A calculator to assess the economics of deep placement P over time
Author: Andrew Zull (DAFFQ), Mike Bell (QAAFI), Howard Cox (DAFFQ), Jayne Gentry (DAFFQ) Kaara Klepper (DAFFQ), Chris Dowling (Back Paddock Company)  Date: 01 Mar 2015
Take home message
Recent research has indicated that there are potential yield benefits from replenishing supplies of phosphorus (P) in the subsurface layers (1030cm) if the Colwell and BSES soil tests indicate a potential deficiency; however, it was unknown if it has economic merit.
DeepP placement is a longerterm decision because of the initial investment costs in P fertiliser (MAP), machinery issues and the benefits over many seasons. Additionally, this increases risk due to unknown future season types. We have developed bioeconomic framework which includes soil conditions, PAWC, climatic conditions as well as input and output prices.
A fundamental question of deepP placement is “how much P and how often?” Using a case study with a deepsoil ColwellP of 5 mg/kg in the Goondiwindi region, we compared the risk and benefit of applying amounts of P at depth for a “shortrotation” (3 years) against a “longrotation” (7 years).
The results indicate that the optimal MAP rate was 135 kg/ha and 270 kg/ha for the short and longrotations, respectively, resulting in realannual returns of $43/ha/year and $76/ha/year. However, there is risk of a loss with the shortrotation ($14/ha/year) under the worstcase scenario (consecutive lowrainfall years). Under the bestcase scenario (highrainfall years) the longrotation resulted in far better net benefits ($139/ha/year).
Due to the lower investment cost with the shortrotation, the expected return on investment was 142%, compared to 67% p.a. for the longrotation. However, the shortrotation had the risk of a negative return on investment. The payback period for both decisions was around 2years.
These results will greatly change when biophysical or economic parameters change. As with all risky decisions, the farmer will have to weigh up the benefits, risks and their financial situation when making a decision.
Introduction
Soil moisture storage during fallows and the subsequent extraction of deep subsoil moisture and nutrients during a crop season are important to most of the northern grains region (NGR) (Bell et al., 2014). Nutrients removed from subsoil layers have to be replenished to maintain crop yields. Some nutrients like nitrogen (N) and sulfur (S) can move back into those layers when soil water is replenished, this transfer method is ineffective for immobile nutrients like phosphorus (P) and potassium (K). Replacing subsoil P and K requires either placing fertiliser into those layers directly, or moving fertilised topsoils deeper into the profile with some sort of inversion tillage. Deep placement of these immobile nutrients is currently considered the most efficient way to rectify this stratification.
Phosphorus (P) is an increasingly important nutrient for NGR cropping systems. Small amounts of P is needed (but at high plant tissue concentrations) during the early growth of crops, to promote higher grain numbers. Thus starter P is applied at the time of planting with the seed. However, as the plant develops it needs increasingly larger amounts of P to establish a high tiller density (in cereals), to promoted vigorous root systems, increase plant biomass and ultimately fill grains (in all species). Historically, this P has been available from native subsoil P reserves; however, through years of removal in the grain, P levels at depth have diminished to low levels. The placement of starter P fertiliser meets the demands of a young seedling with a very small root system; however, it doesn’t meet the demands of wellestablished plants surviving on subsoil moisture during flowering and grain filling. During this time the plants need to access nutrients such as P where the moisture is, in the lower soil profiles.
From an economic perspective, nutrient decisions can broadly be categorised into short and longterm decisions (Table 1). Application of P deeper in the soil will inevitably result in some moisture loss and soil disturbance. Thus the placement of deepP needs to be done well before planting to allow time for replenishment of the surface soil moisture and the soil to settle. In addition, the cost of application and the high application rate of P results in the economic analysis for more than a single season. This is in contrast to starter P and N rate decisions that are based on crop requirement in the current season.
Table 1. Factors involved with short and longterm P decisions
Starter P and N Shortterm decisions 
DeepP Longterm decisions 

