EFFECTS OF FEDERAL RISK MANAGEMENT PROGRAMS ON INVESTMENT, PRODUCTION, AND CONTRACT DESIGN UNDER UNCERTAINTY. A Dissertation SANGTAEK SEO

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1 EFFECTS OF FEDERAL RISK MANAGEMENT PROGRAMS ON INVESTMENT, PRODUCTION, AND CONTRACT DESIGN UNDER UNCERTAINTY A Dissertation by SANGTAEK SEO Submitted to the Office of Graduate Studies of Texas A&M University in artial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY December 004 Major Subject: Agricultural Economics

2 EFFECTS OF FEDERAL RISK MANAGEMENT PROGRAMS ON INVESTMENT, PRODUCTION, AND CONTRACT DESIGN UNDER UNCERTAINTY A Dissertation by SANGTAEK SEO Submitted to Texas A&M University in artial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Aroved as to style and content by: David J. Leatham (Chair of Committee) Bruce A. McCarl (Member) Paul D. Mitchell (Member) Victoria Salin (Member) Clair J. Nixon (Member) A. Gene Nelson (Head of Deartment) December 004 Major Subject: Agricultural Economics

3 iii ABSTRACT Effects of Federal Risk Management Programs on Investment, Production, and Contract Design under Uncertainty. (December 004) Sangtaek Seo, B.Econ., Chungbuk National University; M.Econ., Korea University Chair of Advisory Committee: Dr. David J. Leatham Agricultural roducers face uncertain agricultural roduction and market conditions. Much of the uncertainty faced by agricultural roducers cannot be controlled by the roducer, but can be managed. Several risk management rograms are available in the U.S. to hel manage uncertainties in agricultural roduction, marketing, and finance. This study focuses on the farm level economic imlications of the federal risk management rograms. In articular, the effects of the federal risk management rograms on investment, roduction, and contract design are investigated. The dissertation is comrised of three essays. The unifying theme of these essays is the economic analysis of cro insurance rograms. The first essay examines the effects of revenue insurance on the entry and exit thresholds of table grae roducers using a real otion aroach. The results show that revenue insurance decreases the entry and exit thresholds comared with no revenue insurance, thus increasing the investment and current farming oeration. If the olicy goal is to induce more farmers

4 iv in grae farming, the insurance olicy with a high coverage level and high subsidy rate is effective. In the second essay, a mathematical rogramming model is used to examine the effects of federal risk management rograms on otimal nitrogen fertilizer use and land allocation simultaneously. Current insurance rograms and the Marketing Loan Program increase the otimal fertilizer rate % and increase the otimal cotton acreage % in a Texas cotton-sorghum system. Assuming nitrogen is harmful to the environment and cotton requires higher nitrogen use, these risk management rograms counteract federal environmental rograms. The third essay uses a rincial-agent model to examine the otimal contract design that induces the best effort from the farmer when cro insurance is urchased. With the introduction of cro insurance, the investor s otimal equity financing contract requires that the farmer bear more risk in order to have the incentive to work hard, which is achieved by increasing variable comensation and decreasing fixed comensation.

5 v DEDICATION To my arents, my wife, and my kids

6 vi ACKNOWLEDGEMENTS I would like to thank God for his salvation and unfailing love for me. His love drove me to finish this dissertation and my Ph.D. courses. I deely areciate my committee members: Dr. David J. Leatham, my advisory chair, Dr. Bruce A. McCarl, Dr. Paul D. Mitchell, and Victoria Salin. Dr. Leatham is my mentor who guided my research hilosohy and showed constant suort. Dr. McCarl gave me valuable hel in mathematical rogramming and GAMS. Dr. Mitchell showed me rofessional manners as a researcher and teacher, his suort and friendshi will be remained in my heart. Dr. Salin heled me out with new toics and endurance. In addition, I would like to thank Dr. Dhazn Gillig for her hel in GAMS and Vicky Heard and Lindsey Nelson for their kind business works. A secial thank you is given to the Deartment of Agricultural Economics and Dr. Leatham for financial suort for all of my years with the deartment. I also give thanks to the Korean students in my deartment. Friendshis and discussions with them made my life as a Ph.D. student a lot easier to bear. Chungbuk Agricultural Research & Extension Services is also credited for allowing and suorting me to study here. The memory of my work with comanions gave me a strong background for my study and my life. I thank rofessors at Chungbuk National University and Dr. Doo Bong Han at Korea University. They encouraged and suorted me to study as a Ph.D. student.

7 vii I would like to thank my arents, brothers, and sisters including my in-laws for their love and encouragement. I always remember their love and it gives me strength whenever I am deressed. I also give secial thanks to Pastor Seongkwon Lee, and all the members at the Hansarang Church, as well as Pastor Chong Kim and all the members at the Vision Mission Church. Their love, suort, and rayer heled me to stand as firm as a rock when I struggled. A secial thank you is given to Dr. Yong- Suhk Wui for his love and rayers. I give secial thanks to my wife, Nameun Kim, and my kids, Inyoung, Eulji, and Seongmin for their unfailing love and sacrifice. Without their love, encouragement, and rayers, I could have never finished my dissertation and Ph.D. courses.

