# Contingency

*Construction Industry Computer Consultants Ltd.*

The development and management of contingency on a project is more of an art than the relatively scientific techniques of developing and managing escalation provisions. As such, there are many methods used to formulate and track contingency, and these are often shrouded in mystery and understood by few.

The initial development of the value of the contingency to be carried is often based on precedent and past practices. More recently, steps have been taken by introducing comprehensive statistical techniques to quantify the uncertainty relative to the project estimates, and thereby enable the owner to select an original contingency provision which will have a satisfactory probability of being sufficient. These techniques, of necessity, must represent complex correlations between interdependent resources and commodities. This tends to limit their use to the earlier estimating stages of the project, as they would become too cumbersome to assist in cost control.

The approach described herein was developed to make available to the users of the EMSCO^{*} program the power of risk analysis in the dynamic project cost control environment, thereby achieving two things:

- applying a systematic approach to the management of contingency; and,
- bringing to the attention of those who are in a position to affect the future course of events, those aspects of a project where high uncertainty and risk exist.

Once the original contingency provision is determined, movements of funds to and from it must be explicitly identified and controlled as the project proceeds. The depletion of the contingency, and the trends that are produced, must be watched carefully.

The normal expected course of events is the expansion of the forecast of final costs being more or less absorbed by reducing the contingency. This is caused by the following:

• *Pre-Award*

Prior to placing an order, design progress reviews by estimators may result in a forecast that will vary from the original or previous estimate.

• *Award*

When placing an order, a variance will invariably exist between the pre-tender check estimate value and the award price.

• *Post-Award*

Change orders, cost overruns/underruns on unit price and cost plus contracts, and claims will create a further variance from the awarded price.

Thus, as the project proceeds, two aspects affect the contingency: the first is the net depletion of the contingency due to these movements; the second is the determination of the remaining contingency referred to herein as contingency in reserve.

**Depletion of Contingency**

The Authorized Budget for a project is composed of cost estimates for tangibles, and a contingency provision to cover the anticipated increase over the tangible costs due to unforeseens. The expected course of events is depicted in Figure 1. This exhibits the change through the project of the Forecast of Final Cost at each reporting period until the actual final cost. The expansion of the Forecast of Final Cost of the contract packages is absorbed by a corresponding contraction of the contingency reserve. For simplicity, this diagram assumes that the contingency in reserve is the net of the original provision and the depletion.

The movements to and from the contingency result from the monthly schedule and cost updates and reviews, which record the progress and increased precision in the forecast time and cost to completion. During the pre-award stage of a contract package, any estimating reviews that result in a Forecast of Final Cost, different from the Authorized Budget, will cause a variance that we label a Forecast Depletion of Contingency.

In order to more rigorously discuss the post-award status of these packages, it is necessary to digress somewhat to define what we refer to as Appropriations.

**Appropriations**

The project manager, as the owner’s agent, enters into legal and financial commitments on the owner’s behalf with the various suppliers and contractors. The project manager can involve the owner by formulating an appropriation request that is registered with the owner and itemizes its essential financial components, which can comprise:

- funds to cover the contractual commitment associated with placing an order;
- funds to cover explicitly identified extras that may have been or are to be negotiated with the contractor, that have come to light during the bid analysis but are not covered in the basic contract;
- funds to cover the anticipated costs of any contractual escalation clause; and,
- funds to cover intangibles and unforeseens that may be required to complete the work of this contract.

The fourth item involves the allocation to this contract package of a Provisional Sum which may be committed. As such, the value of this item will be drawn from the project Contingency and reside with the contract package. The actual process of authorizing commitments against this provisional sum still involves rigid controls, but this authority can be relegated to a lower executive level. Typically, this latter procedure involves extra work order and change order authorizations, for which specific signing authorities up to certain stipulated amounts are established.

When it becomes evident that the Provisional Sum remaining will not be required, it is eliminated and these funds are “transferred” back into the project Contingency Reserve.

In the event that the existing appropriation against the contract package is foreseen to be insufficient, the project manager then seeks an additional appropriation for which the conditions causing the need are fully documented. Therefore, we recognize an Appropriation as a transfer, from the owner to the project manager, of the authority to commit funds up to the amount of the Appropriation, in accordance with the scope as detailed in the project manager’s Appropriation Request.

Any Appropriation at variance with the Authorized Budget will cause an Appropriated Depletion from (or addition to) the contingency. Similarly, any Forecast of Final Cost in excess of the Appropriation will cause a variance that we label an Unappropriated Depletion of Contingency. This is illustrated in the diagrams of Figure 2. Diagram A traces a typical depletion history for the whole project. Diagram B is a “snapshot” of the status as at July 1st, 1975. The manner in which this is presented by computer is shown in Figure 3.