• Main benefit in current season • Unknown season type or yield but known starting moisture • Fixed crop $ prices (can contract) • Good knowledge of response functions • Fixed N and P prices at application • Assume no other nutrients constraints 
• Benefits for many seasons • Unknown season type or yield & unknown starting water after 1st season • Unknown future crop prices • Poor knowledge of response functions • Unknown future P and N prices • Need to assume future decisions will provide sufficient starter P & N • Fixed P prices at time of the decision • Time value of money & inflation ($$$ in the ground vs bank) 
When considering the outcomes of longterm decisions there are two fundamental economic considerations: risk and the time value of money. The further we look into the future the greater the uncertainty and therefore the risk. However, the longer we have to wait for a reward the lower its current value, and impact on our decision. The outcome in a 100 years is very risky but of little value, or impact, for many of us. Most longterm farmlevel decisions are limited to 1020 years in the future. Therefore a bioeconomic framework is needed to obtain the optimal application rates (which in some cases may be zero) and the associated risk for longterm nutrient decisions.
Research method
We developed this framework using APSIM and Excel® for 12 regions within the NGR; and, the focus of this paper is the application of the framework and the learnings from the results. This framework design can accommodate other nutrients such as potassium (K), and even lime for aluminium/ manganese toxicity amelioration.
The optimal deepP application rate is driven by both biophysical and economic components of the cropping system of a paddock. A graphical outline of the bioeconomic model is shown in Figure 1:
Figure 1. Schematic of the bioeconomic framework of longterm decisions of deepP placement using APSIM® and Excel®
DeepP bioeconomic framework thresholds
Based on previous analysis, we have assumed that soil will be deepP responsive when Colwell P is <10 mg/kg and BSES P is < 30 mg/kg in the 10‐30cm layer, and that the residual benefit of deep bands will occur if the PBI is < 200 (Bell et al., 2014). Of course, a soil test below this threshold does not guarantee a crop response, and therefore should be used as an indicator of a probable response.
In this study we have assumed that 1 mg/kg Colwell P represents 1 kg plantavailable P/ha in a 10cm layer, and that each kg of crop P removal is equivalent to 1 mg Colwell P/kg extracted across the crop root zone. However, we know from previous research that >90% of that net removal comes from the top 30cm of the profile, with roughly half from the 010cm and the other half from the 1030cm layers. The 1030cm soil test layer represents two soil bands 10cm thick (1020 and 2030 cm), therefore the amount of P in that layer is twice the soil test value (called P* in the setup).
There is little historic data in the NGR on responses to deep P for any crops – other than what we have generated in the last few years (Bell et al., 2014). Therefore we have used three basic season types, with characteristics that influence crop response to deep P, as suggested by Bell et al. (2014):
 Dry start – those years with little or no effective rainfall from planting until after tillering;
 No stress – no severe crop stress, with an expectation that more regular rainfall will ensure the top soils have plenty of active roots; and
 Late stress – those with enough rain to ensure good early growth, secondary root development and tillering but serious later water deficits that ensure a strong reliance on subsoil moisture.
Case study
The case study is based on a paddock in the Goondiwindi region, producing sorghum, chickpea and wheat, on soil with a PAWC of 180 mm, nitrateN of 50 kg N/ha, soil organic carbon between 0.85 and 0.95%, ColwellP soil test in the 1030 cm of 5 mg/kg, and PBI of 100, meaning the soil is very likely to be P responsive. We compared the risks and benefits of applying a low rate of MAP at depth for a 3year “shortrotation” of sorghum, chickpea, wheat, wheat crops against a higher rate of MAP for a 7year “longrotation.”
The climatic records (18902013) from Goondiwindi were used to estimate season types and to run APSIM for yield distributions for soils of 120 and 240 mm PAWC. The bioeconomic framework is designed so that any PAWC can be selected between 120240 mm, using a linear regression between these two values.
Inputs for our case study site (Table 2 and below):
 DeepP placement is by a currently owned John Deere® 8400 tractor and planter attachment set at a soildepth of 200250 mm. The cost includes fuel, oil, repairs, maintenance, efficiency losses, and additional depreciation based on machinery hours totalling $31.58/ha.
 DeepP placement will result in increased yields and therefore 10% more N will also be placed in shallow soil layers for sorghum and wheat crops at a cost of $800/t.
 MAP (P = 22%) is used for the deepP application at a cost of $730/t.
Table 2. Input criteria relating to P and N removed, the yield benefit from applied deepP (from Bell et al. 2014) and croprelated costs and prices

Nutrients removed from soil by crops (kg/ harvested t) 
Damage (discount) to crop when ColwellP<10mg/kg (P*<20kg/ha) 
Variable costs 
Farm gate prices 


Crop 
120mm PAWC 
240mm PAWC 

P* 
Net N 
Dry start 
No stress 
Late stress 
Dry start 
No stress 
Late stress 
$/ha 
$/t 

