10. PLANNING FARM SYSTEMS OVER TIME

10.1 TIME EFFECTS IN AGRICULTURAL PRODUCTION
10.2 OPTIMAL USE OF TIME
10.3 TIME CLASSIFICATION OF ACTIVITIES
10.4 BASIC INTEREST-RATE CONCEPTS AND PROCEDURES
10.5 SUBJECTIVE (INTERNAL) AND OBJECTIVE (EXTERNAL) INTEREST RATES
10.6 EVALUATING FUTURE COSTS
10.7 EVALUATING FUTURE NET RETURNS
10.8 ANNUITIES: EVALUATING REGULAR COST AND RETURN STREAMS OVERTIME
10.9 PERPETUITIES: EVALUATING REGULAR COST AND RETURN STREAMS WITH AN INDEFINITE LONG LIFE
10.10 AMORTIZATION: LIQUIDATING A PRESENT VALUE OVER TIME
10.11 SUMMARY OF PROCEDURES FOR FINANCIAL EVALUATION OF LONG-TERM INVESTMENTS
10.12 EXAMPLE EVALUATION OF A PROPOSED LONG-TERM ACTIVITY
10.13 EVALUATION CRITERIA FOR LONG-TERM INVESTMENTS
10.14 DIFFICULTIES IN PLANNING FARM SYSTEMS OVER TIME
10.15 REFERENCES

'... and that old common arbitrator, Time ... '

Shakespeare, Troilus and Cressida

So far, except for consideration (i) of resources providing a flow of services over time in Section 3.3.4, (ii) of depreciation as an element of capital fixed costs in Section 5.4 and (iii) of the time frames relevant to whole-farm planning in Section 9.1, the time dimension of whole-farm systems and their subsystems has not been considered. It has been assumed that all farm activities occur concurrently within a time frame of a single season or year so that their performance can be evaluated and compared without reference to the length of time over which their resources are tied up or their output generated. However, planning and evaluation of activities extending beyond the coming season or year generally require that their time dimension (and associated uncertainty) be explicitly recognized and taken into account - and the more so, the longer the timespan of the activity, regardless of whether it is of a resource- or product-generating nature or a capital investment in the farm service matrix.

10.1 TIME EFFECTS IN AGRICULTURAL PRODUCTION

Time plays a pervasive role in all production activities but in none more so than agriculture. The reason for this is that, because of its biological nature, agriculture is very time-dependent. Compared with industrial production, agricultural production both takes more time and is generally time-related in terms of the seasons. Thus, e.g., while grain production requires some three to six months of time and the correct seasons, factory production of a car requires only a day and is independent of such seasonal elements as rainfall, temperature, day length etc.

In terms of farmers' decision making, the influence of time occurs in five ways (Dillon and Anderson 1990, Ch. 6; Doll and Orazem 1984, Ch. 7). First, there is what can be called the flexibility effect. By its nature, time gives the farmer flexibility in the form of options that would not be available if production were instantaneous. These options relate to the operation of both resource- and product-generating activities. They relate to the fact that the output of any activity is dependent on both the pattern of input injections over time and the pattern of output harvests over time. Thus the yield of a tea crop varies with both the frequency and level of fertilizer application as well as the time-pattern and intensity of plucking. Within the timespan of any particular activity, decisions about its operation (including marketing of the product, if relevant) can be revised or new decisions taken, perhaps on a sequential contingency basis relating, e.g., to market or climatic conditions. In particular, relative to production activities, time gives the farmer the opportunity to sequence input injections and/or output harvests in varying ways. Thus the farmer has to decide not only the amount of fertilizer, irrigation water, livestock feed etc. to be used, but also the pattern of its use over the coming production period. Should he or she, e.g., apply all of a crop's fertilizer at sowing or should its application be spread throughout the growing period or should it be applied only if rain is imminent? While, theoretically, such questions fall in the domain of response analysis (Chapter 8), they are not easily answered analytically (Dillon and Anderson 1990, Ch. 6). Generally, they are decided on the basis of trial-and-error experience combined with an appreciation of the constraints imposed by agronomic and biological logic. Thus farmers know that it is best if fertilizer application is complemented by rain and that it is best if livestock receive feed daily rather than less frequently.

Second, in many activities time may be a variable input under the farmer's control, i.e., a decision variable to be manipulated by the farmer through his or her choice of a time-length of run for the production process (Dillon and Anderson 1990, Section 6.8). This is particularly the case for livestock-fattening and aquaculture activities, as well as for many vegetative crops, and also relative to the replacement decision for long-term perennial tree crops and woodlots. Such time-dependence of output, of course, always exists in agriculture. Often, however, it can be ignored because the input of time required is fixed as, e.g., in the case of most grain crops once a particular cultivar has been chosen for planting. Note also that time may have an indirect effect on production through the influence of input-carryover effects as, e.g., when there is a carryover of nutrients from fertilizer application in prior production periods. The extent of such carryover is a function of the time elapsed and may influence the farmer's current decision on input use (Dillon and Anderson 1990, Section 6.9.4).

The third influence of time is that, again by its nature, it introduces uncertainty into farmers' decision-making. Because of the complex processes of change, evolution and growth that accompany the passage of time, farmers cannot be sure of the future either in terms of the outcomes of today's decisions or of the opportunities (including new products and technologies) that may become available or of the developments that may occur in their family, social, political and economic environments. Given the information available to him or her, the best that a farmer can do is to make those decisions which are expected to best achieve his or her goals. Until it becomes possible to remember the future (i.e., time becomes reversible!), there can be no guarantee that these decisions will, with hindsight, turn out to have been the best that could have been made. While uncertainty is an inexorable consequence of future time, for simplicity in exposition, planning over time is here considered without regard to the presence of uncertainty. Planning of farm systems under uncertainty is considered in Chapter 11.

The fourth influence of time arises from the fact that time is a resource which offers options in the way other resources can be used. Thus a farmer might either invest savings from this year's income in a bank at some rate of interest or reinvest these savings in the farm. Likewise, year by year over its potential lifespan, the owner of a plot of coffee has to decide whether it would be better to keep the existing stand for another year or to replant it with a new stand or to replace it by some other activity. Such choices imply alternatives in the use of time and hence an opportunity cost for time. Thus the old adage that 'time is money'. This opportunity cost of time is measured as a rate of interest (or, equivalently, as a time-preference discount rate reflecting the degree to which future payments need to be discounted to give their equivalent present value). This interest rate may be determined objectively as the rate at which money would grow over time if invested in the best available alternative. Often this objective interest rate can conveniently be taken as the market rate, i.e., the price that has to be paid to borrow money per unit of time. Such an objective interest rate is useful for purposes of economic rationalism, i.e., to assess in money terms the actual time-opportunity cost of alternative investments. More generally, however, farmers measure the opportunity cost of time subjectively (as is their right) in terms of their personal time-preference interest or discount rate which (as outlined in Section 10.5.2) corresponds to their rate of time-preference tradeoff between present and future income.

Fifth, over time, the value of money, i.e., its purchasing power, may change. Usually this takes the form of inflation whereby the value of money decreases so that fewer goods can be bought than before with the same amount of money. Sometimes, but only rarely, deflation or an increase in purchasing power may occur. In the presence of inflation or deflation, the rate of interest needs to be corrected to allow for their effect. This correction is easily made: if the nominal rate of interest is i* per annum and w denotes the annual rate of inflation (w > 0) or deflation (w < 0), the corrected or real rate of interest i is [(1 + i*)/ (1 + w) - 1] per annum. Thus, if there is an annual rate of deflation of four per cent (i.e., w = -0.04) and the nominal rate of interest is ten per cent, the real annual rate of interest will be [(1 + 0.10)/(1 - 0.04)] - 1 = 0.146 or 14.6 per cent. Note that if the rate of inflation w exceeds the nominal rate of interest i*, the real rate of interest or growth will be negative. Except for Example 1 in Section 10.4.1 below, throughout the remainder of this presentation it is assumed that the rate of inflation or deflation is zero so that i* = i.

10.2 OPTIMAL USE OF TIME

When time is a variable input to an activity, the farmer has to decide how much of it to use, i.e., for how long to let the activity run before replacing it either with a new run of the same activity or a different activity. In making such decisions, two principles should be borne in mind. The first is that a dollar in the future is generally worth less than a dollar today; and the further into the future the dollar is, the less it is worth today. The objective rationale for this is that to receive a dollar in the future, less than a dollar needs to be invested today. It may also be justified subjectively on, e.g., the basis that 'a bird in the hand is worth two in the bush'. This principle leads to the need to use interest-rate or discounted cash-flow procedures in the planning and evaluation of activities extending more than a year or two into the future.

