# Cross River Rail Dice Roll? In this note we consider there is a 25% possibility that Cross River Rail may fail to achieve a positive economic net present value and explain how we arrive at that opinion.

Building Queensland reported in its cost benefit analysis summary that Cross River Rail produces a Net Present Value (NPV) of \$966 million with a Benefit Cost Ratio (BCR) of 1.21. However, its summary did not publish the actual present value totals of the benefits or costs from the study. The full report is not available for public scrutiny.  Also, the government’s website for Cross River Rail has still not published the business case.

The BCR was expressed in terms of P50, which implies there is a 50% probability that it could be lower than 1.21. Similarly, if the NPV was expressed as P50 that implies a 50% probability the NPV could be less than \$966 million. Interestingly, no formal sensitivity analysis was presented in the summary.

Is it possible to assess the probability that the net present value of the project could be less than zero or the benefit cost ratio less than one?

Using the NPV and BCR information from the summary we calculate the implied present value of benefits (B) and the present value of costs (C). Since NPV = B – C = \$966 million, and BCR = B / C = 1.21, we can solve for C. This gives us a present value figure for C of \$4,742 million. Therefore, the present value for B is \$5,738 million.

Since we do not know the risk profile of these values, let’s assume variability in the estimates are normally distributed around the benefit and cost values implied by the NPV and BCR figures. This is a generous interpretation of the variability of the actual result compared to the estimate because we know that costs are typically skewed towards overruns and realized benefits fall short of estimates more often than exceed them.

We assume a standard deviation that is approximately 20% for each cost and benefit estimate. We assume in the absence of any guidance that the estimate is the mean for the purpose of this analysis. This applies both to costs and benefits. Under a standard normal distribution the estimate statistic is also a P50 estimate.

Benefits and costs in the tails of each distribution are likely to be extreme values. We assume that values in the 5% tails either side of the mean are not sampled. That is, values are drawn from a normal distribution that represents 90% of possible values for benefits and costs.

One final consideration – no correlation is assumed between benefits and costs. What it costs to build and operate Cross River Rail has no influence on the level of demand achieved. The same project is delivered irrespective of cost.

Running @Risk probability software over this, we find that running the NPV calculation through 1,000 iterations there is a 25% chance that the project will generate a negative NPV. No formal consideration is given to optimism bias, which would tend to increase this value.

Is this a risk worth taking? Hard to say because some of the fundamental information is still not in the public domain. Also, components of both benefit and cost may be well identified and estimated. As a consequence, their probability profiles might be within a much smaller range.

Within the project, further work would be required to minimise and mitigate risks that could affect benefit realisation or lead to increased costs. Release of further detail about the project would enable the public to assess this.

Image: Brisbane Times.