Straight line
method
- The depreciation charges are constant every year.
- There is no interest calculated on the depreciation charge every year.
Diminishing method
- The depreciation charge depends upon the annual rate of depreciation.
- If the cost of equipment is Rs. 80,000 and its salvage value is zero after useful life of 10 years.
- The annual rate of depreciation is Rs. 80000 / 10 = Rs. 8000
Depreciation charges
after first year
- Rs. 80,000 – Rs. 8000 = Rs. 72,000
Depreciation charges
after 2nd year ( Rs. 72,000 / 10 = Rs.7200 )
- Rs. 72,000 – Rs 7200 = Rs. 64,8000
Depreciation charges
after 3rd year ( Rs. 64800 / 10 = Rs. 6480 )
- Rs. 64,800 – Rs. 6480 = Rs. 58,320
- The depreciation charges decreases from Rs. 8000, Rs. 7200, Rs. 6480 and so on.
Sinking fund
method
- The fixed depreciation charges are made every year and annually interest is calculated on it.
- The cost of replacement of equipment after useful life is sum of total annual installment plus interest of it.
|
Depreciation method |
Annual depreciation charges |
Value of equipment after n years |
|
Straight line method |
( P – S ) / n |
P – Annual Depreciation × n |
|
Diminishing method |
x = 1 – ( S / P )1/n |
P ( 1 – x )n |
|
Sinking Fund method |
q = ( P – S ){ r / ( 1 + r )n
– 1 } |
Sinking fund after nth year = q {
( 1 + r )n – 1 / r }] Value of equipment after n year =
P – q { ( 1 + r )n – 1 / r }] |
Where
P = Cost of
equipment
S = Salvage
value after useful life
n = Number of
years
r = Rate of
interest
x = Depreciation
value in the diminishing method
q = Depreciation
value in the sinking fund method.
Example ( Compare
all three methods )
The cost of an
electrical equipment is Rs.75,000 and its useful life is 10 years. The salvage
value of equipment is Rs.5,000. Calculate annual depreciation charges using ( 1
) Straight line method ( 2 ) Diminishing method and ( 3 ) Sinking fund method
if the rate of interest is 5%. Calculate the cost of equipment after 5 years
considering all three methods.
Solution
( 1 ) Straight line
method
P = Rs 75,000
S = Rs. 5,000
n = 10 years
Annual
Depreciation charges = ( P – S ) / n
= ( Rs. 75,000 –
Rs. 5,000 ) / 10
= Rs. 70,000 /
10
Rs. 7000
The value of equipment after 5 years
=
P – ( Annual Depreciation × 5 )
=
Rs 75,000 – ( Rs. 7000 × 5 )
=
Rs 40,000
( 2 ) Diminishing
method
Annual
Depreciation x = 1 – ( S / P )1/n
= 1 – ( 5,000 /
75,000 )1/10
= 1 – ( 0.0667 )0.1
= 1 – ( 0.762 )
= 0.238
Value of
equipment after 5 years
= P ( 1 – x )5
= Rs, 75,000 ( 1
– 0.238 )5
= Rs. 75,000 (
0.762 )5
= Rs. 75,000 (
0.2569 )
= Rs. 19268
( 3 ) Sinking
fund method
P = Rs. 75,000
S = Rs. 5,000
n = 10 years
r = 5%
q = ( P – S ) {
r / ( 1 + r )n – 1 }
= ( Rs. 75,000 – Rs. 5000 ) { 0.05 / ( 1 +
0.05 )10 – 1 }
= Rs. 70,000 { 0.05 / 1.6288 – 1 }
= Rs. 70,000 { 0.05 / 0.6288 }
= Rs. 70,000 { 0.0795 }
= Rs. 5566
Sinking fund
after 5th year
= q { ( 1 + r )n
– 1 / r }
= Rs. 5566 { ( 1
+ 0.05 )5 – 1 / 0.05 }
= Rs. 5566 { ( 1
+ 0.05 )5 – 1 / 0.05 }
= Rs. 5566 {
1.2762 – 1 / 0.05 }
= Rs. 5566 {
0.2762 / 0.05 }
Rs. 30746.60
Value of
equipment after 5 year
= Rs 70,000 – Rs
30746
= Rs. 39254
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