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

Agricultural Systems 127 (2014) 61–69

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The impact of field size and energy cost on the profitability of supplemental corn irrigation 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, USA Department of Agricultural and Resource Economics, The University of Tennessee, 302 Morgan Hall, Knoxville, TN 37996, USA c Department of Agricultural and Resource Economics, The University of Tennessee, 308B Morgan Hall, Knoxville, TN 37996, USA d Department of Plant Sciences, The University of Tennessee, West Tennessee Research and Education Center, 605 Airways Blvd., Jackson, TN 38301, USA e Department of Biosystems Engineering and Soil Sciences, The University of Tennessee, West Tennessee Research and Education Center, 605 Airways Blvd., Jackson, TN 38301, USA b

a r t i c l e

i n f o

Article history: Received 6 December 2012 Received in revised form 12 July 2013 Accepted 15 January 2014 Available online 11 February 2014 Keywords: Corn Economics Irrigation Linear response stochastic plateau Nitrogen

a b s t r a c t Supplemental irrigation in corn production is increasing for humid regions across the world. Little is known 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 irrigation would be profitable in Tennessee. We considered the effects of field size, energy price, and energy source on the breakeven price of corn. We estimated yield response to nitrogen (N) for irrigated and nonirrigated corn, and allowed expected yield and economically optimal N fertilization to vary with the breakeven price. Field size and the cost of running electricity to the center-pivot were two important factors in choosing between diesel and electricity as the energy source. The breakeven price of corn ranged between $249–$283 Mg1 for the small-sized field, $168–$190 Mg1 for the medium-sized field, and $149–$171 Mg1 for the large-sized field. As field size increased, electricity became more economically viable relative to diesel. At current corn prices, irrigating corn appears profitable on fields greater than 51 ha. However, historically, the probability for the breakeven corn price occurring is zero for the small-sized field, between 6–14% for the medium-sized field, and 12–27% for the large-sized field. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Demand for food crops has been increasing in response to a number of factors including a growing global population, expanding economies in developing countries, and rising biofuels production among other factors (Trostle, 2008). To meet the growing demand for food, more than half of world cereal production is anticipated to be produced using irrigation by 2050 (Rosegrant et al., 2009). Globally, irrigation is expected to expand in humid regions that generally receive sufficient annual rainfall to grow crops without irrigation in most years (Mullen et al., 2009; Rosegrant et al., 2009; Schaible and Aillery, 2012). The primary purpose of irrigation in humid regions is to supplement rainfed crop production during periodic short-term droughts. Research has shown that timely supplemental irrigation in humid regions can increase yields (Bruns et al., 2003; Smith and Riley, 1992), decrease crop disease (Smith and Riley, 1992; Vories ⇑ Corresponding author. Tel.: +1 865 974 7468; fax: +1 865 974 7484. E-mail addresses: [email protected] (C.N. Boyer), [email protected] (J.A. Larson), [email protected] (R.K. Roberts), [email protected] (A.T. McClure), dtyler@utk. edu (D.D. Tyler). http://dx.doi.org/10.1016/j.agsy.2014.01.001 0308-521X/Ó 2014 Elsevier Ltd. All rights reserved.

et al., 2009), and stabilize yields (Apland et al., 1980; Dalton et al., 2004; Epperson et al., 1993; Evans and Sadler, 2008; Henning, 1989; Vories et al., 2009; Salazar et al., 2012). Another advantage of supplemental irrigation in humid regions is the availability of abundant water for irrigation, and that water is often inexpensive or free (Gonzalez-Alvarez et al., 2006; Mullen et al., 2009). For example, the doctrine of riparian water rights is followed by most states in the humid subtropical zone of the southeastern United States (Christy et al., 2005; Myszewski et al., 2005). The riparian doctrine states that water rights are not quantitatively fixed and water is not explicitly priced (Griffin, 2006). When water is inexpensive or free, farmers make irrigation decisions based on water needs and the energy cost of pumping water, not the price of water (Gonzalez-Alvarez et al., 2006; Mullen et al., 2009). In the United States, supplemental irrigation of crops in humid regions such as the southeast has been growing rapidly (Dalton et al., 2004; Gonzalez-Alvarez et al., 2006; Schaible and Aillery, 2012). Schaible and Aillery (2012) reported that the largest increase in irrigated crop production in the United States since 1998 has been in the southeastern states of Georgia, Alabama, and Mississippi. The majority of the growth in irrigation for this region has been for corn production (Salazar et al., 2012; Vories

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et al., 2009). Vories et al. (2009) noted that 62% of all corn hectares in the Mid-South (Louisiana, Mississippi, Alabama, Arkansas, Tennessee, and Kentucky) were irrigated in 2003, and Lee (2013) stated that 72% of Georgia corn hectares were irrigated in 2011. A plausible explanation for the increase in irrigated corn production in the southeastern United States may be the increased price for corn since 2006 (Mullen et al., 2009). Even though irrigation in the southeastern United States is increasing for corn production and the price of corn is historically high, little is known about the long-term profitability at the farm-level of irrigating corn in the humid southeastern United States. For example, center pivot irrigation systems are more expensive to install on the smaller and more irregularly shaped fields that are common in the eastern United States (Hatch et al., 1991), but may be profitable under higher corn prices. Our research objective was to evaluate the breakeven corn price above which a center-pivot irrigation system becomes profitable in the southeastern United States. Annual rainfall is sufficient to produce corn but irrigation is used as a supplement. We considered the effects of different energy sources, energy prices, and field sizes on the breakeven corn price. Stochastic yield response to N fertilizer was estimated for irrigated and non-irrigated corn, and expected yields and profit-maximizing N fertilizer rates were allowed to vary with the breakeven corn price. Partial budgets were used to calculate net cash flows over time for irrigated and non-irrigated corn, and a financial analysis was performed over the life of the irrigation system to solve for the time-adjusted breakeven corn price. The breakeven corn prices were compared to historical corn prices to determine the probability that a producer who invests in center-pivot irrigation would achieve a breakeven profit of zero. Our framework and results will help farmers evaluate the profitability of irrigation investment in other southeastern states as well other humid regions in the world. Furthermore, the results have implications for future agricultural water management in the southeastern United States and specifically Tennessee.

