## 13/03/2021

### Straight line, Diminishing & Sinking Fund Method

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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