Agricultural Systems 127 (2014) 61–69

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Agricultural Systems

journal homepage: www.elsevier .com/locate /agsy

The impact of field size and energy cost on the profitabilityof supplemental corn irrigation

http://dx.doi.org/10.1016/j.agsy.2014.01.0010308-521X/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 865 974 7468; fax: +1 865 974 7484.E-mail addresses: cboyer3@utk.edu (C.N. Boyer), jlarson@utk.edu (J.A. Larson),

rrobert3@utk.edu (R.K. Roberts), athompson@utk.edu (A.T. McClure), dtyler@utk.edu (D.D. Tyler).

Christopher N. Boyer a,⇑, James A. Larson b, Roland K. Roberts c, Angela T. McClure d, Donald D. Tyler e

a Department of Agricultural and Resource Economics, The University of Tennessee, 302-I Morgan Hall, Knoxville, TN 37996, USAb Department of Agricultural and Resource Economics, The University of Tennessee, 302 Morgan Hall, Knoxville, TN 37996, USAc Department of Agricultural and Resource Economics, The University of Tennessee, 308B Morgan Hall, Knoxville, TN 37996, USAd Department of Plant Sciences, The University of Tennessee, West Tennessee Research and Education Center, 605 Airways Blvd., Jackson, TN 38301, USAe Department of Biosystems Engineering and Soil Sciences, The University of Tennessee, West Tennessee Research and Education Center, 605 Airways Blvd., Jackson, TN 38301, USA

a r t i c l e i n f o

Article history:Received 6 December 2012Received in revised form 12 July 2013Accepted 15 January 2014Available online 11 February 2014

Keywords:CornEconomicsIrrigationLinear response stochastic plateauNitrogen

a b s t r a c t

Supplemental irrigation in corn production is increasing for humid regions across the world. Little isknown about the profitability of irrigating corn in the humid southeastern region of the United States.Our objective was to determine the breakeven price of corn where investment in center-pivot irrigationwould be profitable in Tennessee. We considered the effects of field size, energy price, and energy sourceon the breakeven price of corn. We estimated yield response to nitrogen (N) for irrigated and non-irrigated corn, and allowed expected yield and economically optimal N fertilization to vary with thebreakeven price. Field size and the cost of running electricity to the center-pivot were two importantfactors in choosing between diesel and electricity as the energy source. The breakeven price of cornranged between $249–$283 Mg�1 for the small-sized field, $168–$190 Mg�1 for the medium-sized field,and $149–$171 Mg�1 for the large-sized field. As field size increased, electricity became moreeconomically viable relative to diesel. At current corn prices, irrigating corn appears profitable on fieldsgreater than 51 ha. However, historically, the probability for the breakeven corn price occurring is zerofor the small-sized field, between 6–14% for the medium-sized field, and 12–27% for the large-sized field.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Demand for food crops has been increasing in response to anumber of factors including a growing global population, expand-ing economies in developing countries, and rising biofuels produc-tion among other factors (Trostle, 2008). To meet the growingdemand for food, more than half of world cereal production isanticipated to be produced using irrigation by 2050 (Rosegrantet al., 2009). Globally, irrigation is expected to expand in humidregions that generally receive sufficient annual rainfall to growcrops without irrigation in most years (Mullen et al., 2009;Rosegrant et al., 2009; Schaible and Aillery, 2012). The primarypurpose of irrigation in humid regions is to supplement rainfedcrop production during periodic short-term droughts.

Research has shown that timely supplemental irrigation inhumid regions can increase yields (Bruns et al., 2003; Smith andRiley, 1992), decrease crop disease (Smith and Riley, 1992; Vories

et al., 2009), and stabilize yields (Apland et al., 1980; Daltonet al., 2004; Epperson et al., 1993; Evans and Sadler, 2008;Henning, 1989; Vories et al., 2009; Salazar et al., 2012). Anotheradvantage of supplemental irrigation in humid regions is theavailability of abundant water for irrigation, and that water is ofteninexpensive or free (Gonzalez-Alvarez et al., 2006; Mullen et al.,2009). For example, the doctrine of riparian water rights is fol-lowed by most states in the humid subtropical zone of the south-eastern United States (Christy et al., 2005; Myszewski et al., 2005).The riparian doctrine states that water rights are not quantitativelyfixed and water is not explicitly priced (Griffin, 2006). When wateris inexpensive or free, farmers make irrigation decisions based onwater needs and the energy cost of pumping water, not the priceof water (Gonzalez-Alvarez et al., 2006; Mullen et al., 2009).

In the United States, supplemental irrigation of crops in humidregions such as the southeast has been growing rapidly (Daltonet al., 2004; Gonzalez-Alvarez et al., 2006; Schaible and Aillery,2012). Schaible and Aillery (2012) reported that the largestincrease in irrigated crop production in the United States since1998 has been in the southeastern states of Georgia, Alabama,and Mississippi. The majority of the growth in irrigation for thisregion has been for corn production (Salazar et al., 2012; Vories

62 C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69

et al., 2009). Vories et al. (2009) noted that 62% of all corn hectaresin the Mid-South (Louisiana, Mississippi, Alabama, Arkansas, Ten-nessee, and Kentucky) were irrigated in 2003, and Lee (2013) sta-ted that 72% of Georgia corn hectares were irrigated in 2011.

A plausible explanation for the increase in irrigated corn pro-duction in the southeastern United States may be the increasedprice for corn since 2006 (Mullen et al., 2009). Even though irriga-tion in the southeastern United States is increasing for corn pro-duction and the price of corn is historically high, little is knownabout the long-term profitability at the farm-level of irrigatingcorn in the humid southeastern United States. For example, centerpivot irrigation systems are more expensive to install on the smal-ler and more irregularly shaped fields that are common in the east-ern United States (Hatch et al., 1991), but may be profitable underhigher corn prices.

