- 2070 Bhadra · 6+6 marks
MACRS schedule and after-tax IRR by AW
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.
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.
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.
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 |
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 |
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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