The construction of Liquefied Natural Gas (LNG) facilities along the pacific coast of the U.S. would allow the western states to tap into a variety of natural gas supply sources from Southeast Asia and South America. With this kind of facility, domestic supply from in-land sources could be complemented with off-shore gas. Essentially, LNG terminals deliver, the option to acquire off-shore gas thus providing the opportunity to profit from domestic price spikes. A fundamental problem is then to evaluate whether the cost of setting up such facilities is justified by the economic benefits they provide. Underlying this problem is also the determination of an optimal strategy regarding the deployment and operation of a facility that ensures that maximum value is extracted out of the project. A discounted cash-flow method is ill-equipped to analyze this kind of investment due to its static nature. A better approach is a state contingent approach (i.e. Real Options) that properly accounts for uncertainty and the managerial flexibility surrounding the decisions or strategies related to a facility. This becomes of special importance in order to have a realistic evaluation that can be compared in a meaningful way to other protection methods such as natural gas derivative contracts and natural gas storage facilities.

Figure 1: Western U.S. main natural gas supply

LNG facility costs
Setting up an LNG facility has considerable costs. To begin with, location candidates are few due to the need for waterway access and docking facilities. In addition, pipeline access must be secured in order to send gas to the market point or hub from which it is sold and distributed. Given the nature of LNG, there is also the need to build on-site re-gasification stations and storage facilities. For our analysis we will assume a set-up cost of $6.74 per unit of capacity. One unit of capacity is one thousand cubic feet per quarter (mcf/q). We assume this set-up cost structure holds for facilities with capacities in the range of 0.5 BCF/D to 0.8 BCF/D (BCF/D=billion cubic feet per day). Fixed costs per quarter are estimated at $0.25 per unit of capacity and include payroll, maintenance, electricity, taxes and insurance. Fixed costs are incurred regardless of whether the facility is in operation or not. Variable costs include ship transportation from overseas, liquefaction and re-gasification and pipeline fees among others. We assume total variable costs add an average $3.75/mcf to off-shore gas prices at the port of origin.

Natural gas prices
Although there exists correlation between domestic natural gas prices and off-shore gas prices, the regional economics governing them are, in many respects, different. The fact that global linkages between regional economics are not perfect establishes the possibility of significant price differentials. In particular, demand surges in the continental U.S. are not likely to have a first order effect on gas prices in Southeast Asia. This would be one particular scenario that opens the possibility of profitable overseas natural gas imports. We shall assume that LNG imports do not disturb price equilibriums in the sense that import activities do not deepen the relationship between domestic and off-shore prices beyond the that indicated by their assumed correlation. The purpose of an LNG terminal is to profit from high domestic gas prices by acquiring off-shore gas. Figure 2 illustrates the profit regions of a facility, in this chart example, profits occur sometime during quarters 7 and 8 and in quarter 12.

Figure 2: LNG import profit zones

Throughout our analysis we assume a price correlation coefficient of 0.77 between average Southeast Asia (SEA) prices and Southern California (SoCal) prices. Figure 3 and Figure 4 show, correspondingly, the price forecasts for SEA and SoCal prices used throughout this analysis. Forecasts are for average quarterly prices going 30 years out. The solid black line represents the expected prices, the solid blue line represents median prices and the upper and lower orange bands represent correspondingly the 90% and 10% confidence levels.

Figure 3: SEA price forecast

Figure 4: SoCal price forecast

Expected prices can be obtained from fundamental forecasting tools such as MarketPoint. A probability distribution for prices is obtained by assuming a long-term volatility of 60% for SoCal and 35% for SEA. It is also assumed that prices revert towards their expected levels. Typically, reversion speeds and volatilities are estimated from observed data but historical estimates may also be combined with estimates based on fundamental modeling scenarios and information implicit in derivative instrument prices (if available).

Simple cash-flow valuation analysis
Having specified facility costs and price information we can evaluate the cash-flows to be derived from the facility. In this quarterly model, the facility operates only if the spread between SoCal gas prices and SEA prices at the domestic market point¹ is positive. If the spread is negative then it is best not to operate. Note, however, that fixed costs are incurred regardless of the operation status of the facility. Let f(k) denote the quarterly cash-flow (per mcf) yielded by the facility during quarter k, let Pd(k) and Po(k) denote the corresponding SoCal and SEA average quarterly prices and let q be the quarterly fixed cost per mcf. The cash-flow f(k) is then given by f(k) = max (Pd(k )- Po(k) - $3.75, 0 ) - q.

Note that the assumption that the facility operates at full capacity is implied in this cash-flow formulation. In addition, we assume the project lasts 120 quarters (30 years) with no terminal value at the end of that period. A cash-flow model as described above can be easily implemented on a spreadsheet. The stochastic models for natural gas prices can be readily defined using the Real Options Calculator (ROC) Excel Add-in which enables us to evaluate the project in a Monte Carlo simulation environment.

