The trap of present value calculation

The second half of the twentieth century brought about increasing socie-tal awareness that the capacities of our Earth were fi nite, whereas earlier, public goods that had previously been considered infi nite and free, such as clean air, healthy drinking water, waste disposal, and certain biosphere services, had been classifi ed as being among the public goods to be pro-vided by governments on a mandatory basis, as part of public services.

One representative of neoclassical economics, Arthur Pigou (Pigou, 2013), proposed that externalities be taxed, then Ronald Coase (Coase, 1960), the founder of institutional economics, sought to internalise externalities by means of market bargaining. However, problems remain, since the market economy, relying on the calculation of present value for its functioning, is hardly capable of managing projects of more than 30 to 50 years, whereas respecting the limits of the Earth would require thinking using a time hori-zon of several hundred years. The social discount rate desirable for sus-tainable development would often be signifi cantly lower than the market discount rate.

Even relatively simple projects that would, for instance, create considerable energy savings, generally involve signifi cant investment costs. Some projects are implemented over a period of 30 to 50 years, and the rules of present value calculation generally produce a negative net present value, where the social discount rate is defi ned at 6 to 8% or above, and practitioners hardly ever ap-ply lower rates.

To illustrate the problem, let us consider a very simple and widely known example. Afforestation is regarded as a means of fighting climate change.

Trees fix carbon dioxide, for which they only use solar energy through pho-tosynthesis. Their growth is often a lengthy process, as a result of which they keep fixing carbon dioxide for extensive periods. Wood is an excellent raw material for a number of industries, and ultimately may also be used as a renewable source of energy. Moreover, forests play an important role in human recreation, and provide a great number of biosphere services. Let us consider it a given that wood is a valuable good: it is not by coincidence that the destruction of forests has been prohibited by law for centuries.

This should obviously make it worthwhile to invest in afforestation. With any investment, the investor assesses the investment opportunities avail-able and identifies the one that offers the highest return. This requires an assessment of the risks of the investment, as well as the expected returns and cash flows associated with it. Underlying those calculations is the answer to the simple question of which is better: purchasing government securities that offer relatively low returns but are virtually free of risk, or

taking part in an undertaking that involves slightly higher risk, but also offers higher annual returns compared to the government securities. The problem is well known, and specialist books on finance recommend using net present value calculations to answer the question (Brealey–Myers–Al-len–Mohanty, 2012).

The net present value of any investment may be calculated using the following formula:

where

t is the time of the cash fl ow concerned (e.g. 3 represents year three);

n is the entire term;

r is the interest or discount rate;

C_t is the net cash fl ow at time t (positive for gains and negative for invest-ments or expenses);

C₀ is the amount of money invested at time 0.

Specialist books offer detailed arguments that demonstrate that when-ever the above formula produces a positive net present value, a return will certainly be made on the investment provided that the presuppositions are valid. One such key presupposition is the estimate of the discount rate in-cluded in the formula. The discount rate shows the investor’s expectations about the returns on the investment. Higher discount rates are applied to riskier investments (e.g. when the economic environment is uncertain, the area is exposed to extreme weather due to climate change, or the protec-tion of property right cannot be fully guaranteed). A higher discount rate is warranted by these and similar circumstances. In a relatively stable and less risky economic environment, expected returns are lower, and so are the discount rates applied. On balance, it may be assumed that if NPV > 0 the investment is viable.

Let us now consider the case of afforestation referred to earlier. With forests, the two extremes are represented by energy forests on the one hand, and forests comprising valuable native species on the other, which provide a variety of benefits but grow at a very slow rate. A good example of the first is a forest of locust trees, which are fast-growing trees but non-native to Hungary, and of the second, an oak or beech forest. Reaching maturity takes 20 to 22 years in the former case, and 110 to 120 years in the latter. The table below shows details of the various utilisation param-eters for the two forest types, taking into account the time that elapses after planting:

Species Clearance Selection Table 4-4. Harvesting methods (University of West Hungary:

Theoretical considerations of evaluating economics of continuous cover forestry, n.d.)

The Hungarian data show that in an oak forest, the fi nal harvest will yield approximately 400 cubic meters of high-quality wood per hectare, with an-other 85 cubic meters of fi rewood produced by thinning. After 30 years, a locust forest will yield 140 cubic meters of wood that is also valuable, but of more limited use. In 100 years, a locust forest will yield approximately 420 cubic meters of valuable wood, and an additional 165 cubic meters of less valuable material.

There is an extensive body of literature about the problems with select-ing the appropriate social discount rates. Usselect-ing data from one such paper (with some adjustments), we have calculated the net present values for the two forest types. Given that the life span of an oak forest is very long, 114 years in our example, whereas that of a locust forest is only 22 years, we assumed that the locust is clear-felled every 22 years and replanted immediately afterwards, which allowed us to obtain comparable data by calculating the net present value of both types for 114 years. As our nu-merical example is fairly well aligned with the fi ndings of professionals from the University of West Hungary (see the table above), we may be excused for dispensing with some of the details. Based on the English paper, the following tables present the expenditure related to plantation and the ex-pected returns on sales of wood.