2. Literature review Several studies analyzed the feasibility of investing in irrigation systems at the farm level (Caswell and Zilberman, 1986; Guerrero et al., 2010; Letey et al., 1990; O’Brien et al., 2001; Peterson and Ding, 2005; Seo et al., 2008). These studies, however, focus on arid regions where water is scarce and irrigation is vital for crop production. The aforementioned analyses are insightful for arid regions because they demonstrate methods to reduce irrigation costs. However, water is relatively cheap and abundant in the southeastern United States and other humid areas, and producers have little incentive to conserve water or increase water use efficiency (Sheriff, 2005; Vories et al., 2009). Therefore, these studies provide little insight into the profitability of irrigating crops in humid regions such as the southeastern United States. Mullen et al. (2009) evaluated the factors driving irrigation water demand in the southeastern United States using a multi-crop production model. Since the riparian doctrine is widely recognized in this region, Mullen et al. (2009) followed Gonzalez-Alvarez et al. (2006) by using the energy cost of pumping water as a proxy for the price of water. They found that energy cost slightly influenced water demand, but crop prices have the greatest influence on irrigation water demand. Other economic research on irrigation in humid regions has primarily focused on production risk management. Boggess et al. (1983) determined optimal irrigation scheduling that maximized net returns, and Boggess et al. (1985) surveyed farmers in the southeastern United States to determine their perception of using irrigation to manage production risk. Dalton et al. (2004)

compared using irrigation with enrolling in crop insurance to manage potato production risk in Maine in the northeastern United States under humid conditions. They found that crop insurance was inefficient to minimize producers’ production risk in humid regions, and that supplemental irrigation was beneficial depending on the scale (i.e., field size) of the system with a larger scale providing more risk-management benefits. More recently, DeJonge et al. (2007) simulated yields for irrigating corn in Iowa, and calculated the breakeven corn price for irrigation on a 52 ha field. They found a breakeven corn price for irrigation of $182.18 Mg1. Irrigation was not profitable since the average price of corn used to calculate net returns was $79 Mg1 ($2 bu1). Although DeJonge et al. (2007) provide useful insights; they used simulated rather than actual yield data to estimate breakeven prices. In addition, irrigating corn in humid regions may be profitable given the higher corn prices since 2006, the last year of their study. In our literature review, we have found no studies evaluating the profitability of irrigated corn production in humid regions using actual corn yield data rather than simulated yield data. The impact of field size, energy source, and energy price on the breakeven price for corn also has not been studied. Another limitation of many corn irrigation studies is the exclusion of inputs other than water (e.g., DeJonge et al., 2007). Along with water, nitrogen (N) fertilizer is likely the most important input in corn production (Stone et al., 2010). Research has shown that N fertilizer provides the largest economic return per dollar spent relative to all other farm inputs (Pikul et al., 2005). A large number of studies have focused on estimating the profit-maximizing N fertilization rate for corn (e.g., Bullock and Bullock, 1994; Cerrato and Blackmer, 1990; Frank et al., 1990; Llewelyn and Featherstone, 1997). These studies show that as the price of corn and N change, the economically optimal N fertilization rate also changes. For a profit-maximizing corn producer, an increase (decrease) in the price of corn results in an increase (decrease) in the optimal N fertilization rate. Irrigation and N fertilizer are complements in row crop production, so irrigating corn will likely increase both yield and the optimal N fertilization rate (Dinnes et al., 2002; Stone et al., 2010; Vickner et al., 1998). Stone et al. (2010) estimated corn yield response functions to N in the southeastern United States, and found that optimal rates vary between irrigated and non-irrigated corn. Therefore, the corn price and the physical relationship between yield, irrigation, and N impacts corn producers’ net returns. To avoid overstating or understating the profitability of irrigation, the physical relationship between yield, irrigation, and N should be considered along with corn and N prices.

3. Data 3.1. Yields and nitrogen rates Corn yield data come from N fertilization experiments conducted at the University of Tennessee Milan Research and Education Center (35°560 N, 88°430 W) from 2006 to 2011. Non-irrigated corn was grown on a Grenada soil (fine-silty, mixed, active, thermic Oxyaquic Fraglossudalfs) and irrigated corn was produced on a Loring soil (fine-silty, mixed, active, thermic Oxyaquic Fragiudalfs), which were considered well suited for corn production in Tennessee (USDA-NRCS, 1999). The two experiments were located on fields that have been under no-till production for over a decade (Yin et al., 2011). Corn (cultivar Pioneer 33N58) was planted in 76-cm rows in April in rotation with soybeans. Each plot was 4.6 m wide and 9.1 m long. The experimental design was a randomized complete block with five or six N fertilization treatments as strip-plots and four

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replications of corn grown after soybeans. The annual N fertilization rates were 0, 62, 123, 185, and 247 kg N ha1 in 2006 and 2007. In 2008, a treatment of 308 kg N ha1 was added to the experiments. The N source was ammonium nitrate (34–0–0; N–P–K), uniformly broadcast on the soil surface around planting time. P and K were applied based on University of Tennessee

soil-test recommendations. The 2006–2011 average price of N from ammonium nitrate of $1.3 kg1 was used in calculating the cash flows (USDA-NASS, 2012). A visual representation of the corn yield data at the various N rates is shown in Figs. 1 and 2. The data suggest a plateau function is an appropriate model and that the plateau varies across years. All other inputs, such as weed, pest and disease control, were the same for the irrigated and non-irrigated experiments and followed the University of Tennessee’s recommended management practices. 3.2. Irrigation rates

Fig. 1. Non-irrigated corn yields (Mg ha1) by nitrogen rates (kg N ha1) from 2006 to 2011 at Milan, TN.

