DNPV: a valuation methodology for infrastructure and Capital investments consistent with prospect theory

Abstract

Traditional valuation methods such as net present value (NPV) utilize increased discount rates to account for risk, in the process introducing a time bias effect that promotes short-termism. Application of NPV often discourages much needed infrastructure projects that require large capital investments yet are slow to generate positive cashflows. NPV also downplays the significance of future liabilities and can lead to risk misallocation amongst investment partners and stakeholders. The decoupled net present value (DNPV) method introduces the risk-as-a-cost concept that prices the risk of obtaining lower-than-expected cashflows and thus represents investors’ compensation for bearing such risks. Capturing the loss-aversion attitudes described by prospect theory, DNPV provides a transparent and consistent valuation framework for long-term investments by: (i) calculating expected values of cashflow components using their probability characterizations, (ii) defining the cost of risk (market and non-market) as the expected downside value, (iii) subtracting/adding the cost of risk from/to expected revenues/expenditures, and (iv) discounting the results using risk-free rates. DNPV’s power is illustrated by re-analyzing a 42-year toll-road concession initially evaluated using NPV and real options. The case study shows how explicit risk quantifications could be used to better structure the concession and reallocate risks among stakeholders.

Keywords:

• Real options
• derivatives
• valuation
• NPV
• DNPV
• prospect theory

Disclosure statement

No potential conflict of interest is reported by the authors.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.

Notes

Notes

1 A discount factor applied to negative cash flows would have the opposite effect (i.e., it would reduce the liability), hence it would increase the project NPV.

2 The risk factor depends on the investor’s degree of risk aversion. For risk-neutral investors, λ = 1 whereas for individuals that cannot tolerate any degree of uncertainty λ=0.

3 In reality, if the option is fairly priced such that there is no risk-free arbitrage opportunity, then the value of the option minus the price paid for it should be zero.

4 The downside for expenditures is opposite to that of revenues, that is, the downside is to the right of the expected value and cost of risk is added to the expenditures expected value.

5 Higher levels of risk neutrality can be defined in a similar fashion.

6 Readers familiar with derivatives can relate Line 1 to a call option and also relate DNPV with real options; however, despite the equivalence, the consistent treatment of the downside risk in the DNPV method to obtain certainty equivalents for the cash flow renders it superior to real options.

7 Put options are financial instruments that work as insurance products that protect stock owners against a potential drop below a specified value.

8 Although not used in the analysis, a review of the census data indicates that the region indeed grew between 1990 and 2010 from 86,000 to 315,500 which equated to an annual population growth rate of 6.5%. This rate was consistent with the assumed long-term traffic growth of 7% assumed the original traffic projections in Table 2.

9 The main difference of the proposed cost of risk with those presented elsewhere for market risk (e.g., Fama, 1977) is that in the proposed DNPV procedure the cost of risk is derived from information of the asset under consideration and not from its correlation with the overall market.