--- title: "After-tax cash flow, sinking fund depreciation" subject: "Engineering Economics" chapter: 7 key: "semester_6/engineering_economics:aftertax-cash-flow-sinking-fund-25000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/aftertax-cash-flow-sinking-fund-25000 site: BCT Engineering --- # After-tax cash flow, sinking fund depreciation Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes - Asked in: 2076 Shrawan, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/aftertax-cash-flow-sinking-fund-25000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7 ## Question A company bought a machine at Rs 25000 which is expected to produce benefit of Rs 8000 per year for five years. Its salvage value at the end of five years is Rs 10000. Calculate after-tax cash flow if tax rate is 40% and depreciation is on sinking fund method. i = 20%. ## Short answer Sinking-fund depreciation yields ATCF: Rs 5,606, 5,768, 5,961, 6,193, and 16,472 (year 5 includes Rs 10,000 salvage). After-tax IRR = 14.8%, below the 20% required return, so the investment is not acceptable. ## Answer Data: P = 25,000; S = 10,000; N = 5; benefit = 8,000/yr before tax; tax rate = 40%; sinking-fund interest i = 20%. #### Sinking-fund depreciation ```text Yearly deposit = (P − S)(A/F,20%,5) = 15,000(0.13438) = 2,016 Depreciation in year k = 2,016(1.20)^(k−1) ``` #### After-tax cash flow Taxable income = 8,000 − depreciation; tax = 40% × taxable income; ATCF = 8,000 − tax. At year 5 the salvage value of 10,000 equals the book value, so there is no tax on disposal. | Year | Depreciation | Book value | Taxable income | Tax (40%) | ATCF | |---|---|---|---|---|---| | 1 | 2,016 | 22,984 | 5,984 | 2,394 | 5,606 | | 2 | 2,419 | 20,565 | 5,581 | 2,232 | 5,768 | | 3 | 2,903 | 17,663 | 5,097 | 2,039 | 5,961 | | 4 | 3,483 | 14,180 | 4,517 | 1,807 | 6,193 | | 5 | 4,180 | 10,000 | 3,820 | 1,528 | 6,472 | ```text Year 0 1 2 3 4 5 (with salvage 10,000) CF −25,000 5,606 5,768 5,961 6,193 16,472 ``` PW of the ATCF at 20% = −Rs 3,267; after-tax IRR = 14.8%. **Answer:** ATCF for years 1 to 5 = 5,606, 5,768, 5,961, 6,193 and 16,472 (year 5 includes the 10,000 salvage). The after-tax return (14.8%) is below 20%, so the machine would not earn the 20% rate. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the yearly sinking-fund deposit? A. 15,000(A/F,20%,5) = Rs 2,016 B. 25,000(A/F,20%,5) C. 15,000/5 = 3,000 D. 15,000(A/P,20%,5) Answer: A. Depreciable amount is P - S = 15,000. (Key point: Deposit) 2. How does depreciation in year k behave? A. Constant at 2,016 B. 2,016(1.20)^(k-1), increasing yearly C. Decreasing at 20% D. 15,000/5 each year Answer: B. Depreciation grows at the sinking-fund interest rate. (Key point: Depreciation pattern) 3. What is year-1 ATCF? A. Rs 8,000 B. Rs 5,984 C. Rs 5,606 D. Rs 2,394 Answer: C. Taxable 8,000 - 2,016 = 5,984; tax 2,394; ATCF 5,606. (Key point: Year-1 ATCF) 4. Why is the year-5 cash flow 16,472? A. 6,472 plus 10,000 less tax B. 8,000 plus 10,000 C. 6,472 only D. ATCF 6,472 plus 10,000 salvage; salvage equals book value so no tax Answer: D. Book value at year 5 is 10,000 = salvage. 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