---
title: "ERR to select best proposal A or B"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:err-proposals-a-b-25"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/err-proposals-a-b-25
site: BCT Engineering
---

# ERR to select best proposal A or B

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2070 Magh, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/err-proposals-a-b-25
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Select the best proposal using ERR (ε = 25%, MARR = 20%).
| EOY | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Proposal A | -6400 | 2620 | 2900 | 3020 | 3100 | 3100 | 2600 |
| Proposal B | -7550 | 2050 | 4060 | 4000 | 3900 | 3500 | 3400 |

## Short answer

ERR at ε=25%: A=30.96%, B=30.82%. Both >20% MARR. Incremental B-A ERR=28.69% > 20%. Select Proposal B.

## Answer

ERR is found by compounding receipts to the end of year 6 at ε = 25% and discounting expenditures to year 0 at ε, then solving for i'. Select by the incremental ERR compared with MARR = 20%.

**Proposal A**: 
- Receipts compounded to year 6 at ε: FW(R) = 2,620(3.0518) + 2,900(2.4414) + 3,020(1.9531) + 3,100(1.5625) + 3,100(1.2500) + 2,600(1.0000) = 32,293
- Expenditures discounted to year 0 at ε: PW(E) = 6,400(1.0000) = 6,400
- ERR: 6,400(1 + i')^6 = 32,293 → (1 + i') = (5.0458)^(1/6) → **ERR = 30.96%**

**Proposal B**: 
- Receipts compounded to year 6 at ε: FW(R) = 2,050(3.0518) + 4,060(2.4414) + 4,000(1.9531) + 3,900(1.5625) + 3,500(1.2500) + 3,400(1.0000) = 37,849
- Expenditures discounted to year 0 at ε: PW(E) = 7,550(1.0000) = 7,550
- ERR: 7,550(1 + i')^6 = 37,849 → (1 + i') = (5.0132)^(1/6) → **ERR = 30.82%**

Both ERRs (30.96% and 30.82%) exceed MARR = 20%, so both are acceptable. B needs more investment, so test the increment.

#### Incremental (B - A)
Cash flows: [-1150, -570, 1160, 980, 800, 400, 800]
ERR(B - A) = 28.69% > MARR 20%

**Answer: Select Proposal B**, because its extra investment of Rs. 1,150 earns 28.7% which exceeds MARR = 20%.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. At what rate and to when are receipts compounded?
   A. ε = 25% to end of year 6
   B. ε to year 0
   C. MARR 20% to year 0
   D. IRR to year 3
   Answer: A. Receipts are compounded to the end of life at the external rate ε. (Key point: Compounding)

2. How do ERRs compare with MARR?
   A. Only B exceeds
   B. Only A exceeds
   C. Both are below 20%
   D. Both (30.96%, 30.82%) exceed 20%
   Answer: D. Both are acceptable, so incremental comparison is needed. (Key point: Own ERRs)

3. Why is B selected?
   A. B has lower cost
   B. A has negative ERR
   C. B has the highest own ERR
   D. Incremental ERR of 28.69% on extra investment exceeds MARR 20%
   Answer: D. The extra Rs 1,150 earns more than MARR. (Key point: Decision)

## Related in Engineering Economics

- [ERR method to select best of three projects](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-select-best-abc) — Engineering Economics, chapter 4
- [ERR to select between projects A and B](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-project-a-b-18-12) — Engineering Economics, chapter 4
- [ERR with MARR 12% and reinvestment 14%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-reinvestment-14) — Engineering Economics, chapter 3
- [IRR to select best of A, B, C (15 years)](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-select-abc-15yr) — Engineering Economics, chapter 4
- [Incremental IRR to select best of A to D](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aincremental-irr-abcd-salvage-25) — Engineering Economics, chapter 4
- [ERR with MARR = ε = 10%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-six-year-cash-flow) — Engineering Economics, chapter 3

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