Years Activities

Real expenses and returns (thousand HUF

per hectare)

0 Preparation of area -20

0 Plantation -80

0 Road construction -30

0-60 Annual operating expenses -8

1 Weed control -20

4,7,10,13 Pruning and thinning

before sale -6

8 Thinning (1) 80

12 Thinning (2) 140

16 Thinning (3) 200

22 Clear felling 1,600

Table 4-5. Plantation and maintenance costs of a locust forest at the time they are incurred (based on Straka–Bullard, 1996; Davis–Johnson, 1987)

Years Activities

Real expenses and returns (thousand HUF

per hectare)

0 Preparation of area -40

0 Plantation and protection -320

0-60 Annual administrative

costs -8

1 Weed control -40

5 Pruning and thinning

before sale -80

60 Thinning (1) 1,600

80 Thinning (2) 3,200

100 Thinning (3) 4,000

120 Clear felling 4,800

Table 4-6. Plantation and maintenance costs of an oak forest at the time they are incurred (based on Straka–Bullard, 1996; Davis–Johnson, 1987)

In both cases, the present value is calculated over a period of 114 years. An-nual cash fl ows are summarised in Table 4-7. The net present value of each al-ternative is shown in Table 4-8. The lowest discount rate that is applied is 1%;

however, an investor who would accept an annual return of 1% is very unlikely to exist in reality. The examples provided in specialist books on fi nance hardly ever assume discount rates of below 6%. Our highest discount rate is 15%. Such high discount rates are also rare in practice, but could actually occur in the case of

high-risk investments or high infl ation; indeed, in developing world countries for-eign investors use even higher discount rates in their present value calculations.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

102 103 104 105 106 107 108 109 110 111 112 113 114 -14 -8 132 -14 -8 -8 192 -8 -8 -8 -8 -8 1,592

0 0 0 0 0 0 0 0 0 0 0 0 4,800

Table 4-7. Cash fl ows for oak and locust trees between years 0 and 114 (author’s own compilation)

The results in Table 4-8. speak for themselves. In the case of oak, whenever the discount rate is higher than 3% all NPV is negative, indicating that the invest-ment should not be made. Conversely, in the case of locust NPV enters negative territory only with discount rates above 12%, showing that locust forests could be planted on a market basis, whereas oak forests most probably could not.

Discount rates NPV (locust) t=114 NPV (oak) t=114 NPV (locust) t=22

1% 4,415 4,512 1,325

Table 4-8. Net present value of locust and oak forests at various discount rates and terms (author’s own compilation)

Figure 4-11. Present value of locust and oak forests assuming a 114-year (and a 22-year) cycle and various discount rates (based on Table 4-8.) (author’s own compilation)

The above fi gure shows clearly that planting oak trees appears to be more advantageous than locust trees only when a discount rate of a very low 1%

is applied. With any discount rate above 1%, it would be better to plant a locust forest. That said, the ecosystem services of an oak forest are known to be much more valuable compared to those of a locust forest, although such intangible services are disregarded for the purposes of present value calculations.

With such long-term projects, it would be reasonable to use tiered discount rates. In Britain, the discounting practice of Her Majesty’s Treasury Department (Treasury, 2003) provides a good example of the discount rates which may be applied to long-term investments. The guidelines recommend the application of a discount rate of 3.5% for the fi rst thirty years of a project, followed by discount rates of 3% to 1% (see Table 4-9.).

Term in

years 0–30 31–75 76–125 126–200 201–300 301+

Discount

rates 3.5% 3.0% 2.5% 2.0% 1.5% 1.0%

Table 4-9. Discount rates recommended in HM’s Treasury Green Book (2003)

Naturally, tiered discount rates are not only suitable for the economic valu-ation of forest plantvalu-ations. Their use is desirable with utility services such as sewerage, fi xed-track public transport, investments in nature conservation, etc. These investments require public participation since private investors cannot be expected to maintain public or even quasi-public goods. In our example, an energy forest (e.g. involving the locust species) which can be clear-felled after twenty years may also be planted on a commercial basis;

however, the plantation of an oak forest with a desirable life span of 100 to 120 years will require artifi cially ‘mandated’ discount rates to show a positive net present value, but will, apart from its timber yield, also play an important role in preserving biodiversity and a healthy environment. In order to ensure the provision of such welfare-increasing services as public goods, it is appro-priate that the state should intervene and grant subsidies to compensate pri-vate investors for the lower returns on such investments. Fortunately, most states do provide such subsidies in order to maintain an adequate supply of public goods.

4.9 The economic valuation of environmental changes –

In document Sustainability, environmental economics, welfare (Pldal 111-117)