Decoupling and Agricultural Investment with Disinvestment Flexibility: A Case Study with Decreasing Expectations

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1 Decoupling and Agricultural Investment with Disinvestment Flexibility: A Case Study with Decreasing Expectations T. Heikkinen MTT Economic Research Luutnantintie 13, Helsinki FINLAND tiina.heikkinen@mtt.fi June 30, 2007 Abstract This paper studies the effect of decoupling on optimal investment in agriculture assuming disinvestment flexibility. Agricultural income being determined by policy processes is subject to policy uncertainty. Case study examples suggest that assuming disinvestment flexibility, decoupling increases income stability, and a higher level of investments can be achieved even with lower subsides. Increased income stability may also diminish the dynamic cost of income uncertainty. When decoupling of income from production, the stability of the compensating direct payments should be ensured. Keywords: decoupling in agriculture, investment analysis 1 Introduction Decoupling is one of the key issues in EU common agricultural policy. This paper addresses the dynamic effects of decoupling on investments, focusing on the role of expectations. Previous work in [OECD2000] and [Heikkinen and Pietola2006] addresses the role of expectations about future payments to investment decisions in a dynamic setting. This paper extends [Heikkinen and Pietola2006] to study the effect of decoupling the national support on investment in agriculture assuming disinvestment flexibility 1. 1 Disinvestment was not considered in [Heikkinen and Pietola2006]. 1

2 The investment model is based on the dynamic optimization model presented in [Heikkinen and Pietola2006], where investments are studied from the point of view of a representative dairy farm, assuming a Markov model of expectations: farmers believe that with high probability the current income level remains the same next year; however, due to decreasing expectations regarding future income support, a positive probability is assigned to lower levels of income 2. In addition to making future income uncertain, political processes may also make the farmer s current income unobservable at the time when the investment decision is made. In [Heikkinen1998] the dynamic uncertainty cost is defined as the loss in the value and amount of investment due to unobservable return; Appendix A summarizes the definition for dynamic uncertainty cost. Assuming nonincreasing income expectations, decoupling the support from production may make production an unprofitable alternative compared to zero production. For example, assuming zero production implies zero labor cost and production cost, the income of an inactive farmer can be defined as equal to a direct payment. This corresponds to assuming a (partial) disinvestment takes place whenever net income from production is negative: most animals are sold under nonincreasing income expectations. If the direct payment is fixed, decoupling associated with disinvestment flexibility may increase income stability. Decoupling accompanied by a compensating fixed income subsidy may potentially be welfare-enhancing in comparison to a more costly subsidy program with more volatile price-based support. The following observations based on a case study illustrate the potential benefits of a fixed national support: A fixed compensating payment stabilizes income, thereby increasing investments even if the aggregate subsidy level is decreased. Assuming disinvestment flexibility with nonincreasing income expectations, when removing both national support and investment subsidies in the case study, a compensating payment 90 % of previous national support increases investment probability to one (from 16 % before decoupling national support). The dynamic uncertainty cost can be reduced by a fixed compensating payment even if at a lower aggregate subsidy level. Assuming disinvestment flexibility, when decoupling both national support and investment subsidies, a compensating payment 90 % of previous national support im- 2 [Heikkinen and Pietola2006] implicitly made a simplifying assumption that investment increases productivity: after investment took place, a new transition matrix was assumed to apply, corresponding to a higher expected return (for simplicity, corresponding to the transition matrix at the beginning of time horizon). Even though there is some evidence of productivity-enhancing effects of investment [A.-M. Heikkilä2004], this paper studies the effect of decoupling on investment and uncertainty cost without assuming a productivity-enhancing effect. The main effect of removing the (somewhat arbitrary) assumption of productivityenhancement is to reduce the investment level. 2

