

Modified Accelerated Cost Recovery System (MACRS) It is the only approved tax depreciation system in the United States. It automatically switches from DDB or DB to SL depreciation. It always depreciates to zero; that is, it assumes S = 0.Recovery periods are specified by property classes.Depreciation rates are tabulated.The actual recovery period is 1 year longer due to the imposed half-year convention.MACRS straight line depreciation is an option, but recovery periods are longer than for regular

MACRS.

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Straight Line

If an asset has a first cost of $50,000 with a $10,000 estimated salvage value after 5 years,

Calculate the annual depreciation.

Solution

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Double Declining Balance (DDB)

A fiber optics testing device is to be DDB depreciated. It has a first cost of $25,000 and an estimated salvage of $2500 after 12 years.

(a) Calculate the depreciation and book value for years 1 and 4. (b) Calculate the implied salvage value after 12 years.

Solution The DDB fixed depreciation rate is d = 2/n = 2/12 = 0.1667 per year. Year 1: D1 = (0.1667)(25,000)(1 - 0.1667)1-1 = $4167

BV1 = 25,000(1 - 0.1667)1 = $20,833

Year 4: D4 = (0.1667)(25,000)(1 - 0.1667)4-1 = $2411

BV4 = 25,000(1 - 0.1667)4 = $12,054

Implied S = 25,000(1 - 0.1667)12 = $2803 Since the estimated S = $2500 is less than $2803, the asset is not fully depreciated when it reaches

its 12-year expected life.

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DB compared with DDB Freeport-McMoRan Mining Company has purchased a

computer-controlled gold ore grading unit for $80,000. The unit has an anticipated life of 10 years and a salvage value of $10,000.

Use the DB and DDB methods to compare the schedule of depreciation and book values for each year.

Freeport-McMoRan Copper & Gold Inc. (FCX) is a leading international mining company with headquarters in Phoenix, Arizona. FCX operates large, long-lived, geographically diverse assets with significant proven and probable reserves of copper, gold and molybdenum. FCX has a dynamic portfolio of operating, expansion and growth projects in the copper industry and is the world’s largest producer of molybdenum. The company’s portfolio of assets includes the Grasberg mining complex, the world's largest copper and gold mine in terms of recoverable reserves; significant mining operations in the Americas, including the large scale Morenci/Safford minerals district in North America and the Cerro Verde and El Abra operations in South America; and the potential world-class Tenke Fungurume development project in the Democratic Republic of Congo.

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Solution An implied DB depreciation rate is determined using

d = 1 – (10,000/80,000) 1/10 = 0.1877 0.1877 < 2/n = 0.2, so this DB model does not exceed twice the straight

line rate. Table 16–1 presents the Dt values using Equation [16.5] and the BVt values

from Equation [16.9] rounded to the nearest dollar. For example, in year t = 2, the DB results are:

D2 = d(BV1) = 0.1877(64,984 next slide) = $12,197

BV2 = 64,984 - 12,197 = $52,787 Because we round off to even dollars, $2312 is calculated for depreciation in

year 10, but $2318 is deducted to make BV10 = S = $10,000 exactly.

Similar calculations for DDB with d = 0.2 result in the depreciation and book value series in Table 16–1.

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DB compared with DDB

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Tax Depreciation The depreciation method that you use for any particular asset

is fixed at the time you first place that asset into service. Whatever rules or tables are in effect for that year must be followed as long as you own the property.

Since Congress has changed the depreciation rules many times over the years, you may have to use a number of different depreciation methods if you've owned business property for a long time.

Corporations may apply any of the classical methods for book depreciation.

For most business property placed in service after 1986, if you don't claim the equipment expensing deduction for the full cost of the item, the IRS requires you to depreciate the asset using MACRS.

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Modified Accelerated Cost Recovery System (MACRS)

MACRS was derived from the 1981 ACRS system and went into effect in 1986.

Defines statutory recovery (depreciation) percentages. Through MACRS, the 1986 Tax Reform Act defined statutory

depreciation rates that take advantage of the accelerated DB and DDB methods.

Incorporates the half-year convention. By current law – MACRS assumes all assets depreciated by

this method will have a “0” salvage value at the end of the recovery life.

Dt = dtB [16.12]

BVt = BVt-1 – Dt [16.13]

BVt = first cost – sum of accumulated depreciation [16.14]

1

t

t jj

BV B D

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The Half-year convention

During a tax year, assets are purchased and installed throughout the first year.

Under past laws, the first year of depreciation had to be prorated by the number of months remaining in the tax year.

Under current federal tax law the first year is handled using the half-year convention.

Half-year convention assumes that assets are placed in service or disposed of in midyear, regardless of when these events actually occur during the year.

This convention is utilized in this text and in most U.S.- approved tax depreciation methods.

There are also mid-quarter and mid-month conventions.

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Omniture, a leading provider of online business optimization software, has acquired new workstations and 3D modeling software for its 100 affiliate sites at a cost of $4000 per site.