Our research objective was to evaluate the breakeven corn priceabove which a center-pivot irrigation system becomes profitable inthe southeastern United States. Annual rainfall is sufficient to pro-duce corn but irrigation is used as a supplement. We consideredthe effects of different energy sources, energy prices, and field sizeson the breakeven corn price. Stochastic yield response to N fertil-izer was estimated for irrigated and non-irrigated corn, and ex-pected yields and profit-maximizing N fertilizer rates wereallowed to vary with the breakeven corn price. Partial budgetswere used to calculate net cash flows over time for irrigated andnon-irrigated corn, and a financial analysis was performed overthe life of the irrigation system to solve for the time-adjustedbreakeven corn price.

The breakeven corn prices were compared to historical cornprices to determine the probability that a producer who investsin center-pivot irrigation would achieve a breakeven profit of zero.Our framework and results will help farmers evaluate the profit-ability of irrigation investment in other southeastern states as wellother humid regions in the world. Furthermore, the results haveimplications for future agricultural water management in thesoutheastern United States and specifically Tennessee.

2. Literature review

Several studies analyzed the feasibility of investing in irrigationsystems at the farm level (Caswell and Zilberman, 1986; Guerreroet al., 2010; Letey et al., 1990; O’Brien et al., 2001; Peterson andDing, 2005; Seo et al., 2008). These studies, however, focus on aridregions where water is scarce and irrigation is vital for cropproduction. The aforementioned analyses are insightful for aridregions because they demonstrate methods to reduce irrigationcosts. However, water is relatively cheap and abundant in thesoutheastern United States and other humid areas, and producershave little incentive to conserve water or increase water use effi-ciency (Sheriff, 2005; Vories et al., 2009). Therefore, these studiesprovide little insight into the profitability of irrigating crops inhumid regions such as the southeastern United States.

Mullen et al. (2009) evaluated the factors driving irrigationwater demand in the southeastern United States using a multi-cropproduction model. Since the riparian doctrine is widely recognizedin this region, Mullen et al. (2009) followed Gonzalez-Alvarez et al.(2006) by using the energy cost of pumping water as a proxy forthe price of water. They found that energy cost slightly influencedwater demand, but crop prices have the greatest influence on irri-gation water demand. Other economic research on irrigation in hu-mid regions has primarily focused on production risk management.Boggess et al. (1983) determined optimal irrigation scheduling thatmaximized net returns, and Boggess et al. (1985) surveyed farmersin the southeastern United States to determine their perception ofusing irrigation to manage production risk. Dalton et al. (2004)

compared using irrigation with enrolling in crop insurance to man-age potato production risk in Maine in the northeastern UnitedStates under humid conditions. They found that crop insurancewas inefficient to minimize producers’ production risk in humidregions, and that supplemental irrigation was beneficial dependingon the scale (i.e., field size) of the system with a larger scale provid-ing more risk-management benefits.

More recently, DeJonge et al. (2007) simulated yields for irrigat-ing corn in Iowa, and calculated the breakeven corn price for irriga-tion on a 52 ha field. They found a breakeven corn price forirrigation of $182.18 Mg�1. Irrigation was not profitable since theaverage price of corn used to calculate net returns was $79 Mg�1

($2 bu�1). Although DeJonge et al. (2007) provide useful insights;they used simulated rather than actual yield data to estimatebreakeven prices. In addition, irrigating corn in humid regionsmay be profitable given the higher corn prices since 2006, the lastyear of their study. In our literature review, we have found no stud-ies evaluating the profitability of irrigated corn production in hu-mid regions using actual corn yield data rather than simulatedyield data. The impact of field size, energy source, and energy priceon the breakeven price for corn also has not been studied.

Another limitation of many corn irrigation studies is the exclu-sion of inputs other than water (e.g., DeJonge et al., 2007). Alongwith water, nitrogen (N) fertilizer is likely the most important in-put in corn production (Stone et al., 2010). Research has shownthat N fertilizer provides the largest economic return per dollarspent relative to all other farm inputs (Pikul et al., 2005). A largenumber of studies have focused on estimating the profit-maximiz-ing N fertilization rate for corn (e.g., Bullock and Bullock, 1994;Cerrato and Blackmer, 1990; Frank et al., 1990; Llewelyn andFeatherstone, 1997). These studies show that as the price of cornand N change, the economically optimal N fertilization rate alsochanges. For a profit-maximizing corn producer, an increase(decrease) in the price of corn results in an increase (decrease) inthe optimal N fertilization rate. Irrigation and N fertilizer arecomplements in row crop production, so irrigating corn will likelyincrease both yield and the optimal N fertilization rate (Dinneset al., 2002; Stone et al., 2010; Vickner et al., 1998). Stone et al.(2010) estimated corn yield response functions to N in the south-eastern United States, and found that optimal rates vary betweenirrigated and non-irrigated corn. Therefore, the corn price andthe physical relationship between yield, irrigation, and N impactscorn producers’ net returns. To avoid overstating or understatingthe profitability of irrigation, the physical relationship betweenyield, irrigation, and N should be considered along with corn andN prices.