Fig. 2. Irrigated corn yields (Mg ha 2011 at Milan, TN.

1

) by nitrogen rates (kg N ha

1

) from 2006 to

Supplemental water was uniformly applied to the irrigated plots using a Valley linear irrigation system (Valmont Irrigation, Valley, NE). The supplemental water rates were based on the MOIST soil moisture management system program, which is an online irrigation scheduler available for corn producers in Tennessee (Leib, 2012a). Summary statistics for annual rainfall, average temperature, and annual quantities of water applied by month at Milan, TN are presented in Table 1. Irrigation was scheduled to occur between June and August, but a drought in 2007 resulted in irrigation application beginning in May. An above average irrigation rate was applied in 2007, a below average rate was applied in 2009, and irrigation rates were similar to the average rate in the other years (Table 1). When the irrigation investment decision is made, the corn producer does not know the future amounts of supplemental irrigation that will be needed. We weighted the annual irrigation rates from the experiments by their respective probabilities of occurring to find an expected future irrigation rate. Drought years such as 2007 and timely rainfall years such as 2009 have relatively small probabilities of occurring, so taking a simple average of irrigation rates would overweight those years. To weight the annual irrigation rates, we followed Lambert et al.’s (2007) method of creating annual weights based on the irrigation data. In our model, the annual weights (ht) were determined as

ht ¼

, T Y Y X /ðwt Þ /ðwt Þ t

t¼0

ð1Þ

t

Table 1 Summary of growing season precipitation, temperature, and irrigation data, Milan, TN, 2006–2011. Source: NOAA, Milan, TN weather station and MOIST (Leib, 2012a). Month

2006

2007

2008

2009

2010

2011

30-year average

Monthly precipitation totals (cm) March April May June July August September Total (March–September)

8.56 8.38 12.75 15.06 8.97 8.38 11.35 73.36

2.64 8.38 5.84 11.18 5.46 2.95 18.69 55.17

21.56 25.96 23.85 3.86 7.87 1.83 1.19 84.28

11.73 8.13 22.86 5.59 20.07 5.59 11.94 86.26

8.00 15.24 53.59 8.13 14.99 5.08 1.02 105.89

16.61 9.78 11.24 6.80 1.42 1.14 10.21 119.61

12.95 12.28 16.12 11.00 11.18 7.21 10.86 81.51

Average monthly temperature (°C) March April May June July August September Average (March–September)

10.17 18.11 19.83 23.89 26.56 26.89 19.83 20.75

14.61 13.06 21.78 24.78 25.33 30.06 23.11 21.77

9.36 14.11 19.22 25.56 23.72 25.17 22.44 20.36

10.58 14.94 19.83 26.00 24.61 24.61 22.44 20.42

9.39 17.06 21.78 27.56 27.61 27.83 23.11 22.04

10.72 17.25 19.69 26.36 27.86 26.42 20.97 21.32

9.44 14.84 19.73 24.07 26.00 25.45 21.35 20.15

Monthly irrigation totals (cm) May June July August Total (May–August)

– 6.25 7.29 3.12 16.66

1.27 8.56 10.13 6.25 26.21

– 5.21 6.25 4.17 15.62

– 4.17 3.12 1.04 8.33

– 5.21 9.37 3.12 17.70

– 5.21 9.37 2.08 16.66

– – – – –

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where wt is the total irrigation water observed in year t (t = 0, . . ., T); and /ðwt Þ is the standard normal probability density function (pdf). The weighting is based on the rule of probability multiplication and assumes that the irrigation rate in time period t is independent of the rates in other periods (Lambert et al., 2007). The expected P irrigation rate was Tt¼1 ht wt . Using the irrigation data and applying Eq. (1) produced an expected irrigation rate of 16.12 cm ha1 yr1. This rate is slightly above the average annual irrigation rate of 15.24 cm ha1 yr1 reported in the 2007 Census of Agricultural Farm and Ranch Irrigation Survey, which summarizes land use in 2008 (USDA-NASS, 2010). 4. Center-pivot costs 4.1. Investment cost A specific irrigation cost is difficult to estimate because costs change with field size, well depth, energy source, and so on. We generalized the cost of irrigating corn by estimating the cost of a typical non-towable center-pivot system (Verbree, 2012; USDANASS, 2010). Three irrigated and non-irrigated field sizes of 25 ha, 51 ha, and 81 ha were selected to reflect the range of corn fields in Tennessee. We separated capital investment into well investment and system investment (Table 2). Well investment included well drilling, the pump and the power unit. System investment included spans, sprinklers and installation. The estimated investment costs were derived from personal communications with irrigation dealerships in West Tennessee and an irrigation expert (Verbree, 2012). The center-pivot system had a useful life of 20 years and a zero salvage value (Ding and Peterson, 2012; Guerrero et al., 2010). We assumed the producer financed the cost of the well and system over five years at 5% interest (Guerrero et al., 2010). The total capital investment cost of the equipment was depreciated under the Modified Accelerated Cost-Recovery System over five years at a 25% marginal tax rate. Finally, the risk-adjusted discount rate was 8%, which is comparable to other irrigation investment studies (Carey and Zilberman, 2002; Guerrero et al., 2010; Price and Wetzstein, 1999; Seo et al., 2008). 4.2. Energy, maintenance, and labor costs An important decision for producers in the southeastern United States is whether to use diesel or electricity to power their irrigation system. The annual energy costs for using diesel and electric power to apply 16.12 cm ha1 yr1 were calculated following Rogers and Alam’s (2006) energy cost formulas. The weighted