The status as presented in this report is highly informative. The Appropriated Depletion of Contingency of $3,360,000 has already been through the reviews accompanying an appropriation request and have received the formal approval of the appropriating body. Of the total commitments in force of $65,260,000 only $338,175, the Unappropriated Depletion of Contingency, resides as an appropriation variance in the system, i.e., the Forecast of Final Costs of all the awarded contracts is projecting a very small relative overrun to the already appropriated amount. This could be indicative of successful contracts administration for this section of the project. Finally, the current projections for as yet unawarded work result in a Forecast Depletion of Contingency of $2,083,795. The components of this depletion are identified against each contract package thus facilitating preemptive attempts at resolution of problems that will have difficulty withstanding the scrutiny of the appropriation process.

**Contingency in Reserve**

The contingency in reserve is the critical element in the management of contingency. At any one period it may be insufficient or excessive in light of the project conditions. The risk analysis procedure determines the expected contingency, against which the adequacy of the actual project contingency in reserve can be tested.

If analysis results in the conclusion that the contingency reserve is insufficient, then project management can investigate more thoroughly to identify precisely what condition or set of conditions is causing this result, and attempt to resolve the problem within the context of his mandate from the owner.

**Developing Expected Contingency**

Personnel intimately concerned with the project are required to provide an expert assessment of the risk that the existing forecasts of final cost of the individual contract packages could vary over a specified range. The boundaries of this range consist of an optimistic or minimum value, and a pessimistic or maximum value that are to be regarded as truly upset limits. Within these ranges, a most likely value is also determined. This exercise results in a statement of the uncertainty associated with the present forecast of final cost of the contract package. This takes the form of an expected cost variance from the present estimated value. The uncertainty associated with the magnitude of this variance is explicitly represented by its probability distribution in Figure 4.

The lower or optimistic boundary of the range, denoted C_{o} and the upper or pessimistic boundary, denoted C_{p}, are indicative of the uncertainty in the estimate. The most likely value, denoted C_{m} is thus appropriately positioned in this context of uncertainty. The probability distribution is the bell-curve which is mathematically derived so as to place a weighted emphasis on C_{m}. The ordinate of this curve is representative of the anticipated frequency of occurrence, and the total area enclosed between any two values represents the probability of the eventual additional cost of the contract package occurring within this range. Therefore, in this example, the statement that the eventual cost increases will fall between $25,000 and $100,000 represents, to all intents and purposes, absolute certainty.

**The Three-Cost Estimates**

The optimistic estimate is regarded as a downward or minimum upward adjustment to the forecast of final cost of the contract package that might occur if everything goes extremely well. The estimator judges that there is only one chance in a hundred of things happening as well as the optimistic prediction indicates.

The most likely estimate reflects the cost adjustment that the estimator judges, on the basis of experience, would most often be required if the item were performed one hundred times. It is the result of what the estimator feels will occur most often in normal circumstances.

If everything that could go wrong, did go wrong, and the maximum cost that could conceivably be spent on the item were spent, the final cost would coincide with the present estimate plus this pessimistic estimate. This does not mean to say that catastrophies, fires, strikes, etc., are considerations. What is considered are those factors over which the estimator has control, but may mismanage, misestimate, etc. The pessimistic estimate does include an allowance for the normal amount of bad luck.

One condition that does not have to hold is that the present estimate for the contract package and the most likely value of the contingency, coincide. This may be the case, but need not necessarily be so. Of necessity, the present estimate is based on tangibles. The possibility of future intangible occurences forms the basis for the development of the three estimates of contingency reserve. It is precisely for this reason that the assignment of the three estimates to evolve a separate contingency reserve was chosen, in preference to assigning a range of values to the present estimate for the contract package.

**Classes of Contingency**

Three types of contingency are recognized. There are two pre-award values and one post-award value, defined as follows:

1. *Design Uncertainty*

This contingency is ascertained as a result of the uncertainty in the design of a contract package. It is not related to the precision of the estimate, i.e., a factored estimate with a stated precision of “plus or minus 25%" can, as design develops, lead to a more definitive estimate of “plus or minus 12% precision”. However, if there is still some vagueness regarding the scope of the work, the contingency that should be carried will remain unaffected. Only when the scope is clarified and well defined can the estimator identify a precise value for the package, and then reduce or eliminate the contingency previously associated with it.

