- The depreciation charge is first applied to the initial cost of equipment, then its value goes on diminishing.
- This method is more accurate than the straight line method.
- The depreciation charges are more in the early years and its value goes on decreasing after some years.

Let

P =
Initial cost of equipment / plant

S
= Salvage / Scrap value of equipment / plant

n
= Life of equipment

r
= Annual rate of interest

x
= Annual depreciation

**Value
of equipment after one year**

S =
P – Px

S
= P ( 1 – x )

**Value
of equipment after second year**

= Diminished
value after first year – Annul Depreciation

= P
( 1 – x ) – [ P ( 1 – x )x ]

=
P ( 1 – x – x + x^{2} )

=
P ( 1 – 2x + x )^{2}

=
P ( 1 – x )^{2}

**Value
of equipment after 10 ^{th} year**

S
= P ( 1 – x )^{10}

**Value
of equipment after nth years**

S
= P ( 1 – x )^{n}

**Annual
depreciation charge**

(
1 – x )^{n} = S / P

(
1 – x ) = ( S / P )^{1/n}

x =
1 – ( S / P )^{1/n}

Depreciation
for the first year = xP

= P { 1 – ( S / P ) }^{}

Depreciation
for the nth year = xP

= P {( 1 – ( S / P )^{n}}

**Disadvantages**

- The depreciation charge is not depending upon rate of interest on annual depreciation.
- The depreciation charges are more during early years and its value goes on decreases in late years when the maintenance cost of equipment is quite high.

**Example
**

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 Diminishing method. Calculate the cost of equipment after 5
years.

**Solution**

P
= Rs 75,000

S
= Rs. 5,000

n
= 10 years

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

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