Exercise 2

Due Monday 2/6

The Bureau of Land Management is the US government agency in charge of administering federal lands that are not National Parks (run by the Dept. of Interior) or National Forests (run by the Dept. of Agriculture). Imagine you're working there and are given responsibility for deciding what to do in the following situation.

A lumber company would like to log a particular parcel of land. If it goes ahead, it will earn profits of $1000 this year (year 0) and each of the following 10 years (years 1 to 10). After the 10th year, assume the forest is entirely gone and does not grow back (this would be true for a rain forest). Also, to keep the problem simple assume that it's not possible to stop logging once it has begun. In other words, you're going to make a once and for all decision whether or not to allow logging.

The standing forest provides external benefits to the local community in the form of recreational opportunities and beautiful scenery. An economist has estimated the value of these benefits to be somewhere between $600 and $800 per year, but can't say precisely (typical!). You may assume that the local area receives these benefits as long as any of the forest is still standing (that is, if the forest is logged they don't lose any of the external benefits until year 11, when they lose them all). One final complication is that no one is sure whether the interest rate will be 4%, 5% or 6% in the future.

Please answer the following questions.

1. Set up a spreadsheet in Excel (or any similar program) to determine the net present value of logging for any given interest rate and benefit value. That is, the spreadsheet should have a single cell where r is set and a single cell where B is set so that different r and B combinations can be evaluated easily. Use the PV formulas from class (also discussed on the web page below) and do NOT use Excel's built in PV and NPV functions. The reason is simple: you won't have Excel available on the exams. The spreadsheet should be clearly labeled. Please print out a copy for the case when r is 5% and B is $700 per year.
2. Would you allow logging if you knew the interest rate were 5% and the benefits were $700 per year? Explain why or why not in detail, including the specifics of any compensation scheme that would be needed. (Who would you have to compensate and how might you do it?)
3. Now make a table showing the net present value benefits from logging under each of the nine possible combinations of three interest rates (4%, 5%, 6%) and three externality values ($600, $700, $800). Indicate when you would allow logging.

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