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In the discussion entitled Entropy and Interest on this website, the entropy law is contrasted with the laws of the conventional interest based financial system. It was argued that, whilst the former determines that physical wealth marches the road of compound decrement towards (but never quite reaching) zero, the latter allows a sum of money loaned at interest to march the road of compound increment towards infinity. The laws of the conventional financial system were thereby held to contradict the laws of the physical system. I hinted that the consequences of this contradiction for our environment can be extremely negative.

In terms of foreign borrowings outstanding, Brazil, Mexico and Indonesia comprise the three most indebted nations in the world. They are also three of the world's top four deforesters. For the very poor and the starving, survival comes before preservation of the rainforest. The conversion of hardwood to ash enables survival for some. Its conversion to timber for export enables survival for others. Meanwhile, our planet's rainforests experience increasing entropy with a long run cost to all of us.

Increasing numbers of academics are now arguing that such phenomena are the result of a conflict between interest and the physical system and not merely a consequence of economic development. Miller in Debt and the Environment : Converging Crises (1991) explicitly links the depletion of natural resources to the payment of interest on international debt. The academic argument hinges largely on the nature of discounting, for which two examples are now given.

Let us begin by developing an idea due to Michael Lipton at the University of Sussex (1992). Imagine a farmer who wishes to buy a plot of land and farm it. His purchase and operating costs are to be financed entirely on borrowed funds. The land is capable of supporting a highly intensive technique which is forecast to produce £150 per year of net cash-flow for 15 years and results in the complete destruction of the land's productive potential. Such might perhaps be the case for a farmer operating in lands susceptible to desertification. An alternative production technique produces only £100 per year of net cash-flow, but allows the land to regenerate and maintain its productive potential indefinitely.

Discounted cash-flow analysis allows the modern farmer to compare the two farming approaches and select the more profitable. For each interest rate, the present value ('pv') of each set of cash-flows is calculated. The farming approach offering the highest total present value is deemed the more profitable to implement.

High yield method

pv of cash-flows at 5% = 1556.95
pv of cash-flows at 10% = 1140.91

Low yield method

pv at 5% = 2000
pv at 10% = 1000

The calculation shows clearly that with interest rates at 5% the highest present value (2000) resides in the low intensity farming approach, whilst with rates at 10% the highest present value (1140.91) resides in the high intensity option. In short, the incentive toward intensive farming, and thus desertification, increases as the interest rate increases.

This unfortunate result is entirely due to the familiar way in which the discounting process progressively reduces the present value of the land's output in future years toward zero. £100 of net profit earned in year fifty has a present value of approximately £0.85 if the interest rate is 10% per year. No wonder then that the analyst who relies on discounted cash-flow analysis has little care for what the land can produce in year fifty. Whether the land at that time is desertified or not is of little relevance, since its contribution to present value is almost negligible. Lipton argues that :
Dramatically rising interest rates in 1977-79, sustained ever since, have increased the incentives - to families, businesses and governments - to use up natural resources now, and to ignore the consequences later ... Participants at Rio warned of impending famine, dearth, and depletion. The rate of interest is our spectre at their fast.

Despite the recommendation of the previous analysis, one might be excused for believing that the bankrupting of land for the sake of increased short term returns is senseless. An immortal goose that lays one golden egg per week should not have its immortality traded in for the sake of two golden eggs per week in the meantime. It appears however that some natural assets can be sacrificed at the behest of discounted cash-flow analysis. Whether such sacrifice takes the form of desertification, the extinction of a species or the immensely long-lived pollution of a nuclear power plant, the principle remains the same. Compound interest values the distant consequences of current actions at next to nothing. The problems come home to roost for a future generation that has no say in their creation.

Colin Price in Time Discounting and Value (1994) insists that the type of 'uniform negative exponential' discounting practised above is almost always incorrect as a valuation technique in a physical world which provides a wealth of non-exponential functions. He comments :
We are prepared to go along with discounting, because abandoning it would give our own interests less importance than we would like; it threatens too uncomfortable and too uncompromising a departure from our present shameful indifference to the distant future.

Yet, even where the distant future is not concerned, discounting can still display its encouragement for questionable consumption patterns in the present. Let us use discounting in choosing between two flows of holidays. The first flow involves taking no holiday for the next ten years, and the enjoyment of one holiday per year every year thereafter. The second flow involves one holiday per year for the initial ten year period and no holidays thereafter. A holiday is valued at +1 unit of real monetary value, and those years in which no holiday is taken appear as a zero entry. The time period of the analysis extends to t50, being the individual's expected remaining life span and discounting is undertaken at a rate of 20% per year.

Holidays later

pv at 20% = +0.807

Holidays first

pv at 20% = +4.1924

The choice indicated by discounting is to select the flow that constitutes 'holidays first' (present value 4.1924) in preference to the flow that constitutes 'holidays later' (present value 0.8075). The outcome is of relevance to all those who contemplate the sacrifice of current pleasure for the sake of later reward, and seems to suggest that discounting utility is a highly suspect means of project evaluation. One begins to wonder why it is that money, which purchases such utility, is itself the subject of discounting.

Ah, say the critics, an older individual might prefer to take what holidays he or she could as soon as possible - doesn't this fact justify discounting future consumption? Isn't consumption today better than consumption tomorrow? Such counter-arguments cannot be fairly addressed here, but on this specific point one could easily argue that, sometimes, consumption tomorrow is preferable to consumption today. Even an older person would prefer one breakfast per day for life instead of a remaining lifetime's worth of breakfasts today.

The existence of a market interest rate is not always viewed as an appropriate justification on which to undertake the discounting analysis. As highlighted by William Cline in The Economics of Global Warming (1992), there are alternatives. Nevertheless, the conclusions remain the same :
... the principal reason for discounting future consumption is that in the future people may have higher incomes than today, and a lower marginal utility of consumption ... if one is pessimistic about future per capita income growth, there is an intuitive case for not discounting consumption at all.

With regard to inter-generational discounting on any basis, Cline quotes E. J. Mishan in Cost Benefit Analysis : An Informal Introduction (1975) :
... Person A would therefore have no business in evaluating the future worth of 100 by discounting it for 50 years at 10 percent when he himself is not, in any case, going to receive it ... In such cases a zero rate of time preference, though arbitrary, is probably more acceptable than the use today of existing individuals' rate of time preference or of a rate of interest that would arise in a market solely for consumption loans.

If physical assets did not depreciate, if full reinvestment of yield occurred at the frequencies and in the amounts dictated by the compounding process, if there were no diminishing marginal returns to investment and no long run capacity constraints, we might then have a scenario in which the conventions of compounded fixed interest actually applied to a real world process. Reverse the compounding process and we have a discounting analysis that provides increasingly absurd results as the period under consideration lengthens.

Appropriating tomorrow's value today may form the philosophical underpinning to the commercial activities of some businessmen, but we thank the likes of Sir Christopher Wren for allowing us to enjoy the values of yesterday today. With the former attitude in the ascendancy, there will be fewer St. Paul's Cathedrals, fewer grand infrastructure projects for future generations to enjoy. For those who base their financing decisions on discounting, it simply isn't worth creating value for the long term future.

It is increasingly important that Islamic scholars should provide a viable alternative to discounting. Without it, Islamic financiers will continue to rely on a framework that is attracting increasing criticism even on its home ground. To substitute a 'rate of profit' in place of a 'rate of interest' is simply not good enough. The discounting equation does not discriminate between two different percentage rates just because one of them is not called an interest rate.

Abridged from The Problem With Interest (Ta-Ha Publishers, London, 1997)