Example problem on sum-of-the-years-digits method of depreciation
Example problem on sum-of-the-years-digits method of depreciation -1
A
company has purchased an equipment whose first cost is Rs. 1,00,000 with an
estimated life of eight years. The estimated salvage value of the equipment at
the end of its lifetime is Rs. 20,000. Determine the depreciation charge and
book value at the end of various years using the sum-of-the-years-digits method
of depreciation.
Given data
Purchase
price, P = ₹. 1,00,000
Salvage
value, F = ₹. 20,000
Life
of an asset, n = 8 years
Formula used
Dt = Rate*(P – F)
Bt = Bt–1
– Dt
Solution
Sum
of years = n(n + 1)]/2 =
8(8+1)/2 = 36
Rate
of years
First year = 1/36
Second year = 2/36
Third year = 3/36
Fourth year = 4/36
Fifth year = 5/36
Sixth year = 6/36
Seventh year = 7/36
Eighth year = 8/36
|
End of Year
|
Depreciation (Dt = Rate*(P – F)
in ₹
|
Book Value (Bt = Bt–1 –
Dt)
in ₹
|
|
0
|
|
1,00,000
|
|
1
|
17,777.77
|
82,222.23
|
|
2
|
15,555.55
|
66,666.68
|
|
3
|
13,333.33
|
53,333.35
|
|
4
|
11,111.11
|
42,222.24
|
|
5
|
8,888.88
|
33,333.36
|
|
6
|
6,666.66
|
26,666.70
|
|
7
|
4,444.44
|
22,222.26
|
|
8
|
2,222.22
|
20,000.04
|
Example problem on sum-of-the-years-digits
method of depreciation -2
A
company has purchased an equipment whose first cost is Rs. 1,00,000 with an
estimated life of eight years. The estimated salvage value of the equipment at
the end of its lifetime is Rs. 20,000. Determine the depreciation charge and
book value at the end of 5th year using the sum-of-the-years-digits method of
depreciation.
Given data
Purchase
price, P = ₹. 1,00,000
Salvage
value, F = ₹. 20,000
Life
of an asset, n = 8 years
t
= 5
Formula used
Dt =
{[n − t + 1]/[n(n + 1)]/2} * (P – F)
Bt =
{[(P – F)] [(n – t)/n] [(n − t + 1)/(n + 1)]} + F
Solution
D5 = {[n − t + 1]/[n(n + 1)]/2} * (P – F)
= {[8 − 5 + 1]/[8(8 + 1)]/2} * (1,00,000
– 20,000)
D5 =₹. 8,888.88
B5 = {[(P – F)] [(n – t)/n] [(n − t + 1)/(n
+ 1)]} + F
= {[(1,00,000 – 20,000)] [(8 – 5)/8]
[(8 − 5 + 1)/(8 + 1)]} + 20,000
= 80,000 * (3/8) * (4/9) + 20,000
B5 =₹. 33,333.33
Result
At
the end of 5th year,
Depreciation charge = ₹. 8,888.88
Book value = ₹. 33,333.33