3 plies a saving in uncertainty cost corresponding to approximately 7 % of the value of investment in the case study. The dynamic cost of uncertainty at a given time is the cost due to an unobservable return that time period, e.g. year. Even if the return is not observable at a given time, the dynamic uncertainty cost can be zero if dynamic decision making is based on a relatively more stable income process. When enforcing decoupling, it is important to consider the stability of the compensating payments. The organization of the paper is as follows. Section 2 summarizes the investment problem of an optimizing representative agent following [Heikkinen and Pietola2006]. Section 3 studies the effect of decoupling on investment over time. A decision tree representation for problem (3) subject to (2) it outlined in Appendix B. A simplified decision tree illustrates the complexity of the decision tree representation of the investment problem, motivating a dynamic programming approach to the investment problem. 2 Optimizing Investment At each time t = 1,..., T a representative farm decides the investment at t, I t. Denoting by I the total available budget for the investment at t, the decision I t at t satisfies I t {0, I}, t = 1,..., T. (1) Let r t denote the return on investment (%) per time period at time t. Due to variability in the rate of return, the future value of investment is random. Letting I a denote the aggregate budget, the aggregate budget constraint requires: T I t I a. (2) t=1 Letting ρ denote the internal rate of return, the discount factor b (0, 1] is defined as b = 1/(1 + ρ). The dynamic optimization problem of a representative firm can be written as: max E[ b t (r t I t + b k t r k I t I t (1 p))] (3) t=1 k=t+1 where p denotes the investment subsidy % and E denotes the expectation operator. Two versions of problem (3) subject to (1)-(2) are studied in [Heikkinen and Pietola2006]; in the first model (Model 1), it is assumed that r t is observable when the investment decision is made at time t; in the second model (Model 2) only r t 1 is observable at time t. Since the future values of the investment are unknown in both models, there is an opportunity cost to making the investment decision at the beginning of the time horizon [Dixit and Pindyck1994]; the firm has the option to postpone the investment decision. 3

4 3 Decoupling and Optimal Investment with Disinvestment Flexibility In a dynamic model, expectations matter to optimal investment behaviour. Present policies may affect farmers expectations of future policies. For example, in a dynamic investment model in [OECD2000], a perceived probability of a subsidy payment (consisting of a lump-sum payment and a payment per hectare) is assumed to depend on the level of production in the previous period. [Heikkinen and Pietola2006] assumes the probability distribution of a direct payment depends on the previous payment level. Specifically, [Heikkinen and Pietola2006] studies optimal investment assuming a timecorrelated income, modelled as a Markov chain. In this paper the same numerical optimization model will be applied to evaluate the effect of decoupling of national income and investment support on investment, assuming disinvestment flexibility. The model is based on considering a case of a representative dairy farm with a herd size of 130. Table 1 summarizes the assumed transition probabilities between states in terms of return on investment (ROI %). For example, 5 % corresponds to 2003 ROI % accompanied by a decrease by 20 % in total (subsidized) income 3. To focus on the role of policy expectations, consider a simplified model assuming that costs and parameters other than subsidies remain at 2003 level. The transition probabilities can be interpreted as reflecting uncertainty regarding the compensating direct payments 4, varying between 0 (corresponding to ROI 5 %) and (ROI 30 %). With high probability, the return on investment remains unchanged (except for the highest rate of return r = 0.3 that is assumed to decrease with probability 99 % in Table 1). Disinvestment Flexibility Consider the above case study based on a representative large dairy farm. After decoupling the subsidy no longer depends on production and it is optimal to produce only if the net return from production is positive. Otherwise, it is better to set production to zero and take only the direct decoupled support. With no production, both the labour cost of the farmer and the production cost 3 On average, 2005 income from sales in dairy production of large farms was at 2003 level whereas total subsidies slightly increased. However, profitability decreased 2005 due to increased cost level. 4 A direct payment can be defined to match a producer price change given production. Assuming price-based payments are continued, the transition probabilities could alternatively be interpreted as modeling uncertainty regarding the subsidized price level. However, unlike with direct payments, price-based support is not obtained if ROI % is negative (production is zero). 4

5 Table 1: Transition Probabilities between States (ROI %) are assumed to be zero. This corresponds to assuming a (partial) disinvestment takes place whenever net income from production would be negative: most animals are sold under nonincreasing income expectations. Examples of the effect of decoupling will be studied shortly, assuming disinvestment flexibility under nonincreasing income expectations. Disinvestment flexibility in this paper refers to partial disinvestment as outlined above. In contrast, allowing for full capital disinvestment, reducing available production facilities, would modify constraint (1) to: I t {0, I, I}, t = 1,..., T (4) where I I a is the maximum change per period in cumulative investments. However, in examples with I = I a, full capital disinvestment, implying zero return, was not observed to take place. To study the effect of decoupling on investments, consider the following two modifications to the case study in [Heikkinen and Pietola2006]: 1. the removal of price-based national support, assuming a fixed compensating direct payment and disinvestment flexibility. 2. the simultaneous removal of national support and investment subsides, assuming a fixed direct compensating payment and disinvestment flexibility. Specifically, the national-level compensating direct payments are assumed to be fixed, whereas the direct payments due to previous decoupling are assumed to be uncertain according to Table 1. The farm is assumed to make the production decision based on net return; assuming zero production implies zero labor cost, the income of an inactive farmer is defined as equal to a fixed direct payment. Decoupling National Support Consider scenario 1 first, assuming the complete removal of price-based national support. In the case study example, this implies a saving of approximately per farm. A 100 % direct payment compensation corresponds to a subsidy 7 5

