ECONOMIC VALUATION OF MULTI-UNIT NUCLEAR PLANT PROGRAMS BASED ON REAL OPTIONS ANALYSIS. Abstract

Transcription

1 ECONOMIC VALUATION OF MULTI-UNIT NUCLEAR PLANT PROGRAMS BASED ON REAL OPTIONS ANALYSIS by Arturo G. Reinking, Professor and Department Head Departamento de Sistemas Energéticos, Facultad de Ingeniería Universidad Nacional Autónoma de México México D. F., México Phone , Abstract Since nuclear power is being considered again as an attractive alternative for electricity generation, and since the largest component of nuclear electricity costs are the investment costs, it is suggested that in many cases multi-unit nuclear plant programs should be contemplated in an effort to bring such costs down. Such programs should be subject, among other criteria, to long term economic valuation in the frame of an uncertain future, involving when possible, both the benefits of standardization and the impact of learning to lower investment costs as well as possible program adjustments as the future unfolds. Conventional Net Present Value (NPV) analysis is poorly suited for valuations with such a scope. Real Options Analysis (ROA) is considered an improvement to conventional discounted NPV estimates as it reflects the value of the flexibilities available to management to respond to the way uncertainties evolve during project implementation and operation [1]. In this case, building a first unit would give the utility the option, but not the obligation, to build a second unit at a lower investment cost, only if economically attractive. The evaluation of a first unit should then include the value of the flexibility to build a second unit. Likewise building a second unit opens the option to build a third unit and so on. The procedure to solve this problem via ROA is discussed, results are presented and analyzed and possible extensions are then summarized. 1. Real Options Analysis Project evaluation is one of the most straightforward applications of ROA approach as discussed by Boyer, M. [2]. Before ROA, the standard evaluation procedure was discounted cash flow net present value (NPV). The real options approach is considered as an improvement to conventional discounted NPV (CNPV) estimates as it reflects the value of the flexibilities available to management to respond to the way uncertainties evolve during project implementation and operation. ROA starts by identification of sources of uncertainty, and anticipating relevant future decisions by recognizing the flexibility embedded in a project. Next, a computational model must be developed aimed at estimating an expanded (ENPV) that reflects the value of optimal decisions available to management to respond to uncertainty. If uncertainties do exist, and proper actions are suitably identified, ROA yields larger, credible estimates of project values. The reason is that the anticipated responses open to management when uncertainties evolve, are modeled in such a way that responses are only adopted if beneficial to the project, in the same way as financial options are rationally exercised only when profitable, as the holder of such options has the right, but not the obligation, to exercise them. Project evaluation results can typically be expressed as: Expanded NPV = Conventional NPV + Project Flexibility Value

2 or ENPV = CNPV + PFV Most of the calculational methods used in ROA yield a figure for ENPV, so that the PFV is known by the difference to CNPV. The intent of the models adopted is to build them in such a way as to be able to simulate the impact of the identified flexibilities, that is the actions or decisions that can be adopted only if beneficial to the project. In this application, the adopted scheme is known as compound real options in ROA parlance, as the value of an option depends in turn on the value of a later option. In our study, the uncertain variable is the electricity costs that the nuclear units would be competing against. The model assumes a binomial evolution of the electricity prices. The computational scheme calculates the expanded NPV backwards - starting from the lattice points for the future date and folding back towards the present - on a binomial lattice following the Cox, Ross and Rubinstein options valuation procedure [3]. The study is aimed at evaluating a possible agreement with a contractor/vendor, allowing four units to be ordered within fixed expiration dates, with progressively lower investment costs, both because repeated equipment orders, as well as by learning to build identical units more efficiently. The purpose of the study is to estimate the value of the flexibilities embedded in a possible agreement with a contractor/vendor. ROA yields the aforementioned ENPV for a four unit program to be committed over a period of several years. Since the type of real option involved is a compound option, the value of an option depends on the value of a later option, care must be taken to process the data in the correct binomial valuation tree. Thus the model considers both the values of the future real options that exercising them would generate, as well as the incremental cash flows that could be realized. Also, since the volatility of the underlying involved in the Cox, Ross and Rubinstein foldback evolves as the valuation proceeds from the lattice points further into the future towards those closer to the present as the ENPV is estimated, care must be taken to adjust the foldback parameters, in particular the risk neutral probability. The ENPV of the second unit, for example, must reflect both the postulated evolution of the electricity prices at the time it s being evaluated, plus the discounted ENPV of the third unit[3]. 2. Computational model The following model simulates the rational behaviour of a utility management under a long term agreement with a contractor/vendor, under which a kind of partnership is established. The utility s choice of a contractor/vendor is beneficial to the latter because of the possibility that its order books would be more likely to be filled up, plus the utility is basically adopting a given power reactor technology, so changing to some other would not be straightforward. In return, the utility would expect to benefit from the contractor/vendor learning to build identical plants as well as repeated equipment and component manufacturing that would be reflected in lower costs for repeated units. The agreement would thus involve the commitment of a first unit at a given cost and he right, but not the obligation, to order additional identical units at progressively lower costs within a given time frame in this case every four years. The utility would be able to decide whether to place additional orders, that is, exercising the options as new information on the competitiveness of new unit operation becomes available. In exchange for such right the utility compensates the contractor/vendor through a premium. This scheme replicates the basics of buy and sell transactions of financial and/or commodity options.