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

Field size 25 ha

51 ha

81 ha

Well setup Drilling Pump Power unit

$20,000 $20,000 $10,000

$20,000 $24,500 $15,200

$20,000 $26,500 $25,500

Irrigation rig Sprinklers Spans Installation

$2,000 $48,000 $6,700

$2,600 $65,000 $8,000

$4,500 $99,000 $9,300

Total costs Field ha1

$106,700 $4,268

$135,300 $2,692

$184,256 $2,256

average pump operating pressure of 6.89 kilopascals (kPa) was chosen using data from the 2007 Census of Agricultural Farm and Ranch Irrigation Survey (USDA-NASS, 2010). An average pump-lift distance of 76.2 m was used, which is a typical well depth in Tennessee (Verbree, 2012; USDA-NASS, 2010). The amount of energy required to pump 16.12 cm ha1 yr1 of water annually was 185.49 l ha1 yr1 of diesel and 689.42 kW h ha1 yr1of electricity. Three farm diesel prices of $0.52 l1, $0.79 l1 and $1.06 l1, and three commercial electricity prices of 0.07 kW h1, 0.09 kW h1 and 0.11 kW h1 were used to evaluate the sensitivity of irrigation costs to energy prices. These prices were chosen to reflect the range of historic diesel and electricity prices in Tennessee. Leib (2012b) demonstrated the importance of including the fixed cost of running electric power lines to the pump, so we used three fixed costs of $10,000, $15,000 and $20,000 to run electricity to the center-pivot. No clear estimate for repair and maintenance costs was available since these costs are not published in the American Society of Agricultural and Biological Engineering Standards. Jensen (1980) and McGrann et al. (1986a,b) estimated annual repair and maintenance costs for irrigation equipment as a percentage of the initial costs of the equipment, as proposed in the American Agricultural Economic Association (AAEA) Commodity Costs and Returns Handbook (2000). We used 1.7% of the initial costs, which falls within the range specified in the AAEA Handbook (2000). We assumed an annual irrigation labor cost of $6 ha1, including labor costs for monitoring soil water status and other irrigation management activities (Leib, 2012b). 5. Yield response estimation The physical relationship between yield, irrigation, and N as well as the price of corn and N determine the optimal N fertilization rates and yields. If non-optimal N fertilization rates and yields were selected to compare non-irrigated and irrigated corn, the result might overestimate or underestimate the returns to irrigation. For example, if irrigated and non-irrigated yields were compared at 150 kg N ha1, the yield gains from irrigating corn might be underestimated since irrigated corn will likely require more N fertilizer than non-irrigated corn. Therefore, selecting the profit-maximizing N fertilization rates for irrigated and nonirrigated corn at the same price of corn and same price of N, levels the playing field for yield and revenue gain comparisons. Many researchers have found that a plateau function for modeling corn yield response to N fits experimental data as well or better than polynomial models (Bullock and Bullock, 1994; Cerrato and Blackmer, 1990; Frank et al., 1990; Llewelyn and Featherstone, 1997). More recently, several researchers found stochastic plateau functions more suitable than their deterministic plateau function counterparts (Boyer et al., 2012; Biermacher et al., 2009; Roberts et al., 2011; Tembo et al., 2008; Tumusiime et al., 2011). Boyer et al. (2013) found that the linear response stochastic plateau (LRSP) function fit non-irrigated corn yield data well. The LRSP function assumes yield responds linearly to N until yield reaches a 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 functions for both irrigated and non-irrigated corn as

yti ¼ minðb0 þ b1 xti ;

l þ ut Þ þ v t þ eti

ð2Þ

where yti is the corn yield in Mg ha1 in the tth year on plot i; b0 and b1 are the yield response parameters; xti is the quantity of N fertilizer applied in kg N ha1; l is the expected plateau yield in Mg ha1; ut  Nð0; r2u Þ is the year plateau random effect;

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v t  Nð0; r2v Þ is the year intercept random effect; and eti  Nð0; r2e Þ is the random error term. Independence is assumed across the three stochastic components. A limitation of this model is N carryover from previous years is not specifically estimated in the model due to data limitations. The year plateau random effect weights the variation in plateau yields using a standard normal distribution, which is the same distribution used in Eq. (1). Eq. (2) is estimated using the NLMIXED procedure in SAS 9.1 (SAS Institute Inc., 2003). The profit-maximizing N fertilization rate is (Tembo et al., 2008) x ¼

1 ðl þ Z a ru  b0 Þ; b1

ð3Þ

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

Eðyti Þ ¼ ð1  UÞa þ Uðl 

ru / U

Þ;

ð4Þ

where U = U[a  l/ru] is the cumulative normal distribution function; a ¼ b0 þ b1 x; and / = /[a  l/ru] is the standard normal density function. Note that the expected yield (Eq. (4)) and the profit-maximizing N fertilization rate (Eq. (3)) are functions of the price of corn (p); thus, the optimal expected yield and N fertilization rate change as the price of corn changes. 6. Financial analysis framework A deterministic programming model was used to find the breakeven corn price for investing in an irrigation system using net present value (NPV). To calculate the NPV, annual net returns were first determined using a partial budget for corn production that is expressed as