6 %- 9 % of gross revenue depending on the uncertain component of the income subsidy. In Table 1, ROI % before decoupling national support may take 5 values: r = [0.3, 0.16, 0.11, 0.05, 0]. The ROI % after decoupling depends on the level of direct compensation. Let r c [4] denote the ROI % corresponding to the fourth element in ROI-vector at direct compensation level c. For example, letting b = 0.94 and the start state r c 0 = r c [4] for each compensation level c, the effects of decoupling with a fixed compensating payment can be summarized as follows: A fixed income compensation corresponding to 70 % of the support level before decoupling suffices for making the cumulative investment probability equal to one. The dynamic cost of uncertainty is zero assuming a fixed compensation corresponding to 70 % (or higher) of the previous support. This corresponds to a saving in average uncertainty cost by approximately 7 % of the value of investment. Figure 1 plots the cumulative investment probability over 6 years as function of the fixed direct payment in the case study assuming b = 0.94 and r c 0 = r c [4]. The cumulative investment probability over a six year period before decoupling the national support was approximately 16 %. Assuming a fixed compensating payment, a higher level of investment can be achieved at a much lower cost. By increasing income stability, it is thus possible simultaneously to reduce the total support increase investments decrease the dynamic cost of uncertainty Decoupling Investment Subsidies Investment subsidies in terms of a given percentage of investment expenditure are by definition directly linked to the value of investment and to production. Full decoupling investment subsidies here means setting the subsidy percentage (0.35 % in the case study) to zero. For example, letting b = 0.94 and r c 0 = r c [4], the effects of removing both national support and the investment subsidy with a fixed compensating payment can be summarized as follows: Assuming a compensating payment 90 % or higher of the previous national subsidy increases the investment probability to one; before decoupling national support the investment probability was 16 % over 6 years. Assuming a compensating payment 90 % or higher implies the dynamic uncertainty cost is zero. 6

7 cumulative investment probability direct compensating payment relative to national subsidy before decoupling Figure 1: Cumulative investment probability over 6 years as function of direct payment, when removing national price-based support, with b = 0.94, r c 0 = r c [4], assuming observable value (solid curve) and with unobservable value (*) 7

8 cumulative investment direct compensating payment relative to national subsidy before decoupling Figure 2: Cumulative investment probability over 6 years as function of direct payment, when removing both national support and investment subsidy assuming observable value (solid curve) and unobservable value (*), with b = 0.94, r0 c = r c [4] Figure 2 depicts the investment probability over 6 years as function of direct payment (% previous national subsidy level), when removing both national support and the investment subsidy in the case study. Figure 3 depicts the dynamic cost of uncertainty over time as function of direct compensating payment. With a compensating payment 90 % or more of previous national support the uncertainty cost is zero. With compensation lower than 90 %, the dynamic uncertainty cost averaged over time depends on the compensating payment, varying between 2 % (70 % compensation) and 8 % (85 % compensation), as compared to 7 % before decoupling. The underlying reason for the outcomes listed above is the greater income stability due to the assumed fixed compensating support along with assumed disinvestment flexibility. Assuming production is zero unless the net return is positive, ROI % will improve relatively more in cases where ROI % would be zero or negative without direct decoupled support. To illustrate the effect of the flexibility in production (zero disinvestment cost), consider the above example assuming production is always at full capacity level. Figure 4 depicts the investment probability when unprofitable production is continued. This scenario could be motivated e.g. by a delivery contract implying a penalty for failing to meet a target supply. Comparing Figures 2 and 4, it can be seen that 8

9 REVPI(t) time index Figure 3: Dynamic uncertainty cost relative to expected investment, when removing both national support and investment subsidy assuming direct payment 70 % of previous national support (+ sign), 80 % (solid curve), 85 % (dashed curve), 90 % or more (*), with b = 0.94, r0 c = r c [4] 9

