--- title: "Double declining balance depreciation, 15000 machine" subject: "Engineering Economics" chapter: 7 key: "semester_6/engineering_economics:ddb-15000-salvage-900" source: https://www.bctengineer.com/q/semester_6/engineering_economics/ddb-15000-salvage-900 site: BCT Engineering --- # Double declining balance depreciation, 15000 machine Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes - Asked in: 2069 Bhadra, 8 marks - Video: [DOUBLE DECLINING BALANCE Method of Depreciation](https://www.youtube.com/watch?v=M-VzJ51zZoM) — Accounting Stuff - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/ddb-15000-salvage-900 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7 ## Question 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. ## 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. ## Answer 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 | ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For a 5-year asset, what rate does double declining balance apply, and to what base? A. 20% of the original cost B. 40% of the opening book value C. 40% of (cost - salvage) D. 20% of the opening book value Answer: B. DDB rate = 2/N = 2/5 = 40%, applied to the opening book value of each year. (Key point: DDB rate) 2. With P = Rs 15,000, what are the DDB depreciation charges in years 1 and 2? A. 6,000 and 3,600 B. 6,000 and 6,000 C. 5,640 and 3,384 D. 3,600 and 2,160 Answer: A. Year 1 = 0.4 x 15,000 = 6,000 (BV 9,000); year 2 = 0.4 x 9,000 = 3,600. (Key point: Year 1 and 2 depreciation) 3. Why is the year-5 charge 1,044 and not the pure DDB value of 777.6? A. Because DDB always ends with straight-line in the final year regardless of values B. Because the tax rate changes in year 5 C. Because the book value must reach the salvage value of 900, and straight-line on the remaining amount (1,944 - 900) is larger D. Because the DDB rate falls to 20% in the last year Answer: C. Pure DDB would leave BV 1,166, above S = 900; switching to the larger straight-line charge 1,944 - 900 = 1,044 makes BV5 = 900. (Key point: Salvage limit) 4. What are the book values at the end of years 3 and 4? A. 3,240 and 1,166 B. 5,400 and 3,240 C. 2,160 and 1,296 D. 3,240 and 1,944 Answer: D. BV3 = 5,400 - 2,160 = 3,240 and BV4 = 3,240 - 1,296 = 1,944. 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