3 In order to establish such an agreement, the utility would ask for bids among several contractor/vendors and choose the most attractive. As explained below, another piece of information would be requested, and that s the overnight investment cost of a single unit, not part of a program as the utility would also want to consider and evaluate the possibility of ordering units one by one. Thus the utility would need an evaluation tool that must basically answer the question: how does the requested premium compare to the benefit of acquiring such options? Such a tool is rendered by the compound options scheme of ROA as applied in this paper. 3. Results For demonstrations sake, the following parameters are adopted: Table 1. Base unit parameters PARAMETER VALUE UNITS Unit capacity 1,000 MWe Overnight stand alone investment cost 3,250 Millions of US$ Capacity factor 90 % Estimated operation, maintenance and fuel costs 20 US$/MWh Competing electricity price 55 US$/MWh Discount rate 12 % per year These parameters allow a conventional NPV evaluation, one of the building blocks of the ROA model. The option premium is established as the difference between the overnight cost of the programs first unit and the investment cost of a single unit, and is referred to as a fraction F 1 of the latter. It is assumed that the first unit of the program is F 1 more costly than the single unit bid separately. The other information needed is the percentage reduction on the investment costs that the contractor/vendor is willing to offer for the second, third and fourth unit. In the following description of model results these are referred to as F 2 the fraction of the second unit investment cost in relation to the investment cost of the aforementioned single unit, then F 3 as the fraction of the third unit investment cost in relation to the second unit investment cost, and F 4 as the fraction of the 4 th unit investment cost in relation to the 3 rd unit investment cost. These fractions are thus cumulative. One of the basic steps in ROA is identifying the parameter that has a bearing in the sought after results. In this case, the electricity rates, as determined by alternate competing technologies, are adopted as the parameter that the utility management doesn t control, but to which it can respond, if means are identified at the onset. The following table shows the starting ROA parameters. Table 2. ROA parameters PARAMETER VALUE UNITS Risk free rate 4 % per year Standard deviation of electricity price 4.5 % per year Length of binomial steps 4 years Number of steps in the binomial lattice expansion 4 steps

4 Common in these models is assuming that as rates fluctuate randomly (actually pushed by other generation technologies performance and fluctuating alternative fuel costs) the new attained level determine the average rates from then on, so they can be used to estimate conventional net present values. Thus, to recap, as the future unfolds electricity rates may fluctuate up or down, making new nuclear units more or less profitable, so management can commit new units same as exercising the option if it s to its advantage, but is not obliged to do so (if not profitable). At every turn where a unit is committed its investment costs would drop a known preestablished amount. 3.1 Base case The classic backward solving procedure [4] for his compound option model yields the following lattice for the ENPV, considering F 1 = 0.1 and F 2 = F 3 = F 4 = That is, the investment cost of the first unit of the program would be 10% higher than the investment of the stand alone unit,. The 2 nd unit would be 5% lower than the $3,200 million. The 3 rd unit s investment cost would be 5% lower than that of the 2 nd unit and the 4 th also 5% lower than the 3 rd. Table 3. Base case ENPV (all figures in Millions of $) $2,214 $4,074 $4,399 $3,046 $492 $1,374 $1,234 The way to read these results is: the lattice represents the ENPV in each node of the binomial lattice where the electricity prices move up or down at a standard deviation of 4% a year. The first row is the sequence of three up movements; the diagonal is the sequence of three down movements. The other cells hold the results for other sequences of up and down movements. These figures are given in Millions of dollars and can be compared to a CNPV of $81.8 Millions for the stand alone unit. The ENPV for the whole program is $2,214 Millions. Some initial results are highlighted now. The zeroes at the bottom of the 3 rd (and 4 th ) columns mean that after a sequence of three down movements in the electricity rates the options to order the 3 rd (and 4 th ) units are not exercised, regardless on whether the last movement is up or down. The exercise must be run again, this time for a sequence four stand alone units outside the possible agreement, and thus with no investment cost reductions. The results are shown below: Table 4. Base case ENPV (without investment cost reductions) $1,914 $3,250 $3,686 $2,583 $691 $771 The interpretation of this case is similar to the one before: units are only ordered for sequences of at least two up movements in the electricity prices. The ENPV figures are lower than the first case because the investment costs for subsequent units do not drop. They are still considerably high because the units would only be

