## Price tag of project delays

How to calculate the cost of project delays? This article describes an approach, which shows the cost of delays in the percentage of net present value  (NPV) of projects. The theory is not prepared to use on a single project. The target is to show the cost of delays generally for a given organisation, which runs several project in parallel, since the method uses generalities. The result is usable to help avoid or eliminate the bottlenecks in the company or organisation.

The calculation prescinds from the every day’s business but still focuses to the real problem, which is the accurate delivery of project targets, by effective resource allocation.

All we agree that the project delays have costs, means losses. In general, the losses have two main types: the additional resources and the delayed incomes.

The extra expenses are the simpler problem. Usually the delay, declares the extra resource-needs, assuming linear resource needs for the overtime. Normal project planning toolset would be used if the resource need is not linear.

The problem of this costs, that the scale of them is varying per each and every project. It means that the specialities of the projects cause high deviation between their costs of additional resources. As a result of this high variation, no general correlation can be found, which can help to build awareness of this affect in the workers.

We also should mention the cost of the additional resources, which seriously depends on the options they would start to be used. Since the project environment is not countable as a standard it is another reason why not to try calculate this type of loss. We should find a good way to handle them!

Delaying incomes

The net present value (NPV) and the internal rate of return (IRR) of a project – a suitable value of them is the condition of project start-up in project-based organisation – can be calculated from the analysis of the expected cash-flow of a given project. As in the case of the costs, the incomes are too special for each project to produce a generic method to investigate their affects to the project losses.

It seems we reached a dead-end. If we would focus on individual project we did. We have to use statistical approach instead! If a company has relevant number of projects, then we can take statements of an „average” project, which will reflect to the organisation. Again, we need a good approach!

Calculation approach

The starting point is, that the cash-flow items of a project should be handled as random variable, that are shown on the following figure. This case statistics will help us. The Central limit theorem declares, that the mean of a sufficiently large number of independent (in our case mostly independent) random variables will be there properly normalized sum tends toward normal distribution.

In the real life there are projects, which are not independent from each other, but they can be handled as phase of the same big program/project. If we do this grouping, dozens of projects still remain, which are – because of the different resources used or the timing – are really independent. This amount seems enough to model them using normal distribution.

Finding the common picture doesn’t affect the further steps of the deduction, but still important to show the summary of the project as one generic item, which helps understanding and approving the results. The next basic statement of the model analysis, that theoretically unlimited number of different cash-flows can result the same net present value. The consequence of the combining the two statements above, that we can find model cash-flow for the aggregation of the projects (although not to a given one), which simplifies the further calculations.

The most appropriate model for this approach is the annuity, so we will replace the cash-flow above by an annuity for the analysed timeframe.

Simply the net present value – cash-flow statement seems to be enough first, since it can be used for any cash-flows but the aggregation of projects are still more secure since it screen the non-typical projects. Non-typical projects are for example those, when the incomes are coming only on a given date (like Christmas campaigns), when the delays are totally kill the business case, or there is no affect at all. Cost of delay

Let’s see what happens, if a project sustains delay? Practically the incomes for the first month will not flow in for the originally calculated cash-flow period. Assuming the duration of cash-flows of projects is 3 years, the model uses 3 years long monthly annuity, the first x month incomes won’t be realised, so no cash movements will happen in the delaying period.

In case of 4 month delay only 32 movements will happen starting from the 5th month, instead of the original 36. The effects of the delay can be calculated by the ratio of the annuity of the delayed and the original situation. The relevance of this ratio is dual: it is possible to show the impact as percentages, and what is more important makes the result independent from the size of the cash movements.

The present value of an n-element annuity starting x month later from now is the difference of the present value of the n-element and the x-element annuity.

The deduction requires the equation of the annuity calculation: The relation of the delaying and the original project value is given by: where N stands for the original cash-flow duration and M means the number of lost cash movements.

Placing the annuity equation into the step 2., do the possible simplifications we get: The equation above shows, that the ratio of the cash-flows does not depend on the size of cash movements, but only on the interest rate (required rate of return - RRR) and the duration. This is so great, since the interest rate and the duration is a well-known constant for the companies, and commonly used for project return calculation.

Localisation of the calculation

The following attributes you should collect at your company to calculate the cost of delay as the ratio of NPV of a project.

 Financial duration: 36 month Required Rate of Return for 1 year: 20% Required Rate of Return for 1 month: 1.67%

Finally the result of calculation is detailed in the following table. Just look on the 6 month delay, which is all we saw on IT projects: more than 20% of the original NPV is lost!

Delay (month) Absolute loss Relative loss
1 3.66% 3.66%
2 7.25% 3.60%
3 10.79% 3.54%
4 14.27% 3.48%
5 17.69% 3.42%
6 21.05% 3.37%

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35 97.95% 2.08%
36 100.00% 2.05% 