---
title: "PW, AW and FW decision for equipment"
subject: "Engineering Economics"
chapter: 3
key: "semester_6/engineering_economics:pw-aw-fw-equipment-500000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/pw-aw-fw-equipment-500000
site: BCT Engineering
---

# PW, AW and FW decision for equipment

Engineering Economics · Chapter 3: Basic Methodologies of Engineering Economic Analysis

- Asked in: 2069 Poush
- Video: [Present Worth Annual Worth |Engineering Economics |Board Exam Solution in NEPALI](https://www.youtube.com/watch?v=-fuKCBcpQGc) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/pw-aw-fw-equipment-500000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3

## Question

An equipment costing Rs. 5,00,000 is estimated to have life of 10 years and expected annual revenue is Rs. 1,10,000 with annual cost of Rs. 20,000. Determine the investment decision from PW, AW and FW method to this equipment when salvage value is Rs. 1,00,000 and MARR is 12%.

## Short answer

Net annual cash flow = Rs 90,000. PW = Rs 40,717, AW = Rs 7,206 per year, FW = Rs 126,462. All positive, so the equipment should be purchased.

## Answer

Net annual revenue = 1,10,000 − 20,000 = Rs 90,000. I = 5,00,000; S = 1,00,000; N = 10 years; MARR = 12%. Assumed that revenue and cost occur at the end of each year.

```text
 yr 0: -5,00,000      yr 1..10: +90,000      yr 10: +1,00,000
```
Factors at 12%, 10 years: (P/A) = 5.6502, (P/F) = 0.3220, (A/P) = 0.17698, (F/P) = 3.1058

#### PW method
PW = −5,00,000 + 90,000 (P/A, 12%, 10) + 1,00,000 (P/F, 12%, 10)
= −5,00,000 + 508,520 + 32,197 = **Rs +40,717**

#### AW method
AW = PW (A/P, 12%, 10) = 40,717 × 0.17698 = **Rs +7,206 per year**

Check: AW = −(5,00,000 − 1,00,000)(A/P) − 1,00,000 × 0.12 + 90,000 = −70,794 − 12,000 + 90,000 = 7,206

#### FW method
FW = PW (F/P, 12%, 10) = 40,717 × 3.1058 = **Rs +126,462**

| Method | Value | Decision |
|---|---|---|
| PW | +40,717 | > 0, accept |
| AW | +7,206 | > 0, accept |
| FW | +126,462 | > 0, accept |

**Answer: PW, AW and FW are all positive, so the equipment should be purchased. (All three methods always give the same decision.)**

## Check yourself

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

1. What annual net amount is used?
   A. 1,10,000
   B. 1,10,000 - 20,000 = 90,000
   C. 1,30,000
   D. 20,000
   Answer: B. Cost is subtracted from revenue. (Key point: Net annual revenue)

2. What is the PW?
   A. +Rs 40,717
   B. -Rs 40,717
   C. +Rs 7,206
   D. +Rs 126,462
   Answer: A. -500,000 + 90,000x5.6502 + 100,000x0.3220. (Key point: PW)

3. How are AW and FW obtained from PW?
   A. AW = PW(P/A), FW = PW(P/F)
   B. AW = FW(F/P)
   C. AW = PW(A/P), FW = PW(F/P)
   D. They need a separate cash flow
   Answer: C. Each is an equivalent restatement of PW at the same rate. (Key point: Linking AW and FW)

4. What is the conclusion?
   A. Reject, because FW is large
   B. PW and AW disagree
   C. Buy only if AW > PW
   D. All three are positive and give the same decision: buy
   Answer: D. PW, AW and FW always give the same accept/reject decision. (Key point: Decision)

## Related in Engineering Economics

- [AW sensitivity to investment and net annual cash flow](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-aw-500000-75000) — Engineering Economics, chapter 6
- [Sensitivity to investment, revenue and life](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-investment-revenue-life-500000) — Engineering Economics, chapter 6
- [Sensitivity on investment, revenue and life; interpret](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-initial-100000-useful-10) — Engineering Economics, chapter 6
- [IRR by AW, both BCR by FW, and ERR](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-aw-bcr-fw-err-250000) — Engineering Economics, chapter 3
- [Sensitivity of PW to investment and MARR](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-investment-marr-10-50) — Engineering Economics, chapter 6, asked 2×
- [Both BCR with FW, gradient revenue](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Abcr-fw-gradient-revenue-250000) — Engineering Economics, chapter 3

## Related in other subjects

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- [Capitalised value from Rs 20,000 monthly rent](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Avalue-building-20000-rent-2078) — Construction Management, chapter 13
- [EPS and book value; capital Rs 5,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-capital-500000-2000-shares) — Project Engineering, chapter 6
- [EPS and book value; ABC project Rs 6,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-abc-project-600000-b79) — Project Engineering, chapter 6