Optimal subsidies and guarantees in public–private partnerships

Abstract

In this paper, we analyse how certain subsidies and guarantees given to private firms in public–private partnerships should be optimally arranged to promote immediate investment in a real options framework. We show how an investment subsidy, a revenue subsidy, a minimum demand guarantee, and a rescue option could be optimally arranged to induce immediate investment, compensating for the value of the option to defer. These four types of incentives produce significantly different results when we compare the value of the project after the incentive structure is devised and also when we compare the timing of the resulting cash flows.

Keywords:

• option to defer
• early exercise
• incentives
• public–private partnerships

JEL Classification::

• D81
• G31

Acknowledgements

We acknowledge the Portuguese Foundation for Science and Technology – Project PTDC/GES/78033/2006 – for the support. We thank the editor and the anonymous referees for the valuable comments that have substantially improved the quality of the paper. We also thank Dean Paxson and Ana Carvalho for their helpful comments.

Notes

Airports can be presented as a typical example of large-scale infrastructures. This type of project demands significant amounts of capital to be invested and offers no alternative use after construction. This is an important characteristic: the invested capital can be considered sunk after being spent. Other examples of large-scale infrastructures are highways, railways, and ports.

For more details on real options theory, refer to Dixit and Pindyck (1994).

Unless there is a contractual obligation for immediate investment.

For example, the number of passengers of an airport.

For more details, refer to Dixit and Pindyck (1994).

If this payment occurs later, the time value of money (and risk) should be considered, and it does not influence the optimal investment threshold, since it is independent of the value of Q in the future.

The next section presents an analytical comparison of the incentive structures and their cash flows patterns which produces generic comparative results.

Lines representing the NPV before and after subsidy are omitted from the graph for the sake of clarity. We also omit from the text a sensitivity analysis of other parameters for the sake of brevity. The results are similar to those obtained for the investment subsidy.

It is straightforward to show that smooth pasting between F(Q) and NPV(Q) is impossible.

If we assume that construction takes time, abandonment during the construction phase becomes a real option, and a different type of incentive should be arranged.

However, any incentive can be deferred or anticipated at the risk-free rate.

Alternatively we could have shown that .