- 2071 Bhadra · 4 marks
Both types of payback period for Machine A
Short answer
Net annual inflow = Rs 2,000. Simple payback = 6,000/2,000 = 3.00 years (marginal accept). Discounted payback using 10% = 3.75 years, exceeding the 3-year standard, so project is rejected.
Machine A: initial investment Rs. 6000, annual benefits Rs. 3000, O & M cost Rs. 1000, salvage value Rs. 1500, MARR 10%. Evaluate both types of payback period. Useful life = 5 years. (Take standard payback period = 3 years.)
Net annual cash flow = benefit − O&M = 3,000 − 1,000 = Rs 2,000. Salvage Rs 1,500 comes only at year 5 and is not needed for payback. Standard payback = 3 years, MARR = 10%.
yr 0: -6,000 yr 1..5: +2,000 each (yr 5 also +1,500 salvage)
| EOY | Net CF | Cumulative CF | PW at 10% | Cumulative PW |
|---|---|---|---|---|
| 1 | 2,000 | -4,000 | 1,818.18 | -4,181.82 |
| 2 | 2,000 | -2,000 | 1,652.89 | -2,528.93 |
| 3 | 2,000 | 0 | 1,502.63 | -1,026.30 |
| 4 | 2,000 | 2,000 | 1,366.03 | 339.73 |
| 5 | 2,000 | 4,000 | 1,241.84 | 1,581.57 |
Simple payback
θ = Investment / annual net inflow = 6,000 / 2,000 = 3.00 years. This equals the standard period of 3 years, so it is acceptable (just at the limit).
Discounted payback
PW of 3 years of inflows = 2,000 × (P/A, 10%, 3) = 2,000 × 2.4869 = 4,973.70, which is less than 6,000. The balance of 1,026.30 is recovered in year 4, where the PW of the inflow is 2,000 × 0.6830 = 1,366.03.
θ_d = 3 + 1,026.30 / 1,366.03 = 3.75 years
Decision
| Method | Payback | Standard | Result |
|---|---|---|---|
| Simple | 3.00 yr | 3 yr | Accept (marginal) |
| Discounted | 3.75 yr | 3 yr | Reject |
Answer: simple payback = 3 years (accept, at the limit); discounted payback = 3.75 years (more than 3 years, reject). Since the discounted payback accounts for the time value of money, the machine does not meet the 3-year requirement.
✓ Answer checked by Claude Opus 5.5 (high effort)
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