What does the repeatability assumption assume?

Cash flows of the first life cycle repeat identically in later cycles

Each alternative is sold at market value at the end of the study period

The shorter-lived alternative is leased for the remaining years

Costs rise with inflation in each cycle

When is the co-terminated assumption appropriate?

When the need is for a fixed, known study period

When all alternatives have equal lives

Under co-termination, how are an alternative that outlives and one that falls short of the study period treated?

Longer one is sold at estimated market value at the study period end; shorter one is covered by renting, leasing or a replacement

Longer one is repeated; shorter one is ignored

Both are assumed to have zero salvage value

2066 Magh · 8 marks

Repeatability and co-termination 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.

Explain repeatability and coterminated assumptions.

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:

The cash flows of each alternative in its first life cycle repeat in every later cycle, and
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:

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.
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

✓ Answer checked by Claude Opus 5.5 (high effort)

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Repeatability and co-termination assumptions

Repeatability assumption

Co-terminated (co-termination) assumption

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