8 viii TABLE OF CONTENTS Page ABSTRACT...iii DEDICATION... v ACKNOWLEDGEMENTS...vi TABLE OF CONTENTS...viii LIST OF FIGURES... x LIST OF TABLES...xi CHAPTER I INTRODUCTION...1 II EFFECT OF REVENUE INSURANCE ON ENTRY AND EXIT DECISIONS IN TABLE GRAPE PRODUCTION: A REAL OPTION APPROACH Introdution Entry and Exit Thresholds for Standard NPV and Real Otions Entry and Exit Thresholds with Standard NPV Entry and Exit Thresholds with Real Otions Model Model Assumtions Entry and Exit Model with No Revenue Insurance Entry and Exit Model with Revenue Insurance Data Data without Revenue Insurance Data with Revenue Insurance Results The Entry and Exit Thresholds with Real Otions Aroach The Effect of Revenue Insurance on the Entry and Exit Thresholds Conclusion...41 III EFFECTS OF FEDERAL RISK MANAGEMENT PROGRAMS ON OPTIMAL ACREAGE ALLOCATION AND NITROGEN USE IN A TEXAS COTTON-SORGHUM SYSTEM...44

9 ix CHAPTER Page 3.1. Introduction Federal Risk Management Programs Concetual Framework Emirical Model Utility and Profit Prices, Yields, and Correlations Cro Production Function Model Imlementation Emirical Results and Discussion Conclusion...67 IV RISK SHARING AND INCENTIVES WITH CROP INSURANCE AND EXTERNAL EQUITY FINANCING Introduction Princial-Agent Model of an External Equity Investor and a Farmer Otimal Contract for External Equity Financing with Cro Insurance Emirical Analysis Conclusion...89 V SUMMARY AND CONCLUSIONS...91 REFERENCES...97 APPENDIX A APPENDIX B...10 APPENDIX C...16 VITA...131

10 x LIST OF FIGURES FIGURE Page.1. Entry thresholds with real otions and standard NPV Two cases of revenue flow to derive the entry and exit model under revenue insurance...4

11 xi LIST OF TABLES TABLE Page.1. Parameters Used for Table Grae Farming with and without Revenue Insurance Entry and Exit Thresholds by NPV and Real Otions Aroaches Entry and Exit Thresholds and Their Sensitivity to Changes in Selected Parameters Entry and Exit Thresholds by Insurance Premium Rate Otimal Farmer Choices without the Marketing Loan Program (MLP) Otimal Farmer Choices with the Marketing Loan Program (MLP) Exected Net Indemnity ($/acre) for Each Insurance Program Certainty Equivalent and Mean and Standard Deviation of Profit ($1,000 s) with Otimal Farmer Choices Comarative Static Results of the External Equity Financing with Cro Insurance on Otimal Level of Effort e *, Variable Comensation b *, and Fixed Comensation w * Sensitivity Analysis of Selected Variables on Otimal Level of Effort e *, Variable Comensation b *, and Fixed Comensation w *...88

12 1 CHAPTER I INTRODUCTION Agricultural roducers face uncertain agricultural roduction and market conditions. Yield and rice fluctuations largely define this uncertainty. Yield uncertainty is mainly caused by weather. Price uncertainty arises from the interaction of suly and demand conditions ultimately involving many underlying international and domestic factors, including weather. This uncertainty makes agricultural income unstable. Much of the uncertainty faced by agricultural roducers cannot be controlled by the roducer but can be managed. Thus risk management is imortant to farmers and agricultural olicy makers. Several risk management aroaches are available in the U.S. to hel manage uncertainties in agricultural roduction, marketing, and finance. Two widely adoted risk management rograms are the cro insurance and marketing loan rograms rovided by the federal government. These rograms rotect income and market rices in the face of uncertain roduction and market conditions. Yield insurance and revenue insurance are the most commonly used among the cro insurance rograms. Yield insurance guarantees a minimum level of yield (however, the indemnity is given in terms of monetary value) and revenue insurance guarantees a minimum level of revenue. The Agricultural Risk Protection Act (ARPA) of 000 resulted in increased remium subsidies from the government and an exansion This dissertation follows the style and format of the American Journal of Agricultural Economics.

13 in the tyes of olicies available, the cros covered, and the geograhic availability. Total acres covered by cro insurance increased from 18 million in 1998 to 16 million in 00 with total liability, a maximum indemnity that should be aid in case of total loss, increasing from $8 billion to $37 billion (USDA-RMA 00a). The Farm Security and Rural Investment Act of 00 continued the nonrecourse marketing assistance loan rogram and loan deficiency rogram (LDP) that guarantees the minimum level of selected commodity rices, called the marketing loan rate. The former rovides a marketing assistance loan to meet cash flow needs of farmers at harvest time by requiring commodities as collateral. This loan is non-recourse because the farmer can reay the loan with rincial lus interest or forfeit the commodity to the government. The LDP is defined as the difference between the marketing loan rate and the osted county rice (PCP) rovided by the government at harvest time. If the PCP falls below the marketing loan rate at harvest time, then the farmer benefits from the LDP. Unlike cro insurance, those rograms do not require the ayment of a remium for articiation. Marketing loan gain and the magnitude of LDP ayments exceeded $1 billion and $6 billion for the 000 cro year (USDA-FSA 00a), resectively. Risk management rograms reduce downside risk faced by the farmer. Such rovisions affect cro returns and thus farm investment and roduction decisions as well as leasing contracts. Those rograms may induce farmers to grow cros that use more nitrogen, herbicides, and insecticides with ossible detrimental effects on the environment (Goodwin and Smith; Skees). Cro insurance may encourage or discourage investment in erennial cros and may lead existing farmers to stay in

14 3 farming longer or leave earlier. Cro insurance may alter agricultural contracts. The imacts that these decisions have need to be considered by olicy makers and farm decision makers. This study focuses on the farm level economic imlications of federal risk management rograms. Secifically, the work will focus on cro insurance and the marketing loan rogram that are used to rotect farmers from yield, income, and rice uncertainties. In articular, the effects of federal risk management rograms on the investment, roduction, and contract design will be investigated. The dissertation will be comrised of three essays. The sections that follow include a descrition of the three essays, each with its own urose and rocedure. The unifying theme of these essays is the economic analysis of cro insurance rograms. Collectively through the three studies we will examine how the resence of cro insurance and LDP rovisions changes farm decisions regarding investment in risky assets, choice of cros and inut uses, and contract rovisions between investors and farmers.