EðNRtik Þ ¼ E½pytik ðxtik Þ  rxtik  kðcwti þ l þ mÞ;

ð5Þ

where E(NRtik) is the expected net return in $ ha1 in year t for the ith plot; k is a binary variable that is k = 1 for irrigation and k = 0 for non-irrigation; p is the price of corn in $ Mg1; ytik ðxtik Þ is yield in Mg ha1 and is a function of the N fertilizer rate xtik in kg N ha1; r is price of N fertilizer in $ kg1; c is the cost of energy for pumping water in $ cm1 ha1; wti is the irrigation water rate in cm ha1; l is the labor cost for monitoring soil water status and other labor activities related to irrigation in $ ha1; and m is irrigation maintenance and repair costs in $ ha1. The optimal N fertilizer rate in Eq. (3) and the optimal expected yield in Eq. (4) were used in Eq. (5) to calculate expected net returns. The price of N, labor cost, irrigation water rate, and maintenance costs were assumed to be deterministic in the model and are summarized in Table 3. Several energy prices are selected to show the sensitivity of net returns for different energy sources and prices. Expected annual cash flows were calculated for a corn producer financing the purchase of the irrigation system and for one who does not invest in irrigation. Depreciation and annual interest were

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

TNRtik ¼ NRtik  kDep  kInt;

ð6Þ

where TNRtik is the annual taxable net returns; Dep is the annual depreciation of the irrigation system; and Int is the annual interest payment on the loan. The annual interest rate is shown in Table 3. The total taxable net returns was multiplied the by tax rate to determine the amount paid in taxes annually. The annual cash flows were determined by subtracting annual loan payment for the irrigation system and the annual tax payment from the net returns, expressed as

CF tik ¼ NRtik  kPMT  kðTNRtik sÞ;

ð7Þ

where CFtik is the annual cash flow; PMT is the annual loan payment for the irrigation system; and s is the annual tax rate shown in Table 3. The expected annual cash flows for irrigated and non-irrigated corn were used for each year of the 20-year useful life of the irrigation systems. The NPV of investing in an irrigation system over its useful life is solved for the corn price p that makes NPV equal zero. The NPV = 0 calculation is

minNPV ¼ IC þ p

T X CF t1  CF t0 t¼1

ð1 þ gÞt

¼ 0;

ð8Þ

where IC is the initial investment in irrigation equipment in year t = 0; CFt1 is the annual cash flow for irrigated corn; CFt0 is the annual cash flow for non-irrigated corn; T = 20 is the useful life of the irrigation equipment; and g is the risk-adjusted discount rate. The discount rate is the producer’s opportunity cost of investing in the irrigation equipment, representing the net return a producer would receive from an alternative investment (e.g., Treasury bond, new tractor, precision farming technology). The discount rate is equal to the risk-free discount rate plus the risk premium (Seo et al., 2008). The NPV = 0 calculation assumes that the present value of the benefit from irrigating corn (CF t1  CF t0 ) equals the opportunity cost of irrigating corn (i.e., the benefit from an alternative investment). When NPV equals zero, the non-irrigated corn producer is indifferent between investing in an irrigation system and an alternative investment. We solved Eq. (8) for the minimum time-adjusted corn prices (breakeven corn prices) for different energy sources, energy prices and field sizes. The breakeven corn price represents the price required over the 20-year useful life that allows 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 changes the maximum net returns for both irrigated and non-irrigated corn; thus, comparisons are made when both producers maximize profit, providing a level playing field for comparisons. The LRSP function allows us to include year-to-year yield variability in determining the breakeven price of corn—a unique contribution to the irrigation feasibility literature. 7. Results 7.1. Breakeven price of corn

Table 3 Input prices and quantities for the corn budgets. Inputs

Unit

Price

Nitrogen Labor Maintenance Irrigation rate Discount rate Marginal tax rate Interest rate

kg ha % of initial cost cm ha1 yr1 % % $

$1.33 $6 1.7 16.12 8 25 5

Parameter estimates from the LRSP models for irrigated and non-irrigated corn are presented in Table 4. All parameter estimates were significant (a 6 5%). The slope parameter estimates (yield response to N fertilizer) were similar for irrigated and nonirrigated corn, but the intercept and plateau parameter estimates were larger for irrigated corn. The estimated plateau was about four Mg ha1 higher, indicating the yield gain from timely application of irrigation. Additionally, the intercept and plateau random

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effects for irrigated corn were smaller than the random effects for non-irrigated corn, indicating year-to-year yield variability was reduced with irrigation, which suggests production risk decreases. The parameter estimates from the LRSP functions were substituted into the net return equation (Eq. (5)) to solve for the time-adjusted breakeven price of corn. Breakeven corn prices are presented in Table 5 for various energy costs, energy sources, and field sizes. The energy source that provides the lowest breakeven price of corn for a given field size is the preferred energy source for that field size because it provides the best opportunity for the irrigation investment to be profitable. For the small field (25 ha), the breakeven corn price was $249 Mg1 for $0.52 l1 diesel, and $271 Mg1 for $1.06 l1 diesel (Table 5). For every 27 cent l1 increase in the price of diesel, the breakeven price of corn increased by $11 Mg1. With electricity as the power source for the center-pivot, the breakeven price of corn ranged from $257 to $283 Mg1 depending on the fixed investment cost of running electricity to the center-pivot and the per-unit electricity rate (Table 5). For every two cent increase in the per-unit electricity rate, the breakeven corn price increased by $3 Mg1. With diesel at $1.06 l1 and the fixed cost of running