The second principle relevant to the optimal use of time is that for processes/activities whose time length t is at the discretion of the farmer, his or her choice of t will be optimal when (a) the present value of the activity's marginal profit per unit of time at t is equal to (b) the amortized flow of profit which could be obtained by allocating that last unit of time to the best available alternative activity (which may be a new run of the same activity) (Dillon and Anderson 1990, Section 6.6.2). Part (a) of this criterion corresponds to the additional gain to be made by continuing the current activity for one more unit of time; part (b) is the cost incurred in the form of forgone profit by not using this last unit of time for the best alternative activity. Thus equality between (a) and (b) implies that the basic requirement for optimality in resource use and profit maximization, i.e., that marginal revenue equals marginal cost, is satisfied. Conversely, so long as (a) is greater (smaller) than (b), the activity should be continued (replaced). This criterion applies whether the time-length decision variable t is a matter of weeks (as in the case of broilers) or of months (as in pig fattening) or of years (as for tree crops). However, when t is only a matter of weeks or months so that time preference is not significant, the criterion for optimal choice of t simplifies to the requirement that marginal profit per unit of time be equal to average profit per unit of time (Dillon and Anderson 1990, Section 6.6.1; Doll and Orazem 1984, Ch. 7). Application of this simpler criterion is illustrated in Figure 10.1 which depicts a single run of a repetitive time-dependent production process. Profit or net gain as a function of the time-length t of a run of the activity is shown by the curve OAB. Maximum profit from a single run of the activity occurs at B with t = OH. In contrast, for repeated runs of the activity, maximum profit per unit of time occurs at A where the slope of the profit curve (i.e., marginal profit per unit of time) equals maximum average profit per unit of time AG/OG and t = OG. Thus the criterion for optimal t is satisfied at A. Clearly OG is less than OH. This reflects the fact that maximizing profit from a sequence of runs of an activity implies that the time-length of each run should be shorter than if the activity was only to be run once. The logic of this is that, in a particular run, as inputs are used beyond t = OG, marginal profit per unit of time is less than the maximum average profit per unit of time that could be obtained by using these inputs in a new run of the activity beginning at time G.

FIGURE 10.1 - Profit in relation to Time for a Particular Run of a Repetitive Production Process having Time as a Decision Variable in the Absence of Time-preference

The influence of time through its opportunity cost on the long-term planning of farm systems is the topic of this chapter. For simplicity, future outcomes are assumed to be known with certainty. In large part, assessment of time opportunity-cost effects involves the use of a variety of interest-rate or discounted cash-flow procedures which are standard to financial and actuarial analysis - see, e.g., Alien (1956, pp. 228-237), Chisholm and Dillon (1988), Mao (1969, Chs 6 and 7), Rae (1977, Chs 9, 10 and 11), Robison and Barry (1996) and Thuesen (1957, Chs 3 and 4). If done by hand, these interest-rate procedures can involve much tedious calculation and chance of error. However, they are readily available in general spreadsheet programs for personal computers such as, e.g., Microsoft Excel.

10.3 TIME CLASSIFICATION OF ACTIVITIES

10.3.1 Short-term activities
10.3.2 Intermediate- and long-term activities

Possible types of farm activities were outlined from a planning perspective in Section 9.3.1. In terms of their timespan, all these types of activities fall into one of the following three groups:

Short-term activities have a useful lifespan of a year or less. Typical examples are annual crops such as grains, pulses and oilseeds, vegetables etc. and such livestock activities as pigs, broiler chickens and pond fish when these are produced on an 'all in-all out' batch basis. However, when livestock activities are self-generating (i.e., more-or-less permanent herds of cattle, flocks of sheep etc.), they are better regarded as long-term activities.

Intermediate-term activities fall somewhere between short- and long-term activities; the dividing lines are not fixed. Their lifespan often depends on how they are managed. Thus most fodder crops can be grown either as a one-year annual or as a semi-perennial crop maintained over two, three, four ... years. This also applies to some grains: e.g., sorghum in South Asia is commonly ratooned to give three, four, five crops over two to three years and thus becomes an intermediate crop. Likewise, sugarcane is a short-term crop in Java, an intermediate two- to four-year crop in Australia, but a long-term crop of 15 years or more in southern Sri Lanka.

Long-term activities are those having a long or indefinite useful life. The lower limit is not precisely defined and the upper limit ranges from around 25 years for coffee and cacao to 65 to 80 years for coconut to over 100 years for the older varieties of tea and nutmeg.

Resource-generating activities also fall into these same classification groups, according to the length of time over which the resources are generated. Thus investment in the construction of a farm reservoir would be regarded as a long-term activity because it would generate a resource, irrigation water, over its life of 30, 40... years. However, the time dimension of activities is not always obvious: e.g., investment in the construction of a chicken shed might be a short-term activity if it is built only roughly using coconut atap intended to last only one year, or an intermediate activity if it is built using higher quality sago atap lasting four years, or a long-term activity if it is built using mud bricks.

10.3.1 Short-term activities

In both ex ante planning and ex post evaluation of the results of short-term activities, the time dimension may often be ignored. This will be the case when the purpose is comparison of activities which all have approximately similar lifespans: e.g., when the economics of a four-month paddy crop are to be compared with a six-month maize crop. Here small time differences do exist but their recognition would make little difference in the comparative evaluations. The results can be expressed, e.g., as 'crop net returns of $500 per ha vs $400 per ha', without specifying that the first crop occupies the land for four months while the second uses six months of land resource.

A second situation occurs when all the activities are again 'short-term' but there are nevertheless significant time differences between them; e.g., when a four-month paddy crop is to be compared with an 11-month cassava crop. Obviously it would now be misleading to express the comparative results as, e.g., '$500 per ha from paddy vs $700 per ha from cassava'. Here a more accurate comparison would introduce time as a specific dimension of returns, in which case the real comparison would be expressed as $500/4 = $125 per ha-month from paddy vs $700/11 = $64 per ha-month from cassava, which conveys quite a different picture.

At high latitudes and elevations, or where, because of limited water supply, the growing season is short, usually only one crop annually is possible. This fact will be understood and there is no need to attach a time dimension to the analysis. But in the wet tropics and where year-round production is possible, specification of a time dimension in the analysis of activities is often mandatory.

There is another situation where time can be ignored. This is in the analysis of the seasonal or annual economics of long-term activities, e.g., assessment of the current annual returns from tree crops (coconut, rubber etc.) and from time-stable livestock activities such as a dairy herd. In this type of analysis these long-term activities are treated as if they were short-term activities. Using such methods as presented in Chapter 7, they are evaluated relative to some short-term period; the fact that the respective activities might have had quite different cost/return profiles in the past (and may again have in the future) is irrelevant for the purpose of evaluating their current performance.

10.3.2 Intermediate- and long-term activities

The planning of intermediate- and long-term activities requires a different approach. Here the problem is to evaluate the likely future performance of, e.g., a new coffee activity over its entire future life of up to 25 years or a coconut activity over its future life of up to 70 years. However, in some situations ex ante evaluation may need to extend over only part of the activity's future life, e.g., over only the first 15 years of a new or proposed coffee crop, or over the next ten years of an old coffee crop.

Long-term ex ante evaluation is required for a range of purposes, e.g.:

(i) to determine the economics of some planned or potential long-term crop or livestock activity without reference to other comparative activities. Here the operating objective is to determine expected profitability (future expected returns vs future anticipated costs) and the time profiles of these future return and cost streams, e.g., to determine the future break-even point of the investment.

(ii) to allow comparisons among alternative crop or livestock investment possibilities. Here the operating objective is to bring the cost and return streams of all the alternatives to some common basis in time so that, e.g., the average annual return from a 20-year crop can be compared with that of a 35-year or a 65-year crop.

(iii) to obtain similar comparisons between long-term crops on the one hand and sequences of alternative short-term crops on the other.

(iv) to determine the optimal age at which to replace a long-term crop by a new activity or to determine whether an existing activity should be replaced by a new long-term activity.

Procedures for evaluating long-term activities are discussed below. In essence, they reduce to either (a) the process of discounting, i.e., the transference of future cost and return payments backward through time to the present or, less frequently, (b) the process of compounding, i.e., transferring present and future costs and returns forward through time to a common future point in time. This is done in order to bring streams of payments having different time profiles to some common basis of equivalence so that they can be compared.

10.4 BASIC INTEREST-RATE CONCEPTS AND PROCEDURES

10.4.1 Compounding or taking a present value forward through time
10.4.2 Discounting or bringing a future amount back to present value

10.4.1 Compounding or taking a present value forward through time

In its simplest and most usual form, compounding is the procedure of taking some initial amount or present value (PV) forward through time to find that future amount An which is equivalent to PV (i.e. to which PV will grow) when PV increases at some uniform annual rate i over some specified number of years n. Note that PV may be positive (i.e., a credit or a revenue amount) or negative (i.e., a debit or a cost amount). Given that in the first year PV will grow to (PV+iPV) = PV(1+i), in the second year from PV(1+i) to [PV(1+i)+iPV(1+i)]= PV(1+i)², and so on, the general formula for compounding is thus

A_n = PV(1+i)ⁿ.

This procedure of taking some initial sum through time to find its future equivalence can be applied to a wide range of problems. Compounding factors (1+i)ⁿ are listed in Table 10.1 for a range of interest or growth rates i and time periods n. Note that, throughout the presentation of this chapter, it is assumed that periods are measured in years so that i and n are on an annual basis, and that the compound interest rate i is constant over time. It is also assumed that any payments made (i.e., costs) or received (i.e., revenues) occur at year's end. If these various assumptions do not hold, the procedures outlined need to be adjusted appropriately¹ (Chisholm and Dillon 1988).

¹ In particular, if compounding (or discounting) is to occur q times per year and the interest rate per period of length 1/q years is r, then the annual interest rate i equivalent to r is given by:

i = (1+r)^q - 1.

Conversely, if i and q are given,

r = (1+i)^1/q - 1.

If the annual rate of interest is i and compounding (or discounting) is carried out q times per year, then:

A_n = PV [1 + (i/q)]^nq.

