Question

3. The company accountant is uncertain which of three depreciation methods the firm should use for welding equipment that costs $150,000 and has a zero-salvage value at the end of a 5-year depreciable life. Compute the depreciation schedule for the welding equipment using the methods listed: a. Straight line b. Double declining balance c. Sum-of-years' -digits Based on your analysis, which depreciation method is most profitable for the firm?

Answer 1

We have the following information

Equipment Cost = $150,000

Useful Life (n) = 5 years

Salvage Value = 0

Straight Line Depreciation

In this method of depreciation, a fixed sum is charged as the depreciation amount throughout the lifetime of an asset such that the accumulated sum at the end of the life of the asset is exactly equal to the purchase value of the asset.

P = First cost of the asset

F = Salvage value of the asset

n = Life of the asset

B_t = Book value of the asset at the end of period t

D_t = Depreciation amount for the period t

The formulae for the depreciation and book value are as follows

D_t = (P – F)/n

B_t = B_t–1 – D_t = P – t × [(P – F)/n]

D_t = (P – F)/n

D_t = (150,000 – 0)/5

D_t = 30,000

End of the year (t)	Depreciation (Dt)	Book Value (Bt = Bt–1 – Dt )
0		1,50,000.00
1	30,000.00	1,20,000.00
2	30,000.00	90,000.00
3	30,000.00	60,000.00
4	30,000.00	30,000.00
5	30,000.00	-

Double Declining Balance Depreciation

In this method of depreciation, a constant percentage (i.e., double meaning 200% of the straight line rate of depreciation) of the book value of the previous period of the asset will be charged as the depreciation amount for the current period.

P = First cost of the asset

F = Salvage value of the asset

n = Life of the asset

B_t = Book value of the asset at the end of period t

D_t = Depreciation amount for the period t

K = a fixed percentage (it is 0.2 in the case of double declining balance depreciation)

D_t = K × B_t–1

B_t = B_t–1 – D_t

End of the year (t)	Depreciation (Dt)	Book Value (Bt = Bt–1 – Dt )
0		1,50,000.00
1	30,000.00	1,20,000.00
2	24,000.00	96,000.00
3	19,200.00	76,800.00
4	15,360.00	61,440.00
5	12,288.00	49,152.00

Sum of the Years Digits Method of Depreciation

In this method it is assumed that the book value of the asset decreases at a decreasing rate. First the sum of the years is computed

Sum of the years = n(n + 1)/2

In the present case n = 5 years, so

Sum of the years = 5(5 + 1)/2

Sum of the years = 30/2

Sum of the years = 15

The rate of depreciation charge for the first year is assumed as the highest and then it decreases. The rate of depreciation for the years 1 to 5, respectively are as follows: 5/15, 4/15, 3/15, 2/15, and 1/15.

For any year, the depreciation is calculated by multiplying the corresponding rate of depreciation with (P – F).

D_t = Rate × (P – F)

D_t = Rate × (150,000 – 0)

D_t = Rate × 150,000

B_t = B_t–1 – D_t

The formula for D_t and B_t for a specific year t are as follows.

D_t = {(n – t + 1)/[n(n + 1)/2]} × (P – F)

B_t = {(P – F) × [(n – t)/n] × [(n – t + 1)/(n + 1)]} + F

End of the year (t)	Rate	Depreciation (Dt)	Book Value (Bt)
0			1,50,000.00
1	5/15	50,000.00	1,00,000.00
2	4/15	40,000.00	60,000.00
3	3/15	30,000.00	30,000.00
4	2/15	20,000.00	10,000.00
5	1/15	10,000.00	-