15 4 CHAPTER II EFFECT OF REVENUE INSURANCE ON ENTRY AND EXIT DECISIONS IN TABLE GRAPE PRODUCTION: A REAL OPTION APPROACH.1. Introduction The assage of the Agricultural Risk Protection Act (ARPA) in 000 greatly exanded the availability of cro insurance to farmers. Not only have remium subsidies increased, but also the tyes of olicies available and the cros that can be insured. As a result, total acres covered by cro insurance increased from 18 million in 1998 to 16 million in 00 (USDA-RMA 00a). By buying cro insurance, farmers reduce the risk that they face in exchange for some remiums. This behavior changes the exected future cash flow and its distribution and thus affects the investment or disinvestments decisions. Also, increased subsidies affect those decisions through the change in the exected cash flow and its distribution. Thus, the effect of cro insurance on the investment and disinvestments decision needs to be investigated for olicy makers and farmers so that they make better decision-making. However, the effect of cro insurance on the investment and disinvestments decisions has not been studied yet. Many investment studies in agricultural literature have focused on the land valuation (Robison, Hanson, and Lins), asset relacement decision (Leatham and Baker; Perrin), and facility urchase (Griffin et al.) using the net resent value (NPV) aroach. Some studies include the effect of the government tax olicy on the agricultural investment decision using the NPV (Musser, Tew, and Clifton; Rossi). Musser, Tew,

16 5 and Clifton studied the tax benefit of the investment in irrigation equiment and Rossi studied the imact of the Tax Reform Act of 1986 on feeding investments using NPV. Also Baker, Leatham, and Schrader studied the effect of inflation on a confinement swine oeration. However, no studies include cro insurance in the investment analysis using the NPV. The decision rule of NPV requires that the NPV be nonnegative for the investment to be accetable and then choose the highest NPV among different scenarios. These decisions are made at current time and the oortunity cost from the loss of future ossible investments is not reflected in the NPV. investment timing (called the investment flexibility). That is, the NPV ignores the The investment flexibility is valuable because, by adjusting investment timing, the investor may ossibly avoid investing in rojects that results in large sunk costs if there are subsequent unfavorable market conditions. Thus, the NPV aroach has been criticized because it only considers the current decision, not the investment flexibility to invest at later date (Myer). As an alternative to NPV, the concet of real otions has been used to overcome the shortcomings of standard NPV (Trigeorgis). Dixit (1991) analyzed the effect of rice ceiling and rice floor on the investment decision using a real otion aroach. This study incororates the investment flexibility and investment timing. The investment criterion is a trigger value that secifies when to enter the business (called entry threshold). An investor currently in business must also make the decision to continue oerating or exit the business. In this case, the trigger value to exit the business (called exit threshold) is given as a disinvestment decision criterion. This aroach alies the

17 6 financial otion concet to the investment in real assets when the decision is made under uncertainty (Dixit and Pindyck; Trigeorgis). That is, this aroach regards the investment flexibility in real assets as an otion to undertake an investment over a given eriod. This is similar to an American otion in which the holder of the otion can exercise the otion at any oint of time from when the otion is urchased. Recent real otion studies in the agricultural economics literature include the entry-exit decision (Price and Wetzstein; Isik et al., 003), the equiment relacement decision (Hyde, Stokes, and Engel), the sequential investment decision in cro management (Isik, Khanna, and Winter-Nelson), and technology adotion (Purvis et al.). Salin studied the imact of food safety risks on caital investment. However, no studies use the real otion aroach to consider the effect of cro insurance on the investment decision. This study incororates cro insurance into real otion model to see the effect of cro insurance on investment decision. Secifically, the urose of this study is to set u a real otion model with cro insurance and investigate the effect that cro insurance has on the entry threshold as an investment criterion and exit threshold as a disinvestment criterion. For the alication, we choose table grae roduction in California that accounts for 90% of domestic grae roduction (USDA-ERS). Currently, only yield insurance is available for table graes as a cro secific insurance in California. However, adjusted gross revenue (AGR) and the recently develoed AGR-Lite rovides revenue insurance as whole farm insurances that include several cros in several states such as California, Oregon, and Florida (USDA- RMA 003). There is a high otential to introduce revenue insurance for table graes as

18 7 a cro secific insurance in other states including California according to the ARPA in 000. Thus revenue insurance also is considered in this study. It is exected that using the real otion aroach to evaluate the effect of cro insurance on investment decisions will contribute to the investment literature. This study also will include the effects of cro insurance on investment decision, such as the effect of minimum level of revenue guarantee or subsidy effect on investment decisions. In addition, the results of this study will be useful to other otential regions, such as southern Arizona, northern New Mexico, and Texas that may grow table graes (Stein and McEachern). In the following section, we intuitively exlain the entry and exit thresholds for standard NPV and real otion aroaches. Then the actual model, data, and results follow... Entry and Exit Thresholds for Standard NPV and Real Otions Entry and exit thresholds are art of the decision criterion when using the real otion method. The entry and exit thresholds can be different when the NPV is used instead of real otions. This section illustrates these differences. To make the comarison easier, we assume a totally irreversible investment that roduces no salvage value. The inclusion of the salvage value comlicates the model derivation without adding anything to the comarison. This assumtion is relaxed in the section.3 so that the effect of the salvage value on investment decision is exlored using the real otion aroach.

