A net present value is calculated for each intervention. The decreased number of isolated trips is calculated as well but it is not included in the net present values as it is challenging to give a dollar value to disrupted trips. The net present value (NPV) for intervention _i_ follows the equation below: Where ME is maintenance expenditure, EAD is expected annual damage, RUC is road user cost, TR is traffic volume, EAUL is expected annual user losses, CI is capital cost of intervention, d is the discount rate and _y_ the years going from 1 to 20. The cost is different for each of the interventions. Each of the interventions includes periodic and recurrent maintenance that happens at different times during the lifecycle. For instance, a surface treatment road will include periodic maintenance every 9 years, while a gravel road will be maintained every year and an earth road every 4 years (values can be found in the annex and were provided by ANE). The benefits are calculated every year as described in the previous section.

To capture the uncertainty that may affect the performance of some of the interventions, we calculate the NPV of each intervention in 2,000 scenarios, combining values on:<sup>5</sup>

- Climate projections: current, low, medium and high

- Flood duration, -50% to +50% increase compared to the results of the hydrological model<sup>6</sup>

- Traffic growth in the absence of interventions, 0 to 6%<sup>7</sup>

- Traffic growth to agriculture increase elasticity, 0.5 to 1.5

- Discount rate, ranging from 3 to 12%

- Repair time, -50% to +50% of original

- Capital Cost, -50% to +50% of original

- Bridge Repair, -50% to +50% of original

Each of the selected districts has different characteristic and vulnerabilities. For this reason, each district may require a unique combination of the five interventions above in each of its link of the road network, that will maximize the net present value and increase robustness of the road network. Some of these combinations will be: (1) surface treatment to the most vulnerable road and ensure proper maintenance on the rest, (2) repair bridges in most critical link and rebuilt culverts in secondary roads, (3) upgrade to gravel the most critical road and ensure maintenance on secondary road, (4) upgrade to gravel secondary roads only or (5) repair and replace culverts in most critical links only – other combinations may be suggested here by the team.

Once we calculate the NPV of several investment combinations for each of the 2,000 scenarios, we will look for those conditions that are the most robust, that is that have a high NPV under many future conditions.

# **Robustness analysis**

There are many ways of testing the robustness of an investment plan:

> 5 We use a Latin Hypercube Sampling (LHS) method for generating the 2,000 scenarios.

> 6 SSBN developed the flood maps and the hydrological model that calculated water levels and flood duration (more details about the model are in the annex). Flood durations are however difficult to assess in the hydrological model, so we assume it can vary.

> 7 The projected GDP growth for 2018 in Mozambique (Mahdi et al. 2016) is calculated at 6.5%. Traffic and agriculture are expected to grow at a similar rate as GDP. The range of uncertainty applied in these variables is intended to capture the uncertainty on GDP growth.

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