- 2070 Magh · 4 marks
IRR by trial and error; investment decision
Short answer
PW equation: -25,000 + 8,000(P/A,i,5) + 5,000(P/F,i,5)=0. Trial and error yields IRR=21.6%, which exceeds MARR of 20%, so accept the project.
Compute IRR by using trial and error process of the following project. Determine also investment decision. Initial investment = 25,000 Annual revenue = 8,000 Salvage value = 5,000 Useful life = 5 years MARR = 20%
yr 0: -25,000 yr 1..5: +8,000 each yr 5: +5,000 (salvage)
IRR is the rate at which PW = 0:
PW(i) = −25,000 + 8,000 (P/A, i, 5) + 5,000 (P/F, i, 5)
Trial and error
| Trial i | (P/A, i, 5) | (P/F, i, 5) | PW(i) |
|---|---|---|---|
| 20% | 2.9906 | 0.4019 | +934 |
| 25% | 2.6893 | 0.3277 | -1,847 |
| 22% | 2.8636 | 0.3700 | -241 |
| 21% | 2.9260 | 0.3855 | +336 |
PW is positive at 21% (+336) and negative at 22% (-241). Interpolating:
IRR = 21 + 1 × 336 / (336 − (-241)) = 21 + 0.58 = 21.58%
Decision
IRR = 21.58% > MARR = 20%, so the investment is acceptable.
Answer: IRR ≈ 21.6%; accept the project.
✓ Answer checked by Claude Opus 5.5 (high effort)
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