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Depreciation Methods

Chapter 10

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.

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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