electricity to the center-pivot at $10,000, the breakeven price of using electricity was lower, which makes it the preferred energy source. When the investment cost of running electricity to the pump was greater than $10,000, diesel was the more economical energy source. Breakeven corn prices were $167 Mg1 for $0.52 l1 diesel and $190 Mg1 for $1.06 l1 diesel on a medium-sized field (51) (Table 5). The breakeven price of corn using electricity ranged from $168 to $182 Mg1 depending on the fixed investment cost and per-unit electricity rate (Table 5). With diesel at $0.52 l1, the breakeven price of corn was lower for diesel than electricity with the exception of the lowest electricity cost scenario (Table 5). Thus, diesel would be preferred over electricity. When the diesel price is $0.79 l1, the breakeven corn price indicates that electricity was preferred over diesel expect for the highest electricity cost scenario. For the large-sized field (81 ha), the breakeven price of corn decreased to $149 Mg1 for $0.52 l1 diesel, and $171 Mg1 for $1.06 l1 diesel (Table 5). The breakeven price of corn using electricity ranged from $144 to $156 Mg1 depending on the fixed investment cost and per-unit electricity rate (Table 5). When diesel was $0.52 l1, the breakeven price of corn was lower for diesel than electricity with the expectation of a few electricity-cost scenarios, which suggests that diesel would likely be preferred over electricity at $0.52 l1 diesel (Table 5). With the price of diesel at $0.79 l1 or higher, the breakeven price indicates that electricity was preferred over diesel. A probability density function was found for historical real corn prices from 1990 to 2012. The CPI index with a base year of 2001 was used to adjust nominal corn prices to real corn prices. The probability density function for the real corn price was used to determine the probability of the corn price being greater than the breakeven price of corn (Table 6). These probability estimates serve as proxies for the probability of NPV being positive. For the small-sized field, the probability of the corn price being greater than the breakeven corn price was zero (Table 6). The probability of a corn price greater than the breakeven price for the mediumsized field was low, and the probability of the corn price being above the breakeven price for the large-sized field was also low but higher than for the medium-sized field (Table 6). The probability of receiving a corn price sufficiently high to breakeven on investing in supplemental irrigation is low when comparing the breakeven price with the historical distribution of corn prices.

Table 5 Breakeven corn price ($ Mg1) for investing in a center-pivot by energy source, energy cost, and field size.

Table 6 Probability of the breakeven corn price ($ Mg1) for investing in a center-pivot occurring based on real corn prices (1990–2012), by energy source, energy cost, and field size.

Table 4 Estimated corn yield (Mg ha1) response to N (kg ha1) for irrigated and non-irrigated corn grown after soybeans using a linear response stochastic plateau function. Parameter

Response functions Irrigated corn

Non-irrigated corn

Intercept

6.705a (0.221)

5.379a (0.194)

N

0.046b (0.002)

0.044a (0.002)

Plateau

14.878b (0.164)

10.596a (0.172)

Plateau random effect

1.429b (0.468)

4.683a (0.743)

Intercept random effect

0.659b (0.169)

5.132a (0.881)

Random error

1.149a (0.131)

0.912a (0.105)

2 Log-likelihood

494.0

469.4

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

Per-unit energy costs

Field size

Per-unit energy costs

25 ha

51 ha

81 ha

$248.78 $259.57 $270.86

$167.36 $178.56 $189.77

$148.88 $160.04 $171.22

Diesel energy $0.52 l $0.79 l $1.06 l

Electric energy with a $10,000 fixed cost investment 0.07 kW h $256.94 $165.78 0.09 kW h $260.12 $168.93 0.11 kW h $263.40 $172.08

$143.70 $146.83 $149.97

Electric energy with a $15,000 fixed cost investment 0.07 kW h $267.00 $170.67 0.09 kW h $270.18 $173.82 0.11 kW h $273.36 $176.97 Electric energy with a $20,000 fixed cost investment 0.07 kW h $277.08 $175.56 0.09 kW h $280.26 $178.71 0.11 kW h $283.44 $181.87

Diesel energy $0.52 l $0.79 l $1.06 l

Field size 25 ha

51 ha

81 ha

0% 0% 0%

5% 2% 1%

12% 7% 4%

Electric energy with a $10,000 fixed cost investment 0.07 kW h 0% 0.09 kW h 0% 0.11 kW h 0%

5% 4% 3%

15% 13% 12%

$146.76 $149.90 $153.04

Electric energy with a $15,000 fixed cost investment 0.07 kW h 0% 0.09 kW h 0% 0.11 kW h 0%

4% 3% 2%

13% 12% 10%

$149.82 $152.97 $156.11

Electric energy with a $20,000 fixed cost investment 0.07 kW h 0% 0.09 kW h 0% 0.11 kW h 0%

3% 2% 2%

12% 10% 9%

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7.2. Optimal yield and nitrogen rate We report profit-maximizing corn yields—a function of the corn price (Eq. (4))—at the breakeven prices in Table 7. Expected yield was higher for irrigated corn than non-irrigated corn, and varied little with the change in the breakeven price of corn. We also report the profit-maximizing N fertilization rates—also a function of corn price (Eq. (3))—for irrigated and non-irrigated corn at the breakeven prices in Table 8. Consistent with the literature, irrigated corn has a higher optimal N fertilizer rate than non-irrigated corn (Sheriff, 2005; Vickner et al., 1998). Given the breakeven corn prices, the profit-maximizing N fertilization rates ranged from 200 to 211 kg N ha1 for irrigated corn and from 159 to 180 kg N ha1 for non-irrigated corn. The parameter estimates suggest that irrigation increased the yield plateau of corn, which resulted in higher N fertilizer rates. 8. Discussion Irrigation investment is expanding in humid regions of the United States as well as globally (Mullen et al., 2009; Rosegrant et al.,