Example 1. If a family places $100 in a savings account or invests it on the farm or lends it to a neighbour, in each case at an earning rate of nine per cent annually, in the absence of inflation or deflation this $100 sum will in four years increase to an amount of A₄ = $(100)(1 + 0.09)⁴ or, taking the compounding factor (1 + 0.09)⁴ = 1.412 from Table 10.1, A₄ =$(100)(1.412) or $141. Should there be an annual inflation rate of six per cent, the real rate of interest will be [(1.09)/(1.06)] - 1 = 0.028 or approximately three per cent. In real terms, i.e., in terms of today's dollars (rather than the inflated dollars of four years' time), the $100 will grow to $(100)(1.03)⁴ = $112.

Although most commonly used in a financial context, the compounding factors of Table 10.1 are also applicable to non-financial growth problems.

Example 2. As a result of his or her development program, a farmer's annual paddy yield, now three tonnes per ha, is increasing at an average annual rate of six per cent. What yield can be expected in five years' time? Applying the compounding formula, A₅ = 3(1 + 0.06)⁵ = 3 x 1.338 (Table 10.1), the farmer can expect four tonnes per ha.

Often both the initial sum or PV and the equivalent future amount A_n are known and the rate of increase is to be determined.

TABLE 10.1 - Compound Growth Factors (1+i)ⁿ

Source: Chisholm and Dillon (1988, Appendix I).

Example 3. Paddy yields on a sample of farms are now six tonnes per ha; ten years ago they were only 3.5 tonnes. The average annual rate of increase i has therefore been such that 6 = 3.5(1+i)¹⁰ or, rearranging, 1.71 = (1+i)¹⁰. From Table 10.1, this equality condition is met at a growth rate i of about 0.055 or 5.5 per cent.

10.4.2 Discounting or bringing a future amount back to present value

Discounting is the reverse of compounding. It is the procedure for finding the present value, denoted PV, equivalent to some known future amount A_n to be paid or received n years from now. As would be expected from rearranging the formula for compounding, the formula for discounting is:

PV = A_n(1+i)n

where i is the annual discount rate or interest rate. Discount factors 1/(1+i)ⁿ = (1+i)^-n are the reciprocals of the compounding or growth factors of Table 10.1. Values of the discount factor 1/(1+i)ⁿ for a range of i and n values are given in Table 10.2.

Example 4. A farmer has fuelwood trees which will mature in four years' time and will then be worth Rs 500. What is their PV if the farmer's subjective discount rate (see Section 10.5 below) is nine per cent? Under these conditions the trees have a PV of Rs (500)/(1 + 0.09)⁴ = Rs (500)(0.708) (using Table 10.2) or Rs 354.

Example 5. In Example 2 above, crop yield was increasing. But on some other farm, because of continuing soil erosion or salinity etc., yield may be decreasing. If present yield is four tonnes and declining at an annual rate of six per cent, what will yield be in five years' time? This can be found approximately by using the reciprocal of the relevant value from Table 10.1 as PV = 4 x 1/(1 + 0.06)⁵ = 4 x 1/1.338 or, more directly, by using the relevant discount factor from Table 10.2 as 4 x 0.747 = 2.99 tonnes. Note that this example involving a negative growth rate has been conveniently approximated by reversing the time order and thus converting the problem to one involving positive growth. The accurate solution to this problem of negative growth would be found as A₅ = 4(1 - 0.06)⁵ = 4 x 0.94⁵ = 4 x 0.734 = 2.94 tonnes.

Many activities involve a stream of future income and/or costs rather than simply a single future item of income or cost.

Example 6. A farmer has an old kitul palm which is nearing the end of its useful life, but which will still yield toddy to the value of Rs 100, 70 and 40 over the next three years and which, at the end of the third year, can be cut down and sold as fuelwood for Rs 400. However, the village merchant would like to buy the palm immediately for making axe handles. If the farmer sells now and has a discount rate of nine per cent, what minimum amount should he or she charge the merchant? In the farmer's hands, the palm represents the following stream of nominal income values by years:

Year (n):	0	1	2	3	3
Nominal income (Rs):	0	100	70	40	400
Discount factor 1/(1 + 0.09)n:	1	0.917	0.842	0.772	0.772
Discounted income equivalent (Rs):	0	92	59	31	309

Assuming the nominal income payments are received at the end of their respective years, as shown above their PV can be ascertained by applying the relevant discount factors from Table 10.2. To the farmer the PV of this activity is thus Rs (0 + 92 + 59 + 31 + 309) = Rs 491. He or she would have to charge the merchant at least this price to obtain an income equivalent to that obtainable from continuing to tap the palm for a further three years.

Note that in the above cash-flow tabulation. Year 0 has been included for completeness. It corresponds to the immediate present (end of Year 0 or start of Year 1) when, in some situations, payments may occur.

10.5 SUBJECTIVE (INTERNAL) AND OBJECTIVE (EXTERNAL) INTEREST RATES

10.5.1 Objective interest rates
10.5.2 Subjective interest rates

So far, the opportunity cost of time as measured by the rate of interest or discount i has been assumed to be given. Before proceeding further, it is useful to consider the basis and justification for using some particular rate rather than another. The appropriate rate to use in any particular problem may be set by subjective (internal) factors or by objective (external) factors (Pearse and Turner 1990, Ch. 14). Some problems will involve consideration of both types of rate (as in Example 9 below).

10.5.1 Objective interest rates

Objective interest/discount rates are set by factors external to the value structure of the farm household. Money which can be put in a bank account at ten per cent or borrowed in the souk at 30 per cent is an obvious example. The farm family can only accept or reject such market-set rates. Or income might be re-invested in the farm where it will return 15 per cent and this also is determined by factors external to the household (although they are internal to the farm). This on-farm rate is also fixed, at least in the short run, although obviously the family, as farmers, can work to change it over time.

Objective or external rates may be set by such external factors as the local supply and demand for credit; or, if invested on the farm, by crop yields and prices; or by government regulation, custom, tradition or religious law. Being external and thus not under the control of the farmer, the future values of objective interest rates are subject to uncertainty. Such uncertainty is considered in Section 11.16.

10.5.2 Subjective interest rates

Subjective interest rates are set internally by the value structure of the farm household itself and thus vary both over the life of the household and between households. Whereas objective rates are given and explicit, subjective rates are implied in what goals the farm family pursues - its preference for consumption or saving; whether it prefers one activity over another; whether it judges a high-return but exploitive farm plan as superior or inferior to a low-return but sustainable plan. All these various attitudes, and their expression as decisions affecting the use of resources and outputs, can be quantified - at least implicitly - in terms of the farm family's rate of time-preference tradeoff for present vs future income, consumption or other rewards (Doll and Orazem 1984, pp. 251-255).

The subjective time-preference interest rate or discount rate is determined by many factors. Beyond the general influence of the external interest-rate environment, some of the more important of these are probably the following:

(i) Poverty or wealth in relation to a family's material needs. Other things equal, a poor family will usually have a greater preference for near-term income than for income that is to be received at some distant time in the future. It will therefore have a high discount rate for future income as compared with more immediate income and will tend to adopt a farm plan which yields short-term rather than long-term returns. If the degree of poverty is great, the family will possibly pay no attention to the long-term sustainability of its farm system. Only after today's needs are met can there be concern about resources for tomorrow. Poverty can thus be a significant cause of resource degradation (Chopra and Rao 1992; von Braun 1992).

(ii) Opportunities for making income-increasing investments, on or off the farm. Where good investment opportunities exist, the family will have a high demand for capital and other resources to exploit them. If borrowing is limited or too expensive, the family's time-preference for current farm income, from which the additional capital has to be saved, will be high. Where investment opportunities are few (e.g., on the already highly developed paddy farms of Java), there will be low demand for investment resources and time-preference will tend to be relatively low (although this might well be offset by (i) above or the following factors).

(iii) Age and the planning horizon. An individual family might not be much interested in future relative to near-term income because the decision makers are old. Their time-preference will be relatively high but again this might be cancelled by the other factors listed.

(iv) Social and cultural environment. This factor establishes the general framework within which the other factors operate. In some societies, saving and the accumulation of wealth is highly regarded; in others, social status is achieved through present consumption, lavish expenditure and generous giving.

(v) Personal characteristics of individual families. These characteristics occur within the framework of (iv) and refer to relative personal values as these determine attitudes to change and development, saving, investment, risk etc. Basically they are of a psychological nature.

TABLE 10.2 - Discount Factors 1/(1+i)ⁿ

Source: Chisholm and Dillon (1988, Appendix II).

To summarize, the way in which a family manages its farm resources and chooses between activities which have a short- or long-term payoff implies some quantitative level of preference for near-term income vs future income. This time-preference is usually positive: most families attach a higher subjective value to $100 to be received today than to $100 to be received in a year's time. Such preference is reasonable since $100 today can be invested to yield an amount of $(100)(1+i) in a year's time. However, time-preference might sometimes be negative: some families will place a higher value on the conservation of their farm for future support of their children than on their own immediate consumption of income (above some necessary minimum). The direction and degree of time-preference will be determined by factors (i) to (v) above. In turn, the direction and degree of time-preference can be measured in terms of the subjective interest rate which time-preference implies. Once this subjective interest/discount rate is measured - by implication of what farmers actually do or the choices they actually make - it can be applied to a wide range of planning problems on their individual farms.

