- 2065 Chaitra · 16 marks
Payback, ERR and BCR for four projects
Short answer
Simple payback: B has shortest at 3.64 years. ERR: only B (15.49%) exceeds 15%. BCR: only B (1.021) exceeds 1. All methods select project B.
From the following four mutually exclusive projects recommend the best one using Payback Period, ERR and BCR methods. The study period is 5 years and MARR = ε = 15%.
| Project | A | B | C | D |
|---|---|---|---|---|
| Initial investment | 500000 | 400000 | 700000 | 600000 |
| Net annual revenue | 125000 | 110000 | 170000 | 135000 |
| Salvage value is 20% of the initial investment. |
Data: N = 5 years; MARR = reinvestment rate ε = 15%; salvage value S = 20% of the initial investment (A: 100,000; B: 80,000; C: 140,000; D: 120,000). Net annual revenue is the annual benefit.
Factors: (F/A,15%,5) = 6.7424; (P/A,15%,5) = 3.3522; (P/F,15%,5) = 0.4972.
1. Payback period (simple)
Payback = initial investment / net annual revenue (salvage ignored).
| Project | Investment | Net annual revenue | Payback = I / annual |
|---|---|---|---|
| A | 500,000 | 125,000 | 4.00 yr |
| B | 400,000 | 110,000 | 3.64 yr |
| C | 700,000 | 170,000 | 4.12 yr |
| D | 600,000 | 135,000 | 4.44 yr |
Shortest payback: B (3.64 years). Payback ignores the cash flows after recovery and the time value of money, so it is only a screening measure.
2. External rate of return (ERR)
All receipts (annual revenue and salvage) are compounded to year 5 at ε = 15%, and ERR is the rate i' with I(1 + i')⁵ = FW.
FW = A(F/A,15%,5) + S
Project B: FW = 110,000(6.7424) + 80,000 = 821,662
ERR = (821,662 / 400,000)^(1/5) − 1 = 15.49%
| Project | FW of receipts at yr 5 | ERR = (FW / I)^(1/5) − 1 | Acceptable (≥ 15%)? |
|---|---|---|---|
| A | 942,798 | 13.52% | No |
| B | 821,662 | 15.49% | Yes |
| C | 1,286,205 | 12.94% | No |
| D | 1,030,221 | 11.42% | No |
Only B has ERR above MARR = 15%.
3. Benefit–cost ratio (conventional)
BCR = PW(annual revenue + salvage) / initial investment.
Project B: PW(B) = 110,000(3.3522) + 80,000(0.4972) = 408,511
BCR = 408,511 / 400,000 = 1.021
| Project | PW of benefits | BCR = PW(B) / I | Acceptable (≥ 1)? |
|---|---|---|---|
| A | 468,737 | 0.937 | No |
| B | 408,511 | 1.021 | Yes |
| C | 639,471 | 0.914 | No |
| D | 512,202 | 0.854 | No |
Only B has BCR > 1.
Decision
| Method | Best project |
|---|---|
| Payback | B |
| ERR | B (15.49%) |
| BCR | B (1.021) |
A, C and D fail ERR and BCR tests at 15% (their PWs are negative), so no incremental comparison is needed.
Answer: Select project B. It has the shortest payback (3.64 years), ERR = 15.49% > 15% and BCR = 1.021 > 1.
✓ Answer checked by Claude Opus 5.5 (high effort)
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