19 8..1. Entry and Exit Thresholds with Standard NPV The NPV is defined as the discounted value of the difference between future revenue flow R t and future cost flow C t minus initial investment cost (sunk cost) I 0. With finite time horizon and discrete time notation, standard NPV can be denoted as T Rt Ct (.1) NPV = t t I0 t= 0 (1 + ρ) (1 + ρ), where ρ is the risk adjusted rate that consists of the risk free rate and the risk remium rate and T is the number of years of the roject s life. It requires a non-negative NPV at t=0 for the investment to be accetable. To maintain the consistency with the real otion aroach, the investment is assumed to be eretual, and R and C are constant through time. In addition, the risk free rate, r, is chosen to discount the relatively stable cost C. By assuming a rate of growth or drift (trend) rate α in revenue, the NPV is (.) NPV = R C I δ r, where δ is the risk and growth adjusted discount rate that is ρ minus the drift rate α, such that δ = ρ - α (Dixit and Pindyck). This adjustment is justified when the revenue flow has a constant-growth rate (trend) because it revents underestimating the true revenue flow. The use of continuous time analytics is helful to make the transition from the standard NPV decision criterion to the revised decision criterion for investments under real otions. The first ste is to consider the decision criterion, the entry threshold, to

20 9 answer the question of when to invest, not simly invest or not invest that is inherent in the NPV criterion. In equation (.), the entry threshold is denoted as R H and is defined as the level of revenue flow R that makes the NPV zero and thus guarantees at least no loss from investment. The entry threshold rovides a trigger value such that a decision maker invests when R is at least as high as R H. Thus the entry threshold R H is denoted as (.3) RH δc = + δ I, r where the right hand side of equation (.3) is the long-run average cost. The decision rule of equation (.3) is to enter the business if the revenue flow is equal to or greater than the entry threshold R H and not to enter the business otherwise. After the investor enters the business, the investor must decide when to disinvest. The investor must consider the loss of revenue that is incurred from disinvestment, the savings in costs, and the exit cost E. Thus, the NPV in equation (.) can be altered to reflect the decision to disinvest and is written as (.4) NPV = R C E δ + r. In equation (.4), the exit threshold denoting R L, the trigger value to disinvest, is defined as the level of revenue flow R that makes the NPV zero and thus guarantees at least no loss from disinvestments. Thus, the exit threshold R L is denoted as δc (.5) RL = δ E. r

21 10 The decision rule of equation (.5) is to exit the business if revenue flow is less than the trigger value R L and to stay in business otherwise. The entry and exit thresholds with the real otions are comared with those with the NPV aroach in the following section.... Entry and Exit Thresholds with Real Otions In this section, intuitive exlanations of the real otion aroach are rovided. The differences between the entry and exit thresholds using NPV and the real otion aroach are resented for the intuitive understanding. To determine the entry threshold with real otions, we assume that the farmer has an exclusive right to invest so that the revenue movement is not restricted from cometition. This assumtion makes the model derivation easier but this assumtion is relaxed later and a cometitive market is modeled. Also the disinvestment (exit) decision is not considered for the entry threshold decision here because it requires simultaneous decision making with entry decision and this makes the comarison with standard NPV difficult. An inactive farmer is a farmer who is currently not farming but can otentially invest in a farming oeration. If an inactive farmer gets in farming roduction, he must buy land and machinery. While the farmer is inactive, he has an otion to invest and this otion has a value, V 0 (R). The value of this otion results because of the uncertainty and irreversibility of the investment. By waiting, the inactive farmer gains more information and can avoid investing if later the investment turns out to be unrofitable. If an inactive

22 11 farmer enters farming by exercising an otion to invest, he/she looses the otion to invest and instead becomes an active farmer who is currently engaged in farming. That is, by entering farming, an inactive farmer gets a value of V 1 (R) with the exense of the investment cost I and becomes an active farmer. The entry decision is made when the V 1 (R) I is at least greater than or equal to V 0 (R), where the entry threshold to exactly meet this condition is denoted by R H. Intuitively, the value of V 1 (R) I reresents the NPV but the value of the otion to invest V 0 (R) is unique in the real otions aroach. For the mathematical comarison with NPV, denote V 1 (R) as the value of an active (current) farm, V 0 (R) the value of an inactive (otential) farm that is called the value of waiting or the value of the otion to invest, I as the investment cost, and R is the revenue flow with a Brownian Motion rocess. 1 Then the value of waiting V 0 (R) is defined as 1 (.6) V ( R) = A R β, 0 1 where A 1 > 0 and β 1 > 1 and A 1 is the constant to be determined, and β 1 is the ositive root of the fundamental quadratic equation (The derivation of this formula is obtained in the equation (A.) through (A.4) of the aendix A). The otion value of waiting V 0 (R) is nonnegative because the farmer can avoid the bad state of nature by waiting. This value is also an increasing function of revenue flow R because the otion to invest works as the American call otion, where the call otion value increases with the market rice of the underlying asset. 1 The origins of Brownian motion rocesses are in hysics, secifically the characteristics of a heavy article being bombarded by lighter articles (Salin).