Chickpea DC 
3.8 
0 
5% 
10% 
15% 
30% 
10% 
25% 
342 
409 
Sorghum LF 
2.3 
17 
5% 
15% 
10% 
10% 
15% 
25% 
462 
230 
Wheat 
2.6 
23 
5% 
15% 
10% 
10% 
15% 
25% 
319 
257 
When dealing with longterm investments we need to consider the opportunity cost of not investing the money elsewhere or financing. We do this by discounting future cash flows to a net present value (NPV). The discount rate will be different for different people based on their opportunity costs, cost of finance, and/or compensation for undertaking the risky venture. In our analysis we have assumed that this deepP venture will use bank financing and added risk, so the farmer will need to receive 10% p.a. for the duration of the crop rotation. However, when you have longterm investments of different time horizons, the analysis will bias towards the longerterm investment due to longer cash flows. Therefore, to compare these projects we need to convert NPVs into annuities, we call this the annual net benefit ($/ha/year). This is basically the current value of additional income per year over the project life, i.e. the farmer should be indifferent if they received the lump sum NPV or if they received the annual amounts. Although the first crop is longfallowed, the investment horizon of deepP will start at the time of application just prior to planting.
Another longterm investment measure is the internal rate of return (IRR) which is basically the return on investment for longterm investments represented in % p.a. Any P* depleted from or left in the soil after this point has been ignored. This deepP framework is meant to be used in a stepwise fashion through time, in that after a few seasons another Colwell test is needed to evaluate if there is still sufficient P* and if it is economical to replenish the P* pool, this likely after consecutive high yielding years.
Results
Returns vs risk
The calculator is able to determine the optimal P fertiliser rate and the annual net benefits of applying the deepP compared to nil applied deepP. The calculator also measures the risk associated with the alternative deepP strategies. Based on these findings a farmer may opt for a lower risk and expectedreturn or viceversa based on their risk preference.
Optimal P fertiliser rate
Based on the expected (median or 50 percentile) outcomes, the optimal deepP application rate for the short and long rotations used in the case study are approximately 135 kg/ha and 270 kg/ha of MAP respectively as shown by the maximum point on median line and the annual net benefits (Figure 2).
Comparison of net benefits over the short and long rotation
The maximum median annual net benefit was $43/ha/year and $76/ha/year in the short and long rotations respectively.
Under the worstcase scenario (0 percentile), being a series of poor seasons, the optimal application rate for the longrotation did not change but resulted in the annual net return of only $6/ha/year; however, for the shortrotation the optimal rate decreased by 34 kg to 101 kg/ha MAP and resulted in a loss of $9/ha/year.
Under the bestcase scenario (100 percentile), rain when you want it, the optimal application rate increases to 338 kg/ha MAP for the longrotation, with an annual net benefit of $150/ha/year. That is, increasing MAP application by 68 kg/ha it is possible to get an extra $11/ha/year with exceptionally good run of seasons but this amount of MAP would be excessive for all other seasons.
Figure 2. The real annual net benefit of deepP (MAP) placement of a short and long rotations with respect to different seasonal outcomes: percentile = 0 is the worstcase scenario, 100 is the best case, and 50 is the expected outcome. The red circles indicate the optimal application rate for the given seasons.
Quantifying the risk and variability of potential outcomes
Assuming that the farmer is risk neutral and the optimal decision is to maximise the expected value, the annual returns will be between $14 and $93/ha for the shortrotation and $6 and $139/ha for the longrotation. These distributions are one measure of risk. Although not graphically presented here, the framework reported a 7% probability of not breaking even for the shortrotation, the longrotation was almost certain to breakeven. The framework also showed that the longrotation was always better (stochastic dominance) over the shortrotation, meaning that it will always result in a higher annual net return.
Effect of deepP on crop yields and net benefit over time
The calculator quantifies the median change of yields and net benefits over the example rotations (Table 3). The cumulative crop length (years) indicates the time series of the proposed rotation.
There are three streams of expected (median) yields from each of rotations: unconstrained (APSIM) without any penalties from insufficient nutrients, yields with added deepP and starter P, and no applied P. The lower net benefit with both rotations in the first season is due to the cost of deepP application, which proves that it is a longterm investment over multiple seasons.
Table 3. Yield and economic output from the economic framework calculator
Long rotation
Sorghum LF 
Chickpea DC 
Wheat 
Wheat 
Sorghum LF 
Chickpea DC 
Wheat 
Wheat  

