UNIVERSITY OF SCIENCE AND TECHNOLOGY
OF SOUTHERN PHILIPPINES
Alubijid | Cagayan de Oro | Claveria | Jasaan | Oroquieta | Panaon
Depreciation Methods
Subject: Engineering Economy
Instructor: Engr. Ma. Leona Maye B. Pepito
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What is
Depreciation ?
- a reduction in the value of an
asset with the passage of time,
due in particular to wear and
tear.
-is an accounting method of
allocating the cost of a tangible
or physical asset over its useful
life or life expectancy.
-it represents how much of an
asset's value has been used up.
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Depreciation Terms
Fixed Asset - the asset which bought for a long run, which is bought by a
business for its operational use e.g. Building, Machinery, Lant Et.c
Book Value (BV) - the asset's first cost minus the asset's accumulated
depreciation.
Original Value or First Cost (FC)- is related to the original value or we
can say buying value of the fixed Asset.
Rate of Depreciation (ROD) - it is a fixed rate of depreciation which we
have reduced every financial or calendar year from the original value of
the fixed Asset.
Scrap Value (SV) - is the value of an asset when it is no longer usable.
Scrap value is also referred to as Salvage Value or Residual Value.
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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1. Straight Line Method
In straight-line depreciation, the expense amount is the
same every year over the useful life of the asset.
Depreciation Formula for the Straight Line Method:
Annual Depreciati on, A D = (First Cost – Scrap Value) / Useful life
= (FC - SV) / n
Total Depreciation after “x” years, DT =
(FC - SV)
( x)
n
Book Value , BV = FC - D T
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1. Straight Line Method
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1. Straight Line Method
Example:
Consider a piece of equipment that costs Php 25,000 with an estimated
useful life of 8 years and a no salvage value. How much is the depreciation
expense per year for this equipment using straight line method.
Solution:
Annual Depreciation, AD = (FC – SV) / n
Annual Depreciation, AD = (Php25,000 – 0) / 8yrs
Annual Depreciation, AD = Php 3,125 / yr
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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2. Sinking Fund Method
Sinking Fund Method is a depreciation method wherein
funds will accumulate for replacement purposes.
The formulas for Sinking Fund Method of Depreciation are:
Annual Depreciation, A D =
(FC - SV) (i )
(1  i) n  1


A (1  i) x  1
Total Depreciati on after “x” years , D T =
i
Book Value, BV = FC - D T
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2. Sinking Fund Method
Example:
A machine costs Php 300,000 with a salvage value of Php 50,000 at
the end of its life of 10 years. If money is worth 6% annually, use
Sinking Fund Method and determine the depreciation at the 6th year.
Solution
a. Solve for the annual depreciation.
(FC - SV) (i)
Annual Depreciation, A D =
(1  i) n  1
(300,000 - 50,000) (0.06)
AD =
(1  0.06)10  1
A D = Php 18,967
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2. Sinking Fund Method
b. Solve for the depreciation in the 6th year.
Total depreciation after x years, DT


A (1 i)x 1
DT =
i
(18967)(1 0.06)6 1
DT =
0.06
DT = Php132,300.86

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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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3. Sum of the Years Digit Method
Sum of the Years Digit Method (SOYD) is an accelerated
depreciation technique based on the assumption that
tangible properties are usually productive when they are
new, and their use decreases as they become old.
The formulas for the SOYD Method of Depreciation are:
Sum of years = (n / 2) (n + 1)
Annual depreciation at 1st year= (FC - SV) (n / Sum of years)
Annual depreciation at 2nd year = (FC -SV) ((n-1) / Sum of years)
Book Value = FC - Total depreciation at the end of nth year
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3. Sum of the Years Digit Method
Example:
An equipment costs Php 1,500,000. At the end of its economic life of five
years, its salvage value is Php 500,000. Using Sum of the Years Digit
Method of Depreciation, what will be its book value for the third year?
Solution:
a. Solve for the sum of years.
Sum of years = (n / 2) (n + 1)
Sum of years = (5 / 2) (5 + 1)
Sum of years = 15 years
b. Solve for the total depreciation up to the third year.
Total depreciation = (FC - SV) (5 + 4 + 3) /15
Total depreciation = (1,500,000 - 500,000) (12) / 15
Total depreciation = Php 800,000
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c. Solve for the book value in the third year.
Book Value = FC - Total depreciation
Book Value = 1,500,000 - 800,000
Book Value = Php 700,000
Therefore, the book value for the third year is Php 700,000.
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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4. Declining Balance Method
Declining Balance Method is sometimes called the
Constant-Percentage Method or the Matheson formula.
The assumption in this depreciation method is that the
annual cost of depreciation is the fixed percentage (1 - K)
of the Book Value (BV) at the beginning of the year.
The formulas for Declining Balance Method of Depreciation are:
Annual Rate of Depreciati on(K)  1 - n
SV
where, SV = FC (1 - K) n
FC
Book Value = FC (1 - K) m
Depreciati on at m th year = FC (1 - K) m -1 (K)
Total Depreciati on = FC - SV
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4. Declining Balance Method
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4. Declining Balance Method
Example: The first cost of a machine is Php 1,800,000 with a salvage
value of Php 400,000 at the end of its life of five years. Determine the
depreciation after three years using Constant-Percentage Method.
Solution:
a. Solve for K.
Annual Rate of Depreciation(K)  1 - n
K  1- 5
SV
FC
400,000
1,800,000
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4. Declining Balance Method
b. Solve for the book value at the end of the third year.
BV = FC (1 - K)m
BV = 1,800,000 (0.74)3
BV = Php 730,037.21
c. Solve for the total depreciation after three years.
Total depreciation = FC - BV
Total depreciation = 1,800,000 - 730,037.21
Total depreciation = Php 1,069,962.79
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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5. Double Declining Balance Method
The double declining balance depreciation method is a
form of accelerated depreciation that doubles the regular
depreciation approach. It is frequently used to depreciate
fixed assets more heavily in the early years, which allows
the company to defer income taxes to later years.
DDB Formula:
Depreciation at any " nth" year (D n ),
2FC  2 
Dn 
1 