Example 7. The farmer of Example 4 could cut his or her trees in four years' time and then sell them for Rs 500. Suppose he or she also has the option of selling the trees now, at the lower price of Rs 300 because they are still immature. If he or she in fact makes this latter choice, what subjective discount rate is implied by this decision? In the farmer's eyes, Rs 500 in four years' time is equivalent to or has a PV of Rs (500)(1+i)^-4 = Rs 300 so that the discount factor (1+i)^-4 = 0.6. For a term of four years this discount factor of 0.6 is found by interpolation from Table 10.2 to correspond to a (subjective) interest rate of 0.14 or 14 per cent. But the farmer might be willing to sell the trees now for an even lower price. Suppose this final rock-bottom price is Rs 250. His or her real discount rate then implies a discount factor of 250/500 = 0.5, which for a four-year term is found from Table 10.2 to correspond to an interest rate of (about) 19 per cent. It will be noted that this decision by the farmer has nothing directly to do with the discount or interest rates which prevail in the outside world. The equivalence of Rs 250 now and Rs 500 in the future exists only in the farmer's mind, and it arises from some combination of the underlying factors (i) to (v) above which are operative for this particular individual or household. If the farmer were poorer or richer, or had more or fewer opportunities for investment, or lived in a different socio-cultural environment, he or she might well have some other subjective discount rate.

Example 8. If three families were to be asked whether they would prefer to sell a calf now for $100 or wait and sell the full-grown ox at a higher price in four years' time, they would probably reply that (because of their positive time-preferences) they would in general prefer the money now, but that it depended on how much higher than $100 the future price was to be. Family A, a very poor family concerned with meeting its immediate needs, might say that it is willing to wait four years for the income only if it could then get $250 for the ox. Family B, which has good opportunities for developing its farm if it invests money now, might be prepared to wait if the future expected value of the ox is at least $200. Family C, which is well off, might say it would be happy to wait if a future ox price of only $150 could be anticipated. Given this information and using the relation A_n = PV (1+i)ⁿ, by interpolation from Table 10.1 the implied subjective interest rates for the families A, B and C are respectively 0.26, 0.19 and 0.11.

Example 9. In some situations it is necessary to consider both subjective and objective interest rates. Suppose, e.g., the government plans to introduce some (unrelated) agricultural development program in which the farmers of Example 8 can participate if they are willing to bear the cost. The program is guaranteed to give participants an annual return of 15 per cent (an external rate) on their outlay. If families A, B and C are equally typical, how many families could be expected to participate? A comparison of their subjective interest rates with the external rate of 15 per cent indicates that only well-off families like family C (or one third of farmers) might be interested. For families A and B, with their respective discount rates of 26 and 19 per cent, the guaranteed future return of 15 per cent is not high enough to be attractive. Respectively, they would need a return of at least 26 or 19 per cent.

10.6 EVALUATING FUTURE COSTS

Discussion so far has concerned the equivalence of future revenues or returns. Exactly similar procedures are used respectively to determine the present value of future costs or, less frequently, the future value of present costs. There are three main situations in which such calculations are necessary.

First, in order to compare the future income stream from a long-term activity against its costs, and so determine the activity's net return over its lifetime, it is necessary to bring both to the same time basis. The most convenient common basis is usually the PV of each of these streams (although other time bases are also possible.)

Example 10. A farm activity will mature and return the farmer Rs 1 000 in four years' time. It will also require outlays on inputs of Rs 80 now and Rs 100 in three years' time. What are activity net returns if the relevant interest rate is nine per cent? Problems such as this are conveniently sketched in an input-output time chart as shown in Figure 10.2. On an annual accounting basis (Chapter 7), the time profile of net returns to the activity over the next four years would be Rs -80, 0, 0, -100, 1 000. But if concern is with the performance of the activity over the whole of its life rather than in its one-year phases, the PV of total returns is Rs (1 000)(0.708) = Rs 708 and the PV of total costs is Rs [(80)(1.000) + (100)(0.772)] = Rs 157. The activity therefore has a net worth of Rs (708 - 157) = Rs 551 in terms of PV. Note that, as made clear by the time chart of Figure 10.2, in applying interest-rate procedures it is important to specify whether payments occur at the start or end of the relevant time periods.

FIGURE 10.2 - Example of an Input-output Time Chart

The second situation involving the discounting of future cost occurs in making provision for the future replacement/repair of items of physical farm capital (Section 5.4).

Example 11. An irrigation channel will require desilting costing Rs 1 000 in five years' time. What provision should be made now for this future expenditure if the interest rate is nine per cent? Using Table 10.2, a depreciation fund of Rs 650 if established now would generate the necessary Rs 1 000 in five years' time.

The third situation arises where a single future stream of costs is to be evaluated, or where two or more such streams are to be compared.

Example 12. A farmer has budgeted out the likely per unit costs of establishing passionfruit and cinnamon activities. These data are listed below. Given the farmer has a time-preference rate of ten per cent and assuming that the respective costs are incurred at the end of each year, which activity has the higher establishment cost?

Activity	Establishment Cost at End of Year (n)				Nominal Total	PV
	0	1	2	3
Passionfruit (Rs):	0	1 200	500	300	2 000	1 729
Cinnamon (Rs):	0	300	900	800	2 000	1 617

In nominal (i.e., undiscounted) terms, both crops have the same cost of Rs 2 000 over the establishment period of three years. However, because of the farmer's time-preference and the difference in sequencing of the respective cost streams, the PV of the cost of passionfruit establishment (Rs 1 729) is higher than that of cinnamon (Rs 1 617).

10.7 EVALUATING FUTURE NET RETURNS

Planning of a long-term activity involves finding the PV of the activity's stream of annual net returns (i.e., annual 'return minus cost' differences). This is known as discounted cashflow analysis.

Example 13. The separate annual cost and return streams for the first seven years of a proposed cardamom activity are shown in lines 1 and 2 of Table 10.3 and annual return minus cost differences or net returns in line 3. Note that net returns are constant (in nominal terms) in this example for Year 6 onwards. It is necessary to apply the appropriate discount rate of, say, ten per cent only to line 3. The relevant discount factors (from Table 10.2) are shown in line 4. Extended to the full 30-year life of the activity, financial evaluation might be largely in terms of line 6 which shows cumulative total discounted net returns to the end of each year. (However, as discussed in Section 10.13, there are also other criteria pertinent to evaluation of long-term investments.) Note that Year 7 is the first year having a positive cumulative PV, i.e., it will take seven years before the PV of the returns' stream exceeds that of the costs' stream. The break-even period for this cardamom investment is thus seven years.

TABLE 10.3 - Example of Discounted Cash-flow Analysis

Item	Year
	0	1	2	3	4	5	6	7
(1) Costa ($)	500	300	900	800	200	200	200	200	...
(2) Returna ($)	0	0	0	100	500	1 000	1 600	1 600	...
(3) Net return ($)	-500	-300	-900	-700	300	800	1 400	1 400	...
(4) Discount factorb	1.000	0.909	0.826	0.751	0.683	0.621	0.564	0.513	...
(5) PV of net return ($)	-500	-273	-743	-526	205	497	790	718	...
(6) Cumulative PV ($)	-500	-773	-1 516	-2 042	-1 837	-1 340	-550	168	...

^a Payments are assumed to occur at year end.
^b From Table 10.2 with i = 0.10.

As noted previously, discounted cash-flow evaluation of a long-term activity will extend over the full 30-, 40-, 50-... year life of the activity if the total crop cycle is of interest. Or it might be limited to some shorter period of only, say, five or ten years. This will depend on analytical circumstances and the planning horizon of the farmer which might be much less than the lifespan of a very long-term crop.

10.8 ANNUITIES: EVALUATING REGULAR COST AND RETURN STREAMS OVERTIME

10.8.1 Terminal value of an annuity
10.8.2 Annuity equivalent to a future lump sum
10.8.3 Present value of an annuity

So far the costs and returns used in the examples have been either single discrete quantities or some irregular series of payments occurring at points in the life of the activities. Fortunately, as in the example of Table 10.3, many long-term activities become fairly stable after their establishment years; from this point on they often generate rather uniform streams of annual costs and returns. From that point in time when they become uniform - or can be assumed to be uniform without excessive distortion of the facts - they can be evaluated as annuities. This greatly reduces the required calculation effort. Indeed, it often makes practical sense to regard cost and return streams as annuities even when, strictly speaking, they are not.

An annuity is a series of equal annual payments which occur over some medium or long but limited time period. These payments are usually of a future nature and may be either incoming (i.e., revenues and thus positive) or outgoing (i.e., costs and thus negative). Annuities are particularly useful in evaluating long-term production activities or investments. The usual problems to which annuities are applied involve either (a) finding the final terminal amount which the annuity will generate over its life or (b) finding the PV of this future amount or, equivalently, of the annuity.

10.8.1 Terminal value of an annuity

The terminal value A_n of an annuity A payable at the end of each year for a period of n years is the value to which the series of annual payments will accrue if, as each is received, it is invested at the compound rate of interest i until the end of Year n. This terminal value is obtained as:

A_n = A[(1+i)ⁿ - 1]/i.

Values of the annuity factor [(1+i)ⁿ - 1]/i are easily calculated using the compound growth factors of Table 10.1.

This terminal value A_n actually consists of two components: (i) the total of all successive uniform payments over the life of the annuity, i.e., an amount equal to nA, and (ii) the total interest earned by all of these payments on the assumption that each payment is invested at some uniform interest rate over the remaining life of the annuity. Thus the terminal value of a $100 annuity over five years at nine per cent would consist of $100 received at the end of the first year with interest on this for four years; plus $100 received in the second year with interest on this for three years etc. The total amount by the end of the fifth year would be $599 made up of $500 from the annual payments plus $99 interest earned on these payments. This terminal value is calculated, using the relevant annuity factor [(1 + 0.09)⁵ - 1]/0.09 = 0.539/0.09 = 5.989, as A₅ = $(100)(5.989) = $599.