10 optimal investment can be sensitive to the production decision. A special case of decoupling is to assume a fully deterministic compensating payment. In this case investment decision is made at t=1 provided ROI % meets the internal interest rate. Continuing the example discussed above assuming b = 0.94, the direct fixed compensation required for investment to take place corresponds to approximately 95 % national support before decoupling (cf. Figure (2)). On the Size of the Investment Problem The dynamic investment model is a simplified framework that can be extended in many ways to a more realistic model. For example, a more realistic scenario model would result allowing both national policy and common agricultural policy each have 5 possible states. A single aggregate budget constraint corresponds to two possible budget states: {0, I a }. The vector of possible states then can be defined as S = [z, s 11, s 12,..., s 54, s 55 ] where z is a 25-vector of zeros corresponding to each possible state where the budget has been used up, and s ij is the state of return before investment has taken place when the state of national policy is i and the state of common policy is j. In a Markov decision process, each possible action (invest, do not invest) is associated with a transition matrix. Letting the submatrix P1 s denote the transition matrix between 25 possible states in terms of national and CAPsupport, the transition matrix P1 when investing at time t will be P1 = [ P1s 0 P1 s 0 ], (5) where 0 is a matrix of zeros. The transition matrix when not investing at time t is: [ ] P1s 0 P2 =. (6) O P1 s Thus, allowing both national policy and common agricultural policy each have 5 possible states would increase the size of the transition matrix to 50 50, assuming a single aggregate financial constraint. The size of the transition matrix can be reduced by introducing an artificial state modeling the situation when the budget has been used up 5 ; the size of the transition matrix will then be reduced to There is a trade-off between the accuracy of the scenario model and the size of the computational problem. An extension to explicitly allowing a disinvestment option as formalized in (4) further increases the computational cost. In this case, the decision-maker 5 the additional state corresponds to ROI=0; after investment has been made, a new transition probability matrix applies: one where each state leads to this additional state with probability one. 10

11 cumulative investment probability direct compensating payment relative to national subsidy before decoupling Figure 4: Cumulative investment probability over 6 years as function of direct payment, when removing both national support and investment subsidy assuming production at full capacity with observable value (solid line) and unobservable value (*), b = 0.94, r0 c = r c [4] faces three possible actions: to invest, to hold current investment and to disinvest. Letting I a = I, the transition matrix P1 in (5) corresponds to making investment and P2 in (6) corresponds to holding current investment. The transition matrix when disinvesting can be foramlized as [ ] 0 P1s P3 =. (7) 0 P1 s With m possible budget states the size of each transition matrix will be 25m 25m. 4 Conclusion In a dynamic setting expectations of future agricultural policies are relevant for investment decisions. This paper studies the effect of decoupling on optimal investment assuming disinvestment flexibility. A case study in Finnish agriculture is studied assuming decreasing income expectations. If the compensating payment is paid as a fixed income subsidy, decoupling implies a greater income stability. Greater income stability may increase investments even if accompanied by a lower subsidy level. The stability of the compensating payment is a key issue in policy planning. 11

12 More work on the role of expectations for agricultural investment is needed. Appendix A Consider problem (3) subject to (1)-(2). First, it is assumed that r t is observable when the investment decision is made at time t (Model 1); in the second model (Model 2) only r t 1 is observable at time t. Let {It } denote the solution to Model 1 and let {It } denote the solution to Model 2, assuming the investment decision can be made at any time. Let y t denote the net value of investment in terms of income obtained when investing I t at t: y t (r t, I t ) = r t I t + E[ k=t+1 b k t r k ]I t I t (1 p) (8) where p denotes the investment subsidy percentage. cost, EVPI(t), can be defined for period t as A dynamic uncertainty EV P I(t) = E[y t (I t )] E[y t (E(r t r t 1 ), I t )] (9) where the first term corresponds to the expected value obtained at t when solving the wait-and-see model (Model 1) and the second term formalizes the corresponding expected value when the investment decision at time t is based on E(r t ), given the observed return r t 1 (Model 2). Let P r t denote the probability of investment at time t when the state r t is observed, and let P r t denote the corresponding probability with expected value maximization (Model 2). Assuming P r t > 0, define the unit value of investment at time t, v 1 (t), in Model 1 as v 1 (t) = E[y t(i t )] P r t I a and assuming P r t > 0 define the unit value in Model 2 as: v 2 (t) = E[y t(e(r t r t 1 ), I t )] P r ti a. If P r t = 0, let v 1 (t) = 0 and if P r t = 0 let v 2 (t) = 0. An uncertain state in terms of ROI % lowers the value of investment in two ways: by lowering the unit value of investment given the expected amount of investment and by reducing the expected investment for a given unit value. Accordingly, the dynamic value of information, EVPI(t) can be decomposed into two components: EV P I(t) = (v 1 (t) v 2 (t))p r t I a + v 2 (t)(p r t P r t)i a. (10) EVPI(t) can be negative due to overinvestment under uncertainty. E.g. in the special case of a stationary distribution, at t = 1, P r t = 1 or P r t = 0. In 12

