In line with their corporate responsibility targets, DataAnalytics, an analytics firm, has committed to satisfy 100% of its electricity demand using clean energy in the year 2022. They are currently in the process of planning how to achieve this target. In order to hedge against possible variations in the price of electricity in 2022, Data Analytics plans to contract solar capacity from SolarNow, a nearby solar farm, through a Corporate Power Purchase Agreement (CPPA). SolarNow has offered two possible CPPA contracts: Contract A: 100 MW of capacity; Data Analytics must purchase all the output of its contracted 100 MW of solar capacity at a price of 50/MWh. Contract B: 150 MW of capacity; Data Analytics must purchase all the output of its contracted 150 MW of solar capacity at a price of 40/MWh. . However, because of variations in weather, the amount of electricity output that SolarNow's solar panels will produce is uncertain. In particular, every MW of capacity is projected to produce p MWh of electricity per year, where p has a mean of 1500 MWh and a standard deviation of 120 MWh. The distribution is symmetric around its mean. Given the current work-from-home arrangements under which DataAnalytics is operating, it is unclear how many employees will be working from home versus in the offices in 2022. With probability 25%, all their employees will be back in the office and the firm's 2022 electricity demand d will be 210,000 MWh. With probability 75%, only half their employees will be back in the office, and the electricity consumption d will be 140,000 MWh. If Data Analytics' electricity demand d falls short of the amount of electricity delivered by the contract, they must still honour the terms of the contract and pay SolarNow the entire amount, as per the contract terms. However, if d exceeds the amount of electricity delivered by the contract, they must make up the shortfall by purchasing wind or solar energy from the spot market at a price s/MWh. Expert projections suggest that s will be somewhere between 30/MWh and 70/MWh, with equal probability DataAnalytics is seeking your help to understand which of the contracts to choose, based on the total cost to associated with each contract. You decide to simulate the performance of both contracts using a 10000-iteration simulation. After performing the simulation, you obtain summary statistics of the resulting output distributions (Tables 1 and 2), and plot the associated cumulative distribution functions of the output distributions (Figure 2). Summary Statistics Contract A Contract B 8,292,719 9,006,185 1,391,999 685,399 Mean St. Dev Table 1: Summary statistics of the output from the simulation Cumulative Distribution of Total Cost Contract A Contract B 0.0% 0.5% 6,434,238 6,807,344 6,861,018 6,927,454 6,973,858 5,909,147 7,181,025 7,393,249 7,655,098 1.0% 2.5% 5.0% 7,902,607 10.0% 7,010,445 8,181,205 8,360,084 15.0% 7,061,124 7,139,003 20.0% 8,442,475 25.0% 7,233,177 7,332,629 7,438,955 8,536,878 8,622,942 30.0% 35.0% 8,712,966 40.0% 7,538,802 45.0% 7,637,415 7,742,085 8,806,180 8,899,689 8,986,699 9,077,417 50.0% 55.0% 7,856,388 60.0% 9,164,362 65.0% 9,255,924 70.0% 9,358,809 7,988,681 8,149,006 8,376,985 9,157,284 9,816,263 10,269,846 75.0% 9,464,706 80.0% 9,587,282 85.0% 9,721,398 9,896,266 90.0% 10,737,336 95.0% 11,197,635 97.5% 11,444,343 10,151,662 10,387,113 10,643,191 10,832,431 99.0% 99.5% 11,645,447 11,756,747 12,187,547 100.0% 11,609,436 Table 2: Cumulative Distribution of Total Cost for Each Contract 100% 80% 60% 40% 20% 0% 6,500,000 7,500,000 8,500,000 9,500,000 10,500,000 11,500,000 Cost -- Contract A Cost -- Contract B Figure 2: Comparison of Cumulative Distribution Functions for cost associated with Contract A and Contract B a) What are the realistic maximum and minimum costs associated with each of the contracts? [4 marks] b) Which contract is associated with a higher probability of a cost less than 8 million? Which contract is associated with a higher probability of a cost greater than 11 million? [2 marks] c) If your decision was based on minimizing the expected value of the cost, which contract would you choose? Does this agree with your assessment in Q5c, and if not, why not? [5 marks] d) Does any one of the contracts dominate the other? Explain. [3 marks] In line with their corporate responsibility targets, DataAnalytics, an analytics firm, has committed to satisfy 100% of its electricity demand using clean energy in the year 2022. They are currently in the process of planning how to achieve this target. In order to hedge against possible variations in the price of electricity in 2022, Data Analytics plans to contract solar capacity from SolarNow, a nearby solar farm, through a Corporate Power Purchase Agreement (CPPA). SolarNow has offered two possible CPPA contracts: Contract A: 100 MW of capacity; Data Analytics must purchase all the output of its contracted 100 MW of solar capacity at a price of 50/MWh. Contract B: 150 MW of capacity; Data Analytics must purchase all the output of its contracted 150 MW of solar capacity at a price of 40/MWh. . However, because of variations in weather, the amount of electricity output that SolarNow's solar panels will produce is uncertain. In particular, every MW of capacity is projected to produce p MWh of electricity per year, where p has a mean of 1500 MWh and a standard deviation of 120 MWh. The distribution is symmetric around its mean. Given the current work-from-home arrangements under which DataAnalytics is operating, it is unclear how many employees will be working from home versus in the offices in 2022. With probability 25%, all their employees will be back in the office and the firm's 2022 electricity demand d will be 210,000 MWh. With probability 75%, only half their employees will be back in the office, and the electricity consumption d will be 140,000 MWh. If Data Analytics' electricity demand d falls short of the amount of electricity delivered by the contract, they must still honour the terms of the contract and pay SolarNow the entire amount, as per the contract terms. However, if d exceeds the amount of electricity delivered by the contract, they must make up the shortfall by purchasing wind or solar energy from the spot market at a price s/MWh. Expert projections suggest that s will be somewhere between 30/MWh and 70/MWh, with equal probability DataAnalytics is seeking your help to understand which of the contracts to choose, based on the total cost to associated with each contract. You decide to simulate the performance of both contracts using a 10000-iteration simulation. After performing the simulation, you obtain summary statistics of the resulting output distributions (Tables 1 and 2), and plot the associated cumulative distribution functions of the output distributions (Figure 2). Summary Statistics Contract A Contract B 8,292,719 9,006,185 1,391,999 685,399 Mean St. Dev Table 1: Summary statistics of the output from the simulation Cumulative Distribution of Total Cost Contract A Contract B 0.0% 0.5% 6,434,238 6,807,344 6,861,018 6,927,454 6,973,858 5,909,147 7,181,025 7,393,249 7,655,098 1.0% 2.5% 5.0% 7,902,607 10.0% 7,010,445 8,181,205 8,360,084 15.0% 7,061,124 7,139,003 20.0% 8,442,475 25.0% 7,233,177 7,332,629 7,438,955 8,536,878 8,622,942 30.0% 35.0% 8,712,966 40.0% 7,538,802 45.0% 7,637,415 7,742,085 8,806,180 8,899,689 8,986,699 9,077,417 50.0% 55.0% 7,856,388 60.0% 9,164,362 65.0% 9,255,924 70.0% 9,358,809 7,988,681 8,149,006 8,376,985 9,157,284 9,816,263 10,269,846 75.0% 9,464,706 80.0% 9,587,282 85.0% 9,721,398 9,896,266 90.0% 10,737,336 95.0% 11,197,635 97.5% 11,444,343 10,151,662 10,387,113 10,643,191 10,832,431 99.0% 99.5% 11,645,447 11,756,747 12,187,547 100.0% 11,609,436 Table 2: Cumulative Distribution of Total Cost for Each Contract 100% 80% 60% 40% 20% 0% 6,500,000 7,500,000 8,500,000 9,500,000 10,500,000 11,500,000 Cost -- Contract A Cost -- Contract B Figure 2: Comparison of Cumulative Distribution Functions for cost associated with Contract A and Contract B a) What are the realistic maximum and minimum costs associated with each of the contracts? [4 marks] b) Which contract is associated with a higher probability of a cost less than 8 million? Which contract is associated with a higher probability of a cost greater than 11 million? [2 marks] c) If your decision was based on minimizing the expected value of the cost, which contract would you choose? Does this agree with your assessment in Q5c, and if not, why not? [5 marks] d) Does any one of the contracts dominate the other? Explain. [3 marks]