Example 14. A stand of coconut palms is expected to yield an annual net return of $200 over the next 20 years. As each of these income payments is received, the farmer will invest it at a rate of eight per cent. At the end of the 20 years, what sum will have been accrued by this coconut + investment activity? This terminal value is found as A₂₀ = $(200)(1.08²⁰ - 1)/0.08 or $(200)(45.75) = $9 150. Note that this value is in nominal dollars of 20 years hence. It is not in terms of dollars in hand today.

10.8.2 Annuity equivalent to a future lump sum

For a presumed interest rate i, the annual payment or annuity A equivalent to a lump sum A_n due at the end of n years is obtained as:

A = A_ni/[(1+i)ⁿ - 1].

This is known as the sinking-fund formula since it gives the amount A which should be put aside at the end of each year 1, 2, 3... n and invested at an annual interest rate i to the end of Year n (i.e., invested in a 'sinking fund') in order to meet a lump-sum commitment due at the end of Year n. This lump-sum commitment might be, e.g., a debt, a dowry or a sum needed to replace worn out or obsolescent capital items. Values of the sinking-fund factor i/[(1+i)ⁿ - 1] are easily calculated using the compound growth factors of Table 10.1.

10.8.3 Present value of an annuity

For most purposes, whether an annuity represents a stream of future net income (as in Example 14) or of costs, the value of the annuity will need to be assessed on the basis of its PV. Thus, if the coconut activity of Example 14 is to be compared with other activities which have different lengths of life and different time profiles of costs and returns, it is necessary that all these activities be assessed on some standard time basis. The most convenient such basis is usually their PV. This is calculated as:

PV = A_n(1+i)ⁿ = A[(1+i)ⁿ - 1]/[i(1+i)ⁿ]

where, as before, payments of size A occur at the end of each year over the n-year life of the annuity and i is the presumed rate of interest. The annuity discount factor, represented by the quotient [(1+i)ⁿ - 1]/[i(1+i)ⁿ] in the above equation, is given in Table 10.4 for a range of i and n values.

Example 15. What is the PV of the 20-year stream of coconut + investment income of the previous example? As noted, this is a 20-year annuity of $200 at eight per cent. The PV of this is found by applying the appropriate annuity discount factor from Table 10.4: PV = $(200)(9.818) = $1 964. At first glance there is such a large difference between the terminal value of this annuity ($9 152. Example 14) and its PV equivalent of only $1 964 that a check on the results might seem warranted. For this the $9 152 amount, which is due in 20 years' time, can be discounted directly using the appropriate discount factor from Table 10.2: PV = $(9 152)(0.214) = $1 958. Apart from a slight difference due to rounding, no error is present. The large difference between the value of $9 152 in 20 years' time and the value of $1 964 today indicates dramatically the effects of time and the discount rate in the valuation of long-term activities.

Example 16. If the cardamom proposal of Table 10.3 has a lifespan of 30 years, what is its PV if i = 0.10? To the end of its break-even period, Year 7, the activity has a PV of $168. Thereafter, the activity constitutes an annuity of $1 400 for n = (30 - 7) = 23 years. The value of this annuity discounted to the start of Year 8 (or end of Year 7) is $(1 400)(8.883) = $12436. Discounting this value back a further seven years to the present, its PV is $(12 436)(0.513) = $6 380. Thus the full PV of the 30-year cardamom activity is $(168 + 6 380) = $6 548.

Example 17. An ageing family needs funds but at the same time wants to reduce its work load. Its members will not sell their land, but are considering selling leases to operate the following activities on their land: (a) a stand of coconut palm with 15 years of useful life remaining and returning $100 net annually; (b) a block of coffee with ten years of useful life remaining and returning $50 net annually; and (c) a grove of fuelwood trees which will be ready for harvesting in six years' time and will then be worth $150. The old coconut palms will also have a residual value of $120 as construction timber in the 15th year. If the family specifies a discount rate of nine per cent, what are reasonable prices at which to sell the leases for these respective activities? For the coconut activity, annual net returns constitute a 15-year $100 annuity with, from Table 10.4, a PV of $(100)(8.061) = $806 while the sale of timber for $120 in Year 15 has, using Table 10.2, a PV of $(120)(0.274) = $33. The price for the 15-year coconut lease should thus be at least $(806 + 33) = $839. Annual net returns from the coffee activity constitute a ten-year $50 annuity with a PV of $(50)(6.418) = $321 so the price of the ten-year coffee lease should be at least this much. Likewise, the sale of fuelwood in six years' time for $150 implies a six-year lease price of no less than $89 for this activity. These prices would only be attractive to buyers who had a discount rate of less than nine per cent. Thus a buyer with a discount rate of seven per cent would value the 15-year coconut lease at $(100)(9.108) + (120)(0.362) = $954 which compares favourably with its suggested offer price of $839.

Note that if the family in the above example were to sell its land, as distinct from the activities supported by that land, and if it can be assumed that such land will generate a more-or-less uniform and constant stream of future income, then they would be selling a perpetuity rather than an annuity. Perpetuities are discussed in the following section.

10.9 PERPETUITIES: EVALUATING REGULAR COST AND RETURN STREAMS WITH AN INDEFINITE LONG LIFE

10.9.1 Perpetuities in the valuation of land and farms

A perpetuity is an annuity that continues on forever. Strictly speaking, there is no such thing; however, many cost and/or return streams can be assumed to be perpetual and this greatly facilitates their evaluation. The PV of a perpetuity is obtained as:

PV = R/i

where R is the perpetual annual uniform payment (either revenue or cost) and i is the relevant interest rate.

Example 18. If the appropriate interest rate is ten per cent, what is the PV of a hectare of paddy land that annually earns a net return of $500? Assuming that the land is going to remain in this use indefinitely, its annual yield of $500 is an annuity without apparent end, thus a perpetuity. Its PV is $500/0.10 = $5 000.

Example 19. Assuming an interest rate of ten per cent, what is the PV of a hectare of young seedling tea expected to yield a net return of $600 annually? Seedling tea has a very long lifespan and may well continue producing for 80, 90,... years. Its income stream is not a perpetuity but is close to being so. Its value therefore can be estimated as $600/0.10 = $6 000. In fact, whether the tea is regarded as a perpetuity or as a very long-term annuity would not make much practical difference. Valuing it as a 50-year annuity would give a PV of $(600)(9.915) or $5 949 which, given the uncertainties attached to such a long period, is in a practical sense about the same as $6 000.

TABLE 10.4 - Annuity Discount Factors [(1+i)ⁿ - 1]/[i(1+i)ⁿ] for obtaining the Present Value of an Annuity: PV = A[(1+i)ⁿ - 1]/[i(1+i)ⁿ]

Source: Chisholm and Dillon (1988, Appendix III).

10.9.1 Perpetuities in the valuation of land and farms

Perpetuities are used widely in the valuation of land and farms. There are three main alternative bases for such valuation: market value; value based on cost of production of the land or similar asset; or economic value based on future productivity of the resource.

Obtaining a market-based value is purely empirical: a piece of land is worth exactly what some 'willing buyer' is prepared to pay for it. If a willing buyer is not on hand, then reference is made to the prices which other willing buyers have recently paid for similar land. Such a market-based value might approximately correspond to productivity-based value (below), or differ considerably from it. In commercial Western societies there is usually a fairly close relationship between market-based and productivity-based values. But in most Asian societies people are usually willing to pay higher prices for land than would be justified by reference to its productivity alone. This is because they are purchasing land for its other attributes as well, i.e., its properties as a secure store of wealth, as an insurance policy against bad times or for the social prestige which land ownership confers.

In agricultural societies where a land market has not yet emerged and where there is little market trading of agricultural products, the value of agricultural land is probably best determined on the basis of its cost of production - which usually implies the value of the labour required to create new farms from a virgin environment (as, e.g., in new settlement areas of Kalimantan and West Irian).

In commercial situations, land and farms are usually valued according to an estimate of the value of their future productivity. Here 'value' has an economic basis rather than a 'market opinion' or cost-of-production basis. As noted in Example 18, this future productivity is regarded as a perpetuity. (But nonetheless the legal profession in most Western countries prefers valuations based on market price.)

10.10 AMORTIZATION: LIQUIDATING A PRESENT VALUE OVER TIME

From Section 10.8.1 the terminal amount A_n to which an n-year stream of uniform future payments will grow is found by evaluating it as an annuity; the PV of this terminal amount (and thus of the annuity) can then be found by discounting it. Or the PV of the annuity can be found directly by using the annuity discount factors of Table 10.4. Amortization is the reverse of this procedure. A PV or lump sum is amortized - i.e., liquidated or literally 'killed' - by taking it forward through time as an equivalent stream of equal (usually annual) payments. The formula for finding the size of each of these equal future payments A is:

A = PV[i(1+i)ⁿ]/[(1+i)ⁿ-1]

where A is the annual payment and PV is the sum to be amortized over n years at an interest rate of i. As would be expected, this formula is the reverse of the formula for the PV of an annuity A. The amortization factor [i(1+i)ⁿ]/[(1+i)ⁿ - 1] is simply the reciprocal of the annuity discount factors of Table 10.4.

Probably the most common use of amortization is in calculating the repayment schedule of a fixed-term loan, i.e., 'killing off the amount borrowed by repaying it in equal annual instalments.