13 this case, [Heikkinen and Pietola2006] suggests a dynamic option value O(t) for as a measure for a dynamic uncertainty cost relative to expected investment: O(t) = E[y t(i t )] P r t I a max{max t E(y t ), 0} I a, (11) where the nominator in the second term models the net value obtained when maximizing expected forward start NPV at the beginning of the time horizon. If P r t = 0, O(t) is not defined. Note that at t = 1, (11) is equivalent to the first term in (10) (if P r 1 = 1, the quantity cost due to uncertainty could be considered as zero; on the other hand, if P r t = 0 t, the first term is equivalent to the value lost due to uncertainty: EVPI(t)=E[y t (I t )]). In general, whenever overinvestment due to uncertainty takes place with P r 1 = 1, (11) could be applied for the dynamic cost of uncertainty. Appendix B Figure 5 outlines a decision tree representation for the first three time periods for the investment problem (3) subject to aggregate budget constraint (2) with I a = I. In Figure 5 y t (r t, I t ) denotes the net value of investment made at time t as formalized in (8). At time t = 1 there are five decision problems, one for each possible state r i1, i = 1,..., 5. If at time t I t = I, the expected net value of investment at t, y t (r t, I), is obtained, assuming r t is observable (Model 1). If r t is not observable at time t, the decision maker obtains y t (E(r t ) r t 1, I) when investing at time t (Model 2). After each branch with decision I t = 0, 5 new branches will emerge. Thus, at t = 2, there are 25 decision problems, three of which are explicitly depicted in Figure 5: the investment problem when r 1 = r 11 and r 2 = r 12 and the corresponding problems when r 1 = r 51 and r 2 = r 12 or r 2 = r 52. With 20 time periods there are 5 20 decision problems in the decision tree representation. This motivates applying dynamic programming (DP) to the investment problem. DP Formalization for Model 1 Problem (3) subject to (1)-(2) can be solved recursively applying Bellman equation: v(r t ) = max{(y t ) + bev(r t+1 )}, (12) I t where v(r t ) denotes the value function given state r t and where y t denotes the expected net value of investment at t, as formalized in (8). DP Formalization for Model 2 In Model 1, like in [Dixit and Pindyck1994], the value of investment at any time t is observable. In the case study summarized above, due to a high degree of 13

14 policy uncertainty, the return rate r t can be uncertain at the beginning of period t. Assuming r t is observed at the end of period t, all terms affecting the value of investment are random. A risk-neutral decision maker in this case solves the Bellman equation: v(e(r t )) = max I t {E[y t (r t, I t )] + bv[e(r t+1 )]}, (13) where y t denotes the expected net value of investment at t, as formalized in (8). According to formulation (13) the decision maker has the flexibility to make the investment decision at any time; the expected return can be determined based on the return observed previous time period. Assuming a stationary income process, however, there is no motivation for postponing investment; in this case NPV maximization is optimal. Using the terminology in [Keswani and Shackleton2006], the special case where the investment decision is made at the beginning of the time horizon corresponds to optimizing forward start net present value (NPV). References [A.-M. Heikkilä2004] A.-M. Heikkilä, L. Riepponen, A. H.: 2004, Investment in New Technology to Improve Productivity of Dairy Farms. EAAE Seminar University of Crete September 2004 CD-ROM. [Dixit and Pindyck1994] Dixit, A. and R. Pindyck: 1994, Investment under Uncertainty. Princeton: Princeton University Press. [Heikkinen1998] Heikkinen, T.: 1998, Dynamic Pricing and Power Control of A Multimedia Network. In: Conference on Information Sciences and Systems. Princeton, NJ, USA. [Heikkinen and Pietola2006] Heikkinen, T. and K. Pietola: 2006, Investment and the Dynamic Cost of Income Uncertainty: the Case of Diminishing Expectations in Agriculture. MTT Discussion Paper 5, 2006 (previous version also in proc. ERSA 2006, Volos). [Keswani and Shackleton2006] Keswani, A. and M. Shackleton: 2006, How real option disinvestment flexibility augments project NPV. European Journal of Operational Research 168, [OECD2000] OECD: 2000, Decoupling: a conceptual overview. OECD Publication. 14

15 Figure 5: Outline of a Decision Tree Representation of the Investment Problem 15