Nice post. I'll look forward to the discussion on this one.

However I have doubts about two elements in your argument:

  1. Use of interest rate as discount rate
  2. Role of interest rate in liquidation decision

Interest rate as discount rate

A project's cash flows are not discounted at an interest rate. They are discounted according to the weighted average cost of capital of the project owner - called a discount rate. The important distinction here is that cost of capital contains both time value and risk elements.

This is most commonly derived using the Capital Asset Pricing Model (CAPM) according to the formula:

Risk free rate + beta * (Market return - Risk Free rate)

Here the risk free rate is the equivalent of your treasury bill. The second term is made up of beta (a measure of the risk of the individual project relative to the market of projects) times the spread over the risk free rate that a project of market level risk demands.

This is important because the majority of the CoC capital of the forest (or any other) project could come from the risk element, not the risk free element.

This would imply that stable political systems that provide some assurance of returns over the longer term are far more protective of resources than those that do not. This is intuitive and seems to be proven in reality. If you could lose the forest in five year, the incentive to cut goes way up. This is the case in many developing countries where politicians or land owners would rather have a million dollars in a Swiss bank account than 10 million dollars in forest assets.

Maybe the reason that Maxxam was pressured to cut down their holding was not the prevailing interest rate, but rather the contribution to their cost of capital (discount rate) from junk bonds, which require a higher rate of interest than most other debt financing.

If you are looking for a very rough and easy number to use as a discount rate, try 10%. This is not far off of the average return of on US publicly traded stocks over most time periods going back as far as 100 years. While an individual stand alone project with concentrated ownership would require a premium and forest project have their own risk features (more or less than the market), we can ignore that for now.

Plus, a question:

I am a bit confused by the meaning of 41 years in the post, although I expect this is my fault. If we use my 10% discount rate figure, this comes down to 11 years (1.1/.1). Are we now better off after only 11 years?

I think it means that $X = an annuity of $kX for that number of years. An annuity of 10% of X for 11 years is worth X today. An annuity of 2.5% of X for 41 years is worth X today. I can't relate this to your use of 41 years in the post, but again expect this is my fault. It's just after lunch here and my mind is not yet clear.

2) Role of interest rate in liquidation decision

Unless the interest rate only impacts your project, the situation seems far more complex. In the Maxxam case, junk bonds force up their cost of capital, but not those of competitors. However, the underlying interest rate is the same for everyone and thus must be subject to adjustments in the greater economy.

If everyone saw higher rates and wanted to cut, there would be a lumber surplus and prices would go down. To the degree that the interest rate reflects inflation, the increases in discount rates (in the denominator) would be balanced by an increase in prices (in the numerator).

Is there any evidence that resource liquidation follows trends in interest rates? Was it high in the 70s and low in the 90s.

I don't know the answer to this one. I'll try to figure it out while hoping someone else provides the answer first.

Nice comments Jack.  I agree about the use of higher internal discount rates (and alluded to it in comments like "in reality companies use higher internal discount rates to account for the various risks/uncertainties that plague projects", but didn't want to make an already long post longer.

The 41 comes from 102.5/2.5.  If a higher (real) discount rate was used, then the number would be smaller (eg at 10% it would be 110/10 = 11).  As you say, it's the point at which an annuity paying at the discount rate would exactly balance the income from sustainably managing the forest if the forest's characteristics allowed the sustainable income to be k times the income from consuming the forest this year.  Probably no forest would stand much of a chance at a 10% discount rate, which would require that the sustainable income is only 1/11th of the immediate consumption income.  (Then I suspect equipment capacity constraints become important also - borrowing to invest in new equipment in order to do more clearcutting will be disfavored also and that provides a negative feedback - I have a whole nother post in mind on the issues with capital investment).

I agree that Maxxam's junk bonds were likely a particularly important feature of that particular situation.  However, the graph I posted above does suggest that the cut-rate generally increased in the 1970s and 1980s.  However, this point could certainly stand to have further evidence adduced.  I intend, when I get around to it, to have a look at the international statistics.  We might posit that the cutting will show some tendency to move around to wherever discount rates are highest.

In a healthy economy, I agree with you that "If everyone saw higher rates and wanted to cut, there would be a lumber surplus and prices would go down".  However, in an economy where resource constraints were causing aggregate supply to struggle to meet aggregate demand, thus sparking inflation, there is excess demand for the products of the biosphere and the high interest rates (plus a high risk premium due to the uncertainties as you note) will provide financial justification for unsustainable consumption of natural capital.  We might imagine a world in which an already slightly strained biosphere is now being used also for biofuels to replace depleting petroleum looking that way.

