Real Options Application Portfolio:

Transcription

1 Real Options Application Portfolio: Sizing a Pulverized Combustion Boiler Power Plant and Determining When to Add Carbon Capture Technology to the Plant December 10, 2005 ESD.71 Professor deneufville Konstantinos Kalligeros

2 Abstract Recent concern and uncertainty about global warming caused by emissions have inspired this application portfolio. The fixed engineering system is a pulverized coal combustion boiler power plant that will be sized based on the uncertainty of future coal prices. Since consumer power demand continues to grow at a strong rate, demand is assumed to exist for any sized plant between 500 and 2500 MW. A lattice method was used to determine low, median, and high coal prices to be $19.21, $35.00, and $63.77 per ton at project-mid point. The three prices represent coal price uncertainty and were used to analyze optimum power plant design size. The optimum size was determined by modeling power plant performance using the Carnegie Mellon Integrated Environmental Control Model (IECM) to calculate outputs of power plants between 500 and 2500 MW. IECM financial outputs, such as annual levelized operating and capital costs, were input into a lifetime levelized spreadsheet model to determine Net Present Values of different power plant sizes. Results showed economies of scale and lower required capital per MW of electricity as plant size increased; therefore, the largest analyzed power plant size of 2500 MW was chosen as the fixed system size. The next study step was to refine the power plant strategic plan to determine at which carbon tax per ton it becomes preferential to install carbon capture technology rather than pay carbon taxes. Optimum carbon tax rates were modeling using the IECM for a 2500 MW power plant with carbon emissions tax levels of $12.50, $25, $37, and $50. The lifetime levelized spreadsheet was used next to compare power plant net present values for each carbon tax. This flexibility modeling technique estimated minimum carbon tax rates necessary to incentivize capital expenditures to implement amine carbon dioxide capture technology. Analysis determined that optimum carbon taxes ranged from between approximately $17.00 per ton CO 2 based on low coal prices of $19.21 per ton to $17.50 per ton CO 2 for median coal prices of $35.00 per ton to $25.00 per ton CO 2 for high coal prices of $63.77 per ton. Results indicate that carbon taxes of $25.00 per ton would incentivize plant owners to install carbon capture technology under low, median, and high coal prices.

3 Acknowledgments Special thanks to Konstantinos Kalligeros for taking the time to provide feedback and direction on this application portfolio. He went out of his way to make sure that the project was clear and guided. Professor Richard de Neufville also provided support and clarification. Both inspired the creation of real-life problem solving using Real Options Analysis.

4 TABLE OF CONTENTS 1.0 Defining the System Scope of Study Contextual Factors Design and Uncertainty Parameters System Model Defining the Salient Uncertainties Uncertainty Modeling Lattice Analysis of the Evolution of a Major Uncertainty Calibrate the Lattice Develop the Lattice Model Fixed System Design Results Flexible System Design Results Flexible Systems Design Further Discussion Decision Analysis Using Lattice 5 Year NPV Conclusions Comments/Assignment Reflections 20 Appendix A Example IECM Power Plant Modeling I Appendix B Example Simple Spread Sheet Financial Modeling VII Appendix C PowerPoint Presentation of Work XII

5 INDEX OF TABLES AND FIGURES Figure 1 Study Process 2 Figure 2 Prices between November 2002 and November Figure 3 Annual Price Volatility 7 Table 4 Outcome Lattice Calculation Process 8 Table 5 Lattice Node Probability Calculation Process 8 Table 6 Outcome Lattice of Price of per Ton by Project Year 9 Table 7 Probability Distribution of Each Lattice Node 9 Table 8 Probability Distribution for Price of 9 Figure 9 Probability Distribution Function for Price of Trends 10 Table 10 Power Plant Characteristics Based on Plant Size and Cost 11 Figure 11 Cost of Electricity (COE) by Plant Size 12 Figure 12 Capital Required per MW by Plant Size 12 Figure 13 NPV of 0% Carbon Capture vs 90% Carbon Capture based on Price per Ton (2500 MW Plant Size) 14 Table 14 Zero and 90 Percent Carbon Capture Power Plant Characteristics 15 Figure 15 NPV per ton CO 2 per Carbon Tax based on Price Per Ton 16 Table 16 Five Year Price Uncertainty Lattice Based on One Year Steps 17 Table 17 Five Year NPV Lattice Based on Price Uncertainty 19

