Rosa owns a property in Minot, North Dakota. She is considering drilling and sel
ID: 3222366 • Letter: R
Question
Rosa owns a property in Minot, North Dakota. She is considering drilling and selling natural gas. However, she is uncertain about the amount of natural gas under her property. With 50% chance, the land only conserves a limited amount of natural gas, in which case, she has enough natural gas to sell for 2 years. With a 50% chance, the amount of natural gas is enough to sell for 10 years. The revenue of selling natural gas is $2,000,000 per year. There is a fixed cost of $1,000,000 per year for labor. If Rosa shuts down the business, she doesn't need to pay the labor cost In the first year, Rosa needs to purchase drilling equipment that would cost her an additional $5,000,000. The following table summarizes the information. Assume Rosa is risk-neutral and her discount factor is 1. a. Would Rosa invest in the business of drilling and selling natural gas? For part (b)-(c), suppose the union requires that the labor contracts must last at least 5 years. In other words, if Rosa hires workers for the project in the first year, she needs to pay the labor cost of $1,000,000 every year at least 5 years. So in the event that her land conserves a low amount of natural gas, Rosa can only drill and sell for 2 years, but she still needs to pay the labor cost for Years 3-5 because she would have to hire the workers for at least 5 years regardless of how much natural gas is conserved on the land. b. Would Rosa invest? c. Suppose that the North Dakota government is considering offering incentives to natural gas producers, which would boost Rosa's revenue by $x each year that Rosa produces natural gas. What is the minimum x such that Rosa would invest in this case?Explanation / Answer
a. Total cost for 2 years = $6M + $1M = $7M
Total cost for 10 years = $6M + 9 * $1M = $15M
Total revenue for 2 years = $2M + $2M = $4M
Total revenue for 10 years = 10 * $2M = $20M
Expected profit Rosa makes = 0.5 * (Total revenue for 2 years - Total cost for 2 years) + 0.5 * (Total revenue for 10 years - Total cost for 10 years)
= 0.5 * ($4M - $7M) + 0.5 * ($20M - $15M)
= $1M
As the expected profit is positive, Rosa should invest.
b. In this case, total cost for 2 years will change.
Total cost for 2 years = $5M + 5 * $1M = $10M
Expected profit Rosa makes = 0.5 * (Total revenue for 2 years - Total cost for 2 years) + 0.5 * (Total revenue for 10 years - Total cost for 10 years)
= 0.5 * ($4M - $10M) + 0.5 * ($20M - $15M)
= - $0.5M
As the expected profit is negative, Rosa should not invest.
c. Rosa should invest if the expected profit is positive.
Expected profit Rosa makes = 0.5 * (Total revenue for 2 years - Total cost for 2 years) + 0.5 * (Total revenue for 10 years - Total cost for 10 years) > 0
Total revenue for 2 years = 2 * $x M = $2x M
Total revenue for 10 years = 10 * $x M = $10x M
= 0.5 * ($2x M - $10M) + 0.5 * ($10x M - $15M) > 0
=> x - 5 + 5x - 7.5 > 0
=> 6x > 12.5
=> x > 2.083
So the minimum x should be $2.083M so that Rosa would invest.
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