- 2069 Bhadra · 8 marks
Double declining balance depreciation, 15000 machine
Short answer
DDB rate 40%. Annual depreciation: Rs 6,000; 3,600; 2,160; 1,296; 1,044 (switch to straight-line in year 5 to reach salvage). Book values: Rs 9,000; 5,400; 3,240; 1,944; 900.
A machine costs Rs 15000. Its useful life is 5 years and salvage value is Rs 900. Compute the annual depreciation allowances and resulting book values using double declining balance depreciation methods.
Data: P = Rs 15,000; N = 5; S = Rs 900. Double declining balance rate = 2/N = 2/5 = 40% of the opening book value. Depreciation cannot take the book value below S. When the straight-line charge on the remaining depreciable amount, (BV − S)/(remaining years), is larger than the DDB charge, the method switches to straight line so that BV₅ = S.
| Year | Opening BV | DDB = 0.4 × BV | SL = (BV − 900)/years left | Depreciation | Closing BV |
|---|---|---|---|---|---|
| 1 | 15,000 | 6,000.0 | 2,820.0 | 6,000.0 | 9,000.0 |
| 2 | 9,000 | 3,600.0 | 2,025.0 | 3,600.0 | 5,400.0 |
| 3 | 5,400 | 2,160.0 | 1,500.0 | 2,160.0 | 3,240.0 |
| 4 | 3,240 | 1,296.0 | 1,170.0 | 1,296.0 | 1,944.0 |
| 5 | 1,944 | 777.6 | 1,044.0 | 1,044.0 | 900.0 |
Year 1: 0.4 × 15,000 = 6,000 BV₁ = 9,000
Year 2: 0.4 × 9,000 = 3,600 BV₂ = 5,400
Year 3: 0.4 × 5,400 = 2,160 BV₃ = 3,240
Year 4: 0.4 × 3,240 = 1,296 (SL = 1,170, DDB larger) BV₄ = 1,944
Year 5: 0.4 × 1,944 = 778 (SL = 1,044, larger) → charge 1,044 BV₅ = 900
Without the switch, the pure DDB charge of 778 in year 5 would leave BV₅ = 1,166, which is above the salvage value of 900; so the last-year charge is raised to 1,944 − 900 = 1,044.
Answer: Annual depreciation = 6,000; 3,600; 2,160; 1,296; 1,044 and book values = 9,000; 5,400; 3,240; 1,944; 900 (Rs) for years 1 to 5.
✓ Answer checked by Claude Opus 5.5 (high effort)
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