23 1 The value of an active farm V 1 (R) is assumed as the same as the standard NPV without investment cost from equation (.) for the comarison urose. A more secific derivation of the value of an active farm is obtained from Aendix A. Then the value of an active farm V 1 (R) is defined as (.7) ( ) R C V1 R = δ r, where δ and r are defined in section..1. The two value functions V 0 (R) and V 1 (R), are grahed in the figure.1 (Dixit 199) to examine the investment (entry) decision with the real otion aroach. In the grah, the vertical axe V denotes the roject value and I denotes the initial investment cost. The horizon axe denotes revenue flow R. Project value (V) The value of an inactive farm [ V ( R ) 0 ] The value of an active farm [V1(R) I] 0 R 0 R 1 Revenue flow (R) Investment cost (- I) Figure.1. Entry thresholds with real otions and standard NPV

24 13 In the figure.1, the R 0 and R 1 are the entry thresholds with standard NPV and the real otion aroaches, resectively, and V 0 (R) and V 1 (R) I are the value of an inactive farm and the value of an active farm net of investment cost (sunk cost), resectively. As mentioned, standard NPV requires a non-negative roject value as the investment rule so that the entry threshold hits the zero roject value at R 0 (see equation (.3)). On the other hand, the real otion aroach requires two conditions, value matching condition and smooth asting condition, for the investment criterion. Value matching condition is a condition that the value of an active farm is equal to the value of an inactive farm. That is, it requires an entry threshold R H that makes the value of an inactive farm (otential farm) V 0 (R) equal the value of an active farm V 1 (R) when an inactive farm sends the investment cost I and in return gets a roject value V 1 (R). Smooth asting condition is a tangency condition that requires the marginal value of an inactive farm is equal to the marginal value of an active farm. That is, it requires that, at the entry threshold R H, the sloes of the value of an inactive farm and the value of an active farm net of the investment cost be the same. In the figure.1, the restriction of smooth asting condition ushes the curve of V 0 (R) above that of V 1 (R) and makes a tangency oint by adjusting unknown A 1. This tangency oint determines the entry threshold that makes the marginal value of inactive farm equal to the marginal value of an active farmer. In the figure.1, the entry threshold R 1 meets those conditions. If revenue flow R is less than the entry threshold R 1, then the value of an inactive farm V 0 (R), called the value of waiting, is greater than the value of an active farm V 1 (R) net of investment cost

25 14 I and thus waiting is the better olicy. If revenue flow R exceeds at least the entry threshold R 1, then exercising the investment otion by sending investment cost I and getting a roject is the better olicy. At this time, by exercising the investment otion and getting a roject, the farmer loses the otion value of waiting. The real otion aroach requires higher entry threshold than standard NPV by the difference between R 1 and R 0. The difference of entry thresholds between the two aroaches is caused by the otion value of waiting. The real otion aroach catures the value of waiting, while the NPV does not. In reality, business decision-making should consider oerating flexibility and thus requires higher investment threshold than the NPV (Donaldson and Lorsch). If the otion value of waiting is zero, then the real otion aroach roduces the same entry threshold R 0 as standard NPV. Mathematically, the value matching condition and the smooth asting condition for the entry decision are reresented as (.8) V 0 (R H ) = V 1 (R H ) I, (.9) V ( R ) = V ( R ). ' ' 0 H 1 H Equation (.8) and (.9) can be solved for R H from equation (.6) and (.7), where A 1 and R H are unknowns to be determined. To get the solution for R H, first relace equation (.8) and (.9) with equation (.6) and (.7). Then divide equation (.8) by equation (.9) and then rearrange for R H. The solution for the entry threshold is β1 δc (.10) RH = + δ I β r, 1 1

26 15 where β 1 /(β 1-1) is greater than 1 because β 1 > 1. Equation (.10) shows that the entry threshold with real otions is greater than the entry threshold with standard NPV in equation (.3) by a factor of β 1 /(β 1-1). Second, the exit threshold in a real otion aroach can be easily derived and comared with the exit threshold in standard NPV when we follow the same rocedure exlained in the entry threshold with real otions. All the definitions and terms used for the entry threshold both in NPV and real otions and used for the exit threshold in NPV are used for the exit threshold in real otions. The exclusive right to exit and no investment (entry) decision are assumed with the same reasons as in the entry threshold. An active farmer can exit the farming when he/she exects unfavorable market or roduction conditions. The exit decision can be done any time in the future deending on the state of nature. Thus, the exit decision at the current time creates an oortunity cost by losing the future oortunity for the decision-making and this is referred to as the otion value to exit. The Real otions aroach can cature this disinvestment (exit) flexibility as the otion value to exit. This otion value increases the roject value and thus decreases the exit threshold comared with NPV. For the understanding of the exit threshold in real otions, we simly resent the mathematical comarison between the NPV and real otions aroaches. Given the assumtions and definitions above, the value function for an inactive farm V 0 (R) is zero and the value function of an active farm V 1 (R) is defined as β R C (.11) V1 ( R) = B R +, δ r

