**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 2 ^{nd} year** ( Rs. 72,000 / 10 =

**Rs.7200**)

- Rs. 72,000 – Rs 7200 = Rs. 64,8000

**Depreciation charges
after 3 ^{rd} 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 ) |
P ( 1 – x ) |

Sinking Fund method |
q = ( P – S ){ r / ( 1 + r ) |
Sinking fund after nth year = q {
( 1 + r ) Value of equipment after n year =
P – q { ( 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 5 ^{th} 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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