11/25/2023

Bicol University College of Engineering

Civil Engineering Department

Annual depreciation deductions are

intended to “match” the yearly fraction of value
used by an asset in the production if income over
the asset’s actual economic life. The actual
amount of depreciation can never be established
until the asset is retired from service. Because
BY: depreciation is a non-cash cost that affects income
taxes, we must consider it properly when making
ENGR. JEFFERSON M. CIPRIANO, MET
Assistant Professor IV after-tax engineering economy studies.

DEPRECIATION  To provide for the recovery of capital that has

 Is the decrease in value of physical properties been invested in physical property.
with the passage of time and use.  To enable the cost of depreciation to be
 In accounting, it establishes an annual charged to the cost of producing products or
deduction against before-tax income such that services that result from the use of the
the effect of time and use on asset’s value can property. Depreciation cost is real, as are
be reflected in a firm’s financial statements labor and material costs, and it is deductible
benefits of one project has no effect on the in computing profits on which income taxes
benefits of another project. are paid.

 Economic depreciation measures the expected decline DEPRECIABLE PROPERTY

in the real market value of the asset in each period. Is a property for which depreciation is allowed under
federal, state, or municipal income tax laws and
 Depreciation lowers income taxes via the relation: regulations.
Taxes = (income - deductions)(tax rate) Basic requirements of depreciable property:
 It must be used in business or held to produce income.
 It must have a determinable useful life and the life must
be longer than one year.
 It must be something that wears out, decays, gets used
up, becomes obsolete, or loses value from natural
causes.
 It is not inventory, stock in trade, or investment property.

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 Federal tax law states that: Any productive Book Value – represents the remaining,
asset with a finite life (greater than one year) undepreciated capital investment on the books
must be depreciated for tax purposes rather after the total amount of depreciation charges to
than “expensed” in the year of purchase. date have been subtracted from the basis.
 Depreciation amounts represent a prorated k
BVk =adjusted cost basis   (depreciation deduction)j
amount per year that can be treated as an j=1

“expense” (deduction) but is not a real cash Recovery Period – is the depreciable life n of the
flow. asset in years.
 Depreciation amounts represent a form of tax Market Value – a term also used in replacement
savings to the profitable firm. analysis, is the estimated amount realizable if the
asset were sold on the open market

 Assume a tax rate of 30% of taxable income. Salvage Value – is the estimated trade-in market
 For every $1 of eligible deductions the resultant value at the end of the asset’s useful life.
tax savings is: Depreciation Rate – is the fraction of the first
 (0.30)($1.00) = $0.30. cost removed by depreciation each year.
 $1 of additional deductions saves the firm Personal Property – one of the two types of
$0.30. property for which depreciation is allowed, is
the income-producing, tangible possessions of
a corporation used to conduct business.

Book Depreciation – term use by a corporation Real Property – office buildings, manufacturing
or business for internal financial accounting. structures, and other structures. Also land but
Tax Depreciation – term used in tax calculations it’s not depreciable.
per government regulations. Half-year convention – assumes that assets are
First Cost – is the delivered and installed cost of placed in service or disposed of in midyear,
the asset including purchase price, delivery regardless of when these events actually occur
and installation fees, and other depreciable during the year.
direct costs incurred to prepare the asset for
use.

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 It writes off capital investment linearly over n years. Annual Depreciation:

 The estimated salvage value is always $4,000  0
considered. d  $400
 This is the classical, nonaccelerated depreciation 10
model. Book Value @ end of 1  year :
Formula: C0  Cn
d  1($4,000  0)
n BV  $4,000   $3,600
L (C 0  C L ) 10
Dm 
n
L (C 0  C n )
Cm  C0 
n

C0 = the original cost, EOY,k dk BVk

0 $400 $4,000
Cn = value after “n’ years(salvage value or scrap
1 400 3,600
value)
2 400 3,200
n = life of the property, 3 400 2,800
d = the annual depreciation, 4 400 2,400

Dm = total depreciation after “m” years. 5 400 2,000

6 400 1,600
= d(m)
7 400 1,200
Cm = the book value after “m” years 8 400 800
L = depreciable years of a property 9 400 400
10 400 0

A new electric saw for cutting small pieces of lumber a) Annual depreciation charge
in a furniture manufacturing plant has a cost basis
C0  Cn
of $4000 and a 10-year depreciable life. The d 
estimated SV of the saw is zero at the end of 10  (1  i ) n  1 
years. Determine the annual depreciation
amounts, using the straight-line method. Tabulate b) Book value at end of “m” years
the annual depreciation amounts and the book
value of the saw at the end of each year. D m  C 0  C m

w h e re :
d (1  i ) n  1
D m 
i

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An equipment cost P10,000 with a salvage A machine costing P 720,000 is estimated

value of P500 at the end of 10 years. to have a book value of P 40,545.73
Calculate the annual depreciation cost by when retired at the end of 10 years.
sinking fund method at 4% interest. Depreciation cost is computed using a
constant percentage of the declining
book value. What is the annual rate of
depreciation in %?

( )  𝐶 = 𝐶 1−𝑘
 𝑑=
( )

 40,545.73 = 720,000 1 − 𝑘
( , )( . )
 =
( . )
 1−𝑘 = 0.0563
 = 𝑃791.26
 𝑘 = 0.25 𝑜𝑟 25%

Also known as Diminishing Balance Method or a) Sum of the years digit

Constant percentage method.
( n ) ( n  1)
 y e a rs 
2
Use the Matheson formula:
b) Respective depreciation charges
C C
k  1 n
or k  1 m
n

C C n
0 0
d1  (C  Cn)
0
 y e a rs
Note: This method is not applicable if the salvage ( n  1)
d 2  (C  Cn)
value is zero. 0
 y e a rs

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A company purchases an asset for

P10,000.00 and plans to keep it for 20
years. If the salvage value is zero at the
end of 20th year, what is the depreciation
in the third year? Use SYD method.

 𝑑 = 𝐶 −𝐶 ∑

 𝑑 = 10,000 − 0
∑▒