AMT 661

VALUE ANALYSIS
MANAGEMENT
Engr. Joshua C. Castañeda

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DEPRECIATION
LESSON 7

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DEPRECIATION
➢It is the decrease in value of physical properties with
passage of time.

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Methods of Depreciation
1. Straight Line Method (SLM)
2. Sinking Fund Method (SFM)
3. Declining Balance Method (DBM)
4. Sum of the Years Digit Method (SYDM)

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Straight Line Method (SLM)
➢It assumes uniform annual depreciation. It is the
most extensively used method of depreciation
because of its simplicity.

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Straight Line Method (SLM)
𝐹𝑜𝑟𝑚𝑢𝑙𝑎𝑠: Where:
𝐶𝑂 − 𝐶𝐿 d : Annual cost of depreciation
𝑑=
𝐿 𝐶𝑂 : Original cost
𝐷𝑛 = 𝑛𝑑 𝐶𝐿 : Salvage Value
L : Useful life of a property (years)
𝐶𝑛 = 𝐶𝑂 − 𝐷𝑛 𝐷𝑛 : Total depreciation after “n” years
𝐶𝑛 : Book value

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Straight Line Method (SLM)
Problem 1
An equipment costs ₱ 60,000 and the salvage value is
₱ 10,000 after 10 years. Find the depreciation using
straight line method.
𝑑 = ₱ 5,000

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Straight Line Method (SLM)
Problem 2
A business man bought a machine for ₱ 500,000.
Other expenses including installation amounted to
₱30,000. At the end of its estimated useful life of 10
years, the salvage value will be 10% of the first cost.
Using straight line method, what is the book value
after 5 years?
𝐶5 = ₱290,000

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Sinking Fund Method (SFM)
➢It is a depreciation technique used to determine the
annual loss in value of an asset by assuming that a
fixed amount is set aside each year, with interest
accumulation, to fully replace the asset at the end of
its useful life.

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Sinking Fund Method (SFM)
𝐹𝑜𝑟𝑚𝑢𝑙𝑎𝑠: Where:
𝐶𝑂 − 𝐶𝐿 (𝑖) d : Annual cost of depreciation
𝑑=
1+𝑖 𝐿−1 𝐶𝑂 : Original cost
1+𝑖 𝑛
−1 𝐶𝐿 : Salvage Value
𝐷𝑛 = 𝑑 L : Useful life of a property (years)
𝑖
𝐷𝑛 : Total depreciation after “n” years
𝐶𝑛 = 𝐶𝑂 − 𝐷𝑛 𝐶𝑛 : Book value

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Sinking Fund Method (SFM)
Problem 3
An equipment costs ₱10,000 with a salvage value of
₱500 at the end of 10 years. Calculate the annual
depreciation cost by sinking fund method at 5%
interest rate.

𝑑 = ₱755.2935

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Sinking Fund Method (SFM)
Problem 4
A car was bought for ₱300,000. Other expenses
including change oil and transaction fee amounted to
₱20,000. The vehicle is expected to have a life of 12
years with a salvage value of 10% of the purchase
price. Determine the book value at the end of 10 years
using sinking fund method at 8% interest rate.
𝐶10 = ₱ 98,622.8003

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Declining Balance Method (DBM)
➢It is an accelerated depreciation method in which the
depreciation expense declines with age of the asset.

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Declining Balance Method (DBM)
𝐹𝑜𝑟𝑚𝑢𝑙𝑎𝑠: Where:
𝑛−1
𝑑 = 𝐶𝑂 1 − 𝑘 𝑘 d : Annual cost of depreciation
𝑛 𝐶𝑂 : Original cost
𝑛 𝐶𝐿 𝐿
𝐶𝑛 = 𝐶𝑂 1 − 𝑘 or 𝐶𝑛 = 𝐶𝑂 𝐶𝑂
𝐶𝐿 : Salvage Value
L : Useful life of a property
𝑛 𝐶𝑛 𝐿 𝐶𝐿 𝐶𝑛 : Book value
𝑘 =1− 𝑜𝑟 𝑘 = 1 −
𝐶𝑂 𝐶𝑂 k : Rate of depreciation

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Declining Balance Method (DBM)
Problem 5
Determine the rate of depreciation and the book value
at end of the 8 years for an asset that cost ₱15,000,
and has an estimated salvage value of ₱ 2,000 at the
end of 10 years. Use declining balance method.

𝑘 = 18.2488%
𝐶8 = ₱2,992.5557

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Declining Balance Method (DBM)
Problem 6
A machine initially worth ₱ 50,000 depreciate in value
each year by 20% of its value at the beginning of that
year. Find its book value when it is 9 years old.
𝐶9 = ₱6,710.8864

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Sum of the Years Digit Method (SYDM)
➢A form of depreciation that is based on the
assumption that the productivity of an asset decreases
with the passage of time.

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Sum of the Years Digit Method (SYDM)
𝐹𝑜𝑟𝑚𝑢𝑙𝑎𝑠: Where:

𝑑𝑛 = (𝐶𝑂 −𝐶𝐿 )
𝑅𝐷 𝑑𝑛 : Depreciation at 𝑛𝑡ℎ year
𝑆𝑌𝐷 𝐷𝑛 : Total depreciation
after “n” years
𝑆𝑅𝐷
𝐷𝑛 = (𝐶𝑂 −𝐶𝐿 ) 𝐶𝑛 : Book Value
𝑆𝑌𝐷
𝐶𝑂 : Original cost
𝐶𝑛 = 𝐶𝑂 − 𝐷𝑛 𝐶𝐿 : Salvage Value

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Sum of the Years Digit Method (SYDM)
𝐹𝑜𝑟𝑚𝑢𝑙𝑎𝑠: Where:
𝐿 𝑆𝑌𝐷 : Sum of the years digit
𝑆𝑌𝐷 = (𝐿 + 1)
2 𝑅𝐷 : Reverse digit
𝑅𝐷 = 𝐿 − n + 1 𝑆𝑅𝐷 : Sum of reverse digit
L : Useful life of a property
𝑛
𝑆𝑅𝐷 = (2𝐿 − n + 1)
2

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Sum of the Years Digit Method (SYDM)
Problem 7
Michael bought a CPU for his computer during its
release in 2017. The CPU was bought $330 and is
estimated to be relevant up to 2023 -even then, it
would still cost $70. Using SYDM, how much does this
CPU cost in 2020?
𝐶3 = $144.2857

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Sum of the Years Digit Method (SYDM)
Problem 8
An equipment has a first cost of ₱ 500,000 and the
cost of installation is ₱30,000. If the salvage value is
10% of the equipment cost at the end of its useful life
of 5 years. Compute the book value of the equipment
after 3 years using SYDM.
𝐶3 = ₱146,000

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Sum of the Years Digit Method (SYDM)
Problem 9
A rebar cutting machine which was advertised to have
a useful life of 12 years bought at ₱80,000. If the
machine is projected to have a salvage value of
₱5,000 find the amount of depreciation at its fourth
year of use
𝑑4 = ₱8,653.8462

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