Example 20. A farmer borrows a sum of $400 at nine per cent compound interest and agrees to repay it with a series of equal annual payments over 15 years. What will be the size of each uniform payment A? From Table 10.4 the amortization factor is 1/8.061 = 0.124. Each payment will thus be $(400)(0.124) = $49.60. Moreover, since each uniform payment consists of some amount of principal and some amount of interest, and since the farmer will repay a total of $(49.60)(15) = $744 while he or she borrowed only $400, the farmer will pay a total interest charge of $(744 - 400) = $344 on this loan.

Amortization is especially useful in bringing irregular series of future costs or returns to the equivalent basis of a uniform series. In this way, series having different time profiles can be compared as uniform streams rather than simply on a lump-sum PV basis.

Example 21. A farmer can install either of two alternative irrigation systems: system A which involves constructing a dam and pumping water through sprinkler pipes; or system B which involves pumping directly from a creek and using gravity-flow surface application. Both systems will yield the same increase in crop returns, $500 per year. But these systems will have different construction and future maintenance costs for periodic desilting of channels, replacement of pipes and pumps etc. The farmer wants to know: (a) the relative annual cost of each system and (b) the expected increase in annual net returns using each system. Two other pieces of information are necessary: the length of the farmer's planning horizon and the appropriate interest rate. Although both systems would - if maintained and periodically renovated - have an indefinite life, the farmer specifies the planning horizon to be 20 years and the relevant interest rate as 15 per cent. The time-schedule of construction and periodic system maintenance costs is given as follows:

Planning year:	0	1	7	10	15
System A costs ($):	0	1 000	200	600	100
System B costs ($):	600	500	0	400	400
Discount factor:	1	0.870	0.376	0.247	0.123

The first step is to bring each cost stream to its equivalent total PV by discounting each future cost item (using Table 10.2) and summing. These total PV sums and their amortized equivalents are:

	Total PV of Costs	Amortization Factor	Amortized Annual Value of Costs
System A:	$ 1 106	0.160	$ 177
System B:	$1 183	0.160	$ 189

Increased crop returns from both systems are already on an annual basis, $500 per year. To compare system costs with these returns it is therefore convenient to bring costs to this same annual basis. System A has a nominal total cost of $(1 000 + 200 + 600 + 100) = $1 900 but when these separate items - which occur at different points over time - are brought to a common basis (by discounting), they have a total PV of $1 106. But returns are on an annual basis; so to compare returns vs costs, the costs of $1 106 must be 'spread out' or amortized over the 20 years of the investment. The annual equivalent of $1 106 is $(1 106)(1/6.259) = $177 (using Table 10.4). The annual-equivalent costs of system B are found in the same way as $189; and both can be compared with the annual increase in returns of $500. Thus system A implies an annual increase in net returns of $(500 - 177) = $323 while system B yields $311. If the farmer wants only to compare the two alternatives on a total basis, i.e., over the full 20-year planning horizon, amortization is not necessary. The comparison can be based on the total PV of the cost streams, $1 106 and $1 183, vs the PV of the associated returns stream of $500. $500 annually over 20 years is an annuity: its PV for i = 0.15 is $(500)(6.259) or $3 129 (Table 10.4). The comparison then is $ 1 106 vs 1 183 vs 3 129.

Amortization can also be used to calculate the regular amount that should be invested at the end of each year in a depreciation fund to cover the replacement cost of capital items as they become worn out or obsolescent.

Example 22. A farmer's irrigation pump will need to be replaced ten years from now at a cost of $1 000. How much should the farmer invest each year in a depreciation fund to finance this replacement if the relevant interest rate is eight per cent? The amount to be invested at the end of each year constitutes a ten-year annuity and may be found directly by applying the sinking-fund formula of Section 10.8.2. Thus A = $(1 000)(0.08)/(1.08¹⁰ - 1) = $69. Alternatively, as shown in Figure 10.3, the annual depreciation cover may be found by first finding the PV of the $1 000 replacement cost and then amortizing this amount to determine the needed equivalent annuity. Thus PV = $(1 000)/(2.159) = $463.18 so that A = $(463.18)(0.08)(2.159)/(1.159) = $69.

10.11 SUMMARY OF PROCEDURES FOR FINANCIAL EVALUATION OF LONG-TERM INVESTMENTS

The interest-rate procedures outlined in preceding sections are summarized in Figure 10.3 which shows schematically the relationships between PV, A and A_n assuming an annual interest rate of i and a period of n years. Application of these discounted cash-flow procedures to the evaluation of a long-term farm activity or investment implies the following sequential steps:

(i) Determine the time-perspective from which the activity is to be evaluated: whether ex ante, limited ex ante, current year or ex post.

(ii) Define the time period over which the activity is to be analysed. This might or might not correspond to (iii) below.

(iii) Define the time profile of the activity. This is conveniently done in terms of a yield curve sketched over the life of the activity (as in Figure 10.4 below). Data for such yield curves may be available from records or obtained by means of a survey of farms with comparable conditions.

(iv) Based on this time profile, prepare a set of budgets giving the cost/return streams for the activity over the time period to be analysed.

(v) Bring all relevant cost/return streams from (iv) to a common basis in time using an appropriately chosen interest or discount rate.

(vi) Select and apply appropriate evaluation criteria to (iii), (iv) and(v). There are several alternative criteria (Section 10.13 below).

FIGURE 10.3 - Relationships between a Terminal Value (A_n) due at the End of Year n, its Present Value (PV) and an Equivalent Annuity (A) for an Interest Rate of i

Before applying these steps to an illustrative example, the time-perspective of evaluation warrants a little further discussion. An ex ante perspective is required if the problem is the forward planning of an activity over its entire future life. A limited ex ante perspective is appropriate if planning concerns only some part of the future life of the activity: the first 20 years of life of a 70-year coconut crop, or the next ten years of an already mature nutmeg crop etc.

An ex post perspective is required if the problem is to evaluate the past performance of some existing or past crop, over all or pan of its lifespan. Such backward-looking analysis is usually limited to historical studies of old crop stands, but the purpose might be to obtain agro-economic guides to the planting of future crops. Ex post analysis in the form of comparative analysis is routinely applied to short-term crops and farms growing such crops (Chapter 7). It is also applied to the immediately past phases of long-term crops (current-year perspective, below). It is not often applied to full evaluation of all past phases of long-term crops (e.g., for a fall evaluation of a tea crop planted in 1910), but it is often applied to some particular aspect of the historical past; e.g., the only way to determine the likely future impact of typhoons on yields and returns of coconut in parts of the Philippines is to analyse the effects of past typhoons on past crops - and the farther back in time such studies can be extended the more valid will be the guides obtained for future planning (Chapter 11).

A current perspective is required if all past and likely future events can be ignored and attention restricted to what happened to an activity in the immediate past few months or year and what will happen in the next few months or year. The time dimension is ignored in such analyses.

10.12 EXAMPLE EVALUATION OF A PROPOSED LONG-TERM ACTIVITY

The general steps (i) to (vi) above are now applied to the evaluation of a proposed cardamom activity.

(i) Time-perspective: A proposed cardamom activity is to be evaluated (a) to determine the probable economic performance of the investment measured in financial terms (money returns in relation to money costs) and the break-even point in time when returns will have covered costs, and (b) to obtain these data in a form which will allow financial comparison of this activity with other possible investments. The time-perspective is thus ex ante.

(ii) Time period: For planning purposes, the cardamom activity is postulated to have an economic lifespan of 25 years from planting. It is judged by the farmer that it would then be more profitable to replace the cardamom rather than continue it for another year.

(iii) Time profile: The time profile of a long-term crop such as cardamom is best constructed in two stages. A yield curve (Figure 10.4) is sketched over the period extending from initial land preparation to the end of the plants' useful life; then - as per (iv) below - budget tables of inputs, costs, outputs and returns are prepared on the basis of this curve. The yield curve allows the sequential economic crop phases to be distinguished and cost and return items identified as, e.g., from the example cardamom yield curve of Figure 10.4:

Phase 1 (Years 1 to 3): land preparation, planting and annual maintenance costs; no returns.

Phase 2 (Years 4 to 15): routine maintenance plus harvesting, processing and marketing costs; yields annually increasing.

Phase 3 (Years 16 to 30): same as Phase 2 but yields decreasing.

(iv) Activity budgets: Three budgets are needed. The first, a base budget as presented in Table 10.5, details the costs of crop establishment and maintenance on a per unit (here per ac) of activity basis over the years from planting up to when crop maintenance costs become stable, here from Year 1 to Year 4 inclusive. Because labour is usually the most important input, it is a useful practice to show labour units explicitly, not just labour cost. (The budget can then easily be up-dated by applying new unit-labour costs as these might change in future years.) For most long-term crops, annual maintenance inputs/costs will be fairly uniform from the year in which the crop begins to produce (its year of maturity) to the end of its useful life, here Rs 930 annually as shown in Table 10.5 for Year 5 onwards.

The second base budget, as shown in Table 10.6, refers to the unit costs of harvesting, processing and marketing the variable amounts of annual output. This is a 'side' budget which specifies the above costs on a per unit of output basis, not on a per unit of land basis (as was done in Table 10.5), because the levels of output per ac to which these unit costs are applied will change annually according to the yield curve of Figure 10.4. (Of course, if the yield curve is fairly constant over the crop's lifespan, output and returns can also be budgeted on a per ac of crop basis.)

The third budget, as presented in Table 10.7, is a tabulation of returns and costs for each year of the activity. It is derived from the base data of Tables 10.5 and 10.6 and Figure 10.4. The object is to obtain line 5, the stream of annual net returns. These net returns are nominal undiscounted amounts. In themselves they have little significance until they are transformed to a common basis in time.