5 ordered when profitable, regardless of what the future holds. The ENPV for the whole program is $1, 914 Millions. The difference of both ENPV ($2,214 Millions - $1, 914 Millions) = $300 Millions would be the flexibility quantification for the utility of the agreement with the contractor/vendor being in place. It s interesting to note that for this base case the premium, as 10% of overnight investment cost of a standalone unit is $325 Millions, is higher than the flexibility value, so with these figures, the utility would reject such an agreement. (Such premium would have to amount to % in order to match the flexibility value of $312 Millions). 3.2 Deep investment cost reductions The case for larger investment cost reductions is instructive to highlight the workings of the model. The following table shows the results of lowering factor F 4 as the fraction of the 4 th unit investment cost in relation to the 3 rd unit investment cost from 0.95 to 0.9. Table 5. Deep investment cost reductions $2,316 $4,203 $4,524 $3,193 $573 $1,497 $1,381 $117 Since investment costs are lower in the 4 th period all ENPV are higher and an ENPV of $117 appears in the third cell for the 4 th period as compared to zero in the base case for the same reason. The option would not be exercised in the 3 th period, 3 th row, that is after three drops in electricity rates the 3 th unit would not be profitable. However the third cell for the 4 th period can be reached from the second cell of the 3 th period (with an ENPV of $1,497). That is after one increase and two drops in electricity rates. It must be pointed out that the figure of $1,497 in the second cell of the 3 th period is the result of folding back the ENPV of the next two cells, with $1,381 and $117 plus the NPV of the 3 th unit at the node with one increase and one drop in electricity rates. If the option for the 4 th unit in the third cell for the 4 th period is not exercised, the lattice would look as shown in Table 6: Table 6. Deep investment cost reductions (for comparison to Table 5) $2,293 $4,198 $4,524 $3,193 $543 $1,490 $1,381 In this case the figure of $1,490 in the second cell of the 3 th period is the result of folding back the ENPV of the next two cells, with $1,381 and zero plus the NPV of the 3 th unit at the node with one increase and one drop in electricity rates.

6 Comparing the two foldbacks yielding $1,497 and $1,490 in these two cases we notice that the only difference is the ENPV of $117 in the first case. And yet the difference is only $7. The reason for this small effect is that the risk neutral probabilities involved in folding $117 and zero are very small, being Finally, if the option agreement with the contractor/vendor specifies a factor of F 4 = 0.9 as the fraction of the 4 th unit investment cost in relation to the 3 rd unit investment cost instead of 0.95, it becomes more attractive to the utility. The theoretical premium could be 11.2% above the of overnight investment cost of a standalone unit for the first unit of the four unit program and that would result in a flexibility value of $364 Millions. 4. Conclusions This approach can widen the depth and breadth of evaluating and comparing bids for multi-unit nuclear plant programs. The model can be extended to tackle other situations or options, like comparing different reactor types, or considering more than one unit in a single site thus, if exercised a second unit would be built at a lower cost, or possible improvements in capacity factors, or considering a variant of the aforementioned agreement under which if an option for a second or third unit isn t exercised the setup wouldn t expire, but could be retaken if conditions (electricity rates) move in the right direction, or modeling the learning impact on improving fuel performance or lowering operation and maintenance costs, to give just a few examples. References 1. Laughton, D. G. et al, Modern Asset Pricing and Project Evaluation in the Energy Industry, Editor, IAEE (1998), The Energy Journal 19 (1998), 1. (full issue devoted to this and related subjects). 2. Boyer, M. (2003), Création de valeur, gestion de risque et options réeles, Rapport Bourgogne, Centre interuniversitaire de recherche en analyse des organizations, CIRANO Rapport 2003RB-1, 3. Cox, J. C., S. A. Ross, and M. Rubinstein, Option Pricing: A Simplified Approach, Journal of Financial Economics, 7 (1979) Herath, H. S. B., and C. S Park, Multi-stage Capital Investment Opportunities as Compound Real Options, The Engineering Economist, (2002) Jan 1; 47(1) 1-27.