2009; Schaible and Aillery, 2012). Nevertheless, little is known about whether irrigation investment is profitable in humid regions. The calculated breakeven prices suggest that investment in irrigating corn in the humid southeastern United States is not likely profitable, given historical prices of corn. However, the Food and Agricultural Policy Research Institute (FAPRI) (2012) has forecasted the price of corn to remain between $179.52 Mg1 and $234.64 Mg1 through 2022. If this price forecast is realized, investing in a center-pivot irrigation system for a 25 ha field appears to not be profitable regardless of energy source, but investing in center-pivot irrigation systems for 51 and 81 ha fields might be profitable investments for most energy price scenarios. Given current and forecasted corn prices, irrigating corn in humid regions appears to be profitable for large- and medium-sized fields. Although irrigating corn on medium- and large-sized fields appears profitable given forecasted corn prices, a corn producer should consider how irrigation investment impacts various sources of risk in corn production. For example, Mullen et al. (2009) observed that high corn prices have a large impact on irrigation demand in the humid southeastern United States. Today, the price of corn is higher than the historic price of corn due to increased

Table 7 Expected yields (Mg ha1) for the breakeven corn prices by energy source, energy cost, and Field size. Per-unit energy costs

Field size 25 ha

51 ha

81 ha

Irrigated corn

Non-irrigated corn

Irrigated corn

Non-irrigated corn

Irrigated corn

Non-irrigated corn

14.81 14.82 14.82

10.47 10.48 10.48

14.77 14.78 14.79

10.39 10.41 10.42

14.75 14.76 14.77

10.36 10.38 10.40

Electric energy with a $10,000 fixed cost investment 0.07 kW h 14.81 10.47 0.09 kW h 14.82 10.48 0.11 kW h 14.82 10.48

14.77 14.77 14.77

10.39 10.39 10.40

14.75 14.75 14.75

10.34 10.35 10.36

Electric energy with a $15,000 fixed cost investment 0.07 kW h 14.82 10.48 0.09 kW h 14.82 10.48 0.11 kW h 14.82 10.48

14.77 14.78 14.78

10.39 10.40 10.40

14.75 14.75 14.76

10.35 10.36 10.36

Electric energy with a $20,000 fixed cost investment 0.07 kW h 14.82 10.49 0.09 kW h 14.82 10.49 0.11 kW h 14.82 10.49

14.78 14.78 14.78

10.40 10.41 10.41

14.75 14.76 14.76

10.36 10.36 10.37

Diesel energy $0.52 l $0.79 l $1.06 l

Table 8 Profit-maximizing N rates (kg N ha1) for the breakeven corn prices by energy source, energy cost, and field size. Per-unit energy costs

Field size 25 ha

51 ha

81 ha

Irrigated corn

Non-irrigated corn

Irrigated corn

Non-irrigated corn

Irrigated corn

Non-irrigated corn

209.02 209.70 210.34

176.60 177.90 179.13

202.58 203.70 204.74

164.24 166.38 168.36

200.50 201.80 202.98

160.33 162.73 165.00

Electric energy with a $10,000 fixed cost investment 0.07 kW h 209.55 177.61 0.09 kW h 209.74 177.97 0.11 kW h 209.92 178.32

202.42 202.75 203.07

163.92 164.55 165.17

199.86 200.25 200.64

158.98 159.75 160.49

Electric energy with a $15,000 fixed cost investment 0.07 kW h 210.48 179.40 0.09 kW h 210.31 179.06 0.11 kW h 210.48 179.40

202.93 203.24 203.55

164.89 165.50 166.09

200.24 200.63 201.00

159.73 160.47 161.19

Electric energy with a $20,000 fixed cost investment 0.07 kW h 210.68 179.78 0.09 kW h 210.85 180.11 0.11 kW h 211.02 180.43

203.41 203.71 204.01

165.83 166.41 166.98

200.62 200.99 201.36

160.46 161.18 161.88

Diesel energy $0.52 l $0.79 l $1.06 l

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demand for corn, which is likely driving the expansion irrigation in the southeastern United States. Corn producers who invest in irrigation systems must be able to manage the risk of potentially unstable future corn prices (also known as price risk). At the forecasted prices of corn over the next ten years (FAPRI, 2012), investing in a center-pivot may be profitable for corn fields greater than 51 ha. However, agricultural prices historically have had boom and bust periods (Gouel, 2012). Considering the historical price of corn, the probability is fairly low of irrigated corn being a profitable investment on any size field in the southern United States. Therefore, irrigation investment could increase corn producers’ price risk. In addition, higher price risk increases corn producers’ financial risk because a higher breakeven price is required to cover the higher cost of irrigation. Thus, higher corn or commodity prices will be required to maintain positive cash flows with irrigation. Conversely, irrigation has proven to be a useful investment in reducing production risk by reducing yield variability (Apland et al., 1980). Our results in Figs. 1 and 2 and the random effects parameter estimates in Table 4 confirm that supplemental irrigation in a humid climate decreases the year-to-year yield variability for corn producers, which gives producers more certainty about the quantity of corn produced. This paper considers price risk by presenting results for various energy sources, energy prices, and farm sizes. Additionally, the probability of the breakeven price being higher than the historical price of corn is shown. Yield variability (i.e., production risk) was also considered in estimating breakeven prices of corn for investing in irrigation. However, future research is needed to address the tradeoffs among price, financial, production risks from irrigation investment in humid climates. A Monte Carlo simulation model using historical prices and yield variability is a potential approach 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, however, irrigation in the humid southeastern United States is designed to supplement rainfall during drought periods. Less water is applied to corn in a growing season than in more arid regions, so energy costs have less of an impact on the profitability of irrigated corn in humid regions. If diesel prices were at or below $0.52 l1, diesel would be preferred over electricity for most electricity prices and field sizes but, if the diesel price were greater than or equal to $0.79 l1, electricity would become more competitive for fields of 51 ha or larger. Field size and the cost of running electricity to the center-pivot are important factors in the relative profitability of using electricity or diesel as the energy source for irrigation. Corn producers should consider these factors before choosing an energy source. This study has implications for water supplies, water planning, and for future agricultural water management in Tennessee and the southeastern United States. If corn prices remain high, investment in irrigation would likely continue to increase and corn area may continue to expand and replace less water-intensive crops, such as cotton. Thus, it is possible that more intensive water use in humid regions will increase. This increase would be important for policy makers to consider in developing water management policies as water supplies tighten. For example, they could create incentives for corn producers to adopt more efficient irrigation systems or change the water law to regulate water access and quantity used.