(v) and (vi) Evaluation of equivalent net returns: Bringing the cardamom cost and return streams of Table 10.7 to a common basis in time and criteria for their evaluation are considered in the following Section 10.13.

FIGURE 10.4 - Yield Curve for Cardamom Investment Example

TABLE 10.5 - Inputs and Costs for Establishment and Maintenance of Cardamom (per Acre Basis)

Item	Establishment				Year 5 onwards
	Year 1	Year 2	Year 3	Year 4
Labour units (days/operation/year):
Thin jungle	30
Clear planting points	20
Roads, paths, drains	10	5	5		4
Plant shade	2
Plant cardamom	35
Weed	25	20	20	20	20
Fertilize	10	10	10	14	14
. . .	.	.	.	.	.
. . .	.	.	.	.	.
Pest control	2	2	3	3	5
Total labour units:	140	52	64	51	60
Total labour costs (Rs):	1400	520	640	510	600
Material and services (cost/operation/year) (Rs):
Plants	250	50
Chemicals, sprays		20	30	50	50
Fertilizer	100	120	120	240	240
Transport	50
. . .	.	.	.	.	.
. . .	.	.	.	.	.
Tools	40	30	20	20	20
Total material and services costs (Rs):	480	240	200	350	330
Total all costs (Rs):	1880	760	840	860	930

10.13 EVALUATION CRITERIA FOR LONG-TERM INVESTMENTS

Evaluation criteria for farm systems and subsystems were discussed in Section 6.2 (stability, diversity, flexibility, sustainability etc.). These apply to all activities, enterprises and whole farms. In particular, relative to long-term investments, sustainability is of crucial importance from both a private and a social perspective. It is in both the farmer's and society's interest that her or his activities do not cause the degradation of resources either on the farm itself or external to the farm. Long-term investments should therefore always be evaluated from a sustainability and environmental perspective (Markandya 1994). There are also other selection/evaluation criteria of a financial nature which apply specifically to long-term activity/system investments. The most important of these are listed in Table 10.8 and briefly discussed in the context of the cardamom example of Table 10.7.

TABLE 10.6 - Derivation of Cost of Harvesting and Processing Cardamom (Rs per Cured Pound)

Basis: a gang of pickers harvesting 440 lb of green cardamom per day
		Cost/440 lb green
		(Rs)
Harvesting
	Field supervisor	15
	Contract picking	300
Processing
	Labour for weighing and drying	70
	Fuel for drying	140
	Labour for grading and packing	10
	Sacks	40
Total direct cost of harvesting and processing		575
Cost per lb of green cardamom		1.31
Cured-to-green recovery rate ('out-turn')		20%
Cost per lb of cured cardamom		6.55

TABLE 10.7 - Revenue and Cost Streams for Cardamom over 25 Years (Rs per Acre)

Item	Year							Nominal Total
	1	2	3	4	5	6	25
(1) Revenue	0	0	0	700	1 050	1 400	1 890	55 370
(2) E + M costa	1 880	760	840	860	930	930	930	23 870
(3) H + P costb	0	0	0	145	218	290	392	11 475
(4) Total cost	1 880	760	840	1 005	1 148	1 220	1 322	35 345
(5) Net revenue	-1 880	-760	-840	-305	-98	180	568	20 025

^a E + M = establish and maintain; cost from Table 10.5.

^b H + P = harvest and process; cost calculated as cured yield (from Figure 10.4) multiplied by Rs 6.55 (from Table 10.6).

Financial evaluation of long-term farm activities or investments can be on the basis of a number of factors, depending on the Mode, Field and purpose of the analysis (Section 2.1). In all except the most simple cases, evaluation would be by reference to a set of factors rather than to only one. As they are derived for the present cardamom example, these factors are listed in Table 10.8. Factors (1) to (8) are relevant for on-farm or on-estate decision making (i.e., farm management in Field A). Factors (9) to (11) would also be considered if this cardamom activity were part of some larger public investment, such as a publicly funded settlement scheme (i.e., farm management in Field C). In this latter case, the listed factors would be used, e.g., to decide whether the best crop on which to base the scheme is cardamom or robber or tea etc. In the following discussion of the criteria of Table 10.8, an annual interest rate of ten per cent is assumed for discounting and amortization.

TABLE 10.8 - Example of Some Factors relevant to the Choice and Evaluation of Long-term Investments^a

For farms and estates (Farm Management in Field A)	Cardamom
(1) Total life of the activity from establishment:	25 years
(2) Time to maturity (i.e., initial yield):	4 years
(3) Time to full maturity (i.e., maximum yield):	15 years
(4) Operating break-even point:	Year 6
(5) Investment break-even point:	Year 14
(6) Activity establishment costs per acre (Years 1 to 4):	Rs 4 340
(7) Activity net PV per acre:	Rs 2 641
(8) Amortized annual equivalent of net PV per acre:	Rs 291
For public projects (Farm Management in Field C)
(9) Benefit-cost ratio:	B/C = 1.22
(10) Foreign exchange benefit-cost ratio:	B/C = 2.16
(11) Internal rate of return on the investment:	IRR = 15.3

^a Based on the cardamom example of Figure 10.4 and Tables 10.5, 6 and 7.

(1) Activity total life, here specified as 25 years, might or might not be relevant to a farmer/estate manager. A long productive lifespan is generally a positive attribute, but not if the farmer's planning horizon is limited; or if the pace of genetic improvement is such that an estate manager knows that, whatever variety is planted now, it will be able to be replaced by a superior one in the relatively near future (as, e.g., with rubber).

(2) Years-to-maturity, here four years, would be an important consideration on poor farms if the activity under consideration is a food crop (jak, breadfruit etc.). On very poor farms it might well be the dominant one; factors (4), (5), (7), (8) might be irrelevant in this case.

(3) Years to full production maturity, here about 15 years, is also sometimes a critical factor, e.g., inhibiting the planting of some of the palms which are notoriously slow developers, regardless of how productive they might eventually become and how low their cost of establishment.

(4) Years to operating break-even point, here Year 6, when current annual return first exceeds current annual costs. This would be an important consideration on farms/estates experiencing cash-flow problems.

(5) Years to investment break-even point, here Year 14 when, for the first time over the activity's life, the cumulative PV of total costs is exceeded by the cumulative PV of total returns. This factor, too, would be important for farms/estates having cash-flow problems. Where the investment funds must be borrowed, the interest burden on this debt over the period up to when the investment reaches its break-even point might well be the single most important factor inhibiting development.

(6) Establishment costs, particularly for labour in the initial year(s), might encourage or discourage adoption of the activity independent of its possible attractiveness in future years.

(7) Activity net PV is obtained by summing the discounted values of the items of line 5 of Table 10.7. This is the first of the financial values by which the activity might be evaluated. As derived in column (8) of Table 10.9, the PV of the proposed cardamom activity is Rs 2 641 per acre.

(8) Amortized net PV is factor (7) transformed to an annual basis over the life of the investment. Here it is Rs (2 641)(0.110) = Rs 291 (using the amortization factor for ten per cent over 25 years, 1/9.077 = 0.110, from Table 10.4).

TABLE 10.9 - Example of Worksheet for obtaining the Benefit-cost Ratio and Internal Rate of Return of a Long-term Investment^a

Year	Total Cost (Rs/ac)			Total Return (Rs/ac)			Net Return (Rs/ac)
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Nominal	Discounted		Nominal	Discounted		Nominal	Discounted
		at 10%	at 13%		at 10%	at 13%		at 10%
0	0	0	0	0	0	0	0	0
1	1 880	1 709	1 664	0	0	0	-1 880	-1 709
2	760	628	595	0	0	0	-760	-628
3	840	631	582	0	0	0	-840	-631
4	1 005	686	616	700	478	429	-305	-208
5	1 148	713	623	1 050	652	570	-98	-61
6	1 220	688	586	1 400	790	672	180	102
7	1 293	663	550	1 750	898	744	457	235
8	1 365	636	513	2 100	980	790	735	344
9	1 452	616	483	2 520	1 069	839	1 068	453
10	1 535	591	452	2 940	1 133	866	1 405	542
.	.	.	.	.	.	.	.	.
.	.	.	.	.	.	.	.	.
25	1 322	122	62	1 890	174	89	568	52
Total	35 345	12 121	9 539	55 370	14 762	10 675	20 025	2 641

^a Based on the cardamom example of Table 10.7.

Other factors can be obtained from extensions of Table 10.9, e.g., assuming that borrowed funds are to be used, additional relevant factors might be the total amount of the necessary loan and its total interest cost. (Note, however, that many farmers do not like borrowing, or will not or cannot borrow beyond a certain limit regardless of how profitable the investment might eventually turn out to be.)

The remaining three factors of Table 10.8 are relevant for the evaluation of large public investment projects, i.e., to farm management in Field C rather than Field A (Section 2.1.7).

(9) The benefit-cost ratio (B/C) is used primarily for making rapid comparisons among roughly similar alternative investments - see, e.g., Gramlich (1990) and Sinden and Thampapillai (1995). In the present example 'benefits' are simply the activity gross return stream, line 1 of Table 10.7. This is transposed to column (4) of a new table, Table 10.9. Here each annual gross return item is discounted at ten per cent and the results shown in column (5). They are then summed to obtain total discounted gross return over 25 years of Rs 14 762. The same is done for the annual cost stream of line 4 of Table 10.7 and the results shown in column (2) of Table 10.9. These also are then summed to obtain total discounted activity cost of Rs 12 121. The B/C ratio for i = 0.10 is then 14 762/12 121 = 1.22. As calculated, this ratio is purely a measure of an investment's financial attractiveness. It is of limited validity as a measure of an investment's total desirability in relation to factors (1) to (8), or factor (10) below, or - most importantly - in terms of the environmental or social merit or impact of an investment.