6 Real Options Application Portfolio Sizing a Pulverized Combustion Boiler Power Plant and Determining When to Add Carbon Capture Technology to the Plant 1.0 Defining the System Recent concern and uncertainty about global warming caused by emissions have inspired this application portfolio. The fixed engineering system is a pulverized coal combustion boiler plant that will be sized based on the uncertainty of future coal prices. Since consumer power demand continues to grow at a strong rate, it is assumed to exist for any of the study plant sizes. The flexible system will be analyzed based on uncertainties in future carbon taxes. The objective of this application portfolio is to apply real options analysis to determine what carbon emissions tax level will incentivize power plant owners to add carbon capture technology to a pulverized coal combustion boiler plant. 1.1 Scope of Study As shown in Figure 1, developing a strategic plan for the fixed plant size is the first study step. The portfolio will apply Manne s theory to determine the preferred power plant size by comparing the price per MW of electricity generated given power plant sizes between 500 and 2500 MW and uncertainties in coal prices at project mid-point low, median, and high prices of $19.21, $35.00, and $63.77 per ton. The next study step is to revise the strategic plan to determine at which carbon tax per ton it becomes preferential to install carbon capture technology in the plant rather than pay the carbon tax. Carbon tax rates will be derived by comparing net present value of projects given carbon emissions tax levels of $12.50, $25, $37, and $50. This flexibility modeling will be used to determine minimum carbon tax rates necessary to induce capital expenditure for implementing amine carbon dioxide capture technology. 1

7 1. Develop Strategic Plan Fixed Design t = 0 Design Decision: What size plant based on coal price uncertainties? 2. Revise Strategic Plan Flexible Design t =? Uncertainty Revealed: Carbon Taxes At what price add carbon capture technology? Figure 1 Study Process 1.2 Contextual Factors A fairly conservative discount rate of 15 percent will be applied due to the complexity of the project. Experience shows that construction capital costs are largely uncertain and frequently grossly underestimated. In addition, external costs of burning fossil fuels, such as climate changes and health impacts, are extremely difficult to measure qualitatively and quantitatively. Outside system performance incentives and regulations could be built into the overall energy system to accelerate integration of carbon capture into existing power plants. Incentives could include a cap and trade carbon emissions market, direct alternative energy subsidies, feed-in tariffs, quota obligations, removing energy innovation barriers, and energy tax exemptions, while regulations could include emissions, waste, and user taxes, and eliminating subsidies that encourage energy use. As discussed next, this analysis will focus on the affects of implementing a carbon tax. 2

8 1.3 Design and Uncertainty Parameters Since future operating costs are dependent on fuel costs, it is important to analyze their impacts. While coal prices were fairly stable from 1990 to 2002, coal prices and volatility have risen significantly in 2003 and Fuel costs are sensitive to many supply side factors including physical availability, natural disasters, transportation, and political situations; therefore, future prices are difficult to predict. A lattice method will be employed to determine the range of potential coal prices and resulting net present values of plants, as explained in Sections 2.0 and 5.0. prices at project mid-point low, median, and high prices of $19.21, $35.00, and $63.77 per ton will be modeled. Concerns with controlling greenhouse gas emissions in response to climate change will likely spur implementation of carbon emissions taxes or a cap and trade type of system. Since MIT Professor John Deutch favors a carbon tax response, the analysis focused on carbon taxes. In addition, it is difficult to put a price on the qualitative terms of emissions impacts to determine CO 2 costs; therefore, an inducing carbon tax can be approximated by comparing operating costs against power plant Net Present Value (NPV). Carbon emissions tax levels of $12.50, $25, $37.50, and $50 per ton will be modeled. 1.4 System Model The Carnegie Mellon Integrated Environmental Control Model (IECM) is available to analyze the effects of the design and uncertainty parameters of the system. 1 It was designed to model coal-fired power plants to determine the financial and operating impacts of implementing post-combustion CO 2 amine system carbon capture. The model can include post-combustion controls for NO x, particulates, and SO 2, which will be added to both the fixed and the flexible scenarios due to current regulations