3. Data

3.1. Yields and nitrogen rates

Corn yield data come from N fertilization experiments con-ducted at the University of Tennessee Milan Research and Educa-tion Center (35�560N, 88�430W) from 2006 to 2011. Non-irrigatedcorn was grown on a Grenada soil (fine-silty, mixed, active, ther-mic Oxyaquic Fraglossudalfs) and irrigated corn was produced ona Loring soil (fine-silty, mixed, active, thermic Oxyaquic Frag-iudalfs), which were considered well suited for corn productionin Tennessee (USDA-NRCS, 1999). The two experiments were lo-cated on fields that have been under no-till production for over adecade (Yin et al., 2011). Corn (cultivar Pioneer 33N58) wasplanted in 76-cm rows in April in rotation with soybeans. Each plotwas 4.6 m wide and 9.1 m long.

The experimental design was a randomized complete blockwith five or six N fertilization treatments as strip-plots and four

C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69 63

replications of corn grown after soybeans. The annual N fertiliza-tion rates were 0, 62, 123, 185, and 247 kg N ha�1 in 2006 and2007. In 2008, a treatment of 308 kg N ha�1 was added to theexperiments. The N source was ammonium nitrate (34–0–0;N–P–K), uniformly broadcast on the soil surface around plantingtime. P and K were applied based on University of Tennessee

Fig. 1. Non-irrigated corn yields (Mg ha�1) by nitrogen rates (kg N ha�1) from 2006to 2011 at Milan, TN.

Table 1Summary of growing season precipitation, temperature, and irrigation data, Milan, TN, 20

Month 2006 2007 2008

Monthly precipitation totals (cm)March 8.56 2.64 21.56April 8.38 8.38 25.96May 12.75 5.84 23.85June 15.06 11.18 3.86July 8.97 5.46 7.87August 8.38 2.95 1.83September 11.35 18.69 1.19Total (March–September) 73.36 55.17 84.28

Average monthly temperature (�C)March 10.17 14.61 9.36April 18.11 13.06 14.11May 19.83 21.78 19.22June 23.89 24.78 25.56July 26.56 25.33 23.72August 26.89 30.06 25.17September 19.83 23.11 22.44Average (March–September) 20.75 21.77 20.36

Monthly irrigation totals (cm)May – 1.27 –June 6.25 8.56 5.21July 7.29 10.13 6.25August 3.12 6.25 4.17Total (May–August) 16.66 26.21 15.62

Fig. 2. Irrigated corn yields (Mg ha�1) by nitrogen rates (kg N ha�1) from 2006 to2011 at Milan, TN.

soil-test recommendations. The 2006–2011 average price of Nfrom ammonium nitrate of $1.3 kg�1 was used in calculating thecash flows (USDA-NASS, 2012).

A visual representation of the corn yield data at the various Nrates is shown in Figs. 1 and 2. The data suggest a plateau functionis an appropriate model and that the plateau varies across years. Allother inputs, such as weed, pest and disease control, were the samefor the irrigated and non-irrigated experiments and followed theUniversity of Tennessee’s recommended management practices.

3.2. Irrigation rates

Supplemental water was uniformly applied to the irrigatedplots using a Valley linear irrigation system (Valmont Irrigation,Valley, NE). The supplemental water rates were based on theMOIST soil moisture management system program, which is anonline irrigation scheduler available for corn producers inTennessee (Leib, 2012a). Summary statistics for annual rainfall,average temperature, and annual quantities of water applied bymonth at Milan, TN are presented in Table 1. Irrigation wasscheduled to occur between June and August, but a drought in2007 resulted in irrigation application beginning in May. Anabove average irrigation rate was applied in 2007, a below averagerate was applied in 2009, and irrigation rates were similar to theaverage rate in the other years (Table 1).

When the irrigation investment decision is made, the corn pro-ducer does not know the future amounts of supplemental irriga-tion that will be needed. We weighted the annual irrigation ratesfrom the experiments by their respective probabilities of occurringto find an expected future irrigation rate. Drought years such as2007 and timely rainfall years such as 2009 have relatively smallprobabilities of occurring, so taking a simple average of irrigationrates would overweight those years. To weight the annual irriga-tion rates, we followed Lambert et al.’s (2007) method of creatingannual weights based on the irrigation data. In our model, theannual weights (ht) were determined as

ht ¼Y

t

/ðwtÞ,XT

t¼0

Yt

/ðwtÞ ð1Þ

06–2011. Source: NOAA, Milan, TN weather station and MOIST (Leib, 2012a).

2009 2010 2011 30-year average

11.73 8.00 16.61 12.958.13 15.24 9.78 12.2822.86 53.59 11.24 16.125.59 8.13 6.80 11.0020.07 14.99 1.42 11.185.59 5.08 1.14 7.2111.94 1.02 10.21 10.8686.26 105.89 119.61 81.51

10.58 9.39 10.72 9.4414.94 17.06 17.25 14.8419.83 21.78 19.69 19.7326.00 27.56 26.36 24.0724.61 27.61 27.86 26.0024.61 27.83 26.42 25.4522.44 23.11 20.97 21.3520.42 22.04 21.32 20.15

– – – –4.17 5.21 5.21 –3.12 9.37 9.37 –1.04 3.12 2.08 –8.33 17.70 16.66 –

64 C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69

where wt is the total irrigation water observed in year t (t = 0, . . .,T);and /ðwtÞ is the standard normal probability density function (pdf).The weighting is based on the rule of probability multiplication andassumes that the irrigation rate in time period t is independent ofthe rates in other periods (Lambert et al., 2007). The expectedirrigation rate was

PTt¼1htwt . Using the irrigation data and applying

Eq. (1) produced an expected irrigation rate of 16.12 cm ha�1 yr�1.This rate is slightly above the average annual irrigation rate of15.24 cm ha�1 yr�1 reported in the 2007 Census of AgriculturalFarm and Ranch Irrigation Survey, which summarizes land use in2008 (USDA-NASS, 2010).

