- 2067 Mangsir · 8 marks
Best of three mutually exclusive projects, 10-year study
Short answer
Compute net annual benefits (A: Rs. 125,000, B: Rs. 125,000, C: Rs. 145,000). At 12% MARR, PW over respective lives: A -56,780, B -35,411, C 48,580. Only C has positive PW, so select Project C.
Recommend which one is best out of the following three mutually exclusive projects. Study period is 10 years. MARR = 12%.
| Project | A | B | C |
|---|---|---|---|
| Initial Investment | 5,00,000 | 6,00,000 | 7,00,000 |
| Annual Revenues | 1,50,000 | 1,50,000 | 1,70,000 |
| Annual cost | 25,000 | 25,000 | 25,000 |
| Salvage value | 1,00,000 | 1,00,000 | 70,000 |
| Useful life | 4 | 6 | 8 |
Net annual benefit = revenue - cost: A = 150,000 - 25,000 = 125,000; B = 125,000; C = 170,000 - 25,000 = 145,000.
Assumption for the study period (10 years)
Each project is bought once and used for its own life (4, 6, 8 years). At the end of the life it is sold at its salvage value and the money is invested elsewhere at the MARR (12%) up to year 10. Money earning exactly MARR has zero net present worth, so the extra years add nothing to PW and the projects can be compared by PW over their own lives. (Under the repeatability assumption with AW instead, the ranking is the same: AW(A) = -18,694, AW(B) = -8,613, AW(C) = +9,779 per year, so C is still best.)
PW calculations at 12%
| Project | N | (P/A,12%,N) | (P/F,12%,N) |
|---|---|---|---|
| A | 4 | 3.0373 | 0.6355 |
| B | 6 | 4.1114 | 0.5066 |
| C | 8 | 4.9676 | 0.4039 |
PW(A) = -500,000 + 125,000(3.0373) + 100,000(0.6355) = -500,000 + 379,669 + 63,552 = -56,780 PW(B) = -600,000 + 125,000(4.1114) + 100,000(0.5066) = -600,000 + 513,926 + 50,663 = -35,411 PW(C) = -700,000 + 145,000(4.9676) + 70,000(0.4039) = -700,000 + 720,308 + 28,272 = 48,580
| Project | PW (Rs.) | Decision |
|---|---|---|
| A | -56,780 | reject (PW < 0) |
| B | -35,411 | reject (PW < 0) |
| C | 48,580 | accept |
Answer: Select Project C, the only project with positive PW (Rs. 48,580).
✓ Answer checked by Claude Opus 5.5 (high effort)
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