m  m
2

BV  FC 1  
 m
2

SV  FC 1  
 m
n 1
n
m
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5. Double Declining Balance Method
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5. Double Declining Balance Method
Example:
An equipment costs Php750,000 and has a salvage value of
Php25,000 after its 25 years of useful life. Using double declining
balanced method, what will be the book value of the equipment at the
end of 6 years?
Solution:
2

BV  FC 1  
 m
n
2 

BV  750 ,000 1  
 25 
BV  Php 454 ,766 .25
6
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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6. Working Hours Method
Working Hours Method is a depreciation method that
results in the cost basis allocated equally over the expected
number of units produced during the period of tangible
properties. The formula for Working Hours Method of
Depreciation is:
Depreciation per hour = (FC - SV) / Total number of hours
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6. Working Hours Method
Example:
A machine costs Php 400,000 with a salvage value of Php 200,000.
Life of it is six years. In the first year, 4000 hours. In the second year,
6000 hours and 8000 hours on the third year. The expected flow of the
machine is 38000 hours in six years. What is the depreciation at the
end of the second year?
Solution:
a. Solve for the depreciation per hour.
Depreciation per hour = (FC - SV) / Total number of hours
Depreciation per hour = (400,000 - 20,000) / 38000
Depreciation per hour = Php 10
b. Solve for the depreciation at the end of 2nd year.
Depreciation = 10 (6000)
Depreciation = Php 60,000
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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7. Constant Unit Method
Constant Unit Method is the same with Working Hours
Method in the structure of the formula. The formula for
Constant Unit Method of Depreciation is:
Depreciation per unit = (FC - SV) / Total number of units
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7. Constant Unit Method
Example: A coin machine costing Php 200,000 has a salvage value of
Php 20,000 at the end of its economic life of five years. Determine the
annual reserve for depreciation for the third year only. The schedule of
production per year is as follows:
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7. Constant Unit Method
Solution:
a. Solve for the total number of coins.
Total number of coins =100,000 + 80,000 + 60,000 + 40,000 +20,000
Total number of coins = 300,000
b. Solve for the depreciation per unit.
Depreciation per unit = (FC - SV) / Total number of coins
Depreciation per unit = (200,000 - 20,000) / 300,000
Depreciation per unit = 0.60
c. Solve for the depreciation reserve for the third year.
Depreciation = 0.66 (60,000)
Depreciation = Php 36,000
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Methods of Depreciation
1.
2.
3.
4.
5.
6.
7.
8.
Straight Line Method
Sinking Fund Method
Sum of the Years Digit Method
Declining Balance Method
Double Declining Balance Method
Working Hours Method
Constant Unit Method
Output Method
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8. Output Method
The term units-of-output depreciation refers to one of several methods of
allocating the cost of an asset over its expected lifetime. The units-ofoutput depreciation method is based on the assumption the asset will
output a fixed number of units over its lifetime; therefore, the depreciation
expense in a given accounting period is directly related to the asset's
output in that same accounting period.
Output Method Formula:
Units - of - Output Depreciation =
(Cost of Asset - Residual Value)
Total Units of Output
Depreciation Expense = Units of Output Depreciation x Units Produced
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8. Output Method
Example:
A company has a machine with a cost of Php 500,000 and a useful life
that is expected to end after producing 24,000 units of a component
part. Furthermore, the machine's salvage value at that point is assumed
to be Php 20,000.
Solution:
(Cost of Asset - Residual Value)
Total Units of Output
Php(500,00 0 - 20,000)
Units - of - Output Depreciati on =
24,000unit s
Units - of - Output Depreciati on = Php20/unit
Units - of - Output Depreciati on =
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References:
• LT Blank, A Tarquin. Engineering Economy. McGraw Hill,
International Edition, 5th edition, 2002.
• William G. Sullivan et al. Engineering Economy.16th Edition. New
Jersey: Prentice – Hall,Inc, 2015
• GJ Thuesen, WJ Fabrycky, GJ Thuesen. Engineering Economy.
Prentice Hall, Upper Saddle River, NY, 2001.
• Chan S. Park. Contemporary Engineering Economics.2nd
Edition.USA:Addison-Wesley Publishing Company,Inc. 1997
• Matias A. Arreola. Engineering Economy. 3rd Edition. Philippines:
Ken Inc., 1993.
• G.J. Thuesen and W.J. Fabrycky. Engineering Economy.8th Edition.
New Jersey: Prentice – Hall, Inc., 1993
• Max Kurtz. Engineering Economics for Professional Engineers’
Examination.2nd Edition. New York: McGraw-Hill, 1975
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Thank you!
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