---
title: "Repeatability, two mutually exclusive options"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:repeatability-option-1-2"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/repeatability-option-1-2
site: BCT Engineering
---

# Repeatability, two mutually exclusive options

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2076 Shrawan
- Video: [Repeatability assumption |Economics |Board Exam Solution in NEPALI](https://www.youtube.com/watch?v=OfLkWltuILI) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/repeatability-option-1-2
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Consider the following two mutually exclusive alternatives, recommend the best alternative using repeatability assumptions. MARR = 12%
|  | Option-I (Rs.) | Option-II (Rs.) |
|---|---|---|
| Initial Cost | 20,000 | 30,000 |
| Annual receipts | 10,000 | 14,000 |
| Annual cost | 5,000 | 8,000 |
| Salvage Value | 4000 | 0 |
| Useful Life | 6 years | 10 years |

## Short answer

Using repeatability and AW at 12% MARR: Option I AW = Rs. 628/yr, Option II AW = Rs. 690/yr. Both positive; Option II has higher annual worth. Recommend Option II.

## Answer

Repeatability assumption: each option is repeated with identical cash flows, so the unequal lives (6 and 10 years) are compared by annual worth (AW) over one cycle of each. MARR = 12%.

#### Option I (N = 6)
(A/P, 12%, 6) = 0.2432, (A/F, 12%, 6) = 0.1232
AW = -20,000(0.2432) + (10,000 - 5,000) + 4,000(0.1232)
   = -4,865 + 5,000 + 493
   = **Rs. 628 per year**

#### Option II (N = 10)
(A/P, 12%, 10) = 0.1770
AW = -30,000(0.1770) + (14,000 - 8,000) + 0
   = -5,310 + 6,000
   = **Rs. 690 per year**

| Option | Life | AW (Rs./yr) |
|---|---|---|
| I | 6 | 628 |
| II | 10 | 690 |

Both are positive (acceptable), and Option II has the larger AW.

**Answer: Recommend Option II**, which gives about Rs. 62 more annual worth than Option I.

## Check yourself

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

1. Why is AW used for Options I and II?
   A. Lives are equal
   B. MARR differs
   C. Lives are unequal (6 and 10 years) and repeatability makes one-cycle AW comparable
   D. Salvage is the same
   Answer: C. Under repeatability, AW over one cycle compares projects with different lives. (Key point: Why AW)

2. What is Option I's AW?
   A. Rs 628 per year
   B. Rs 5,000 per year
   C. Rs 690 per year
   D. Rs -628 per year
   Answer: A. -4,865 + 5,000 + 493 = 628. (Key point: Option I AW)

3. Which option is recommended?
   A. Neither
   B. Option II, larger AW (Rs 690)
   C. Option I, higher salvage
   D. Option I
   Answer: B. Option II has the larger AW, 690 vs 628. (Key point: Choice)

## Related in Engineering Economics

- [Best of three mutually exclusive projects, 10-year study](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Amutually-exclusive-abc-study-10-years) — Engineering Economics, chapter 4
- [Repeatability, best of A and B](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Arepeatability-a-b-400000-700000) — Engineering Economics, chapter 4
- [Find required annual receipts A](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Arequired-annual-receipts-a-1000000) — Engineering Economics, chapter 3
- [Repeatability assumption, select best of three projects](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Arepeatability-abc-14) — Engineering Economics, chapter 4, asked 2×
- [ERR to recommend best of A, B, C](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-recommend-best-abc-e20) — Engineering Economics, chapter 4
- [Sensitivity on initial cost and life; interpret](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-initial-cost-life-25) — Engineering Economics, chapter 6

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