9 Some of the additional model inputs and project assumptions are listed here: Capacity Factor 85% Capital Charge (CFC) 12%, Illinois #6 $35/ton 1.38 $/MMBtu 10,900 Btu/KWe-hr 61.2% Carbon Annual Operating Hours 7451 Hours Amine System Carbon Capture 90% Efficient Current 2004 Dollars 3.5 percent Inflation Project life 20 years Financial results of each IECM model run will be input into a simple lifetime-levelized cost spreadsheet to determine Net Present Value and generated electricity costs per MW. 2.0 Defining the Salient Uncertainties 2.1 Uncertainty Modeling The IECM model allows for coal costs between $0 and $100 per ton. Current prices for Illinois #6, one of the model s default coals, are about $35.00 per ton. 2 Section 2.2 details a lattice model run to determine future coal prices based on volatility. The lattice results will be used and coal prices will be modeled using project mid-point low, median, and high prices of $19.21, $35.00, and $63.77 per ton. To calculate annual revenue, a current electricity selling price of cents/kwhr based on the October NSTAR electricity bill will be used. To be conservative, zero price growth will be assumed. 2 News and Markets, Energy Information Administration, Department of Energy, November 13,

10 For the flexible design, the application portfolio considers that the California Public Utilities Commission is starting to assign a carbon adder cost for California power plants to include in their energy cost forecasts. This adder cost attempts to represent the external costs of emitting carbon dioxide. In 2008, the California cost adder is proposed to be $12.50 per ton. 3 The IECM model will be used to hypothetically model this using a $12.50, $25, $37, and $50/ton CO 2 tax. 2.1 Lattice Analysis of the Evolution of a Major Uncertainty The lattice analysis depicts the development of coal prices, a major uncertainty input for the power plant. The lattice will analyze coal prices over a 20 year period using five time periods (four years per time period) Calibrate the Lattice prices have grown from $25 to $35 per ton between 1990 and 2005; therefore, a starting coal price of $35.00 per ton, consistent with current Illinois #6 prices, is used. Since it is difficult to forecast coal prices given market volatility, the lattice was developed using the average growth rate between 1990 and 2005 of 2.67 percent per year. 3 On December 16, 2004, the California Public Utilities Commission (CPUC) adopted Decision No requiring the state s largest electric utilities (PG&E, SCE, and SDG&E) to begin accounting for the financial risk associated with greenhouse gas emissions when making new long-term power plant investments. 5

11 Figure 2 Prices between November 2002 and November For many reasons, including an extremely limited futures market, it is difficult to obtain reliable future coal volatility data; however, economists have analyzed and quantified past coal volatility. Illinois #6 volatility has ranged between 10 and 18 percent since For purposes of this exercise, 15 percent volatility will be assumed. 4 News and Markets, Energy Information Administration, Department of Energy, November 13,

12 Figure 3 Annual Price Volatility for Selected US Domestic s 1990 through Therefore, up = u = e (σ * ( t^.5)) = e (0.15 * 4^.0.5) = = u down = d = 1/u = = d probability = p = (v/ (σ* t 0.5 )) = * (0.107/(0.15* ) = = p, where, t = 4 years, v = growth rate (2.67) * 4 years, and σ = 15 percent Develop the Lattice Model The lattice model is developed using a simple spreadsheet calculation. The lattice begins with the initial price, approximately equal to current coal prices of $35.00 per ton. The lattice is developed for the four year time periods using the equations shown in Table 4 below. Table 5 illustrates the application of the probability factor, p, to determine the probability of each node occurring. 5 News and Markets, Energy Information Administration, Department of Energy, November 13,

13 0 Years (P 0 ) Starting Price - P 0 4 Years (P4) P4 1 = P 0 *up P4 2 = P 0 *down Table 4 Outcome Lattice Calculation Process 8 Years (P8) P8 1 = P4 1 *up P8 2 = P4 1 *down + P4 2 *up P8 3 = P4 2 *down 12 Years (P12) P12 1 = P8 1 *up P12 2 = P8 1 *down + P8 2 *up P12 3 = P8 2 *down + P8 3 *up P12 4 = P8 3 *down 16 Years (P16) P16 1 = P12 1 *up P16 2 = P12 1 *down + P12 2 *up P16 3 = P12 2 *down + P12 3 *up P16 4 = P12 3 *down + P12 4 *up P16 5 = P12 4 *down 20 Years (P20) Step P20 1 = P16 1 *up 5 P20 2 = P16 1 *down + P16 2 *up 4 P20 3 = P16 2 *down + P16 3 *up 3 P20 4 = P16 3 *down + P16 4 *up 2 P20 5 = P16 4 *down + P16 5 *up 1 P20 6 = P12 5 *down 0 0 Years (p 0 ) Starting prob - p 0 Table 5 Lattice Node Probability Calculation Process 4 Years (p4) p4 1 = p 0 *p p4 2 = p 0 *(1-p) 8 Years (P8) P8 1 = p4 1 *p P8 2 = p4 1 *(1-p) + p4 2 *p p8 3 = p4 2 *(1-p) 12 Years (p12) p12 1 = p8 1 *p p12 2 = p8 1 *(1-p) + p8 2 *p p12 3 = p8 2 *(1-p) + p8 3 *p p12 4 = p8 3 *(1-p) 16 Years (p16) p16 1 = p12 1 *p p16 2 = p12 1 *(1-p) + p12 2 *p p16 3 = p12 2 *(1-p) + p12 3 *p p16 4 = p12 3 *(1-p) + p12 4 *p p16 5 = p12 4 *(1-p) 20 Years (p20) Step p20 1 = p16 1 *p 5 p20 2 = p16 1 *(1-p) + p16 2 *p 4 p20 3 = p16 2 *(1-p) + p16 3 *p 3 p20 4 = p16 3 *(1-p) + p16 4 *p 2 p20 5 = p16 4 *(1-p) + p16 5 *p 1 p20 6 = p12 5 *(1-p) 0 8