The value of the project is obtained as the expectation of V=f(1)×d(1) + f(2)×d(2) + … + f(120)×d(120)

where d(k) is the risk-free discount factor implied by the term structure of interest rates for cash-flows coming k quarters from now. For simplicity we assume a deterministic term-structure at a constant annual rate of 4% such that d(k) = exp(-0.04/4 k). Running the ROC analysis we find that the value of the project is equal to $12.97 per mcf of capacity. This value already accounts for the probability of operation/non-operation periods given price uncertainty. However, we have not yet subtracted the set-up of facility building costs that amount to $6.74/mcf yielding a net facility value of $6.23/mcf. Note that this value differs from a discounted cash-flow (DCF) analysis that can only account for operation/non-operation periods based on expected prices. In fact, the model value under DCF is highly underestimated as the static expected prices rule out the possibility of upward domestic price shocks. DCF naively ``believes'' that the facility is never profitable and therefore never operated which translates into a waste of fixed costs. In other words, DCF analysis ignores operational optionality and estimates a total value of -$24.67/mcf including set-up costs.

Figure 5: Simple ROC analysis vs. DCF

Figure 5shows a valuation comparison between ROC Analysis and the naive DCF approach. In addition, it shows an estimate, computed during ROC analysis, of the probability of operation throughout the life of the facility.²

Introducing strategy: optimal investment timing
We have determined that given price uncertainty, building an LNG facility is a good idea. However, now we must investigate whether there are strategic alternatives that increase the project's potential. One such strategy is postponement. Is now the best time to build? If not, when and under what conditions should we build the facility? An options interpretation of the postponement problem is to think of it as follows: Presently, we are in a zero cash-flow scenario (as we have done nothing yet) and starting this quarter and throughout the time span of our analysis, we have the (irreversible) option to build an LNG facility and capture the corresponding cash-flow. The cost of exercising such option is given by the facility set-up costs, namely $6.74/mcf. Figure 6 illustrates the structure of the model.

Figure 6: Postponement model structure

Evaluation of the postponement model requires considerable numerical sophistication as it requires methods such as dynamic programming that are capable of solving the valuation problem ``backwards in time.'' While the technicalities are outside the scope of this case study, the need for a ``backwards in time'' procedure can be easily understood by examining the optimal decision for building the facility. At any given time, the facility should be built if: Based on the above condition one can see that in order to determine the optimal decision today one must have knowledge of what the (optimal) actions will be in the future for all possible uncertainty resolution scenarios. In a simple spreadsheet we can define the (trivial) zero cash-flow range corresponding to the ‘postponement’ strategic scenario. Using the Real Options Calculator we define this scenario in addition to the existing LNG facility cash-flow scenario and, correspondingly, define the option that allows us to transition from the former to the latter via an investment of $6.74/mcf. After running the analysis we find that it is not optimal to build the facility right away, but rather wait and see if the price spread between domestic and off-shore natural gas prices becomes larger. The ROC produces an optimal decision policy (Figure 7) that determines when and under what circumstances one should build the facility. The expected value of the project under this optimal policy is $14.28/mcf, an increase of about 230% with respect to building right away.

Figure 7: Optimal decision policy.

The policy indicates, for each quarter, what price spreads, justify building the facility. The policy ensures that the capital expenditure associated with the facility's set-up costs is made only when price spreads allow one to expect maximum profitability. The policy accounts for seasonal patterns (which account for its jagged contour) and price reversion. It's characteristic U shape indicates that early on, unless price spreads are quite high, it is better to wait and see how the spread evolves; towards the end of the analysis time-frame the policy demands higher spreads once again as there is less time to make up for capital expenditures. In fact, there is roughly a 7% chance that the facility will not be built under optimal management.

The fact that the policy tends to avoid unprofitable capital expenditures is not only reflected in higher profit values but also in lower risk levels. This can be seen in the risk-profile reports of the ROC where a detailed distribution of the value of the project is reported taking into consideration all uncertain variables and the optimal action policy. Figure 9 conveys some of this risk information in terms of the 5% and 1% worst case project value outcomes for both the optimal timing policy and a simple ``build now'' policy. Based on this figures, it is clear that optimal timing significantly reduces the project's exposure to losses.

Figure 8: Strategy value comparison.

Figure 9: Worst case loss at 1% and 5%

Conclusion
This case study illustrates the value of using tools that incorporate modern valuation techniques into project evaluation. In particular, we examined the optimal investment timing problem. The solution is based in a few fundamental principles that optimize the transition between available strategic scenarios in order to obtain the cash-flow with maximum value. The same fundamental methodology can be applied to a variety of problems, either as new problems or as additional (strategic) dimensions in the existing analysis. Some examples in the realm of LNG projects include

• Facility location
• Capacity expansion
• Facility liquidation

Another important point is that given its treatment of uncertainty, the analysis delivers not only a value measure but also distribution of possible outcomes at both the value and the cash-flow level. Thus, the Real Options approach as applied here provides a very accurate picture of the risk/reward trade-off in a project. ¹SEA prices at domestic market point include a $3.75/mcf charge for transportation, liquefaction and re-gasification ²Under DCF, given expected price forecasts, the probability of operation is zero throughout the life of the facility.