9. Conclusion Irrigation investment for corn production is expanding into more humid regions across the globe and specifically in the

southeastern United States. However, little is known about the profitability of irrigating corn in these regions. Since interest in irrigation has recently increased among southeastern United States corn producers because of higher corn prices, we determined the breakeven price of corn for investing in a center-pivot irrigation system in Tennessee. Our analysis investigated farm-level irrigation investment using diesel and electric energy sources with three energy prices and three field sizes. We estimated yield response to N for irrigated and non-irrigated corn, and let the yield and N fertilization rates vary with the breakeven price of corn. Yield variability of irrigated and non-irrigated corn was included in calculating 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 N fertilization rates and expected yields for irrigated corn than nonirrigated corn. Yield variability decreased with supplement irrigation application. At current corn prices, which are historically high, irrigating corn appears to be profitable on field sizes greater than 51 ha, but when compared with historic corn prices, the probability of receiving a corn price sufficiently high to breakeven on irrigation investment is low. Field size and cost of extending electricity to the irrigation system were vital factors in selecting diesel or electricity as the energy source. When diesel prices were equal or greater than $0.79 l1, electricity became a more viable energy source than diesel for fields greater than 51 ha. Acknowledgements The authors thank Dr. Blake Brown and the staff at the Milan Research and Education Center, Milan, TN, for field research support. They also thank the anonymous reviewers for comments on an earlier draft. References American Agricultural Economics Association (AAEA), 2000. Commodity Costs and Returns Estimation Handbook. AAEA, Ames, IA. Apland, J., McCarl, B.A., Miller, W.L., 1980. Risk and the demand for supplemental irrigation: a case study in the Corn Belt. Am. J. Agric. Econ. 62, 142–145. Biermacher, J.T., Brorsen, B.W., Epplin, F.M., Solie, J.B., Raun, W.R., 2009. Economic potential for precision agriculture based on plant sensing technology. Agric. Econ. 40, 397–407. Boggess, W.G., Lynne, G.D., Jones, J.W., Swaney, D.P., 1983. Risk-return assessment of irrigation decisions in humid regions. Southern J. Agric. Econ. 15, 135–143. Boggess, W.G., Anaman, K.A., Hanson, G.D., 1985. Importance, causes and management responses to farm risks: evidence from Florida and Alabama. Southern J. Agric. Econ. 17, 105–116. Boyer, C.N., Tyler, D.D., Roberts, R.K., English, B.C., Larson, J.A., 2012. Switchgrass yield response functions and profit-maximizing nitrogen rates on four landscapes in Tennessee. Agron. J. 104, 1579–1588. Boyer, C.N., Larson, J.A., Roberts, R.K., McClure, A.T., Tyler, D.D., 2013. Stochastic yield response functions to nitrogen for corn after corn, corn after soybeans, and corn after cotton. J. Agric. Appl. Econ. 45, 669–681. Bruns, H.A., Meredith, W.R., and Abbas, H.K., 2003. Effects of furrow irrigation on corn in the humid sub-tropical Mississippi delta. Crop Manage. . Bullock, D.G., Bullock, D.S., 1994. Quadratic and quadratic-plus-plateau models for predicting optimal nitrogen rate of corn: a comparison. Agron. J. 86, 191–195. Carey, J.M., Zilberman, D., 2002. A model of investment under uncertainty: modern irrigation technology and emerging markets in water. Am. J. Agric. Econ. 84, 171–183. Caswell, M., Zilberman, D., 1986. The effects of well depth and land quality on the choice of irrigation technology. Am. J. Agric. Econ. 68, 798–811. Cerrato, M.E., Blackmer, A.M., 1990. Comarison of models for describing corn yield response to nitrogen fertilizer. Agron. J. 82, 138–143. Christy, D.R., Myszewski, M., Kundell, J.E., 2005. A Comparison of Surface Water Laws and Regulations from Southeastern States. Carl Vinson Institute of Government, University of Georgia. (accessed 18.07.12). Dalton, T.J., Porter, G.A., Winslow, N.G., 2004. Risk management strategies in humid production regions: a comparison of supplemental irrigation and crop insurance. Agric. Resour. Econ. Rev. 33, 220–232. DeJonge, K.C., Kaleita, A.L., Thorp, K.R., 2007. Simulating the effects of spatially variable irrigation on corn yields, costs, and revenue in Iowa. Agric. Waer. Manage. 92, 99–109.

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