- 2070 Magh · 6 marks
ATCF and IRR with given depreciation schedule
Short answer
After-tax cash flows: year 1 Rs 2,87,500; years 2–4 Rs 3,12,500; year 5 Rs 3,37,500. PW at 15% = Rs 38,239 > 0; IRR = 16.6% > MARR, so the investment is profitable.
Suppose an equipment purchased for Rs. 10,00,000. It is expected to generate income of Rs. 3,50,000 per year during 5 years. Corporate income tax rate is 25% per year. The recovery period depreciation amounts are as follows.
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Depreciation amount | 1,00,000 | 2,00,000 | 2,00,000 | 2,00,000 | 3,00,000 |
| Calculate ATCFs and determine profitability (IRR) when MARR is 15% by using PW method. |
Data: P = Rs 10,00,000; income = Rs 3,50,000/yr for 5 years; tax rate = 25%; MARR = 15%. The depreciation totals Rs 10,00,000, so the book value at year 5 is 0; assume no salvage value.
After-tax cash flow
Taxable income = 3,50,000 − depreciation; tax = 25% × taxable income; ATCF = 3,50,000 − tax.
| Year | Depreciation | Taxable income | Tax (25%) | ATCF |
|---|---|---|---|---|
| 1 | 100,000 | 250,000 | 62,500 | 287,500 |
| 2 | 200,000 | 150,000 | 37,500 | 312,500 |
| 3 | 200,000 | 150,000 | 37,500 | 312,500 |
| 4 | 200,000 | 150,000 | 37,500 | 312,500 |
| 5 | 300,000 | 50,000 | 12,500 | 337,500 |
Year 0 1 2 3 4 5
CF −10,00,000 287,500 312,500 312,500 312,500 337,500
Present worth at 15%
PW = −10,00,000 + 2,87,500(P/F,15%,1) + 3,12,500[(P/F,15%,2) + (P/F,15%,3) + (P/F,15%,4)] + 3,37,500(P/F,15%,5)
= −10,00,000 + 2,87,500(0.8696) + 3,12,500(0.7561 + 0.6575 + 0.5718) + 3,37,500(0.4972)
= −10,00,000 + 2,50,000 + 6,20,438 + 1,67,800 = Rs 38,239
Profitability (IRR)
Solve PW(i) = 0:
PW(15%) = 38,239
PW(18%) = -33,018
IRR = 15% + 3% × 38,239/(38,239 + 33,018) ≈ 16.6%
Answer: After-tax PW at 15% = Rs 38,239 > 0 and after-tax IRR ≈ 16.6% > MARR = 15%, so the investment is profitable.
✓ Answer checked by Claude Opus 5.5 (high effort)
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