27 16 where B > 0 and β < 0 and B is the constant to be determined, β is the negative root of the fundamental quadratic equation (The derivation of this formula is obtained in the equation (A.) through (A.4) of the aendix A), and BR β The otion value to exit BR β is the otion value to exit. is nonnegative because the farmer can exit the farming whenever the bad state of nature is exected in the future. Thus as the ossibility of the bad state of nature increases, the otion value to exit increases, too. This value is also a decreasing function of revenue flow R because the ossibility to exit the farming decreases as revenue flow increases. To get the exit threshold in real otion, value matching condition and smooth asting conditions are required as in the entry threshold. Value matching condition is a condition that the value of an active farm is equal to the value of an inactive farm. That is, it requires an exit threshold R L that makes the value of an active farm V 1 (R) equal the value of an inactive farm V 0 (R) when an active farm sends the exit cost E and in return gets the otion value to invest V 0 (R). Smooth asting condition is a tangency condition that the marginal value of an active farm is equal to the marginal value of an inactive farm. That is, it requires that, at the exit threshold R L, the sloes of the value of an active farm and the value of an inactive farm net of the exit cost be the same. Mathematically, the value matching condition and the smooth asting condition for the exit decision are reresented as (.1) V 1 (R L ) = V 0 (R L ) E, (.13) V ( R ) = V ( R ). ' ' 1 L 0 L

28 17 Equation (.1) and (.13) can be solved for R L from equation (.11) and V 0 (R) = 0, where B and R L are unknowns to be determined. To get the solution for R H, first relace equation (.1) and (.13) with equation (.11) and V 0 (R) = 0. Then divide equation (.1) by equation (.13) and then rearrange for R L. The solution for the exit threshold is β δc (.14) RL = δ E β r, 1 where β /(β -1) is less than 1 because β < 0. Equation (.14) shows that the exit threshold with real otions is less than the exit threshold with standard NPV in equation (.5) by a factor of β /(β -1)..3. Model The entry and exit model in this study is set u with two cases, one without cro insurance, and the other with cro insurance to see the effect of cro insurance on investment decision-making. These models form simultaneous equations to be solved for the entry and exit threshold. The assumtions to derive the models are resented. Then the entry and exit models, without and with revenue insurance, are resented, resectively Model Assumtions First, we assume a cometitive industry to derive the entry and exit model (Leahy). At the farm level, an investment or caital budgeting choice is a long-term and strategic decision. In a long-term ersective, many farmers can join or leave grae

29 18 farming according to market conditions. They act cometitively so that abnormal roject values, either higher or lower roject value comared with zero roject value, disaear. That is, in a cometitive industry, ositive roject values induce more inactive farmers to enter farming, where inactive farmers are farmers who could otentially enter grae farming. Negative roject values lead to active farmers leaving the business, where active farmers are farmers who are currently engaged in farming. The cometition leads to a dynamic equilibrium in the long run through rice and thus revenue adjustment. To emhasize the entry and exit thresholds in a cometitive market, following Leahy, the uer and lower reflecting barriers are interchangeably used for the entry and exit thresholds in model derivation. In a cometitive market, when the rice flow or revenue flow reaches the entry threshold, new farmers enter the business that increases the outut quantities in the market. As a result, the market rice or revenue is slightly brought back to a lower level from the entry threshold immediately. When the market rice or revenue reaches the exit threshold, active farmers exit the farming, thus increasing market rice or revenue slightly. Thus entry and exit thresholds work as the uer and lower reflecting barriers in a cometitive market, resectively. However, in any case, the arbitrage drives the market rice and revenue into the entry threshold for inactive farms and exit threshold for active farms, thus resulting in the equilibrium rices or revenues, resectively. Thus, when making an investment decision, the farmer needs to consider the otential entrance of cometitive farmers. We assume that there are many grae farmers and their cometitive investment decisions affect market rice. We also assume a homogeneous roduct so that each farmer has the same rice.

30 19 Uncertainty in the cometitive industry could be farm secific or industry-wide (or aggregate uncertainty), where the former can be exlained by the uncertainty of management skill (or technology) and commodity secific demand and the latter can be exlained by aggregate demand uncertainty or a widesread disaster in roduction. In this aer, we focus on the industry-wide uncertainty because much of the uncertainties in agriculture are caused by market conditions or roduction deendency on nature. In a cometitive industry, rice is an endogenous variable determined by the demand and roduction relationshis, where both are assumed uncertain, thus, rice moves stochastically. Yield also changes stochastically because of roduction uncertainty. The yield and rice correlation is included in the secification of rice and yield stochastic rocesses in the next section. In the model, the investment costs are assumed artially reversible, which results in salvage values from the roject, such as lands, facilities, and machinery. On the other hand, the exit from the farming entails costs, such as the cost to remove the vineyard. In this study, we assume that the exit costs totally counteract the salvage values so that both factors can be eliminated in the model. However, we conduct sensitivity analysis to see the effect of the exit costs and salvage values on the entry and exit thresholds. Once a farmer exits farming, investment costs to enter farming again are the same as before, so that a temorary susension and resumtion without a enalty is not allowed. Variable cost is assumed relatively redictable and thus the risk free rate is used to discount it (Pindyck; Price and Wetzstein).

31 0 To derive the entry and exit model, we can use a dynamic rogramming aroach or contingent claim analysis that lead to the same solution (Dixit and Pindyck). The latter requires a risk free ortfolio with existing assets to evaluate the otion value to invest. However, a dynamic rogramming aroach can be used to maximize the resent value of cash flow without such assumtion. This aroach requires the assumtion of risk references or risk adjusted discount rates. In this study, we follow the dynamic rogramming aroach because the agricultural uncertainty cannot be easily relicated. We use the risk-adjusted discount rate to discount uncertain revenue flow..3.. Entry and Exit Model with No Revenue Insurance The stochastic evolution of the value of a roject over time affects the investment decision. The stochastic rocesses of relevant variables are needed to obtain the stochastic evolution. We assume rice and yield are stochastic variables that follow geometric Brownian motion (Turvey 199b; Price and Wetzstein). When rice and yield follow geometric Brownian motions, revenue R also follows a geometric Brownian motion: (.15) dr = α R Rdt + σ R Rdz R, where α is the drift rate, σ is the volatility rate, dt is a small time increment, and dz is the increment of the standard Brownian motion (or Wiener rocess). The mathematical rocedures to derive the entry and exit model by Dixit and Pindyck are rovided in aendix A.