The estimated salvage for each system after 3 years is expected to be 5% of the first cost.

The Utah office wants to compare the depreciation for a 3-year MACRS model (tax depreciation) with that for a 3-year DDB model (book depreciation), most curious about the depreciation over the next 2 years.

(a) Determine which model offers the larger total depreciation after 2 years.

(b) Determine the book value for each model after 2 years and at the end of the recovery period.

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The basis is B = $400,000 and the estimated S = 0.05(400,000) = $20,000.The MACRS rates for n = 3 are taken from Table 16–2 (next slide) and the

depreciation rate for DDB is dmax = 2/3 = 0.6667.

Table 16–3 presents the depreciation and book values. Year 3 depreciation for DDB would be (0.6667)$44,444 = $29,629, except that this would make BV3 < $20,000 (44,444 - 29,629 = 14815). BV – tax depr = BV3

Solution

Dt = dtB [16.12]BVt = BVt-1 – Dt [16.13]

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Depreciation rates

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Solution

Only the remaining amount of $24,444 is removed (44,444 - 20,000). (a) The 2-year accumulated depreciation values from Table 16–3 are MACRS: D1 + D2 = $133,320 + 177,800 = $311,120 DDB: D1 + D2 = $266,667 + 88,889 = $355,556 The DDB depreciation is larger. (Remember that for tax purposes,

Omniture does not have the choice in the United States of the DDB model.)

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(b) After 2 years the book value for DDB at $44,444 is 50% of the MACRS book value of $88,880. At the end of recovery (4 years for MACRS due to the built-in half-year convention, and 3 years for DDB), the MACRS book value is BV4 = 0 and

for DDB, BV3 = $20,000. This occurs because MACRS always removes the entire first cost,

regardless of the estimated salvage value. This is a tax depreciation advantage of the MACRS method.

Solution

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Recovery PeriodThe expected useful life of property is estimated in years and used as the n value in alternative evaluation and in depreciation computations. For book depreciation, the n value should be the expected useful life. However, when the depreciation will be claimed as tax deductible, the n value should be lower.

The advantage of a recovery period shorter than the anticipated useful life is leveraged by the accelerated depreciation models that write off more of the basis B in the initial years.

The U.S. government requires that all depreciable property be classified into a property class that identifies its MACRS-allowed recovery period.

Table 16–4, a summary of material from IRS Publication 946, gives examples of assets and the MACRS n values.

Virtually any property considered in an economic analysis has a MACRS n value of 3, 5, 7, 10, 15, or 20 years.

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Class of Property Items Included

3-year propertyTractor units, racehorses over two years old, and horses over 12

years old when placed in service

5-year property

Automobiles, taxis, buses, trucks, computers and peripheral equipment, office machinery (faxes, copiers, calculators etc.), and any property used in research and experimentation. Also includes breeding and dairy cattle.

7-year propertyOffice furniture and fixtures, and any property that has not been

designated as belonging to another class.

10-year propertyVessels, barges, tugs, similar water transportation equipment,

single-purpose agricultural or horticultural structures, and trees or vines bearing fruit or nuts.

15-year propertyDepreciable improvements to land such as shrubbery, fences,

roads, and bridges.

20-year property Farm buildings that are not agricultural or horticultural structures.

27.5-year property Residential rental property.

39-year propertyNonresidential real estate, including home offices. (Note that the

value of land may not be depreciated.)

MACRS categorizes all business assets into classes and specifies the time period over which you can write off assets in each class. The most commonly used items are classified in the chart. http://taxguide.completetax.com/text/Q14_2960.asp (similar to Table 16-4)

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MACRS Recovery Periods

Table 16–4 provides two MACRS n values for each property. The first is the general depreciation system (GDS) value that the text (MSE 304) uses

in examples and problems. The depreciation rates in Table 16–2 (slide 24) correspond to the n values for the GDS

column and provide the fastest write-off allowed. The rates utilize the DDB method or the 150% DB method with a switch to SL

depreciation. Note that any asset not in a stated class is automatically assigned a 7-year recovery period under GDS.

The far right column of Table 16–4 lists the alternative depreciation system (ADS) recovery period range. This alternative method allows the use of SL depreciation over a longer recovery period than the GDS. The half-year convention applies, and any salvage value is neglected, as it is in regular MACRS.

The use of ADS is generally a choice left to a company, but it is required for some special asset situations. Since it takes longer to depreciate the asset, and since the SL model is required (removing the advantage of accelerated depreciation), ADS is usually not considered an option for the economic analysis.

This SL option is sometimes chosen by businesses that are young and do not need the tax benefit of accelerated depreciation during the first years of operation and asset ownership.

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Table 16–4: Example MACRS Recovery Periods for Various Asset Descriptions

31http://www.pine-grove.com/depreciation/MACRS.htm

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Depletion

Up to this point, we have discussed depreciation for assets that can be replaced.

