---
title: "Both payback periods, is project acceptable"
subject: "Engineering Economics"
chapter: 3
key: "semester_6/engineering_economics:payback-both-types-acceptable"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/payback-both-types-acceptable
site: BCT Engineering
---

# Both payback periods, is project acceptable

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

- Asked in: 2076 Shrawan, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/payback-both-types-acceptable
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3

## Question

Would the project be acceptable? Maximum desired payback period is 4 years. Decide from both types of payback period. MARR = 10%.
| EOY | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Net Cash Flow | -5000 | 800 | 1500 | 2500 | 1510 | 1464 |

## Short answer

Simple payback period is 3.13 years, within the 4‑year limit, but the discounted payback at 10% is 4.14 years, exceeding the maximum allowed. The project is not acceptable on a time‑value basis.

## Answer

Maximum acceptable payback = 4 years; MARR = 10%.

```text
 EOY :  0      1     2     3     4      5
 CF  : -5000  +800 +1500 +2500 +1510  +1464
```
| EOY | Net CF | Cumulative CF | PW at 10% | Cumulative PW |
|---|---|---|---|---|
| 0 | -5,000 | -5,000 | -5,000.00 | -5,000.00 |
| 1 | 800 | -4,200 | 727.27 | -4,272.73 |
| 2 | 1,500 | -2,700 | 1,239.67 | -3,033.06 |
| 3 | 2,500 | -200 | 1,878.29 | -1,154.77 |
| 4 | 1,510 | 1,310 | 1,031.35 | -123.42 |
| 5 | 1,464 | 2,774 | 909.03 | 785.61 |

#### Simple (conventional) payback period
Cumulative CF is −200 at the end of year 3 and +1,310 at year 4, so recovery occurs in year 4.

θ = 3 + 200 / 1,510 = **3.13 years** (< 4 years)

#### Discounted payback period
Cumulative PW is −123.42 at the end of year 4 and +785.61 at year 5.

θ_d = 4 + 123.42 / 909.03 = **4.14 years** (> 4 years)

#### Decision
| Method | Payback | Limit | Result |
|---|---|---|---|
| Simple | 3.13 yr | 4 yr | Accept |
| Discounted | 4.14 yr | 4 yr | Reject |

**Answer: the simple payback accepts the project, but the discounted payback (which respects the time value of money at 10%) is 4.14 years, beyond the 4-year limit. The project is therefore not acceptable on a payback basis, although it is marginal (it still has PW = +Rs 785.61 over its 5 years).**

## Check yourself

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

1. How is simple payback found?
   A. Use cumulative PW
   B. Divide investment by MARR
   C. Locate where cumulative undiscounted CF turns positive and interpolate
   D. Average the first two flows
   Answer: C. Cumulative CF is -200 at year 3 and +1,310 at year 4, so 3 + 200/1,510 = 3.13. (Key point: Simple payback)

2. What is the discounted payback period here?
   A. 4.14 years
   B. 3.13 years
   C. 3.00 years
   D. 5.00 years
   Answer: A. Cumulative PW is -123.42 at year 4 and +785.61 at year 5, so 4 + 123.42/909.03. (Key point: Discounted payback)

3. Why is discounted payback longer than simple payback?
   A. It adds extra costs
   B. Future inflows are worth less today at 10%
   C. It ignores later years
   D. It uses a larger investment
   Answer: B. Discounting reduces each inflow, so recovery takes longer. (Key point: Why they differ)

4. With a 4-year limit, what is the conclusion?
   A. Acceptable on both methods
   B. Not acceptable on both methods
   C. Acceptable because PW at year 5 is positive
   D. Not acceptable, because discounted payback exceeds 4 years
   Answer: D. Simple passes (3.13) but discounted fails (4.14); the project is marginal. (Key point: Decision)

## Related in Engineering Economics

- [Both types of payback period, 3000 investment](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Apayback-both-3000-cash-flow) — Engineering Economics, chapter 3
- [Both types of payback period for Machine A](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Apayback-both-machine-a-5yr) — Engineering Economics, chapter 3
- [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
- [Best project for 4-year and 8-year service periods](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aselect-best-project-fw-4yr-irr) — Engineering Economics, chapter 4
- [Payback period to recommend best of A, B, C](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Apayback-recommend-abc-2a) — Engineering Economics, chapter 4
- [After-tax cash flow, DDB with switchover](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aafter-tax-cash-flow-ddb-switchover) — Engineering Economics, chapter 7

## Related in other subjects

- [NPV and payback of a startup project](https://www.bctengineer.com/question.md?key=semester_7%2Fentrepreneurship_development%3Anpv-payback-startup-project) — Entrepreneurship Development, chapter 5
- [Demand of rural municipality, base period 3 years](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-bk79) — Water Supply Engineering, chapter 3
- [Rank projects by payback, PW, IRR, B/C](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Arank-projects-payback-pw-irr-bc) — Project Engineering, chapter 6
- [Conventional vs project financing; ARR, NPV, PI, payback](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aconventional-vs-project-financing-numerical) — Project Engineering, chapter 6