Stuart, I understand why the Fed would raise interest rates to reign in inflation under conditions of rapid economic growth ("over-heated"economy) with more goods and services being produced thereby reducing  associated borrowing and thus slow the economy.  However, why would this same strategy be employed under conditions of inflation due to resource constraits that result directly in economic contraction--no need for interest rates as an economic "brake"?
"I have a whole nother post in mind on the issues with capital investment"

Stuart, my far away favorite website for finance information, data and many free models is that of NYU Sterns school finance prof Aswath Damodaran:

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/

Take a look. I will eagerly await your next post.

*

In my reading 41 (beside being one off the Adams' answer to all things :) gives the minimum portion of the resource you may liquidate sustainably (indefinately) in order to break even with immediate total liquidation now.

That is if you are able to liquidate 1/41 of the resource each  year indefinately you will be in financial tie with cutting it down right now. If you can sustainably take off bigger share per year you would (theoretically) prefer to do so.

I do agree that 10% is more real world discount rate, which immediately poses the question why lumber companies do not liquidate since it seems to be the most profitable decision.

My explanations go along these lines:

  1. If a company liquidates its principal resource in a snap it would have to invest additional resources for the liquidation process which along with the previous invesments will turn obsolate afterwards and will not payoff.

  2. Companies do price in the externalities which clear cut would cause. Ruined reputation, moonlike landscapes and Greenpeace members tied to trees are really bad for business.

  3. The companies (especially bigger once) have much less abstract view of the "market" as economists. Therefore they don't just "produce something" and expect the "market" to absorb it. It is all tied with contracts, and most of them are aware that overproduction by single one of them could cause significant price drop.

  4. Last but maybe most important, companies are made of people, and people usually have family, and most of them plan for retirement. Both of these lead people to prefer security over the long term than immediate profits in the short term. Whatever Adam Smith may have said greed is not always the dominant motivation.

All of these are very well applicable for all companies consuming non-renewable or slowly renewable resources. I think that both psychologically and economically people become worried if they see the business they run will deplete during their lifetime - some 20-30 years ahead or less. Usually you can not get humans to think 50 or 100 years ahead.
1/41th of the resource says nothing about what is sustainable, as far as I can tell.  What is sustainable is governed by ecological processes, not financial ones.

People are not rational actors, but rationalizers, and the math behind financial systems is a great excercise in justifying short-term interests over long-term inhabitability of the planet.  It basically tells people what they want to hear, given our inherent bias towards present rewards.  

Has anyone looked at Richard Douthwaite's work on the issue of responding to inflation from resource constraints by raising interest rates and how damaging that would be?

A quote: "Central bankers must therefore recognise that higher energy prices are necessary to enable the energy companies to develop more expensive sources of fuel, and that, consequently, they must allow the inflation to take its course. They must not choke it off by preventing the higher energy prices being reflected in the prices charged for the goods and services which use fossil energy. Inflation is the only relatively painless way that every price in the global economy can change by a different amount to reflect the new energy price level. The inflation needs to proceed for several years as, initially, firms will put prices up by only the amount their direct fuel costs rise. They will consequently require further increases later when the higher cost of the fuel used in the products they purchase works its way through to them and has to be passed on. Resisting inflation would essentially be an attempt to maintain the purchasing power of money in terms of the amount of energy it buys. This is obviously an inappropriate response if energy is getting scarcer and/or requires more resources to produce."

Source:  http://www.feasta.org/documents/energy/November2005.htm

Oh... think I was not clear enough. 1/41 is the financial threshold, not the physical (or biological etc). Compare this to the physical threshold and you will find whether financially it makes sense to go for sustainability or for caching in.

Example:

The forest has 5% of growth, so you can cut only 5% (1/20) sustainably. If discount rates are such (2.5%) the NPV of the forest would be higher if you manage it sustainably instead of clear cutting it.

If the discount rate is 10% the forest still renovates for 20 years but you have financial incentative to cut it right now, because you don't care that much for the future.

This has some very real world implication. Suppose I borrowed the money to buy that forest (with adjustable IR for simplicity). If interest rate is 2.5% and I get a return of 5% from my forest (skipping over some assumptions here) I could be paying the loan interest and get some profit. If IR of my loan goes to 10% then I will probably decide to clearcut the forest and repay the loan as I am forced to think short-term and get the cache now.

Sorry, missed to comment on the quote which is rather interesting indeed.

Personally as someone who lived once through hyperinflation I could not agree less with it :) What it misses is that with rising rates central banks targed containment rising of general price level, not the energy prices per se. If properly applied tighter monetary policy can suppress uncontrolled devaluation of the currency, while energy prices would be still rising relatively to the other goods and services though slower in nominal terms.

This would in fact benefit energy producers as they would still be facing rising profits in real term, while providing a stable monetary environment.