The search for clarity

In a new paper of the Meridiam/Campbell Lutyens Research Chair at EDHEC-Risk Institute, we propose a dedicated valuation framework for privately-held infrastructure equity investments.

Following the roadmap to create long-term infrastructure investment benchmarks described in Blanc-Brude (2014), this framework takes into account the challenges of valuing privately-held and seldom-traded infrastructure equity investments, while aiming to design a methodology that can be readily applied given the current state of empirical knowledge and, going forward, at a minimum cost in terms of data collection.


The valuation of unlisted infrastructure project equity stakes requires addressing three significant challenges:

Endemic data paucity: While primary and secondary market prices can be observed, sufficiently large and periodic samples, representative of different types of infrastructure projects at each point in their multi-decade lifecycle, are unlikely to be available every year in each regional market.

The term structure of expected returns: The nature of such investments requires the estimation of a term structure of discount factors at different points in their lives that reflects the change in their risk profile. Indeed, in expectation, infrastructure investments can exhibit a dynamic risk profile resulting in the sequential resolution of uncertainty, including the frequent de-leveraging of the project company’s balance sheet.

The absence of a unique price for a given investment in unlisted infrastructure, which springs from the fact that there is no direct traded equivalent to the payoff of infrastructure project equity. It follows that prices are partly driven by investor preferences and that substantial bid/ask spreads are likely.
The first point is partly a mundane aspect of the difficulties encountered when collecting data on private investments, but also a reflection of the nature of long-term equity investment in infrastructure. The type of infrastructure projects that have been financed in the past are not necessarily representative of investment opportunities today. Thus, even if year-23 dividends for projects that were financed 24 years ago can be observed today, they may not be good predictors of dividends in projects financed three years ago, 20 years from now. For example, projects financed in the early 1990s may have been in sectors where fewer projects exist today (e.g. telecoms) or rely on contractual structures or technologies that are not relevant to long-term investors in infrastructure today (e.g. coal-fired merchant power).

If data paucity is an endemic dimension of the valuation of privately-held infrastructure equity investments we must start from the premise that we cannot observe enough data to simply derive prices empirically. Instead, we acknowledge a position of relative ignorance and aim to build into our approach the possibility of improving our knowledge as new cash flow and transaction data become observable that can be used to update models of dividend distributions and asset pricing.

The second point about the term structure of expected returns has long been made in finance literature: using constant and deterministic discount rates is defective if projects have multiple phases and project risk changes over time as real-options are exercised by asset owners.

It also amounts to assuming that the risk-free rate, asset beta, and market risk premium are constant and deterministic, when we know that such variables are time-varying and stochastic. Moreover, the internal rate of return (IRR) of individual investments cannot be easily used to estimate performance at the portfolio level, as the IRR of a portfolio is not the same as the weighted average IRRs of individual investments.

Thus, using methodologies based on discounting at a constant rate, while common in the corporate sector, is inadequate for the purposes of long-term investors who need performance measures that can help them make hedging, risk management, and portfolio management decisions.

The third point (the absence of unique pricing measures) is a reflection of what is usually labelled ’incomplete markets’ i.e. the fact that the same asset can be valued differently by two investors, and yet this does not constitute an arbitrage opportunity (and therefore the bid-ask spread does not narrow) because transaction costs are high and because, in the absence of complete markets, investor preferences partly explain prices.

The existence of a range of (or bounds on) values is also impacted by market dynamics: if a new type of investor (e.g. less risk-averse) enters the private infrastructure equity market, the range of observable valuations for similar assets may change. Likewise, if some investors want to increase their allocations to unlisted assets, given the limited available stock of investable infrastructure projects at a given point in time, their valuations may rise, but not that of others (who may sell).

Hence, the important point that the required rate of return or discount rate of individual investors in infrastructure equity is fundamentally unobservable: it cannot be inferred from observable transaction prices since it is both a function of the characteristics of the asset (e.g. cash flow volatility) and individual investor preferences.


Because of these challenges, existing approaches developed to value private equity investments are mostly inadequate for the purpose of valuing unlisted infrastructure project equity.

In our review of the literature we identify three groups of valuation techniques: repeat sales, public market equivalents and factor extraction from cash flows. Importantly, these techniques all imply that enough data can be observed to compute a price.

The repeat sales approach assumes that asset betas can be inferred from discreet and unevenly timed transaction observations after correcting for price staleness and sampling bias, while the public market equivalent approach implies that public asset betas can be combined to proxy the return of unlisted assets. Cash flow-driven approaches are less normative and aim to derive the unobservable rate of return of unlisted assets by decomposing their implied returns into traded and untraded components ex post facto, that is, once all cash flows have been observed and can be related to equally observable market factors.

Thus, these approaches cannot be directly applied to privately-held infrastructure investments, the value of which is determined by streams of expected and risky cash flows that mostly occur in the future, and for which few comparable realised investments exist today.

Existing approaches also typically fail to take into account the subjective dimension of asset pricing in the unlisted space and compute asset betas and alphas as if a unique pricing measure existed i.e. as if all investors had similar preferences, and in some papers, as if private equity exposures could always be replicated with a combination of traded assets.


To the extent that infrastructure dividend cash flows can only be partially observed today, their expected values cannot be decomposed into exogenous factors (markets, the economy, etc.), the future value of which is not known today and would be very perilous to predict 30 years from now.

Instead, we must derive the relevant discount factors endogenously i.e. using observable information about each private investment in infrastructure equity including, as suggested above, its contractual characteristics, location, financial structure etc. as well as the value of the initial equity investment made, which is also observable.

