Ch16 Lecture Notes

8/2/2019 Ch16 Lecture Notes

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Depreciation Methods

Chapter 16

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Basic Idea

The capital investments of a corporation in tangibleassets (equipment, computers, vehicles, buildings andmachinery) are commonly recovered on the books ofthe corporation through depreciation.

Although the depreciation amount is not an actual cashflow, the process of depreciating an asset, also referredto as capital recovery,accounts for the decrease in anassets value because of age, wear and obsolescence.

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


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Depreciation

An income tax system generally does not allowa deduction for the cost of an asset in the yearthat it is purchased. Instead, it spreads out the

deduction over a period roughly consistentwith the asset's useful economic life.

The amount allowed as an annual deductionroughly reflects the reduction in the value of

the capital asset as it ages, and is calleddepreciation.


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Why Do Capital Assets Depreciate?

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

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

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

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 assetswill 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 theprofitable firm.

Assume a tax rate of 30% of taxable income.

For every $1 of eligible deductions the resultant tax savingsis:

(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 andto represent the diminishing value of the

capital funds invested in it.

The annual depreciation amount Dtdoes not

represent an actual cash flow, nor does it necessarily

reflect the actual usage pattern of the asset duringownership.


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Terminology

Book value represents the remaining, capitalinvestment (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 ormarket value at the end the assets useful life.


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Important Terms

First Cost or Unadjusted Basis (B)

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

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 (bookdepreciation).

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

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

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

MACRS has the DB and SL methods, in slightly different forms, embedded in it, but thesetwo 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 assetreflect the remaining capital invested in it. Additionally, most other countries stillrecognize the classical methods of straight line and declining balance.


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Depreciation Models

There are several models for depreciating assets. Thestraight 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 linemethod.

For the classical methods, straight line, decliningbalance, and sum-of-year digits (SYD), there are Excel

functions available to determine annualdepreciation.


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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 bookdepreciation 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 regularMACRS.


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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. Theunit has an anticipated life of 10 years and a salvage value of$10,000.

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

Freeport-McMoRan Copper & Gold Inc. (FCX) is a leading international mining company with headquarters inPhoenix, 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 worlds largest producer of molybdenum. The companys

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.
http://www.fcx.com/index.htm


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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 straightline rate.

Table 161 presents the Dtvalues using Equation [16.5] and the BVtvalues

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 makeBV10 = S = $10,000exactly.

Similar calculations for DDB withd = 0.2result in the depreciation and

book value series in Table 161.


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DB compared with DDB


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Tax Depreciation

The depreciation method that you use for any particular assetis fixed at the time you first place that asset into service.Whatever rules or tables are in effect for that year must befollowed 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 differentdepreciation methods if you've owned business property for along time.

Corporations may apply any of the classical methods for bookdepreciation.

For most business property placed in service after 1986, if youdon't claim the equipment expensing deduction for the fullcost of the item, the IRS requires you to depreciate the assetusing MACRS.
http://www.irs.gov/


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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 statutorydepreciation rates that take advantage of the accelerated DBand DDB methods.

Incorporates the half-year convention.

By current law MACRS assumes all assets depreciated bythis method will have a 0 salvage value at the end of therecovery life.

Dt= d

tB [16.12]

BVt = BVt-1 Dt [16.13]

BVt = first cost sum of accumulated depreciation [16.14]

1

t

t j

j

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 optimizationsoftware, has acquired new workstations and 3D modelingsoftware for its 100 affiliate sites at a cost of $4000 per site.

The estimated salvage for each system after 3 years isexpected 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-yearDDB model (book depreciation), most curious about thedepreciation 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 thedepreciation rate for DDB is dmax = 2/3 = 0.6667.

Table 163 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 0

(1 )n

nimpS BV B d

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

Ch16 Lecture Notes

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