Can you please answer these questions and show work.

1. A firm has free cash flows of $1,000, $2,000, and $3,000 at the end of years 1, 2, and 3, respectively. Assume a discount rate of 10%. If the firm has a present value of $8572.50, what is its terminal value? What is the present value of its terminal value?

2. You are considering buying an oil field.  If you buy the field, you can extract the oil in one year.  There are 100 barrels of oil that can be extracted from the field; the cost of doing so is $4,000.  You expect the price of oil in one year to be $50/barrel.  If your discount rate is 15%, how much are you willing to pay for the field? Assume that you are going to drill in one year no matter what the price of oil turns out to be- that is, ignore real options.

3. You are considering buying an oil field. If you buy the field, you can extract the oil in one year. There are 100 barrels of oil that can be extracted from the field; the cost of doing so is $4,000. You expect the price of oil in one year to be $50/barrel. However, there are four equally likely prices of oil in one year: $20/barrel, $35/barrel, $40/barrel, and $105/barrel. 

Of the below prices, what is the minimum price at which you would drill in year 1, if you buy the field today? Assume the price of oil never changes after one year.

4. You are considering buying an oil field. If you buy the field, you can extract the oil in one year. There are 100 barrels of oil that can be extracted from the field; the cost of doing so is $4,000. You expect the price of oil in one year to be $50/barrel. However, there are four equally likely prices of oil in one year: $20/barrel, $35/barrel, $40/barrel, and $105/barrel. 

If your discount rate is 15%, how much are you willing to pay for the field? Assume the price of oil never changes after one year.