Hence, we argue that a robust valuation framework for equity investments that solely creates rights to future (and yet largely unobserved) risky cash flows, as is the case of privately-held infrastructure equity, requires two components:

A model of expected dividends and conditional dividend volatility, calibrated to the best of our current knowledge;

A model of endogenously determined discount factors, that is, the combination of expected returns implied by the distribution of future dividends, given observable investment values.
In other words, as for any other stock, the valuation of privately-held equity in infrastructure projects amounts to deriving the appropriate discount rates for a given estimate of future dividends. But while this process is implicit in the pricing mechanism of public stock markets, in the case of privately-held equity with distant payoffs, we have to derive the relevant parameters explicitly, taking into account the characteristics of infrastructure assets.


The dividend stream or cash flow process can be described as state-dependent and we introduce a new metric for infrastructure project dividends: the equity service cover ratio or ESCR, which is computed as the ratio of realised-to-base case dividends.

The base case equity forecast of infrastructure equity investments, while not necessarily accurate, provides a useful and observable quantity, which by definition spans the entire life of each investment. Thus, we propose to describe the behaviour of equity cash flows in infrastructure projects as a function of this initial forecast, in order to create metrics allowing direct comparisons between different equity investments.

In our paper, we show that the value of the ESCR at each point in the lifecycle of infrastructure equity investments can be used as a state variable describing the dynamics of the cash flow process. In combination with a given project’s base case dividend forecast (which is known at the time of investment), knowledge of the distribution of the ESCR at each point in time is sufficient to express the expected value and conditional volatility of dividends.

The fact that new observations are not redundant today (we can still learn about the dynamics of dividends in infrastructure investment by collecting new data), justifies the need for an ongoing and standardised reporting of these cash flows to keep learning about their true distribution and value the infrastructure investments made today, tomorrow.


Since the term structure of expected returns of individual investors/deals is unobservable and lies within a range (or bounds) embodying market dynamics at a given point in time, we adapt the classic state-space model mostly used in physical and natural sciences to capture the implied average valuation (or state) of the privately-held infrastructure equity market at one point in time and its change from period to period. Using such a model also allows us to capture the market bounds on value implied by observable investment decisions for a given stream of expected cash flows.

The objective of state-space models is parameter estimation and inference about unobservable variables in dynamic systems, that is, to capture the dynamics of observable data in terms of an unobserved vector, here the term-structure of discount factors. Hence, we have an observation equation relating observable data to a state vector of discount factors, and a state equation, which describes the dynamics of this state, from one observation (transaction) to the next. Each transaction corresponds to a new state i.e. a given term structure of discount factors matching the price paid in that transaction (the initial investment) with expected cash flows, which may or may not be the same as the previous transaction’s.

Given a stream of risky future dividends, if the price paid in the current transaction is different from that paid in the previous one, it must be because the valuation state has shifted. The valuation state can change due to a change in investor preferences between the two deals, or due to a change in the consensus risk profile of that kind of investment (e.g. projects with commercial revenues after a recession), or because of a change in the overall market sentiment (the average) valuation.

Thus, by iterating through transactions, we may derive an implied average valuation state (a term structure of discount factors) and its range, bounded by the highest and lowest bidders in the relevant period.

Later, when dividend payments are realised, period returns can be computed using the discounted sum of remaining cash flows as the end-of-period value (given the implied term structure of discount factors at that point).

In this paper, we define the observation equation using a dynamic version of the standard Gordon growth model (discounted dividends) and the state equation using an autoregressive (with a one-period lag) model of the term structure of expected returns which can be derived from the kind of factor model of expected excess returns that are commonly found in financial literature. We take the view that expected returns are a function of conditional dividend volatility.

In a simple, linear setting, we show that we can iterate through observable investments, while estimating model parameters on a rolling basis, to capture both the implied expected returns (and discount factors) during a given reporting period and track these values and their range (arbitrage bounds) from period to period.


As an illustration of our approach, we apply the dividend and pricing models to a generic case of privately-held infrastructure investment, assuming an expected ESCR and ESCR volatility profile (including the probability of receiving no dividends in any given period).

Given a base case dividend scenario inspired by an actual infrastructure project financed in Europe in the last decade, we obtain a full distribution of future dividends and apply our valuation framework to this assumed dividend process for an equally assumed range of investment values. Some of the key outputs are shown on the following figures.

Figure 1 shows the resulting filtered term structure of expected period and multi-period (average) expected returns filtered from a range of 20 consecutive initial transactions in this type of project.

Figure 2 shows the resulting values of the dividend discount factor1 at the time of valuation and the expected average price and its range for this group of transactions.

Finally, figure 3 shows how we can implement this model with rolling parameter estimation to track the implied average expected returns and price of consecutive transactions from period to period

These results spring from model inputs that are only inspired by existing data and a number of intuitions about privately-held infrastructure equity investments, and can only be considered an illustration. However, they show clearly that with well calibrated cash flow models and a transparent valuation framework, the kind of performance measures that have so far been unavailable to long-term investors can readily be derived and monitored in time, as new investments are made.


Next steps include the implementation of our data collection template to create a reporting standard for long-term investors and the ongoing collection of the said data. Beyond, in future research, we propose to develop models of return correlations for unlisted infrastructure assets in order to work towards building portfolios of privately-held infrastructure equity investments. These developments will take place with the support of, and in collaboration with, the financial industry and its regulators.

This work continues with the support of Meridiam and Campbell Lutyens, as well as the other members of the Long-Term Infrastructure Investor Association, who are spearheading the standardisation and mass collection of data to calibrate the cash flow and pricing models described above.