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