14 The previous lattice steps were followed to determine the uncertainty of the price of coal. Table 6 depicts the price variations for the 20 year period for each analyzed step of 4 years. Table 6 Outcome Lattice of Price of per Ton by Project Year 0 Years 4 Years 8 Years 12 Years 16 Years 20 Years Step $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Table 7 depicts the probabilities for each period and step for the 20 year period. Table 7 Probability Distribution of Each Lattice Node 0 Years 4 Years 8 Years 12 Years 16 Years 20 Years Step Table 8 is the probability distribution table that summarizes the outcome of the lattice for the five steps at Year 20. Table 8 Probability Distribution at Year 20 for Price of Step Probability Price/ton $ $ $ $ $ $

15 The following probability distribution graphically illustrates the possible costs of coal pear ton and associated probabilities at year 20. Figure 9 Probability Distribution Function at Year 20 for Price of Trends Probability Price of /ton Since the price of coal can be volatile, it is likely that the prices will vary considerably from year to year with a general uptrend. This is confirmed by the Probability Distribution Function for 2025, which shows that coal prices have an approximately 25 percent probability of being lower than current prices of $35.00 per ton, and approximately 75 percent probability of being higher. 3.0 Fixed System Design Results To determine the optimum size of the fixed power plant given that demand exists for any size plant, power plant sizes of 500, 1000, 1250, 1500, 1750, 2000, and 2500 were modeled with the IECM for coal prices of $19.21, $35.00, and $63.77 per ton. Model outputs, such as yearly levelized operating and capital costs, were input into a simple spreadsheet to determine NPV, costs of producing electricity per MW, and capital requirements per MW for each plant size. 6 Table 10 below depicts the results of the 6 Example IECM model input and output screens are shown in Appendix A. Example NPV spreadsheet calculations are shown in Appendix B. 10

16 fixed system modeling. Figures 11 and 12 illustrate how combustion boiler power plants exhibit economies of scale characteristics. As the scale of production increases, the net present value to produce one megawatt of power also increases due to a decrease in production costs per unit. In addition, smaller capital requirements per MW exist as the scale of the production increases. The IECM model limitation is a 2500 MW plant; therefore, given the strong economies of scale, the largest power plant possible for modeling, or 2500 MW, was chosen as the fixed plant size. Table 10 Power Plant Characteristics Based on Plant Size and Cost Gross Electrical Output (MW) Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) Capital Required (Millions) Capital Cost/MW (Millions) Cost of $ $ $ $ $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 2, $ 1.02 Cost of $ $ $47.96 $ $ $ $95.94 $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 2, $ 1.02 Cost of $ $ $87.38 $ $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 1, $ $ $ $ 2, $

17 $75.00 Figure 11 Cost of Electricity (COE) by Plant Size for low, median, and high coal prices COE ($/MWh) $70.00 $65.00 $60.00 $55.00 $50.00 $45.00 $63.77/ton $35.00/ton $40.00 $35.00 $30.00 $19.21/ton Plant Size (MW) Figure 12 Capital Required per MW by Plant Size Capital Required per MW by Plant Size Capital Needed/MW (M$) $1.50 $1.45 $1.40 $1.35 $1.30 $1.25 $1.20 $1.15 $1.10 $1.05 $ Size Plant (MW) 12

