--- title: "MACRS schedule and after-tax IRR by AW" subject: "Engineering Economics" chapter: 7 key: "semester_6/engineering_economics:macrs-after-tax-irr-aw-45000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/macrs-after-tax-irr-aw-45000 site: BCT Engineering --- # MACRS schedule and after-tax IRR by AW Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes - Asked in: 2070 Bhadra, 6+6 marks - Video: [MACRS Method | Calculation of depreciation |Engineering economics](https://www.youtube.com/watch?v=gUEQv5BLuEU) — OPengineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/macrs-after-tax-irr-aw-45000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7 ## Question An asset has installed value of 45,000. Sv = 0. It is classed as a 5 year property. Determine approximate MACRS depreciation schedule. Over 6 years it is estimated to generate revenue of Rs. 23,000 per year with annual operating cost 7300. Required rate of return = 15% after tax. Tax rate = 40%. Evaluate after tax IRR with annual worth method. ## Short answer After-tax IRR = 17.6% (exceeds the 15% MARR), and annual worth at 15% = Rs 812 per year (>0). Therefore, the investment is acceptable. ## Answer #### 1. MACRS depreciation schedule (5-year property) MACRS uses the half-year convention and 200% declining balance (rate 2/5 = 40%), switching to straight line when it gives a larger charge. Salvage value is ignored (S = 0), so the whole 45,000 is depreciated over 6 tax years. ```text Year 1: 40% × ½ = 20.00% of 45,000 = 9,000 Year 2: 40% × (100 − 20)% = 32.00% = 14,400 Year 3: 40% × (100 − 52)% = 19.20% = 8,640 Year 4: 40% × 28.8% = 11.52% (switch to SL) = 5,184 Year 5: 11.52% (SL on remaining balance) = 5,184 Year 6: half-year, 5.76% = 2,592 ``` These are the standard MACRS percentages for 5-year property. #### 2. After-tax cash flow Revenue = 23,000; operating cost = 7,300; tax rate = 40%; asset value at the end = 0 (no disposal tax). ATCF = (23,000 − 7,300) − 0.40 × (23,000 − 7,300 − depreciation). | Year | MACRS % | Depreciation | Taxable income | Tax (40%) | ATCF | |---|---|---|---|---|---| | 1 | 20.00% | 9,000 | 6,700 | 2,680 | 13,020 | | 2 | 32.00% | 14,400 | 1,300 | 520 | 15,180 | | 3 | 19.20% | 8,640 | 7,060 | 2,824 | 12,876 | | 4 | 11.52% | 5,184 | 10,516 | 4,206 | 11,494 | | 5 | 11.52% | 5,184 | 10,516 | 4,206 | 11,494 | | 6 | 5.76% | 2,592 | 13,108 | 5,243 | 10,457 | ```text Year 0 1 2 3 4 5 6 CF −45,000 13,020 15,180 12,876 11,494 11,494 10,457 ``` #### 3. Annual worth and after-tax IRR AW(i) = [−45,000 + Σ ATCF_k (P/F,i,k)] (A/P,i,6) | i | AW (Rs) | |---|---| | 15% | 812 | | 20% | -750 | ```text At 15%: (A/P,15%,6) = 0.26424 AW(15%) = 3,073 × 0.26424 = 812 > 0 At 20%: AW(20%) = -750 < 0 IRR by interpolation = 15% + 5% × 812/(812 + 750) = 17.6% ``` (Exact solution of AW(i) = 0 gives 17.6%.) **Answer:** After-tax IRR ≈ **17.6%**, which is greater than the required 15%, and AW at 15% = Rs 812 per year > 0. The investment is **acceptable**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What convention and rate does 5-year MACRS use? A. Half-year convention with 200% declining balance switching to SL B. Full-year with straight line only C. Sum-of-years digits D. Unit of production Answer: A. This gives 20, 32, 19.2, 11.52, 11.52, 5.76 percent. (Key point: MACRS convention) 2. How is salvage value treated? A. Subtracted from the cost B. Ignored; the full cost is depreciated C. Added to year-1 depreciation D. Used to set the rate Answer: B. MACRS depreciates the whole cost basis. (Key point: Salvage value) 3. What is year-1 ATCF? A. Rs 15,700 B. Rs 9,000 C. Rs 13,020 D. Rs 2,680 Answer: C. Taxable 15,700 - 9,000 = 6,700; tax 2,680; ATCF = 15,700 - 2,680. (Key point: Year-1 ATCF) 4. What is the result? A. IRR about 15%, marginal B. IRR about 20% C. IRR below 15%, reject D. IRR about 17.6% > 15%, so acceptable Answer: D. AW at 15% = +812 and at 20% = -750, so IRR lies between. 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