Depletion, though similar to depreciation, is applicable only to natural resources.

When the resources are removed, they cannot be replaced or repurchased in the same manner as can a machine, computer, or structure.

Depletion is applicable to natural deposits removed from mines, wells, quarries, geothermal deposits, forests, and the like.

There are two methods of depletion - cost depletion and percentage depletion.

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Cost Depletion

Cost depletion, sometimes referred to as factor depletion, is based on the level of activity or usage, not time, as in depreciation.

It may be applied to most types of natural resources. The cost depletion factor for year t, denoted by pt, is the ratio of the first cost of the resource to the estimated number of units recoverable.

The annual depletion charge is pt times the year’s usage or volume.

The total cost depletion cannot exceed the first cost of the resource.

If the capacity of the property is re-estimated some year in the future, a new cost depletion factor is determined based upon the undepleted amount and the new capacity estimate.

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Brookfield Asset Management Inc. (BAM), a global asset manager focused on property, power and other infrastructure assets with approximately $95 billion of assets under management, has negotiated the rights to cut timber on privately held forest acreage for $700,000. An estimated 350 million board feet of lumber are harvestable.

(a) Determine the depletion amount for the first 2 years if 15 million and 22 million board feet are removed.

(b) After 2 years the total recoverable board feet was re-estimated to be 450 million from the time the rights were purchased. Compute the new cost depletion factor for years 3 and later.

Brookfield has a 30-year track record of owning and operating timberlands in North and South America that generate strong, sustainable cash flows.

Today they have 2.5 million acres of high quality timberlands under management which include: Island Timberlands, a private equity investment, Longview Timberlands that encompasses 588,000 acres of high quality fee simple timberlands on the west coast of Washington and Oregon, and Acadian Timber.

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Solution (a) Determine the depletion amount for the first 2 years if 15 million and 22 million

board feet are removed. For $700,000 BAM may cut timber on privately held forest acreage. An estimated 350 million board feet of lumber are harvestable. Use Equation [16.15] for pt in dollars per million board feet.

Multiply pt by the annual harvest to obtain depletion of $30,000 (15 * 2000) in year 1 and $44,000 (22 * 2000) in year 2.

Continue using pt until a total of $700,000 is written off. (b) After 2 years the total recoverable board feet was re-estimated (450 million from the

time the rights were purchased). Compute the new cost depletion factor for years 3 and later.

After 2 years, a total of $74,000 (30000 + 44000) has been depleted. A new pt value must be calculated based on the remaining $700,000 - 74,000 =

$626,000 investment. Additionally, with the new estimate of 450 million board feet, a total of: 450 -15 - 22 = 413 million board feet remain. For years t = 3, 4, . . . , the cost depletion factor is = $1516 per million board feet

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Percentage Depletion

Percentage depletion is a special consideration given for natural resources. A constant, stated percentage of the resource’s gross income may be depleted each

year provided it does not exceed 50% of the company’s taxable income. For oil and gas property, the limit is 100% of taxable income. The annual depletion amount is calculated as using percentage depletion, total

depletion charges may exceed first cost with no limitation. The U.S. government does not generally allow percentage depletion to be applied to

oil and gas wells (except small independent producers) or timber. The depletion amount each year may be determined using either the cost method

or the percentage method, as allowed by law. Usually, the percentage depletion amount is chosen because of the possibility of

writing off more than the original cost. However, the law also requires that the cost depletion amount be chosen if the

percentage depletion is smaller in any year.

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A gold mine was purchased for $10 million. It has an anticipated gross income of $5.0 million per year for years 1 to 5 and $3.0 million per year after year 5.

Assume that depletion charges do not exceed 50% of taxable income. Compute annual depletion amounts for the mine. How long will it take to recover the initial investment at i = 0%?

Agnico-Eagle Mines Limited is an international growth company focused on gold, with operations in Canada and advanced-stage projects and opportunities in Canada, Mexico, Finland, and the USA. Agnico-Eagle's LaRonde Mine in Quebec is Canada's largest gold deposit and is a strong foundation for international expansion.

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Solution

A 15% depletion applies to gold. Depletion amounts are Years 1 to 5: 0.15(5.0 million) = $750,000 Years thereafter: 0.15(3.0 million) = $450,000 A total of $3.75 million is written off in 5 years, and the remaining $6.25

million is written off at $450,000 per year. The total number of years is:

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Equations

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DB Depreciation

max

2d

n

1( )t tD d BV

1(1 )ttd d d

Max. depr. rate by law:

Depreciation for year t:

Actual depreciation rate for year t:

If BVt-1 not known, apply:1(1 )ttD dB d

Book Value amounts (two methods)

1

(1 )tt

t t t

BV B d

BV BV D

Implied Salvage Value

1/

1n

S

B

Implied d for S >0

(1 )nnimpS BV B d

Excel Function: =DDB(B,S,n,t,d)