32 1 Given the stochastic rocess of equation (.15), the value of an inactive farm that has the oortunity to enter the farming, and the value of an active farm that has the otion value to exit the farming are determined simultaneously. In a cometitive industry, the entry and exit thresholds lay roles as the uer and lower reflecting barriers that are the equilibrium revenues for inactive farmers and active farmers, resectively (Leahy). Dixit and Pindyck rovide the simultaneous equations for the solution of thresholds with rice uncertainty under dynamic equilibrium in a cometitive industry. 3 The simultaneous equations are given as β1 β R H C (.16) ( B1 A1 ) RH + ( B A ) RH + = I δ r β1 1 β 1 1 (.17) β1( B1 A1 ) RH + β( B A ) RH + = 0 δ β1 β R L C (.18) ( B1 A1 ) RL + ( B A ) RL + = E δ r β1 1 β 1 1 (.19) β1( B1 A1 ) RH + β( B A ) RH + = 0, δ where β i are the roots of the fundamental quadratic equation. A i and B i are constants to 1 be determined, where A1 R β is the value of the otion to invest for an inactive farm and B R β is the value of the otion to exit for an active farm. A R β is the increase in the 1 value of an inactive farm from the lower reflecting barrier and B1 R β is the decrease in the value of an active farm from the uer reflecting barrier caused by cometitions. As exlained in section.3.1, in a cometitive market, the arbitrage drives the market rice 3 Detailed rocedures are rovided in aendix A.

33 or revenue at the uer reflecting barrier for an inactive farm but does not allow them to rise above that barrier. Thus the value of an inactive farm must be adjusted to the downward direction. Also the arbitrage revents the market rice or revenue from going down below the lower reflecting barrier for an active farm. Thus the value of an active farm must be adjusted the uward direction. C is the variable cost, I is the investment cost, r is the risk free rate of return, δ is the risk and growth adjusted discount rate. E is the exit cost adjusted by the salvage value. δ is commonly assumed to be greater than zero (ρ > α) otherwise no otimum exists and waiting is the best decision. Equations (.16) and (.18) are value-matching conditions, one for the entry threshold and the other for the exit threshold, that require the value of waiting to equal the value of investing at the entry and exit thresholds, resectively. Equations (.17) and (.19) are smooth-asting conditions, one for the entry threshold and the other for the exit threshold, that require the same sloes of the value of waiting and the value of investing at each threshold level. However, in a ersective of the uer and lower reflecting barriers caused by a cometitive equilibrium, those conditions can be interreted as the results of the arbitrage among inactive farmers and active farmers, resectively. The last two terms in equations (.16) and (.18) denote the exected net resent values of an infinite annuity of rofit, where revenue flow is discounted by the risk and growth adjusted discount rate and constant cost is discounted by risk free rate. By setting (B 1 -A 1 ) and (B -A ) as K 1 and K, we can solve the simultaneous equation with four unknowns, K 1, K, R H, and R L. These equations are highly non-linear in the thresholds, R H and R L, thus the symbolic solution cannot be obtained and instead a

34 3 numerical rocedure is required to get the solution. We use the MathCad 8 Professional to solve this simultaneous equation. In the model, the otimal entry and exit thresholds are equilibrium revenue levels worked as uer and lower reflecting barriers, resectively, which result in zero otion value of waiting for inactive farmers (A 1 =A =0). From the entry and exit thresholds, the inaction ga is defined as the difference between the entry threshold and the exit threshold that leads to no action to exit the farming from entering the farming. This concet of inaction ga is sometimes useful for the interretation of the results Entry and Exit Model with Revenue Insurance Revenue insurance guarantees a revenue floor ( R ) but also requires a constant insurance remium, thus increasing the variable cost. Thus, the revenue insurance affects the entry and exit thresholds. The revenue guarantee induces more inactive farmers to invest and more active farmers to stay in farming. However, revenue insurance requires that an active roducer ay the insurance remium, which reduces the net revenue flow and decreases the attractiveness of entry, so that we need to consider the trade off between the revenue guarantee and insurance remium. To see the effect of revenue insurance on the entry and exit decision, the model can be set u in two cases. The first case is when the revenue guarantee, R, is greater δ than the exit threshold, R L, but less than the variable cost C Φ, ( RL R CΦ ), where r the variable cost includes insurance remium Φ, thus defined as C Φ = C+Φ. The second case is when the revenue guarantee is greater than the variable cost but less than the long

35 4 δ δ run average cost ( CΦ R CΦ + δ I ). In this study, we focus on the first case r r because it is rare for the revenue guarantee from cro insurance to exceed the variable cost otherwise buying revenue insurance always guarantees nonnegative rofit that is not common in agricultural roduction. Even though the revenue guarantee is less than the variable cost, two sub-cases must be considered (figure.). Figure. shows these two sub-cases of revenue flow to be modeled for the study, where R L is the exit threshold, R is the revenue flow, R is the revenue guarantee, and R H is the entry threshold. In the figure., the first sub-case is RL R R and the second sub-case is R R RH. In the first sub-case, where revenue is greater than the exit threshold but less than the revenue guarantee, RL R R, the revenue guarantee is binding. In the second subcase, where revenue is greater than the revenue guarantee but less than entry threshold, R R R H, the revenue guarantee is not binding. 1 st Case ( RL R R ) nd Case ( R R RH ) 0 R L R R H R (Exit threshold) (Revenue guarantee) (Entry threshold) (Revenue flow) Figure.. Two cases of revenue flow to derive the entry and exit model under revenue insurance

