--- title: "Depreciation, causes; declining balance for 50,000" subject: "Engineering Economics" chapter: 7 key: "semester_6/engineering_economics:depreciation-causes-db-50000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-causes-db-50000 site: BCT Engineering --- # Depreciation, causes; declining balance for 50,000 Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes - Asked in: 2069 Poush - Video: [#E5 Depreciation | Straight line method | Constant Percentage method | Sinking Fund Method |](https://www.youtube.com/watch?v=pb8uKs5Cn_8) — Kivip Tech 【 Civil Engineering 】 - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-causes-db-50000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7 ## Question What do you mean by depreciation and what are its causes? A machine purchased for Rs. 50,000 by expecting useful life of 10 years. Calculate its depreciation amount for each year by using declining balance method when rate of depreciation is 20% per year. ## Short answer Depreciation is the systematic allocation of cost, caused by wear, obsolescence, inadequacy, etc. With 20% declining balance, annual depreciation: Rs 10,000, 8,000, 6,400, 5,120, 4,096, 3,277, 2,621, 2,097, 1,678, 1,342. ## Answer #### Depreciation Depreciation is the decrease in the value of a physical asset with the passage of time and use. In accounting and tax it is the systematic allocation of the cost of an asset (less its salvage value) over its useful life. It is a non-cash expense, but it is deductible from taxable income. #### Causes of depreciation 1. **Physical deterioration (wear and tear):** use, friction, corrosion, weather and ageing reduce the strength and efficiency of the asset. 2. **Functional obsolescence:** new technology or new designs make the old asset out of date, even though it is physically sound. 3. **Inadequacy:** the asset can no longer meet the growth in demand or capacity. 4. **Changes in requirement or law:** a change in the product, safety rules or environmental standards makes the asset unsuitable. 5. **Depletion:** the asset is a natural resource (mine, quarry) that is used up as material is extracted. 6. **Fall in market price:** a decline in the market value of the asset because of changes in the economy or demand. 7. **Time (lapse of legal right):** a fixed term of use, such as a lease, patent, license or concession, ends. 8. **Accident or damage:** fire, flood, earthquake or accidents shorten the life. #### Declining-balance depreciation: P = Rs 50,000, N = 10, R = 20% D_k = 0.20 × BV_(k−1). | Year | Opening BV | Depreciation | Closing BV | |---|---|---|---| | 1 | 50,000 | 10,000 | 40,000 | | 2 | 40,000 | 8,000 | 32,000 | | 3 | 32,000 | 6,400 | 25,600 | | 4 | 25,600 | 5,120 | 20,480 | | 5 | 20,480 | 4,096 | 16,384 | | 6 | 16,384 | 3,277 | 13,107 | | 7 | 13,107 | 2,621 | 10,486 | | 8 | 10,486 | 2,097 | 8,389 | | 9 | 8,389 | 1,678 | 6,711 | | 10 | 6,711 | 1,342 | 5,369 | Total depreciation = 50,000 − 5,369 = Rs 44,631; the book value after 10 years is Rs 5,369, which is the salvage value implied by the 20% rate. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. With R = 20% on Rs 50,000, what is year-1 depreciation? A. Rs 10,000 B. Rs 5,000 C. Rs 8,000 D. Rs 12,000 Answer: A. 0.20 x 50,000 = 10,000. (Key point: DB year 1) 2. What is year-2 depreciation? A. Rs 10,000 B. Rs 8,000 C. Rs 6,400 D. Rs 4,000 Answer: B. 20% of opening BV 40,000. (Key point: Year 2) 3. What is the BV after 10 years? A. Rs 0 B. Rs 10,000 C. Rs 5,369 D. Rs 44,631 Answer: C. 50,000 x 0.8^10 = 5,369. (Key point: Final BV) 4. Which cause covers fire or flood? A. Depletion B. Inadequacy C. Time D. Accident or damage Answer: D. These events shorten the life of the asset. 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