- 2066 Magh · 10 marks
Best combination with independent and contingent projects
Short answer
Find PW of each project (A: 26,687, B: 18,026, C: 56,699). Feasible combinations within Rs. 120,000 budget and contingency B only with C. A+C yields highest PW of Rs. 83,385 at investment Rs. 90,000.
Select the best combination of the projects where A is independent and B is contingent on C.
| Project | A | B | C |
|---|---|---|---|
| Initial Investment | 40,000 | 70,000 | 50,000 |
| Annual Revenues | 15,000 | 20,000 | 20000 |
| Annual cost | 2,500 | 3,500 | 0 |
| Useful life (Yrs.) | 8 | 8 | 8 |
| The investment is limited to Rs. 120,000. MARR = 10%. |
A is independent; B is contingent on C (B can be taken only if C is taken). Budget = Rs. 120,000, MARR = 10%, life 8 years. Net annual benefit = revenue - annual cost.
(P/A, 10%, 8) = 5.3349
PW of each project
| Project | Investment | Net benefit/yr | PW = -I + NB(P/A,10%,8) |
|---|---|---|---|
| A | 40,000 | 12,500 | -40,000 + 12,500(5.3349) = 26,687 |
| B | 70,000 | 16,500 | -70,000 + 16,500(5.3349) = 18,026 |
| C | 50,000 | 20,000 | -50,000 + 20,000(5.3349) = 56,699 |
Feasible combinations
Because B needs C, the combinations "B alone", "A + B" are infeasible. Remaining combinations (1 = taken):
| Combination | A | B | C |
|---|---|---|---|
| Do nothing | 0 | 0 | 0 |
| A | 1 | 0 | 0 |
| C | 0 | 0 | 1 |
| A + C | 1 | 0 | 1 |
| B + C | 0 | 1 | 1 |
| A + B + C | 1 | 1 | 1 |
Budget test and PW
| Combination | Investment (Rs.) | PW (Rs.) |
|---|---|---|
| Do nothing | 0 | 0 |
| A | 40,000 | 26,687 |
| C | 50,000 | 56,699 |
| A + C | 90,000 | 83,385 |
| B + C | 120,000 | 74,725 |
| A + B + C | 160,000 | exceeds budget |
Answer: Select A + C (investment Rs. 90,000), which has the highest PW of Rs. 83,385. The combination B + C uses the whole budget but gives only Rs. 74,725; A + B + C costs Rs. 160,000 and violates the limit. Each of A, B, C is individually profitable, so the budget and the contingency decide the result.
✓ Answer checked by Claude Opus 5.5 (high effort)
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