- 2076 Shrawan · 6 marks
After-tax cash flow, DDB with switchover
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.
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%.
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.
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 |
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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