4. Center-pivot costs

4.1. Investment cost

A specific irrigation cost is difficult to estimate because costschange with field size, well depth, energy source, and so on. Wegeneralized the cost of irrigating corn by estimating the cost of atypical non-towable center-pivot system (Verbree, 2012; USDA-NASS, 2010). Three irrigated and non-irrigated field sizes of25 ha, 51 ha, and 81 ha were selected to reflect the range of cornfields in Tennessee. We separated capital investment into wellinvestment and system investment (Table 2). Well investmentincluded well drilling, the pump and the power unit. Systeminvestment included spans, sprinklers and installation. Theestimated investment costs were derived from personalcommunications with irrigation dealerships in West Tennesseeand an irrigation expert (Verbree, 2012).

The center-pivot system had a useful life of 20 years and a zerosalvage value (Ding and Peterson, 2012; Guerrero et al., 2010). Weassumed the producer financed the cost of the well and systemover five years at 5% interest (Guerrero et al., 2010). The total cap-ital investment cost of the equipment was depreciated under theModified Accelerated Cost-Recovery System over five years at a25% marginal tax rate. Finally, the risk-adjusted discount ratewas 8%, which is comparable to other irrigation investment studies(Carey and Zilberman, 2002; Guerrero et al., 2010; Price andWetzstein, 1999; Seo et al., 2008).

4.2. Energy, maintenance, and labor costs

An important decision for producers in the southeastern UnitedStates is whether to use diesel or electricity to power their irriga-tion system. The annual energy costs for using diesel and electricpower to apply 16.12 cm ha�1 yr�1 were calculated followingRogers and Alam’s (2006) energy cost formulas. The weighted

Table 2Center-pivot investment costs (US $) by field size. Source: Personal communicationswith irrigation dealerships in West Tennessee and an irrigation expert (Verbree,2012)

Cost item Field size

25 ha 51 ha 81 ha

Well setupDrilling $20,000 $20,000 $20,000Pump $20,000 $24,500 $26,500Power unit $10,000 $15,200 $25,500

Irrigation rigSprinklers $2,000 $2,600 $4,500Spans $48,000 $65,000 $99,000Installation $6,700 $8,000 $9,300

Total costsField $106,700 $135,300 $184,256ha�1 $4,268 $2,692 $2,256

average pump operating pressure of 6.89 kilopascals (kPa) waschosen using data from the 2007 Census of Agricultural Farm andRanch Irrigation Survey (USDA-NASS, 2010). An average pump-liftdistance of 76.2 m was used, which is a typical well depth inTennessee (Verbree, 2012; USDA-NASS, 2010). The amount ofenergy required to pump 16.12 cm ha�1 yr�1 of water annuallywas 185.49 l ha�1 yr�1 of diesel and 689.42 kW h ha�1 yr�1of elec-tricity. Three farm diesel prices of $0.52 l�1, $0.79 l�1 and $1.06 l�1,and three commercial electricity prices of 0.07 kW h�1,0.09 kW h�1 and 0.11 kW h�1 were used to evaluate the sensitivityof irrigation costs to energy prices. These prices were chosen to re-flect the range of historic diesel and electricity prices in Tennessee.Leib (2012b) demonstrated the importance of including the fixedcost of running electric power lines to the pump, so we used threefixed costs of $10,000, $15,000 and $20,000 to run electricity to thecenter-pivot.

No clear estimate for repair and maintenance costs was avail-able since these costs are not published in the American Societyof Agricultural and Biological Engineering Standards. Jensen(1980) and McGrann et al. (1986a,b) estimated annual repair andmaintenance costs for irrigation equipment as a percentage ofthe initial costs of the equipment, as proposed in the AmericanAgricultural Economic Association (AAEA) Commodity Costs andReturns Handbook (2000). We used 1.7% of the initial costs, whichfalls within the range specified in the AAEA Handbook (2000). Weassumed an annual irrigation labor cost of $6 ha�1, including laborcosts for monitoring soil water status and other irrigation manage-ment activities (Leib, 2012b).

5. Yield response estimation

The physical relationship between yield, irrigation, and N aswell as the price of corn and N determine the optimal N fertiliza-tion rates and yields. If non-optimal N fertilization rates and yieldswere selected to compare non-irrigated and irrigated corn, theresult might overestimate or underestimate the returns toirrigation. For example, if irrigated and non-irrigated yields werecompared at 150 kg N ha�1, the yield gains from irrigating cornmight be underestimated since irrigated corn will likely requiremore N fertilizer than non-irrigated corn. Therefore, selecting theprofit-maximizing N fertilization rates for irrigated and non-irrigated corn at the same price of corn and same price of N, levelsthe playing field for yield and revenue gain comparisons.

Many researchers have found that a plateau function for model-ing corn yield response to N fits experimental data as well or betterthan polynomial models (Bullock and Bullock, 1994; Cerrato andBlackmer, 1990; Frank et al., 1990; Llewelyn and Featherstone,1997). More recently, several researchers found stochastic plateaufunctions more suitable than their deterministic plateau functioncounterparts (Boyer et al., 2012; Biermacher et al., 2009; Robertset al., 2011; Tembo et al., 2008; Tumusiime et al., 2011). Boyeret al. (2013) found that the linear response stochastic plateau(LRSP) function fit non-irrigated corn yield data well. The LRSPfunction assumes yield responds linearly to N until yield reachesa plateau (or the knot point where N is no longer a limiting input)while considering the effects of stochastic events such as insects,disease, and weather on yield response and yield potential.

