- 2070 Magh · 5 marks
PW with differential inflation rates
Short answer
Inflate each item by its own rate: sales 5%, labour 8%, materials 0% and 6%, salvage 3%. Discount net actual cash flows at 20%: PW ≈ Rs 9,300. The project is marginally acceptable.
Evaluate the PW of the following project. Initial investment = Rs. 1,00,000 (in constant dollars) Annual sales income = Rs. 40,000 (in constant dollars) Annual labour cost = Rs. 3,000 (in constant dollars) Annual material X = Rs. 2,000 (in constant dollars) Annual material Y = Rs. 1,000 (in constant dollars) Salvage value = 20% of initial investment (in constant dollars) Inflation rate for sales income, labour cost, materials X, material Y and salvage value are 5%, 8%, 0%, 6% and 3% respectively for the project period. Take market interest rate = 20%, project life is 4 years.
Each item inflates at its own rate (differential inflation), so each is converted to actual dollars as constant × (1 + f_item)^n and then all net actual cash flows are discounted at the market interest rate of 20%. The initial investment (year 0) needs no conversion.
Salvage value = 20% × 1,00,000 = 20,000 constant dollars, inflating at 3%: 20,000(1.03)⁴ = 22,510.
| Item | Constant $ | Inflation f |
|---|---|---|
| Sales income | 40,000 | 5% |
| Labour | 3,000 | 8% |
| Material X | 2,000 | 0% |
| Material Y | 1,000 | 6% |
| Salvage | 20,000 | 3% |
| Year | Sales | Labour | Material X | Material Y | Salvage | Net actual CF | PW at 20% |
|---|---|---|---|---|---|---|---|
| 1 | 42,000 | 3,240 | 2,000 | 1,060 | 0 | 35,700 | 29,750 |
| 2 | 44,100 | 3,499 | 2,000 | 1,124 | 0 | 37,477 | 26,026 |
| 3 | 46,305 | 3,779 | 2,000 | 1,191 | 0 | 39,335 | 22,763 |
| 4 | 48,620 | 4,081 | 2,000 | 1,262 | 22,510 | 63,786 | 30,761 |
Net actual CF = sales − labour − X − Y + salvage.
PW = −1,00,000 + 29,750 + 26,026 + 22,763 + 30,761
= Rs 9,300
Answer: PW ≈ Rs 9,300 (positive but small), so the project is just acceptable at the 20% market rate.
✓ Answer checked by Claude Opus 5.5 (high effort)
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