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MER 160 - Design of Thermal Fluid Systems

Engineering Economics – Depreciation Methods

Professor BrunoWinter Term 2005

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Depreciation

• Reduction in the value of an asset with time

• “Book Depreciation:” used by a business to keep track of the value of their assets at any given time

• “Tax Depreciation:” Used to determine write-offs against income caused by depreciation. MUST BE DONE USING A GOV’T APPROVED METOD

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Concepts of Value• Market Value

– Price at which property could actually be sold

• Value to owner– Money amount that would be sufficient to

compensate owner if the owner were to be deprived of the property

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Depreciation TerminologyDepreciation: reduction in the value of an asset

using (government) approved rules

Dt: depreciation amountB: first cost (installed cost of asset)

(Also called the “Unadjusted Basis” or simply “Basis” … hence the “B”)

BVt: book value - represents the remaining un-depreciated investment (value) on the

books. Determined at the end of the year

Note the “t” subscript refers to “time” in years

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Depreciation Terminology

n: recovery period (depreciable life of asset in years)

dt: depreciation rate (fraction of first cost removed by depreciation in a given year).

SV: salvage value (estimated market value at the end of an asset’s useful life).

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Depreciation TerminologyDepreciation is allowed for two types of property:

Personal Property: income producing tangible possessions of a corporation used to conduct business

Real Property: real estate buildings etc (land is not depreciable)

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Methods of Depreciation Accounting

(1)Accelerated methods - give a greater write off in the early years (declining balance, MACRS)

(2) Uniform Methods - give a uniform write off throughout the entire service life. (straight-line)

(3) Decelerated Methods - give a smaller write off in the early years. (sinking fund)

CHOICE IS INFLUENCESD BY TAX LAWS

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Straight Line Depreciation

Dt is the depreciation charge in year t and BVt is the book value at the end of the tth year after the depreciation charge has been made.

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SL Depreciation Example

Consider a machine tool with a first cost of $35,000 an estimated life of 20 years and an estimated salvage value of $3,500. Use SL depreciation and calculate the depreciation charge and the book value of the machine tool after 4 years.

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SL Depreciation ExampleB = $35,000SV = $3500n = 20

= 1/20 = 0.05

=0.05*(35000-3500) =$1575

= $35000 – 4($1575) = $28700

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Declining Balance DepreciationAssets are commonly worth more in initial years – it is sensible to write off costs more rapidly in the early years.

Declining Balance: a given depreciation rate (d) is applied to the remaining book value each year.

i.e. 10% applied to a $35,000 asset

1st year Dt = 0.01*(35000) = 3500

2nd year Dt = 0.10*(35000-3500) = 3150

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Declining Balance DepreciationThe maximum allowable percentage is double the straight line rate: (also called Double Declining Balance or DDB method)

dmax = 2/n

The actual depreciation rate is dt = d*(1-d)t-1

Dt = d*BVt-1

Dt = d*B*(1-d)t-1

BVt = B*(1-d)t

With the DB method the BV never goes to zero.However, no asset can be depreciated below the SV!

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DB Depreciation Example

Assume that an asset has a first cost of $25,000 and an estimate salvage value of $4000 after 12 years, Calculate its depreciation and book value for (a) year one and (b) year four using the DDB method.

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DB Depreciation Example

First Compute the depreciation rate:

d = 2/n = 2/12 = 0.1667

(a) For the first year: D1 = = 0.1667*25000*(1-0.1667)1-1=$4167

BV1 = 25000*(1-.01667)1 = $20,832.50

Year 4 D = 2411.46, BV = 12,054

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MACRS Economic Reform Act (1981) – ACRS

Tax Reform Act (1986) - MACRS

• Applies to property placed in service after 12/31/86

• Doesn’t use useful life or SV

• Property is organized into ASSET Classes and assigned a Class Life.

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MACRS

Dt = dt*B

(dt is set by the government)

BVt = BVt-1-Dt

The first cost is always completely depreciated – assumes SV = 0

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MACRS Depreciation Example

Calculate the depreciation charge and book value for an asset worth $100,000 using MACRS depreciation with a three year recovery period.

year d D BV0 100,000.00$ 1 0.333 33,300.00$ 66,700.00$ 2 0.445 44,500.00$ 22,200.00$ 3 0.148 14,800.00$ 7,400.00$ 4 0.074 7,400.00$ -$