Data from the experiment were used to estimate LRSP functionsfor both irrigated and non-irrigated corn as

yti ¼minðb0 þ b1xti; lþ utÞ þ v t þ eti ð2Þ

where yti is the corn yield in Mg ha�1 in the tth year on plot i; b0 andb1 are the yield response parameters; xti is the quantity of N fertil-izer applied in kg N ha�1; l is the expected plateau yield inMg ha�1; ut � Nð0;r2

uÞ is the year plateau random effect;

C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69 65

v t � Nð0;r2vÞ is the year intercept random effect; and eti � Nð0;r2

e Þis the random error term. Independence is assumed across the threestochastic components. A limitation of this model is N carryoverfrom previous years is not specifically estimated in the model dueto data limitations. The year plateau random effect weights the var-iation in plateau yields using a standard normal distribution, whichis the same distribution used in Eq. (1). Eq. (2) is estimated usingthe NLMIXED procedure in SAS 9.1 (SAS Institute Inc., 2003).

The profit-maximizing N fertilization rate is (Tembo et al., 2008)

x� ¼ 1b1ðlþ Zaru � b0Þ; ð3Þ

where Za is the standard normal probability of r/(pb1) at the a sig-nificance level. The profit-maximizing expected yield is (Temboet al., 2008)

EðytiÞ ¼ ð1�UÞaþUðl� ru/UÞ; ð4Þ

where U = U[a � l/ru] is the cumulative normal distributionfunction; a ¼ b0 þ b1x; and / = /[a � l/ru] is the standard normaldensity function. Note that the expected yield (Eq. (4)) and theprofit-maximizing N fertilization rate (Eq. (3)) are functions of theprice of corn (p); thus, the optimal expected yield and N fertilizationrate change as the price of corn changes.

6. Financial analysis framework

A deterministic programming model was used to find thebreakeven corn price for investing in an irrigation system usingnet present value (NPV). To calculate the NPV, annual net returnswere first determined using a partial budget for corn productionthat is expressed as

EðNRtikÞ ¼ E½pytikðxtikÞ � rxtik � kðcwti þ lþmÞ�; ð5Þ

where E(NRtik) is the expected net return in $ ha�1 in year t for theith plot; k is a binary variable that is k = 1 for irrigation and k = 0 fornon-irrigation; p is the price of corn in $ Mg�1; ytikðxtikÞ is yield inMg ha�1 and is a function of the N fertilizer rate xtik in kg N ha�1;r is price of N fertilizer in $ kg�1; c is the cost of energy for pumpingwater in $ cm�1 ha�1; wti is the irrigation water rate in cm ha�1; l isthe labor cost for monitoring soil water status and other labor activ-ities related to irrigation in $ ha�1; and m is irrigation maintenanceand repair costs in $ ha�1.

The optimal N fertilizer rate in Eq. (3) and the optimal expectedyield in Eq. (4) were used in Eq. (5) to calculate expected net re-turns. The price of N, labor cost, irrigation water rate, and mainte-nance costs were assumed to be deterministic in the model and aresummarized in Table 3. Several energy prices are selected to showthe sensitivity of net returns for different energy sources andprices.

Expected annual cash flows were calculated for a corn producerfinancing the purchase of the irrigation system and for one whodoes not invest in irrigation. Depreciation and annual interest were

Table 3Input prices and quantities for the corn budgets.

Inputs Unit Price

Nitrogen kg $1.33Labor ha $6Maintenance % of initial cost 1.7Irrigation rate cm ha�1 yr�1 16.12Discount rate % 8Marginal tax rate % 25Interest rate $ 5

subtracted from net returns (Eq. (5)) to calculate total taxable netreturns, expressed as

TNRtik ¼ NRtik � kDep� kInt; ð6Þ

where TNRtik is the annual taxable net returns; Dep is the annualdepreciation of the irrigation system; and Int is the annual interestpayment on the loan. The annual interest rate is shown in Table 3.The total taxable net returns was multiplied the by tax rate to deter-mine the amount paid in taxes annually. The annual cash flowswere determined by subtracting annual loan payment for the irriga-tion system and the annual tax payment from the net returns, ex-pressed as

CFtik ¼ NRtik � kPMT � kðTNRtiksÞ; ð7Þ

where CFtik is the annual cash flow; PMT is the annual loan paymentfor the irrigation system; and s is the annual tax rate shown inTable 3.

The expected annual cash flows for irrigated and non-irrigatedcorn were used for each year of the 20-year useful life of the irriga-tion systems. The NPV of investing in an irrigation system over itsuseful life is solved for the corn price p that makes NPV equal zero.The NPV = 0 calculation is

minp

NPV ¼ �IC þXT

t¼1

CFt1 � CFt0

ð1þ gÞt¼ 0; ð8Þ

where IC is the initial investment in irrigation equipment in yeart = 0; CFt1 is the annual cash flow for irrigated corn; CFt0 is the an-nual cash flow for non-irrigated corn; T = 20 is the useful life ofthe irrigation equipment; and g is the risk-adjusted discount rate.The discount rate is the producer’s opportunity cost of investingin the irrigation equipment, representing the net return a producerwould receive from an alternative investment (e.g., Treasury bond,new tractor, precision farming technology). The discount rate isequal to the risk-free discount rate plus the risk premium (Seoet al., 2008). The NPV = 0 calculation assumes that the present valueof the benefit from irrigating corn (CFt1 � CFt0) equals the opportu-nity cost of irrigating corn (i.e., the benefit from an alternativeinvestment). When NPV equals zero, the non-irrigated corn pro-ducer is indifferent between investing in an irrigation system andan alternative investment. We solved Eq. (8) for the minimumtime-adjusted corn prices (breakeven corn prices) for differentenergy sources, energy prices and field sizes. The breakeven cornprice represents the price required over the 20-year useful life thatallows the irrigation system to cover the cost of the investment.

