---
title: "Repeatability and co-termination assumptions"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:repeatability-coterminated-assumptions"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/repeatability-coterminated-assumptions
site: BCT Engineering
---

# Repeatability and co-termination assumptions

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2066 Magh, 8 marks
- Video: [Repeatability Assumption |Co-terminated Assumption | Capitalized Worth](https://www.youtube.com/watch?v=HpsymcMmwxM) — 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-coterminated-assumptions
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Explain repeatability and coterminated assumptions.

## Short answer

Repeatability assumes indefinite need with identical cash-flow cycles, so alternatives can be compared using the annual worth of one life cycle over the LCM of lives. Co-termination sets a fixed study period, crediting salvage for longer lives and adding replacement costs for shorter ones, then comparing PW or AW over that period.

## Answer

When mutually exclusive alternatives have unequal lives, they cannot be compared directly by PW. Two standard assumptions make their service periods equal.

#### Repeatability assumption
The study period is long (or indefinite) and the service is needed beyond the life of the alternatives. It is assumed that:
1. The cash flows of each alternative in its first life cycle repeat in every later cycle, and
2. Costs and revenues stay the same (no inflation or technological change).

Consequence: the annual worth (AW) of one cycle equals the AW over any number of cycles, so alternatives can be compared directly by AW. If PW is used, the alternatives are repeated up to the least common multiple (LCM) of their lives.

Example: A (3 years) and B (5 years): LCM = 15 years, so A is bought 5 times and B 3 times. Comparing AW of one cycle gives the same answer.

Use it when the need is continuing and the same equipment will be bought again.

#### Co-terminated (co-termination) assumption
The service period is limited and known (the study period). All alternatives are made to end at that same date:
1. If an alternative lasts longer than the study period, it is sold at the end of the study period at an estimated market (salvage) value.
2. If it lasts shorter, the shortfall is covered by renting or leasing, or by a replacement bought for the remaining years; its estimated costs for the remaining period are included.

Then PW, FW or AW can be compared over the common study period.

Example: need for 6 years; A lasts 4 years and B lasts 8 years. A is bought once and a short-term replacement is used for years 5-6; B is used 6 years and its market value at year 6 is credited.

#### Comparison
| Basis | Repeatability | Co-termination |
|---|---|---|
| Service need | Long or indefinite | Fixed, known study period |
| Future cash flows | Same as first cycle | Estimated separately for the study period |
| Common period | LCM of lives or AW of a cycle | Study period |
| Salvage value | At the end of each life | Market value at the end of study period |
| Best method | AW (easy) | PW / FW over the study period |

## Check yourself

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

1. What does the repeatability assumption assume?
   A. Each alternative is sold at market value at the end of the study period
   B. The shorter-lived alternative is leased for the remaining years
   C. Costs rise with inflation in each cycle
   D. Cash flows of the first life cycle repeat identically in later cycles
   Answer: D. Repeatability assumes the same cash flows repeat each cycle with no inflation or technology change. (Key point: Repeatability assumption)

2. For A (3 years) and B (5 years) under repeatability using PW, what common period is used?
   A. 3 years
   B. 5 years
   C. 15 years (LCM)
   D. 8 years (sum)
   Answer: C. PW comparison needs the LCM of lives (15 years); alternatively AW of one cycle can be compared directly. (Key point: Comparison basis under repeatability)

3. When is the co-terminated assumption appropriate?
   A. When the need is for a fixed, known study period
   B. When the need is indefinite
   C. When all alternatives have equal lives
   D. When no salvage values exist
   Answer: A. Co-termination applies when the service period is limited and known; all alternatives are made to end at that date. (Key point: When to use co-termination)

4. Under co-termination, how are an alternative that outlives and one that falls short of the study period treated?
   A. Longer one is repeated; shorter one is ignored
   B. Longer one is sold at estimated market value at the study period end; shorter one is covered by renting, leasing or a replacement
   C. Both are repeated to the LCM
   D. Both are assumed to have zero salvage value
   Answer: B. The longer-lived alternative is credited with market value at the study period end, and the shorter one's shortfall years are covered by a lease or replacement with estimated costs. (Key point: Handling unequal lives in co-termination)

## Related in Engineering Economics

- [Modified BCR with co-termination, AW](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Amodified-bcr-cotermination-aw) — Engineering Economics, chapter 4
- [Repeatability, two mutually exclusive options](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Arepeatability-option-1-2) — Engineering Economics, chapter 4