--- title: "Depreciation causes; SOYD and declining balance" subject: "Engineering Economics" chapter: 7 key: "semester_6/engineering_economics:depreciation-causes-soyd-declining-150000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-causes-soyd-declining-150000 site: BCT Engineering --- # Depreciation causes; SOYD and declining balance Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes - Asked in: 2070 Magh, 2+5 marks - Video: [Sinking fund method |Declining balance | SOYD method |Board Exam Solution](https://www.youtube.com/watch?v=4HEjiCzBeeI) — OPengineer - 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-soyd-declining-150000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7 ## Question Define depreciation. What are the causes of it? If a machine costing Rs. 1,50,000 is purchased by expecting salvage value Rs. 40,000 at the end of 6th year, calculate depreciation amount for each year by (i) SOYD (ii) Declining balance. ## Short answer Depreciation is the systematic allocation of an asset's cost over its useful life; causes include physical wear, obsolescence, inadequacy, and legal expiry. SOYD: Rs 31,429, 26,190, 20,952, 15,714, 10,476, 5,238. Declining balance (rate 19.77%): Rs 29,657, 23,794, 19,089, 15,315, 12,287, 9,858; both end at book value Rs 40,000. ## 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 **Functional obsolescence:** new technology or new designs make the old asset out of date, even though it is physically sound. 3.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. #### Depreciation schedule: P = Rs 1,50,000, S = Rs 40,000, N = 6 P − S = 1,10,000. **(i) SOYD:** sum of digits = 6(7)/2 = 21; D_k = 1,10,000 × (7 − k)/21. | Year | Fraction | Depreciation | Book value | |---|---|---|---| | 1 | 6/21 | 31,429 | 118,571 | | 2 | 5/21 | 26,190 | 92,381 | | 3 | 4/21 | 20,952 | 71,429 | | 4 | 3/21 | 15,714 | 55,714 | | 5 | 2/21 | 10,476 | 45,238 | | 6 | 1/21 | 5,238 | 40,000 | **(ii) Declining balance:** the rate that makes BV₆ = S is R = 1 − (S/P)^(1/N) = 1 − (40,000/1,50,000)^(1/6) = 1 − 0.8023 = **19.77%**. D_k = R × BV_(k−1). | Year | Opening BV | Depreciation | Book value | |---|---|---|---| | 1 | 150,000 | 29,657 | 120,343 | | 2 | 120,343 | 23,794 | 96,549 | | 3 | 96,549 | 19,089 | 77,460 | | 4 | 77,460 | 15,315 | 62,145 | | 5 | 62,145 | 12,287 | 49,858 | | 6 | 49,858 | 9,858 | 40,000 | Both methods depreciate a total of Rs 1,10,000 and end with a book value of Rs 40,000; the charges are largest in year 1 (Rs 31,429 by SOYD; Rs 29,657 by DB). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For N = 6, what is the sum of digits? A. 21 B. 36 C. 15 D. 6 Answer: A. 6 x 7/2 = 21. (Key point: SOYD sum of digits) 2. What is SOYD year-1 depreciation? A. Rs 18,333 B. Rs 31,429 C. Rs 25,000 D. Rs 29,657 Answer: B. 1,10,000 x 6/21 = 31,429. (Key point: SOYD year 1) 3. What DB rate brings BV to Rs 40,000 in 6 years? A. 16.67% B. 26.67% C. 19.77% D. 33.3% Answer: C. R = 1 - (40,000/1,50,000)^(1/6). (Key point: DB rate) 4. What is total depreciation by both methods? A. Rs 1,50,000 B. Rs 40,000 C. Rs 31,429 D. Rs 1,10,000 Answer: D. P - S = 1,10,000; both end at book value 40,000. 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