The profit-maximizing yield (Eq. (4)) and N fertilization rate(Eq. (5)) change with the breakeven price, which in turn changesthe maximum net returns for both irrigated and non-irrigatedcorn; thus, comparisons are made when both producers maximizeprofit, providing a level playing field for comparisons. The LRSPfunction allows us to include year-to-year yield variability indetermining the breakeven price of corn—a unique contributionto the irrigation feasibility literature.

7. Results

7.1. Breakeven price of corn

Parameter estimates from the LRSP models for irrigated andnon-irrigated corn are presented in Table 4. All parameter esti-mates were significant (a 6 5%). The slope parameter estimates(yield response to N fertilizer) were similar for irrigated and non-irrigated corn, but the intercept and plateau parameter estimateswere larger for irrigated corn. The estimated plateau was aboutfour Mg ha�1 higher, indicating the yield gain from timely applica-tion of irrigation. Additionally, the intercept and plateau random

Table 4Estimated corn yield (Mg ha�1) response to N (kg ha�1) for irrigated and non-irrigatedcorn grown after soybeans using a linear response stochastic plateau function.

Parameter Response functions

Irrigated corn Non-irrigated corn

Intercept 6.705a 5.379a

(0.221) (0.194)

N 0.046b 0.044a

(0.002) (0.002)

Plateau 14.878b 10.596a

(0.164) (0.172)

Plateau random effect 1.429b 4.683a

(0.468) (0.743)

Intercept random effect 0.659b 5.132a

(0.169) (0.881)

Random error 1.149a 0.912a

(0.131) (0.105)

�2Log-likelihood 494.0 469.4

Note: Standard errors are in parenthesis.a significant at p = 0.01.b significant at p = 0.05.

66 C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69

effects for irrigated corn were smaller than the random effects fornon-irrigated corn, indicating year-to-year yield variability wasreduced with irrigation, which suggests production risk decreases.

The parameter estimates from the LRSP functions weresubstituted into the net return equation (Eq. (5)) to solve forthe time-adjusted breakeven price of corn. Breakeven corn pricesare presented in Table 5 for various energy costs, energy sources,and field sizes. The energy source that provides the lowest break-even price of corn for a given field size is the preferred energysource for that field size because it provides the best opportunityfor the irrigation investment to be profitable.

For the small field (25 ha), the breakeven corn price was$249 Mg�1 for $0.52 l�1 diesel, and $271 Mg�1 for $1.06 l�1 diesel(Table 5). For every 27 cent l�1 increase in the price of diesel, thebreakeven price of corn increased by $11 Mg�1. With electricityas the power source for the center-pivot, the breakeven price ofcorn ranged from $257 to $283 Mg�1 depending on the fixedinvestment cost of running electricity to the center-pivot and theper-unit electricity rate (Table 5). For every two cent increase inthe per-unit electricity rate, the breakeven corn price increasedby $3 Mg�1. With diesel at $1.06 l�1 and the fixed cost of running

Table 5Breakeven corn price ($ Mg�1) for investing in a center-pivot by energy source, energycost, and field size.

Per-unit energy costs Field size

25 ha 51 ha 81 ha

Diesel energy$0.52 l $248.78 $167.36 $148.88$0.79 l $259.57 $178.56 $160.04$1.06 l $270.86 $189.77 $171.22

Electric energy with a $10,000 fixed cost investment0.07 kW h $256.94 $165.78 $143.700.09 kW h $260.12 $168.93 $146.830.11 kW h $263.40 $172.08 $149.97

Electric energy with a $15,000 fixed cost investment0.07 kW h $267.00 $170.67 $146.760.09 kW h $270.18 $173.82 $149.900.11 kW h $273.36 $176.97 $153.04

Electric energy with a $20,000 fixed cost investment0.07 kW h $277.08 $175.56 $149.820.09 kW h $280.26 $178.71 $152.970.11 kW h $283.44 $181.87 $156.11

electricity to the center-pivot at $10,000, the breakeven price ofusing electricity was lower, which makes it the preferred energysource. When the investment cost of running electricity to thepump was greater than $10,000, diesel was the more economicalenergy source.

Breakeven corn prices were $167 Mg�1 for $0.52 l�1 diesel and$190 Mg�1 for $1.06 l�1 diesel on a medium-sized field (51) (Ta-ble 5). The breakeven price of corn using electricity ranged from$168 to $182 Mg�1 depending on the fixed investment cost andper-unit electricity rate (Table 5). With diesel at $0.52 l�1, thebreakeven price of corn was lower for diesel than electricity withthe exception of the lowest electricity cost scenario (Table 5). Thus,diesel would be preferred over electricity. When the diesel price is$0.79 l�1, the breakeven corn price indicates that electricity waspreferred over diesel expect for the highest electricity costscenario.

For the large-sized field (81 ha), the breakeven price of corn de-creased to $149 Mg�1 for $0.52 l�1 diesel, and $171 Mg�1 for $1.06l�1 diesel (Table 5). The breakeven price of corn using electricityranged from $144 to $156 Mg�1 depending on the fixed investmentcost and per-unit electricity rate (Table 5). When diesel was$0.52 l�1, the breakeven price of corn was lower for diesel thanelectricity with the expectation of a few electricity-cost scenarios,which suggests that diesel would likely be preferred over electric-ity at $0.52 l�1 diesel (Table 5). With the price of diesel at $0.79 l�1

or higher, the breakeven price indicates that electricity was pre-ferred over diesel.