36 5 Consider the first sub-case, RL R R. If revenue is greater than the exit threshold and less than the revenue guarantee, then the value of investing for the active farmer 4 is R CΦ β1 β (.0) V ( R) = + B1 R + BR, r r where C Φ is the variable cost with insurance remium, which includes a subsidy from the government, and B 1 and B are the constants to be determined. The first two terms in equation (.0) are the exected resent value of an infinite annuity of rofit with revenue insurance, where the revenue has the lower boundary caused by revenue guarantee and thus discounted by the risk free rate. The other two terms are the value of an active farm adjusted by reaching the revenue guarantee and the otion value to exit for an active farm, resectively, which are caused by revenue insurance and cometitions. As before, we also have the value matching condition V(R L )= -E and smoothasting condition V '( R L ) = 0. This value matching condition is obtained by setting the otion value of waiting to zero (V 0 (R) = 0) because the otion value of waiting in a cometitive market is zero from cometitions. The ositive otion value of waiting means the ossibility of the ositive roject value, which induces more farmers to the farming and thus makes the otion value of waiting disaear in a cometitive market. However, the value of an active farm is adjusted from the reflecting barrier caused by 4 The derivation of equation (.0) is rovided in aendix A.

37 6 cometitions. This adjusted value in a cometitive market works like the otion value of waiting for an inactive farm with the exclusive right to invest. For the second sub-case when revenue is greater than the revenue guarantee, but less than the entry threshold, R R RH, the roject value is R CΦ β1 β (.1) V ( R) = + B3R + B4R, δ r where B 3 and B 4 are the constants to be determined. In equation (.1), the exected resent value of an annuity of revenue is discounted by the risk and growth adjusted discount rate, where the revenue is not bounded from the floor, but the cost is discounted by the risk free rate. The key arameter of the real otion model affected by cro insurance is the discount rate. Thus given cro insurance, we need to adjust the discount rate of revenue because the revenue guarantee eliminates downside risk, thus changing the distribution of revenue. We reduce the risk remium rate in the discount rate of revenue by the insurance coverage level (50-75%) of the exected revenue because the farmer can eliminate the downside risk by that much. However, we still use the same volatility rate to consider the otential movement of revenue flow in equation (.0) and (.1) even though the actual revenue flow is bounded by the revenue floor. When the otential revenue in a cometitive industry is far below the revenue guarantee, the farmer knows that the actual revenue received stays at the revenue guarantee longer than if the otential revenue were close to the revenue guarantee. The farmer refers the latter to the former for the investment decision. Thus, the otential movement of revenue is an

38 7 imortant factor for the farmer s investment decision with cro insurance, which is consistent with the assumtion used by Dixit and Pindyck. Given the arameters and adjustments for cro insurance, the derivation of the otion value model roceeds in the usual way. The other two terms in equation (.1) are the value of an active farm adjusted by reaching the revenue guarantee and the value of the otion to exit for an active farm, resectively, which are caused by revenue insurance and cometitions. The resective value matching and smooth-asting conditions are V(R H ) = I and V '( R H ) = 0. Assuming the value function V(R) is continuously differentiable around R, we get the following equation (.) by equating equations (.0) and (.1) at R and rearranging them. Then by differentiating equation (.) with resect to R at R, equation (.3) is obtained. These are value matching and smooth asting conditions to connect the first sub-case and the second sub-case under the continuous revenue flow in the figure.. R R β1 β (.) + ( B1 B3 ) R + ( B B4 ) R = 0 r δ (.3) 1( B1 B3 ) R β β + β + β( B B4 ) R = 0. δ Additionally, from the value matching and smooth-asting conditions, V(R L )= -E and V '( R L ) = 0 for the exit threshold from equation (.0) and V(R H ) = I and V '( R H ) = 0 for the entry threshold from equation (.1), we have four more equations to solve. R CΦ β1 β (.4) + B1 RL + BRL = E r r

39 8 β1 1 β 1 (.5) β B R + β B R = 1 1 L L 0 RH CΦ β1 β (.6) + B3RH + B4RH = I δ r 1 β1 1 β 1 (.7) + β1b3 RH + βb4rh = 0. δ Now we have six simultaneous equations from (.) to (.7) and six unknowns that include four constants, B 1, B, B 3, and B 4, and two thresholds, R H and R L. These equations also are highly non-linear in the thresholds, R H and R L, thus analytical solution cannot be obtained and thus numerical solution is required..4. Data Table.1 summarizes data on California table graes used in this study (California Agricultural Statistics Service). The rice and yield series are statewide from 1987 to 00. In the next section, we rovide data with and without revenue insurance Data without Revenue Insurance Yield and rice volatility rates and drift rates are estimated from the logarithm of data because the real otion aroach in this study assumes the geometric Brownian motion of the stochastic rocess, where the volatility rate is the rate for variability of revenue flow and the drift rate is the rate for trend of revenue flow. The yield and rice series show ositive drift rates (trends) of and 0.033, resectively, and the yield and rice volatility rates are 0.14 and 0.0, resectively. The correlation between the yield and rice is Given the drift rates and volatility rates in yield and rice, those