Depreciation
Introduction
Straight Line Method
Declining Balance Method
Sinking Fund Method
Sum of Years’ Digit
2
01
Introduction
3
Depreciation refers to the decline in the value of physical
properties over time and with usage. It is an accounting concept
that involves an annual deduction from before-tax income. The
purpose of depreciation is to account for the impact of time and
usage on the value of an asset, allowing this decline to be
reflected in a company's financial statements.
4
Types of Depreciation:
1. Physical Depreciation – due to physical reduction of the
physical ability of an equipment or asset to produce results
2. Functional Depreciation – due to reduction in demand for the
function that the equipment or asset was designed to render.
This type of depreciation is also known as obsolescence.
5
02
Straight Line Method
6
Straight Line Method assumes that the loss in value is directly
proportional to the age of the equipment or asset.
𝑐0 − 𝑐𝑛
𝑑=
𝑛
𝑐𝑚 = 𝑐0 − 𝐷𝑚
d = depreciation
C0 = first cost
Cn = salvage/scrap value
n = life of property
cm = book value at end of m years
Dm = total depreciation after m years
7
Sample Problem
A piece of new equipment has been proposed by engineers
to increase the productivity of a certain manual welding
operation. The investment cost is $25,000, and the equipment
will have a market value of $5,000 at the end of a study period
of five years. Using straight line method, tabulate its
depreciation over 5 years.
8
Solution
𝑐0 − 𝑐𝑛
𝑑=
𝑛
25000 − 5000
𝑑=
5
𝑑 = 4000
Period
Depreciation
0
Book Value
25,000
1
4,000
21,000
2
4,000
17,000
3
4,000
13,000
4
4,000
9,000
5
4,000
5000
03
Declining Balance
Method
10
Declining Balance Method assumes that the annual loss in value is
a fixed percentage of the book value at the beginning of the year.
𝑘 =1−
𝑛
𝑐𝑛
𝑐0
𝑐𝑚 = 𝑐0 − 𝐷𝑚
k = constant percentage
C0 = first cost
Cn = salvage/scrap value
n = life of property
cm = book value at end of m years
Dm = total depreciation after m years
11
Sample Problem
A piece of new equipment has been proposed by engineers
to increase the productivity of a certain manual welding
operation. The investment cost is $25,000, and the equipment
will have a market value of $5,000 at the end of a study period
of five years. Using declining balance method, tabulate its
depreciation over 5 years.
12
Solution
Period
Depreciation
0
𝑘 =1−
𝑛
𝑐𝑛
𝑐0
5000
𝑘 =1−
25000
𝑘 = 0.2752
5
Book Value
25,000
1
(0.2752)25,000
18120
2
(0.2752)18120
13133.38
3
(0.2752)13133.38
9519.07
4
(0.2752)9519.07
6899.42
5
(0.2752)6899.42
5000.7
04
Sinking Fund Method
14
Sinking Fund Method assumes that a sinking fund is established in
which funds will accumulate for replacement purposes.
𝑐0 − 𝑐𝑛 𝑖
𝑑=
1+𝑖 𝑛−1
𝑐𝑚 = 𝑐0 − 𝐷𝑚
d = depreciation
C0 = first cost
Cn = salvage/scrap value
n = life of property
i= interest rate
cm = book value at end of m years
Dm = total depreciation after m years
15
Sample Problem
A piece of new equipment has been proposed by engineers
to increase the productivity of a certain manual welding
operation. The investment cost is $25,000, and the equipment
will have a market value of $5,000 at the end of a study period
of five years. Using declining balance method, tabulate its
depreciation over 5 years.
16
Solution
*Assume i=20%
𝑐0 − 𝑐𝑛 𝑖
1+𝑖 𝑛−1
(25000 − 5000)(0.2)
=𝑑=
= 2687.59
1 + 0.2 5 − 1
𝑑[ 1 + 𝑖 2 − 1] 2687.59[ 1 + 0.2 2 − 1]
=
=
𝑖
0.2
= 5912.71
𝑑[ 1 + 𝑖 3 − 1] 2687.59[ 1 + 0.2 3 − 1]
=
=
𝑖
0.2
= 9782.84
𝑑[ 1 + 𝑖 4 − 1] 2687.59[ 1 + 0.2 4 − 1]
=
=
𝑖
0.2
= 14427
𝑑[ 1 + 𝑖 5 − 1] 2687.59[ 1 + 0.2 5 − 1]
=
=
𝑖
0.2
= 20000
𝑑=
D1
𝐷2
𝐷2
𝐷3
𝐷3
𝐷4
𝐷4
𝐷5
𝐷5
Period
Depreciation
0
Book Value
25,000
1
2687.59
22312.41
2
5912.71
19087.29
3
9782.84
15217.16
4
14427
10573
5
20000
5000
05
Sum of Years’ Digit
Method
18
Sum of Years’ Digit Method is an accelerated method for computing
depreciation which takes the asset's expected life and adds
together the digits for each year.
𝑑 = 𝑐0 − 𝑐𝑛
𝑛
∑𝑦𝑒𝑎𝑟𝑠
𝑐𝑚 = 𝑐0 − 𝐷𝑚
d = depreciation
C0 = first cost
Cn = salvage/scrap value
n = life of property
cm = book value at end of m years
Dm = total depreciation after m years
19
Sample Problem
A piece of new equipment has been proposed by engineers
to increase the productivity of a certain manual welding
operation. The investment cost is $25,000, and the equipment
will have a market value of $5,000 at the end of a study period
of five years. Using straight line method, tabulate its
depreciation over 5 years.
20
Solution
*Assume i=20%
Period
𝑑=
d1 = 𝑐0 − 𝑐𝑛
𝑑2 = 𝑐0 − 𝑐𝑛
𝑑3 = 𝑐0 − 𝑐𝑛
𝑑4 = 𝑐0 − 𝑐𝑛
𝑑5 = 𝑐0 − 𝑐𝑛
𝑛
20000(5)
=
= 6666.67
∑𝑦𝑒𝑎𝑟𝑠
15
𝑛−1
20000(4)
=
= 5333.33
∑𝑦𝑒𝑎𝑟𝑠
15
𝑛−2
20000(3)
=
= 4000
∑𝑦𝑒𝑎𝑟𝑠
15
𝑛−3
20000(2)
=
= 2666.67
∑𝑦𝑒𝑎𝑟𝑠
15
𝑛−4
20000(1)
=
= 1333.33
∑𝑦𝑒𝑎𝑟𝑠
15
Depreciation
0
Book Value
25,000
1
6666.67
18333.33
2
5333.33
12999.67
3
4000
8999.67
4
2666.67
6333
5
1333.33
4999.67