A probability density function was found for historical real cornprices from 1990 to 2012. The CPI index with a base year of 2001was used to adjust nominal corn prices to real corn prices. Theprobability density function for the real corn price was used todetermine the probability of the corn price being greater thanthe breakeven price of corn (Table 6). These probability estimatesserve as proxies for the probability of NPV being positive. For thesmall-sized field, the probability of the corn price being greaterthan the breakeven corn price was zero (Table 6). The probabilityof a corn price greater than the breakeven price for the medium-sized field was low, and the probability of the corn price beingabove the breakeven price for the large-sized field was also lowbut higher than for the medium-sized field (Table 6). The probabil-ity of receiving a corn price sufficiently high to breakeven oninvesting in supplemental irrigation is low when comparing thebreakeven price with the historical distribution of corn prices.

Table 6Probability of the breakeven corn price ($ Mg�1) for investing in a center-pivotoccurring based on real corn prices (1990–2012), by energy source, energy cost, andfield size.

Per-unit energy costs Field size

25 ha 51 ha 81 ha

Diesel energy$0.52 l 0% 5% 12%$0.79 l 0% 2% 7%$1.06 l 0% 1% 4%

Electric energy with a $10,000 fixed cost investment0.07 kW h 0% 5% 15%0.09 kW h 0% 4% 13%0.11 kW h 0% 3% 12%

Electric energy with a $15,000 fixed cost investment0.07 kW h 0% 4% 13%0.09 kW h 0% 3% 12%0.11 kW h 0% 2% 10%

Electric energy with a $20,000 fixed cost investment0.07 kW h 0% 3% 12%0.09 kW h 0% 2% 10%0.11 kW h 0% 2% 9%

C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69 67

7.2. Optimal yield and nitrogen rate

We report profit-maximizing corn yields—a function of the cornprice (Eq. (4))—at the breakeven prices in Table 7. Expected yieldwas higher for irrigated corn than non-irrigated corn, and variedlittle with the change in the breakeven price of corn. We also re-port the profit-maximizing N fertilization rates—also a functionof corn price (Eq. (3))—for irrigated and non-irrigated corn at thebreakeven prices in Table 8. Consistent with the literature, irri-gated corn has a higher optimal N fertilizer rate than non-irrigatedcorn (Sheriff, 2005; Vickner et al., 1998). Given the breakeven cornprices, the profit-maximizing N fertilization rates ranged from 200to 211 kg N ha�1 for irrigated corn and from 159 to 180 kg N ha�1

for non-irrigated corn. The parameter estimates suggest that irriga-tion increased the yield plateau of corn, which resulted in higher Nfertilizer rates.

8. Discussion

Irrigation investment is expanding in humid regions of the Uni-ted States as well as globally (Mullen et al., 2009; Rosegrant et al.,

Table 7Expected yields (Mg ha�1) for the breakeven corn prices by energy source, energy cost, an

Per-unit energy costs Field size

25 ha 51 ha

Irrigated corn Non-irrigated corn Irrigated

Diesel energy$0.52 l 14.81 10.47 14.77$0.79 l 14.82 10.48 14.78$1.06 l 14.82 10.48 14.79

Electric energy with a $10,000 fixed cost investment0.07 kW h 14.81 10.47 14.770.09 kW h 14.82 10.48 14.770.11 kW h 14.82 10.48 14.77

Electric energy with a $15,000 fixed cost investment0.07 kW h 14.82 10.48 14.770.09 kW h 14.82 10.48 14.780.11 kW h 14.82 10.48 14.78

Electric energy with a $20,000 fixed cost investment0.07 kW h 14.82 10.49 14.780.09 kW h 14.82 10.49 14.780.11 kW h 14.82 10.49 14.78

Table 8Profit-maximizing N rates (kg N ha�1) for the breakeven corn prices by energy source, ene

Per-unit energy costs Field size

25 ha 51 ha

Irrigated corn Non-irrigated corn Irrigated

Diesel energy$0.52 l 209.02 176.60 202.58$0.79 l 209.70 177.90 203.70$1.06 l 210.34 179.13 204.74

Electric energy with a $10,000 fixed cost investment0.07 kW h 209.55 177.61 202.420.09 kW h 209.74 177.97 202.750.11 kW h 209.92 178.32 203.07

Electric energy with a $15,000 fixed cost investment0.07 kW h 210.48 179.40 202.930.09 kW h 210.31 179.06 203.240.11 kW h 210.48 179.40 203.55

Electric energy with a $20,000 fixed cost investment0.07 kW h 210.68 179.78 203.410.09 kW h 210.85 180.11 203.710.11 kW h 211.02 180.43 204.01

2009; Schaible and Aillery, 2012). Nevertheless, little is knownabout whether irrigation investment is profitable in humid regions.The calculated breakeven prices suggest that investment in irrigat-ing corn in the humid southeastern United States is not likely prof-itable, given historical prices of corn. However, the Food andAgricultural Policy Research Institute (FAPRI) (2012) has forecastedthe price of corn to remain between $179.52 Mg�1 and$234.64 Mg�1 through 2022. If this price forecast is realized,investing in a center-pivot irrigation system for a 25 ha fieldappears to not be profitable regardless of energy source, but invest-ing in center-pivot irrigation systems for 51 and 81 ha fields mightbe profitable investments for most energy price scenarios. Givencurrent and forecasted corn prices, irrigating corn in humid regionsappears to be profitable for large- and medium-sized fields.

Although irrigating corn on medium- and large-sized fieldsappears profitable given forecasted corn prices, a corn producershould consider how irrigation investment impacts various sourcesof risk in corn production. For example, Mullen et al. (2009)observed that high corn prices have a large impact on irrigationdemand in the humid southeastern United States. Today, the priceof corn is higher than the historic price of corn due to increased

d Field size.

