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PROBLEMS HOMEWORK 1. A biotech firm must decide whether to purchase the patent to a new food additive, a lowcalorie starch substitute. It is estimated that the funds required to bring the additive to the market can be as high as $50 million or as low as $25 million. The payoff is uncertain as well: The present value of profits could be as high as $500 million or as low as $30 million. The risk-free rate is 10 percent, and the standard deviation of rate of return on biotech products is 35 percent. The patent's life is estimated at one year. a. In a worst-case scenario, how much is the patent worth? b. In a best-case scenario, how much is the patent worth? i. 5. An oil company has paid $100,000 for the right to pump oil on a plot of land during the next three years. A well has already been sunk and all other necessary facilities are in place. The land has known reserves of 60,000 barrels. The company wishes to know the market value of this operation. The interest rate is 8 percent and the marginal cost of pumping is $8 per barrel. Both of these costs are expected to remain unchanged over the three-year period. The current price of oil is $10 per barrel. Company economists have estimated the following: (i) Oil will increase in price by 10 percent with a probability of 40 percent, or decrease in price by 12 percent with a probability of 60 percent during each of the next three years. (ii) The cost of storing oil in above ground tanks is $.50 per year. (iii) The company can pump a maximum of 20,000 barrels per year at the site. (iv) The site may be shut down for a year and then reopened at a cost of $2,000. Determine the market value of the operation ignoring taxes. Assume that all cash flows occur at the end of each year