(10) The foreign exchange B/C ratio is the same as (9) except that only those cost and return components of the investment which require or generate foreign exchange are now considered. One would proceed by inspecting the base budget Tables 10.5 and 10.6 and identifying all those items which must be imported - machinery, fuel, fertilizer etc. - and arranging these as a new 'foreign exchange costs' line in Table 10.7. That part of total output which is to be exported would be similarly identified to provide a new 'foreign exchange returns' line. The analysis then proceeds as before. As shown in Table 10.8, the proposed cardamom activity has a foreign exchange B/C ratio of 2.16 as compared with its standard B/C ratio of 1.22. The proposal is thus much more attractive in foreign exchange terms.

Of course, small farmers themselves will not usually be concerned with the foreign exchange aspects of an activity. But commercial estates in some countries are allowed to retain some proportion of foreign exchange earnings and this can greatly influence their choice in enterprise selection. For analysis in support of public agricultural development projects, the foreign exchange dimension is not infrequently the dominant factor in evaluation.

(11) Internal rate of return (IRR). This is that rate of discount which makes the PV of an investment's cost stream equal to the PV of its revenue stream so that the net PV of the investment is equal to zero (Sinden and Thampapillai 1995, Ch. 9). The unknown is the discount rate. (By contrast, in finding the net PV or the B/C ratio of an investment, the discount rate is specified.) As for other types of discounted cash-flow analyses, calculation of IRR is provided by personal computer spreadsheet programs such as, e.g., Microsoft Excel. The procedure for calculation of IRR by hand is illustrated in Table 10.9. Some trial rate, say ten per cent, is first applied to the nominal (undiscounted) cost and return streams and columns (2) and (5) are obtained, the totals of which are respectively Rs 12121 and Rs 14 762. Discounted returns are considerably greater than costs at ten per cent; therefore some higher rate is now applied, say 13 per cent. The results of this are shown in columns (3) and (6). Discounted returns of Rs 10 675 are still higher than discounted costs of Rs 9 539 but not by much. The equality condition is then found graphically by plotting PV against i as shown in Figure 10.5. The point of intersection of the discounted cost and return curves indicates an IRR of 15.3 per cent.

FIGURE 10.5 Graphical Determination of IRR

One note of caution is necessary. In analysis to obtain B/C ratios and IRR values at farm or estate level, objectivity and honesty on the part of the analyst can usually be assumed. This may not be the case where these apparently objective procedures are applied in support of investments intended incidentally to serve some vested interest or to justify investment decisions which have already been taken. By fiddling with assumptions concerning future costs, prices, the time profile of the activity etc., it is possible (within limits) to come up with whatever B/C ratio or IRR will best serve the purpose of the analyst or client. Not infrequently these measurements are predetermined and the technical-economic conditions of the activity (prices, yields etc.) then tailored to achieve them. (Among practitioners of such art, an IRR range of 17 to 27 per cent seems to be preferred ground.)

10.14 DIFFICULTIES IN PLANNING FARM SYSTEMS OVER TIME

Three major factors make whole-farm planning over time difficult and not as reliable as would be wished. Indeed, beyond the immediate short term of the coming season or year, in situations of dynamic change induced by research and development these factors may often make fruitful farm-system planning virtually impossible. Two of these factors have already been mentioned (Section 10.1): first, the flexibility effect whereby time gives the farmer options for the sequencing of activities' input injections and output harvests within years and of activities between years and, second, the inevitable presence of uncertainty. The effect of these factors is compounded by the fact that the longer the planning period, the greater the number of options to be considered and the amount of uncertainty to be faced. This uncertainty facing farmers in their planning can have many sources. It may relate to Nature (yields as affected by the vagaries of climate, pestilence etc.), to the economic environment (technology, prices, interest rates, inflation), to government policy (subsidies, quotas, labour laws etc.), to personal matters (health, family relationships) or to the socio-political environment (social unrest, civil war etc.). Particularly for small farms of Type 1 (subsistence) and Type 2 (semi-subsistence), such uncertainty is multiplied in situations of change where non-traditional farming methods and activities are becoming available or induced as a consequence of agricultural research and/or social change (improved education, better communications, population pressure etc.). Prior to these modem developments, such small farms by trial and error over the centuries had established traditional farm systems well-oriented to their needs and in equilibrium with their natural and social environments. Clearly, disturbance of these traditional systems brings with it significant uncertainty in planning.

The third factor that makes whole-farm planning over time difficult is really due to the combined effect of the above two factors. It is known as the curse of dimensionality. By this is meant the exponential expansion in the number of possibilities to be considered as the length of the whole-farm planning horizon increases. Thus, e.g., suppose a farmer can grow any of six crops. Assuming that only one crop can be grown at a time (i.e., mixed cropping is not allowed), planning for a one-year horizon would involve consideration of six crop options; for a two-year horizon, six by six or 36 two-year crop-sequence options; for a three-year horizon, 6³ or 216 such possibilities. Clearly, even without consideration of crop mixtures or of uncertainty with its array of possible outcomes, the whole-farm planning problem can rapidly become so large as to be unmanageable or to be so complicated that the cost of planning exceeds its benefit. Thus, while multi-period mathematical programming techniques may be applied to the long-term planning of whole-farm systems (Rae 1977, Ch. 10), it is doubtful if the benefits are worth the cost on an individual farm basis. This is particularly so if significant uncertainty is present and the planning horizon is longer than two or three years. The exception to this is if the whole-farm system is so simple as to not suffer the curse of dimensionality in its planning. This is most likely to be the case for mono-crop estates or small specialist farms growing such perennial tree crops as rubber, coconut, tea, coffee etc. and for small or large specialist single-product farms producing such products as milk, broilers, flowers, fish etc. Subject to appropriate consideration of uncertainty (as considered in the following chapter), such mono-crop or single-product systems can be planned using the discounted cash-flow procedures and evaluation criteria outlined in this chapter. Likewise, as indicated in this chapter, these procedures for investment planning and evaluation can be applied to the planning of farm subsystems or individual activities to the extent that they do not suffer as much from the curse of dimensionality as do whole-farm systems.

Given the curse of dimensionality, the best approach to planning over time for non-specialist (i.e., mixed) farms, either small or large, is to adopt a rolling planning strategy. Under this approach a plan is drawn up each year for the next two or three years. Each year the first year of the previous plan is discarded (since it relates to the year that is passing) and a further year into the future is added to the plan, i.e., the plan is rolled forward a year. In essence, the plan drawn up in the previous year is revised in the present year with account taken of whatever relevant new information is available. The process is depicted in Figure 10.6 for a two-year rolling planning horizon: during Year 1, Plan 1 is drawn up covering Years 2 and 3; during Year 2, Plan 2 is drawn up covering Years 3 and 4; and so on for Plans 3, 4,... These plans may be of any desired degree of complexity ranging from a basis in whole-farm budgeting to sophisticated mathematical programming approaches and, as need be, they may include decisions about the initiation, continuance or replacement of longer-term activities (such as perennial tree crops) extending beyond the planning period.

FIGURE 10.6 - Schematic Depiction of a Rolling Planning Strategy

10.15 REFERENCES

Alien, R.G.D. (1950). Mathematical Analysis/or Economists, Macmillan, London.

Chisholm, A.H. and J.L. Dillon (1988). Discounting and Other Interest Rate Procedures in Farm Management, Professional Farm Management Guidebook No. 2, ABRI, University of New England, Armidale.

Chopra, K and C.H.H. Rao (1992). The Links between Sustainable Growth and Poverty', Quarterly Journal of International Agriculture 31(4): 364-379.

Dillon, J.L. and J.R. Anderson (1990). The Analysis of Response in Crop and Livestock Production, 3rd edn, Pergamon Press, Oxford.

Doll, J.P. and F. Orazem (1984). Production Economics: Theory with Applications, 2nd edn, Wiley, New York.

Gramlich, E.M. (1990). A Guide to Benefit-Cost Analysis, 2nd edn, Prentice-Hall, Englewood Cliffs.

Markandya, A. (1994). 'Criteria, Instruments and Tools for Sustainable Agricultural Development', in A. Markandya (ed.), Policies for Sustainable Development: Four Essays, Economic and Social Development Paper 121, Food and Agriculture Organization of the United Nations, Rome, pp. 1-70.

Mao, J.C.T. (1969). Quantitative Analysis of Financial Decisions, Macmillan, London.

Pearce, D.W. and R.K. Turner (1990). Economics of Natural Resources and the Environment, Harvester Wheatsheaf, New York.

Rae, A.N. (1977). Crop Management Economics, Crosby Lockwood Staples, London.

Robison, L.J. and P.J. Barry (1996). Present Value Models and Investment Analysis, The Academic Page, Northport.

Sinden, J.A. and D.J. Thampapillai (1995). Introduction to Benefit-Cost Analysis, Longman, Melbourne.

Thuesen, H.G. (1957). Engineering Economy, 2nd edn, Prentice-Hall, Englewood Cliffs.

von Braun, J. (1992), 'Agricultural Growth, Environmental Degradation, Poverty and Nutrition: Links and Policy Implications', Quarterly Journal of International Agriculture 31(4): 340-363.