81 ha

corn Non-irrigated corn Irrigated corn Non-irrigated corn

10.39 14.75 10.3610.41 14.76 10.3810.42 14.77 10.40

10.39 14.75 10.3410.39 14.75 10.3510.40 14.75 10.36

10.39 14.75 10.3510.40 14.75 10.3610.40 14.76 10.36

10.40 14.75 10.3610.41 14.76 10.3610.41 14.76 10.37

rgy cost, and field size.

81 ha

corn Non-irrigated corn Irrigated corn Non-irrigated corn

164.24 200.50 160.33166.38 201.80 162.73168.36 202.98 165.00

163.92 199.86 158.98164.55 200.25 159.75165.17 200.64 160.49

164.89 200.24 159.73165.50 200.63 160.47166.09 201.00 161.19

165.83 200.62 160.46166.41 200.99 161.18166.98 201.36 161.88

68 C.N. Boyer et al. / Agricultural Systems 127 (2014) 61–69

demand for corn, which is likely driving the expansion irrigation inthe southeastern United States. Corn producers who invest in irri-gation systems must be able to manage the risk of potentiallyunstable future corn prices (also known as price risk). At the fore-casted prices of corn over the next ten years (FAPRI, 2012), invest-ing in a center-pivot may be profitable for corn fields greater than51 ha. However, agricultural prices historically have had boom andbust periods (Gouel, 2012). Considering the historical price of corn,the probability is fairly low of irrigated corn being a profitableinvestment on any size field in the southern United States. There-fore, irrigation investment could increase corn producers’ pricerisk. In addition, higher price risk increases corn producers’ finan-cial risk because a higher breakeven price is required to cover thehigher cost of irrigation. Thus, higher corn or commodity priceswill be required to maintain positive cash flows with irrigation.Conversely, irrigation has proven to be a useful investment inreducing production risk by reducing yield variability (Aplandet al., 1980). Our results in Figs. 1 and 2 and the random effectsparameter estimates in Table 4 confirm that supplemental irriga-tion in a humid climate decreases the year-to-year yield variabilityfor corn producers, which gives producers more certainty aboutthe quantity of corn produced.

This paper considers price risk by presenting results for variousenergy sources, energy prices, and farm sizes. Additionally, theprobability of the breakeven price being higher than the historicalprice of corn is shown. Yield variability (i.e., production risk) wasalso considered in estimating breakeven prices of corn for invest-ing in irrigation. However, future research is needed to addressthe tradeoffs among price, financial, production risks from irriga-tion investment in humid climates. A Monte Carlo simulation mod-el using historical prices and yield variability is a potentialapproach for this future research.

Higher energy costs cause the breakeven price of corn to increase,which matches the literature (Gonzalez-Alvarez et al., 2006;Peterson and Ding, 2005; Mullen et al., 2009; Scheierling et al.,2006; Seo et al., 2008). Unlike the arid western United States, how-ever, irrigation in the humid southeastern United States is designedto supplement rainfall during drought periods. Less water is appliedto corn in a growing season than in more arid regions, so energy costshave less of an impact on the profitability of irrigated corn in humidregions. If diesel prices were at or below $0.52 l�1, diesel would bepreferred over electricity for most electricity prices and field sizesbut, if the diesel price were greater than or equal to $0.79 l�1, elec-tricity would become more competitive for fields of 51 ha or larger.Field size and the cost of running electricity to the center-pivot areimportant factors in the relative profitability of using electricity ordiesel as the energy source for irrigation. Corn producers shouldconsider these factors before choosing an energy source.

This study has implications for water supplies, water planning,and for future agricultural water management in Tennessee andthe southeastern United States. If corn prices remain high, invest-ment in irrigation would likely continue to increase and corn areamay continue to expand and replace less water-intensive crops,such as cotton. Thus, it is possible that more intensive water usein humid regions will increase. This increase would be importantfor policy makers to consider in developing water managementpolicies as water supplies tighten. For example, they could createincentives for corn producers to adopt more efficient irrigationsystems or change the water law to regulate water access andquantity used.

9. Conclusion

Irrigation investment for corn production is expanding intomore humid regions across the globe and specifically in the

southeastern United States. However, little is known about theprofitability of irrigating corn in these regions. Since interest inirrigation has recently increased among southeastern United Statescorn producers because of higher corn prices, we determined thebreakeven price of corn for investing in a center-pivot irrigationsystem in Tennessee. Our analysis investigated farm-level irrigationinvestment using diesel and electric energy sources with threeenergy prices and three field sizes. We estimated yield responseto N for irrigated and non-irrigated corn, and let the yield and Nfertilization rates vary with the breakeven price of corn. Yieldvariability of irrigated and non-irrigated corn was included in cal-culating the breakeven price of corn for irrigation investment,which is a unique contribution to the irrigation feasibility literature.

Results from the yield response functions find higher optimal Nfertilization rates and expected yields for irrigated corn than non-irrigated corn. Yield variability decreased with supplement irriga-tion application. At current corn prices, which are historically high,irrigating corn appears to be profitable on field sizes greater than51 ha, but when compared with historic corn prices, the probabil-ity of receiving a corn price sufficiently high to breakeven on irri-gation investment is low. Field size and cost of extendingelectricity to the irrigation system were vital factors in selectingdiesel or electricity as the energy source. When diesel prices wereequal or greater than $0.79 l�1, electricity became a more viableenergy source than diesel for fields greater than 51 ha.

Acknowledgements

The authors thank Dr. Blake Brown and the staff at the MilanResearch and Education Center, Milan, TN, for field research sup-port. They also thank the anonymous reviewers for comments onan earlier draft.

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