Projects can often be divided into phases. As well as to help set targets, milestones and plan resources, the phasing of projects is very useful if there are critical points at which a project may fail, or its direction should be adapted or modified in some way. The modularisation of projects into sub-projects (modules), allows one to improve and ultimately to maximise the value inherent in a project, as long as the modular structure is designed to be able to fully adapt the nature of the project at every critical point. This has implications not only for the operational management of projects, but also for their valuation from a economic and accounting or regulatory perspective. The correct modularisation of projects will expose inherent “real options” value, and allow it to be realised in practice.
This is illustrated with a simple example in the following.
Consider a project in which one needs to invest $350m and whose most likely outcome is to create a gross value of $1000m in the future (in present value terms). The net value of the project may be considered to be $650m.
Now, if we know that the project is risky, and based on other experience has a 54% chance of success (still the most likely outcome, with failure having a 46% probability), then of course the value is reduced: The average value is -350+54%*1000 or $190m. This can be seen in tree form:
Now, if the investment part of the original project can be split phases, then – ignoring the risk for the moment – one may have a cash flow profile as follows:
Note that since we are assuming that all three investment phases are conducted (but simply in a series), then both the non-risked and risked-valuation is the same: The phasing of the original investment is just a split of the $350m into $10m (Phase 1), $100m (Phase 2) and $240m (Phase 3), so that the (non-risked) value is still $650m in the non-risked case or $190 when a 54% success probability is used to weight the $1000m final value.
Now, if in fact each investment phase is both risky AND allows some form of decision to be taken when this risk has been resolved (e.g. abandon, expand, continues), then the valuation can be improved. The simplest case is where each phase either succeeds or fails, and the project is continued (on success) or abandoned as soon as it fails (i.e. at the end of each of Phase 1, 2 or 3). For example, assume that the probabilities of success in each phase are as shown below (and using the same investment figures for each phase, shown again here for reference):
(the aggregate probability of success at the end of phase 3 is therefore 75%.80%.90% i.e. 54%)
The full tree diagram is:
The value of the project is therefore $311m. The increase in value compared to the single-probability-weighted figure of $190m (i.e. an extra $121m) is due to the phasing of the projects into these risk-decision phases. Concretely, when a phase fails, future investment is stopped. This contrasts with the approaches where the was only a single decision point (whether this came at the end of one long single phase, or at the end of multiple phases with no interim decisions); in the single decision approach investments in subsequent phases were being made even in the cases where in reality the project would fail.
One may say that the value created by this more nuanced approach is $121m. (It is probably more accurate to say that the value was always there, it just had not been exposed in the first project approach nor in the associated calculations).
In fact, this raises the issue as to whether the project could be even more valuable than this: Perhaps there are additional ways of splitting the phases further if there are other key risks/decisions that have not yet been reflected in the three phases above. Perhaps there should be four or five phases and decisions, for example.
This exposes the need to value projects based on a correct or optimised structure, and conversely to structure projects to optimise value through taking decisions to abandon or modify the project at key points in time.
It is also interesting to see the above multi-phase tree split into individual phases. To evaluate a decision tree, one needs to work backwards from the right. The last phase of the tree (Phase 3) looks as:
This can be interpreted as meaning that the situation is worth $660m if one has arrived at that point (i.e. -240+1000*90%).
Therefore the tree for the prior phase looks like:
Thus at that point (beginning of Phase 2) situation is worth $428m if one has arrived at that point (i.e. -1000+660*80%).
Therefore for Phase 1, we have:
The tree for Phase 1 shows the $311m value (i.e. -10+428*75%), as calculated earlier. Once again, one could look at this from a real options perspective (such as saying that Phase 1 represents an option that – for an investment of $10m that may be lost in the end i.e. expire worthless – gives one a 75% chance of winning $428m, or allows access to an asset that is worth 428*75% i.e. $321m).
Finally, it is worth also noting that if one were to be able to perform Phase 1, but did not know of the existence of the possibility to separate Phase 2 and Phase 3 (using the decision at the end of Phase 2), then the tree at the beginning of Phase 1 would look like:
The value of the whole situation would be $275m (-10+340*80%*90%), instead of $311m: The integration of Phase 2 and 3 into a single phase eliminates the abandonment possibility (option) at the end of Phase 2, giving a full tree for this case as:
In this case, the value of the project at the beginning of Phase 1 (and of the option to proceed) is reduced by the elimination of the abandonment option at the end of Phase 2.
The values can be summarised in tabular form as follows: