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An angel investor is evaluating two new startup options related to Large Language Model (LLM) engines that have different capabilities and annual return trajectories. Option A (Engine A) can be trained using current state-of-the-art LLM models. It offers a decent return of $480,000 + CCC per year, which increases by 3% annually after the first year. Option B (Engine B) requires some initial learning from user interaction, resulting in annual returns staying low at $80,000 for the first 5 years. After that, the model will be fully trained and productionized, resulting in returns increasing by a factor of 7 (i.e., 600% increase) at the end of year 5 (beginning of year 6). Then, the returns will increase by 6% annually every year thereafter. Assuming a minimum acceptable rate of return (MARR) of (AAA + 3)%, compounded annually, we want to compare these two options in the short term and long term. a. If the investor intends to exit both investments after 15 years, what is the present worth of each option related to LLM engines? b. Which option (A or B) should the investor choose, if the investor intends to exit after 20 years? 30 years? Clearly explain your decision process and all the steps. Now, we want to look into the impact of your time value of money. Suppose the investor intends to exit after 30 years. c. What would be the level of TVOM that makes her indifferent between the two options at year? d. Now we want to consider the effect of uncertainty: Due to the rapidly changing technological market conditions, the return on LLM Engine B is uncertain. Nevertheless, it is estimated that the uniform return for the first 5 years follows a normal distribution with a mean of $80,000 and a standard deviation of $40,000 (note that its uniform, so if the return is $73,000 for a given sample, it will be the same for all 5 years for that particular sample). Additionally, the increasing factor in year 6 is also uncertain and varies uniformly between 4 and (4 + AAA). Perform a Monte Carlo analysis that includes uncertainty of both parameters using 2000 samples and determine the present value of Engine B in year 10.