--- title: "After-tax cash flow, DDB with switchover" subject: "Engineering Economics" chapter: 7 key: "semester_6/engineering_economics:after-tax-cash-flow-ddb-switchover" source: https://www.bctengineer.com/q/semester_6/engineering_economics/after-tax-cash-flow-ddb-switchover site: BCT Engineering --- # After-tax cash flow, DDB with switchover Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes - Asked in: 2076 Shrawan, 6 marks - Video: [Declining Balance with conversion to Straight Line depreciation method |Board Exam Solution](https://www.youtube.com/watch?v=biBncOCCThA) — OPengineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/after-tax-cash-flow-ddb-switchover - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7 ## Question A company invested Rs 100000 in an equipment which will generate annual benefit of Rs 45000 for 5 years. Its salvage value is expected to be Rs 20000 at the end. Estimate after-tax cash flow. Assume double declining balance method with switchover to straight line depreciation, tax rate = 25%. MARR = 10%. ## Short answer After-tax cash flows for years 1–5 are Rs 43,750, 39,750, 37,350, 34,150, and 53,750 (year 5 includes Rs 20,000 salvage). At 10% MARR, the after-tax present worth is Rs 57,385 (>0), so the investment is acceptable. ## Answer Data: P = 1,00,000; N = 5; S = 20,000; before-tax benefit = 45,000/yr; tax rate = 25%; MARR = 10%. #### Depreciation: DDB with switchover to SL DDB rate = 2/N = 2/5 = 40% of the opening book value, but book value may not fall below S = 20,000. ```text Year 1: 0.40 × 1,00,000 = 40,000 BV = 60,000 Year 2: 0.40 × 60,000 = 24,000 BV = 36,000 Year 3: 0.40 × 36,000 = 14,400 BV = 21,600 (SL = (36,000−20,000)/3 = 5,333 < 14,400, stay DDB) Year 4: DDB = 8,640, but only 21,600 − 20,000 = 1,600 can be taken (SL switchover = 800 is smaller) Year 5: BV already equals S, so depreciation = 0 ``` #### After-tax cash flow (ATCF) Taxable income = benefit − depreciation; tax = 25% × taxable income; ATCF = 45,000 − tax. At the end of year 5 the asset is sold for 20,000 = book value, so there is no gain or loss and no tax on it. | Year | Depreciation | Book value | Taxable income | Tax (25%) | ATCF | |---|---|---|---|---|---| | 1 | 40,000 | 60,000 | 5,000 | 1,250 | 43,750 | | 2 | 24,000 | 36,000 | 21,000 | 5,250 | 39,750 | | 3 | 14,400 | 21,600 | 30,600 | 7,650 | 37,350 | | 4 | 1,600 | 20,000 | 43,400 | 10,850 | 34,150 | | 5 | 0 | 20,000 | 45,000 | 11,250 | 33,750 | ```text Year 0 1 2 3 4 5 (incl. salvage 20,000) CF −1,00,000 43,750 39,750 37,350 34,150 53,750 ``` #### Evaluation PW = −1,00,000 + 43,750(P/F,10%,1) + 39,750(P/F,10%,2) + 37,350(P/F,10%,3) + 34,150(P/F,10%,4) + 53,750(P/F,10%,5) = Rs 57,385; after-tax IRR = 30.3%. **Answer:** ATCF = 43,750, 39,750, 37,350, 34,150 and 53,750 (year 5 includes 20,000 salvage) for years 1 to 5. After-tax PW at 10% = Rs 57,385 > 0, so the investment is acceptable. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What DDB rate applies for N = 5? A. 40% of opening book value B. 20% of cost C. 25% of opening book value D. 40% of (P - S) Answer: A. 2/N = 2/5 = 40% applied on book value. (Key point: DDB rate) 2. Why is year-4 depreciation only Rs 1,600? A. DDB gives 1,600 directly B. Book value may not fall below S = 20,000, and 21,600 - 20,000 = 1,600 C. SL on cost gives 1,600 D. The tax rate limits it Answer: B. Depreciation stops when book value reaches salvage. (Key point: Salvage limit) 3. What is year-1 ATCF? A. Rs 45,000 B. Rs 40,000 C. Rs 43,750 D. Rs 5,000 Answer: C. Taxable income 45,000 - 40,000 = 5,000; tax 1,250; ATCF = 43,750. (Key point: ATCF year 1) 4. Why is year-5 cash flow 53,750? A. 33,750 plus 20,000 minus tax on salvage B. 45,000 plus 20,000 less tax C. 33,750 only D. ATCF 33,750 plus 20,000 salvage with no tax since salvage equals book value Answer: D. Selling at book value gives no gain or loss, so no disposal tax. 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