Saturday, January 26, 2013

The sale of a forest as an NPV problem.

A story in my local paper caught my attention this morning  - it's about the NCSU Department of Forestry which owns a large piece of forest land that they are considering selling.  Apparently, there are significant objections to the sale because of the perceived research and teaching value of the land.

Setting aside these objections for a minute, I thought it might be worth doing a quick NPV analysis on this project.

The proposed sale price is $117 million.   This money would be placed in the university endowment and would be invested to return about 8% per year - with 5% going to the Dept of Forestry.  

So $117 million * 0.05 = $5,850,000.

However, the current forest generates between 1.5 and 2 million dollars annually already and in an NPV analysis, we are interested in the incremental cash flows from a project.  In this case, the incremental cash flows are the difference between $5,850,000 and, lets say, $2,000,000 which is $3.85 million.

This is a perpetuity - it will keep on earning a return forever, so the value of these incremental cash flows is simply:

3.85/0.05 = $77 million.

The astute reader might say - "but won't the income from the forest go up over time with inflation?"   Actually, the income stream from the money invested in the endowment should also rise, as the principal amount will grow at the rate of inflation (this is the other 3% of the 8% return) - so the effects of inflation cancel.

So the decision facing the Department of Forestry is whether the educational and research opportunities of the forest are worth more or less than $77 million.  Alternatively, can these educational and research goals be achieved elsewhere for a sum of less than $77 million.  The cost of providing for these needs has not been included in my analysis.