18 4.0 Flexible System Design Results A similar process was applied to determine the carbon tax necessary to induce carbon capture implementation for the 2500 MW power plant. Carbon taxes of $12.50, $25.00, $37.50, and $50.00 were modeled with the IECM for coal prices of $19.21, $35.00, and $63.77 per ton. Model outputs, such as yearly levelized operating and capital costs, were input into the simple lifetime levelized spreadsheet to determine NPV, costs of producing electricity per MW, and capital requirements per MW for each plant modeling. The NPVs of two different systems were compared to determine the carbon tax break even point: (1) zero percent carbon capture with carbon taxes between $0 and $50 and coal costs between $19.21 and $63.77 per ton; and (2) 90 percent carbon capture with carbon taxes between $0 and $50 and coal costs between $19.21 and $63.77 per ton. According to the results shown in Figure 4 below, as coal costs rise, lower carbon taxes are necessary to induce carbon capture technology implementation. At today s prices of $35 per ton, which is also the expected median price at the mid-point of the project, a carbon tax of approximately $17.50 would induce carbon capture investment. For $19.21 and $63.77 per ton, approximately $25 and $16 would induce technology investment. Figure 13 illustrates how plant owners can introduce flexibility into their system in the event of unexpected carbon tax implementation given current and future coal prices. 13

19 Figure 13 NPV of 0% Carbon Capture vs 90% Carbon Capture based on Price per Ton (2500 MW Plant Size) $6, $5, $4, $3, $2, $1, $- $(1,000.00) $(2,000.00) $(3,000.00) $(4,000.00) $(5,000.00) $(6,000.00) $0.0 $12.5 $25.0 $37.5 $50.0 No CO2 Capture $19.21 CO2 Capture $19.21 No CO2 Capture $35 CO2 Capture $35 No CO2 Capture $63.77 CO2 Capture $63.77 Table 14 summarizes the findings from the modeling effort for zero and 90 percent carbon capture systems based on coal cost and carbon tax uncertainties. Figure 15, derived from the data, illustrates that for the no capture technology system, the NPV per ton of CO 2 emitted remains relatively constant across coal prices. However, for the 90 percent capture system, the NPV per ton of CO 2 emitted is very sensitive to coal prices. 14

20 Table 14 Zero and 90 Percent Carbon Capture Power Plant Characteristics Based on Cost and Carbon Tax CO 2 (ton/yr) Net Present Value Net Present Value ($/ton CO 2 ) Price $19.21 per ton $0 Carbon Tax $ 4, $ $12.50 Carbon Tax $ 2, $ 7.78 $25.00 Carbon Tax $ 1, $ 5.20 $37.50 Carbon Tax $ $ 0.05 $50.00 Carbon Tax -$ 1, $ 5.07 Carbon Capture Technology $0 Tax $ 2, $ Carbon Capture Technology $12.50 Tax $ 1, $ Carbon Capture Technology $25.00 Tax $ 1, $ Carbon Capture Technology $37.50 Tax $ 1, $ Carbon Capture Technology $50.00 Tax $ 1, $ Price $35.00 per ton $0 Carbon Tax $ 3, $ $12.50 Carbon Tax $ 1, $ 4.89 $25.00 Carbon Tax -$ $ 0.25 $37.50 Carbon Tax -$ 1, $ 5.38 $50.00 Carbon Tax -$ 3, $ Carbon Capture Technology $0 Tax $ 1, $ Carbon Capture Technology $12.50 Tax $ $ Carbon Capture Technology $25.00 Tax $ $ Carbon Capture Technology $37.50 Tax $ $ Carbon Capture Technology $50.00 Tax $ $ Price $63.77 per ton $0 Carbon Tax $ 3, $ $12.50 Carbon Tax -$ $ 0.34 $25.00 Carbon Tax -$ 1, $ 5.48 $37.50 Carbon Tax -$ 3, $ $50.00 Carbon Tax -$ 4, $ Carbon Capture Technology $0 Tax $ $ Carbon Capture Technology $12.50 Tax -$ $ Carbon Capture Technology $25.00 Tax -$ $ Carbon Capture Technology $37.50 Tax -$ $ Carbon Capture Technology $50.00 Tax -$ 1, $

