Question

A contractor bought a crane for erecting tall buildings. It was invoiced from Japan CIF (cost, insurance, freight) Manila at P2,500,000. Brokerage, bank, customs’ duties, permits, etc. total P1,200,000. At the end of 10years, he expects to sell it for P500,000. Determine the book value at the beginning of year 5 using the: A)Straight-Line Method. B) Sinking Fund Method at 12%. C) Matheson Formula Method. D) Double Declining Balance Method. E) Sum of the Years Digit Method.

Answer 1

Depreciable basis, B =2,500,000 + 1,200,000 = 3,700,000

Expected salvage, S = 500,000

Life, n = 10 years

A)Straight-Line Method.

Annual depreciation = D = (B - S) / n = (3,700,000 - 500,000) / 10 =  320,000

Hence, book value at the beginning of year 5 = Book value at the end of year 4 = B - 4 x D = 3,700,000 - 4 x 320,000 = P  2,420,000

B) Sinking Fund Method at 12%.

i = 12%

Depreciation for year 1 = D₁ = (B - S) x i / [(1 + i)ⁿ - 1] = (3,700,000 - 500,000) x 0.12 / [(1 + 0.12)¹⁰ - 1] =  182,349.33

Hence, book value at the beginning of year 5 = Book value at the end of year 4

= B - D₁ - D₁ x (1 + i) - D₁ x (1 + i)² - D₁ x (1 + i)³ = 3,700,000 - 182,349.33 - 182,349.33 x 1.12 - 182,349.33 x 1.12² - 182,349.33 x 1.12³ = P 2,828,492.76

C) Matheson Formula Method.

Depreciation factor, D = 1 - (S / B)^1/n = 1 - (500,000 / 3,700,000)^1/10 = 0.18139041

Hence, book value at the beginning of year 5 = Book value at the end of year 4

= B x (1 - D)⁴ = 3,700,000 x (1 - 0.18139041)⁴ = P 1,661,533.25

D) Double Declining Balance Method.

Depreciation factor, D = 2/n = 2/10 = 0.2

Hence, book value at the beginning of year 5 = Book value at the end of year 4

= B x (1 - D)⁴ = 3,700,000 x (1 - 0.2)⁴ = P 1,515,520.00

E) Sum of the Years Digit Method

sum of the years = 1 + 2 + ...+ 10 = 10 x 11/2 = 55

Depreciation for year m = (B - S) x (10 - m + 1) / 55 = (3,700,000 - 500,000) x (11 - m) / 55

Please see the table below:

Year, m	Depreciation
1	581,818.18
2	523,636.36
3	465,454.55
4	407,272.73
Total	1,978,181.82

Hence, book value at the beginning of year 5 = Book value at the end of year 4 = B - total of depreciation in the table above = 3,700,000 -  1,978,181.82 = P 1,721,818.18