2. *Market Trends*

This contingency needs great judgement and foresight, and requires that the construction manager, or design engineer for equipment supply contracts, interprets the trends of the market place. It depends upon whether market conditions indicate, in the judgment of the construction manager or engineer, that the low bidder will be below or above the present estimate for the contract package. The contingency is ascertained in relation to the market conditions for this type of package. The parameters for developing this contingency are:

a) Competitiveness — will the bidders for this type of contract be busy or idle?

b) Commodity Prices — how to these relate now to what they were when the estimates were made?

c) Productivity — what are the bidders going to use versus our own assumptions? What will the effect of new labour agreements on the horizon?

3. *Post-Award Uncertainty*

This contingency is developed by the contracts administrator. This is the construction supervisor for erection contracts, and the design engineer for fabrication contracts. The value results from his judgement of the incremental variance from the present forecast of final cost in respect of anticipated change orders, field orders, and pending or possible claims. On cost plus and unit price contracts, this assumes that the estimate of work to complete is accurate, and is not to include a provision for possible estimating inaccuracies.

There is one very important underlying assumption that is basic to this whole philosophy, which is that the current estimates of final cost are accurate within the constraints of definition of scope. These contingencies are not factors for poor estimating. Rather, they are attempts at educated guesses, made by the “grassroots” supervisors, to envisage the possible future costs based upon present knowledge and trends.

**Treatment of the Data**

If management knew with certainty the exact amount of time or cost necessary to accomplish any item, there would be no need for estimates or management. Any number of factors can cause time or cost variances from the planned values. Management justifies its existence by judging uncertainty.

By regarding each contract package as a statistical sample, we develop a total value of the expected additional cost probably required to complete the project, i.e., the contingency that should be carried in reserve, or expected contingency (denoted C_{e}). In addition, this is associated with a probability distribution, the shape of which yields a qualitative statement of the uncertainty in it. Figure 5 displays the concept.

The probability distribution curve 1 indicates a high uncertainty in C_{e}, and would be typical of a situation early in the project. The curve 2 indicates a low uncertainty associated with C_{e}, and is typical of the situation towards the end of the project.

The mathematics behind the method are conveniently quite simple. The three-cost estimates for the contract packages are fitted to Beta distributions. The expected value and variance of each Beta distribution are simply determined and by assuming no co-variance (this is possible by careful application of the estimating directives) and applying the Central Limit Theorem, we assume that large samples (over 20) of these two values will closely approach a normal distribution of modal value equal to the sum of the expected values, and standard deviation equal to the square root of the sum of the variances.

**Interpreting the results**

Of fundamental importance in the analysis is the interpretation accorded to these results. The central value of the probability distribution is located C_{e} dollars “beyond” the forecast of final cost of the contract packages. The degree of dispersion of the two extremities of the distribution above and below this value is indicative of the uncertainty in the estimate of C_{e}. Of paramount interest to the analysis in the point of intersection of the contingency reserve (denoted C_{r} ) with the probability curve. This is illustrated in Figure 6.

The shaded area under the curve is the probability that sufficient C_{r} remains. The total area under the curve represents absolute certainty. The value of C_{e} , at the midpoint of the distribution, represents a probability that is as likely to occur as not. Thus, it can be appreciated that for the specific configuration of Figure 6, there is a reasonable probability that insufficent contingency remains. This situation, and any trends over the next few monthly reporting periods would warrant close attention and cost-cutting efforts.

In the event of identical cost data but a wider dispersion of the distribution, the probability increases that sufficient C_{r} remains, but this can only be associated with a greater uncertainty in the estimation of C_{e}. With a narrower dispersion of the distribution, the probability reduces that sufficient C_{r} remains, and a greater amount of certainty can be associated with this conclusion.

The typical results of a project risk analysis are shown in the report of Figure 7.

Figure 8 converts this data into a pictorial statement that permits a scaled comparison of the trend between this and the previous reporting period.

The report of Figure 9 exhibits a ranking of the contract packages of the project into high, medium, low and no risk groupings. This draws attention directly to the high risk areas of the project.

**Maintaining the Data**

The basic project management system EMSCO, of which this is a portion, enables the risk analysis data to be readily updated and maintained. The awarding of each contract, identified in the basic system, automatically causes the design and market condition contingency amounts to be dropped. In a similar manner, the completion of a contract, against which no further change order or claims can be expected, causes its corresponding post-award contingency to be eliminated.

The expected contingency and its probability distribution enable powerful analytical conclusions to be drawn from the results. The energies of project management can therefore be more efficiently directed to those areas where greatest benefit accrues as a result of their involvement.

^{*} The EMSCO program is a proprietary project management software package marketed and maintained by Construction Industry Computer Consultants Limited. It is available on several data centers in Canada, and in the U.S.

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