21 $80.00 Figure 15 NPV per ton CO 2 per Carbon Tax Based on Price Per Ton (2500 MW Plant) Price per Ton (2500 MW Plant) $60.00 $40.00 $20.00 $- $(20.00) $(40.00) $(60.00) $0.0 $12.5 $25.0 $37.5 $50.0 No CO2 Capture $19.21 CO2 Capture $19.21 No CO2 Capture $35 CO2 Capture $35 No CO2 Capture $63.77 CO2 Capture $63.77 The power plant owner should introduce carbon capture technologies using the preceding analysis based on future carbon tax implementation. 4.1 Flexible Systems Design Further Discussion The real options flexible design approach may also be used to determine the optimal carbon tax to implement. It was calculated based on the amine system that captures ninety percent of carbon dioxide emissions. To implement a carbon tax today based on the price of $35.00 per ton, an introductory rate of at least $17.50 per ton of CO 2 emitted should be applied to induce carbon technology installation by power plant owners. A better carbon tax of $25.00 per ton of CO 2 would induce carbon capture in systems even if coal costs fall to lows of $19.21 per per ton. Since carbon taxes are 16

22 dependent on coal prices, tax rates should be periodically evaluated for necessary adjustments, much like the Federal interest or Treasury bill rates. Outside the scope of this assignment, future real options analysis could be carried out based on the uncertainty of natural gas prices for different plant configurations such as IGCC and Gas Turbines, as well as for longer plant lives. 5.0 Decision Analysis Using Lattice 5 Year NPV The lattice analysis explained in Section was repeated for a five year time frame to determine coal price uncertainties impact on Year 5 NPV for the power plant. prices and probabilities are shown in Table 16 below. Table 16 Five Year Price Uncertainty Lattice Based on One Year Steps Starting price $35 Prob up Prob down Upside factor Discount rate: 15% Downside factor t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 Price $35.00 $ $47.26 $54.91 $63.81 $ $ $35.02 $40.69 $47.28 $ $25.95 $30.15 $35.03 $ $22.34 $25.96 $ $19.23 $ $ Probabilities: Given the lattice of probabilities and outcomes developed above, the next step is to perform a decision analysis to determine the five year NPV of the system. For purposes 17

23 of developing this decision analysis, the NPV will be calculated based on each node s coal price per ton shown in Table 16 with recommended carbon taxes of $17.50 per ton CO 2 emitted. There is only one option to exercise, the decision to close the plant or not. In other words, if the plant develops a negative NPV and is closed down, it will not be opened back up. The IECM model was run given each price option in the Table 16 lattice and the values were plugged into the lifetime levelized spreadsheet to determine the NPV for each node of the lattice, dependent on the year and step. To determine the Probability Weighted Net Revenue, the NPV for each node was multiplied by the probabilities calculated like in Table 7, except using one year time steps instead of four year steps. Each Year s Probability Weighted Net Revenues were summed and multiplied by the discount factor to determine the year s NPV. The five years of NPV were summed to get a total five year NPV of $410 Million based on coal price uncertainties. Next, the Probability Weighted NPV was compared with the Present Value with Options to determine the value of the Option. As the lattice analysis shows, at $17.50 per ton CO 2 emissions tax with uncertain coal costs, the plant will not need to be shut down within the first five years. The lattice NPV is calculated at approximately $400 million, which means the plant will not shut down and the option is worth nothing. 18

24 Table 17 Five Year NPV Lattice Based on Price Uncertainty Year 1 Year 2 Year 3 Year 4 Year 5 Net Revenue: $ $ $ (39.07) $(119.77) $ (106.13) $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Year 1 Year 2 Year 3 Year 4 Year 5 Probability 0 $ $ $ (7.98) $ (14.41) $ (7.52) Weighted $ $ $ $ $ Net Revenue $ $ $ $ $ $ $ $ 8.13 $ $ 1.80 Year 1 Year 2 Year 3 Year 4 Year E [Revenues] $ - $ $ $ $ $ PV( E[Revenues]) $ - $ $ $ $ $ Total NPV $ PV (Net Revenue) With Options Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 PV(Net Revenue) $ $ $ $ (2.80) $ (73.52) $ (106.13) WITH OPTIONS $ $ $ $ $ (check next year) $ $ $ $ $ $ $ $ $ $ Shut Down? FALSE FALSE FALSE FALSE FALSE FALSE WITH OPTIONS FALSE FALSE FALSE FALSE FALSE (check next year) FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE Value of option = $ $ 410 $ (9) The negative $9 million difference is likely a rounding error between the several spreadsheets that were used to calculate the different NPVs. 19

