## Note on Replacement Analysis (Part II)

• Note
• Things to remember

### Minimum cost life of the challenger:

The minimum cost life of any new (existing) asset is the number of years at which the equivalent uniform annual cost (EUAC) of the ownership is minimized. The minimum cost life is normally shorter than the useful life of the asset because of increasing operating and maintenance cost in the later years of asset life.

The minimum cost life is calculated as the following:

1. Calculate the EUAC for each value of the useful life (e.g. n = 1, 2, 3, etc.)
2. The EUAC decreases to some minimum and increases again.
3. The minimum cost life is the number of years at which the EUAC is minimum.
4. The asset having the lowest minimum cost life of all the challengers is chosen to compete with the defender asset.

### Replacement Analysis when required service life is long

Required Assumption and Decision Framework

It is understood in the previous section that the economic service life of an asset is determined. The question that arises is that how to use this information to decide whether now is the time to replace the defender. If now is not the exact time, when is the optimal time to replace the defender? For answering the above question the following three assumptions are made.

1. Planning horizon (study period)
2. Technology
3. Relevant cash flows information

1. Planning horizon:

By planning the horizon, it is mean that the service period required by the defender and a sequence of the future challenger.

1. Infinite planning period: It is used when we are unable to predict when the activity under consideration will be terminated.
2. Finite planning period: When the project has a definite and predictable duration, replacement policy should be articulated more realistically based on a finite planning horizon.

1. Technology

Prediction of technological patterns over the planning horizon refers to the development of types of challengers that may replace those under study. A number of options exist in predicting purchase cost, salvage value and operating cost dictated by the efficiency of the machine over the life of an asset. If we assume that all future machines will be same as those new in service, there is no technological progress in the area that will occur. In other cases, we may recognize the possibility of the future machine that will be significantly more efficient, reliable or productive than those currently on the market. A good example is Personal computers. This situation leads to the recognition of technological change and obsolescence. Clearly, if the best available machine gets better and better over time, we should certainly investigate the possibility of delaying an asset’s replacement for a couple of years – a viewpoint that contrasts with the situation in which technological change is unlikely.

1. Relevant cash flows information

Many varieties of prediction can be used to approximate the patterns of revenue, cost and salvage value over the life of an asset. Sometimes, revenue is constant but costs increase while salvage value does not, over the life of the machine. In other situations, a decline in revenue over the equipment life can be expected. The specific situation will determine whether replacement analysis is directed towards cost minimization (with constant revenue) or profit maximization (with varying revenue). We formulate a replacement policy for an asset whose salvage value does not increase with age.

Decision framework

The annual worth / annual equivalent (AE) method provides a more direct solution when the planning horizon is infinite (endless). Similarly, when the planning horizon is finite (fixed), the present worth (PW) method is convenient to be used.

Decision Criterion

Although the economic life of the defender is defined as the additional number of years of service which minimizes the annual equivalent cost (or minimizes the annual equivalent revenue) that is not necessarily the optimal time to replace the defender. The correct replacement time depends on data on the challenger as well as on data on the defender.

As a decision criterion, the AE method offers a more direct solution when the planning horizon is infinite. When the planning horizon is finite, the PW method is more appropriate to use. We will develop the replacement decision procedure for both situations. We begin by investigating an infinite planning horizon without technological change. Even though a simplified situation such as this is unlikely to occur in real life, the analysis of this replacement situation introduces methods that will be useful in analyzing infinite horizon replacement problems with technological change.

### Replacement Analysis under the Infinite Planning Horizon

Under the infinite planning horizon, the service is required for a very long time. Either we continue to use the defender to provide the service or we replace the defender with the best available challenger for the same service requirement.

Procedure for replacement analysis for infinite planning horizon:

1. Compute the economic service life of the both defender and challenger. Use ND to indicate the economic service life of defender and NC to the economic service life of challenger respectively. The annual equivalent cost for the defender and the challenger at their economic lives are indicated by AED* and AEC*.
2. Compare the AED* and AEC*. If AED* is bigger than AEC*, we come know that it is more costly to keep the defender than to replace it with the challenger. Thus the challenger should make replacement of the defender now. If AED* is smaller than AEC*, it costs less to keep the defender than to replace it with the challenger. Hence the defender should not be replaced now. The defender should continue to be used at least for the duration of its economic life if there are no technological changes over that life.
3. If the defender should not be replaced now, when should it be replaced? First, we need to continue to use until its economic service life is over. Then we should calculate the cost of running the defender for one more year after its economic life. If this cost is greater than the AEC*, the defender should be replaced at the end of its economic life. This process should be continued until we find the optimal replacement time. This approach is called the marginal analysis, i.e. to calculate the incremental cost of operating the defender for just one more year.

### Replacement Analysis under finite planning horizon

If the planning period is finite, the comparison based on the annual equivalent cost (AEC) method over a defender’s economic service life does not generally apply. The procedure for solving such a problem with a finite planning horizon is to establish all reasonable replacement patterns and then use the equivalent worth value for the planning period to select the most economical pattern.

### BIBLIOGRAPHY:

Chan S.Park, Contemporary Engineering Economics, Prentice Hall, Inc.
E. Paul De Garmo, William G.Sullivan and James A. Bonta delli, Engineering
Economy, MC Milan Publishing Company.
James L. Riggs, David D. Bedworth and Sabah U. Randhawa,Engineering
Economics, Tata MCGraw Hill Education Private Limited.

1. The minimum cost life of any new (existing) asset is the number of years at which the equivalent uniform annual cost (EUAC) of the ownership is minimized.
2. Planning horizon is the service period required by the defender and a sequence of future challenger.
3. Prediction of technological patterns over the planning horizon refers to the development of types of challengers that may replace those under study.
4. As a decision criterion, the AE method offers a more direct solution when the planning horizon is infinite.
5. When the planning horizon is finite, the PW method is more appropriate to use.
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