25 6.0 Conclusions Analysis determined that optimum carbon taxes ranged from between approximately $17.00 per ton CO 2 based on high coal prices of $63.77 per ton to $17.50 per ton CO 2 for median coal prices of $35.00 per ton to $25.00 per ton CO 2 for low coal prices of $19.21 per ton. Results indicate that carbon taxes of $25.00 per ton would incentivize plant owners to install carbon capture technology under low, median, and high coal prices. The modeling efforts used in this application portfolio are limited by their simplicity. The levelized cost discount factor cash flow calculation simple spreadsheet (shown in Appendix B) is a simplified method for calculating NPV. It may have limited accuracy. The lattice analysis NPV may be a more reliable calculation since it considers coal price uncertainties and the probability of each possible price; however, accuracy is limited by the assumptions of volatility and standard deviation. In addition, all simple spreadsheet modeling inputs are determined by the IECM program. It is difficult to determine how accurate these calculations are since they are done automatically by the computer. Overall, despite the simplicity of the some of the modeling techniques, the results are deemed to be an accurate representation of NPVs. 7.0 Comments/Assignment Reflections The flexible approach to design seems to work best for sizing physical projects, such as a power plant, where financial characteristics can be applied to the variables. For instance, if demand varied throughout the plant s lifetime, it would be possible to determine whether to take advantage of economies of scale and build a larger plant or to take advantage of time value of money and build two smaller plants, with some of the capital costs deferred to the future. Valuing the option of closing the plant is a valuable tool to determine the negative impacts of uncertainties, such as coal prices in this case. If the analysis shows negative impacts in the event of extremely high coal prices, it is possible to close the plant and take less of a loss on the overall plant costs. 20

26 Since it took me three tries to choose a topic that I was able to model and analyze given the application portfolio constraints, I learned a tremendous amount about the complexity and value of analyzing projects using real options. My previous two topics were entirely too ambitious for the assignment and proved to be an undertaking too elaborate for the purposes of the class. Reconfiguring the project multiple times allowed me to gain a greater understanding of real options and to see how I could use it for more complicated projects in the future. I enjoyed applying the analysis to determine what carbon tax is necessary to incentivize plant owners to implement carbon capture technology into the system. Although, my project purpose was to determine at which carbon tax that plant owners would implement the technology, a more large-scale use of the information would be for policy makers to determine the best carbon tax to implement to induce carbon capture technology. 21

27 Appendix A Example IECM Power Plant Modeling Example IECM Power Plant Calculation Inputs Overall Plant Set Up and Diagram (No CO 2 Capture) Plant Performance Inputs Capacity Factors, Gross Electrical Output I

28 Plant Performance Inputs Financing Variables Plant Performance Inputs O&M Cost Inputs (Fuel) II

29 Plant Performance Inputs Fuel Parameters Plant Performance Inputs Carbon Dioxide Taxes III

30 Plant Performance Inputs Capital Costs Plant Performance Inputs O&M Costs IV

31 Example IECM Power Plant Calculation Results Overall Plant Performance Stack Contents V

32 Annual Levelized Plant Fixed and Variable Costs Annual Levelized Plant Fixed and Variable Costs VI

33 Appendix B Example Simple Spread Sheet Financial Modeling Spreadsheet calculations of NPV for $35/ton and Various Carbon Taxes or Carbon Capture Costs $35.00/ton 35 $12.50 Carbon Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $1, $2, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) VII

34 $25.00 Carbon Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $76.77 $2, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) $37.50 Carbon Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $1, $2, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) VIII

35 $50.00 Carbon Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $3, $2, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) Carbon Capture Technology 0 Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $1, $3, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) IX

36 Carbon Capture Technology Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $ $3, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) Carbon Capture Technology Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $ $3, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) X

37 Carbon Capture Technology Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $ $3, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) Carbon Capture Technology Tax Net Electrical Output (MW) Operating Hours Annual Power Generation (BkWh/yr) Internal COE $ per MWh Rate ton/hr Costs/Yr (Mil) CO2 (ton/hr) Net Present Value Capital Required (Millions) $ $ $ $3, Time period, n Price, p (cents/kwhr) Revenue, R(n) ($M/yr) O&M cost (inc. fuel), ($M/yr) Operating income, Revenue - O&M Cost Annualized Capital Cost, ($M/yr) Net Income, ($M/yr) NPV Net Present Value ($M) XI