Cumulative crop length (years) 
0.4  1 
2  3  4.4 
5 
6  7 
Yield (kg/ha) unlimited N & P 
4,654 
1,359  3,266 
3,210 
4,654  1,313  2,988  3,081 
Yield (kg/ha) with added P 
4,654  1,359 
3,266 
3,210  4,654  1,313  2,975  2,922 
Yield (kg/ha) without added P 
4,082  1,169 
2,730 
2,715  3,943  1,076  2,528  2,550 
Net benefit of P treatment 
$132  $86  $122  $124  $144  $86  $113  $70 
Short rotation
Sorghum LF 
Chickpea DC 
Wheat  Wheat 


Cumulative crop length (years) 
0.4  1  2  3 
Yield (kg/ha) unlimited N & P 
4,654  1,359  3,266  3,210 
Yield (kg/ha) with added P 
4,654  1,359  3,266  3,081 
Yield (kg/ha) without added P 
4,082  1,169  2,730  2,715 
Net benefit of P treatment 
$33  $86  $121  $108 
Return on investment on deepP
The other consideration for longterm investments is the return on investment was well as the payback period of the initial investment. The internal rate of return (IRR) for the short and longrotation is 142% and 67% p.a., which is far greater than the opportunity cost of 10% (Figure 3). Although the annual returns of the longrotation are higher under all situations, the expected (median) IRR is lower due to the higher initial financial investment. However, the risk (uncertainty) associated with the shortrotation is also far greater. Under the worstcase scenario it is possible to have an 18% IRR and there is a 5% chance of getting a negative IRR. The higher risk of the shortrotation is also indicated by the high IRR under the bestcase scenario of 750% compared to the longrotation 224%. In summary, the longrotation IRR is lower, but it is more predictable (less variable) and is almost guaranteed to have a positive IRR. Although not shown, the short and longrotation has about an 85% chance of getting >10%, which is the opportunity cost.
Figure 3. The distribution of internal rates of return for the short and longrotation option: percentile = 0 is the worstcase scenario, 100 the best case, and 50 the expected.
Payback period
The expected payback period of both the short and longrotations is twoyears (Figure 5). However there is a greater probability of the shortrotation decision being paid back sooner due to the low rate of deep P, hence lower initial investment of the shortrotation. There is a 1% chance of never receiving a payback. Under the worst conditions the cost outlay for fertiliser in the longrotation is expected to be paid pack in the fifth year.
Figure 4. The frequency of which the initial investment is paid back in a particular year. “Never” indicates that it was never fully paid back.
Discussion
The decision to apply deepP is different to most fertiliser decision because it involves a single high application of fertiliser product that is hoped to supply financial benefits over a number of seasons for which future climatic conditions and starting soil moisture are unknown. Hence several technical and economic factors need to be included in the analysis.
The decision to apply deepP has the following considerations that this economic framework (calculator) can address;
1. Is deep P required?
 The framework uses best current research knowledge of critical soil levels, and predicts whether it is likely to be worthwhile proceeding with a deepP application
 P application rates can be varied to find the optimum P rate for the highest financial return.
 Once the optimal rate is identified based on the expected annual net returns for the different crop rotations, then the grower needs to assess the risk: best and worstscenario.
2. What is the optimum deepP rate to apply for a given time horizon?
3. How much P, how often and what is the risk?
4. What is the internal rate of return and payback time?
 For added information about risk and financing, graphs are presented on returns on investment and payback period of different deepP decisions.
The framework can be used to examine the cost/benefit tradeoffs of deepP decisions over time and the implications of expected prices, costs and crop rotation practices.
It demonstrates the potential yield benefits of correcting P deficiencies at depth, as well as the costs and cashflow implications that may be involved.
Moreover this framework can also be used by farmers to communicate the potential returns and even the risk (worstcase scenarios) to financial institutions, when seeking additional finance.
The case study of different application rates is only one example for which this framework could be used. It can also be used to investigate the returns and risk with respect to different levels of ColwellP measurements, soil PAWC, different paddocks on a farm, changing input and output prices and even other longterm amelioration or nutrient decisions.
References
Bell, M., Lester, D., Power, B., Zull, A. F., Cox, H., McMullen, G., & Laycock, J. (2014). Changing nutrient management strategies in response to declining background fertility: The economics of deep Phosphorus use. Paper presented at the GRDC Grains Research Update: Goondiwindi.
Acknowledgements
The research undertaken as part of this project is made possible by the significant contributions of growers through both trial cooperation and the support of the GRDC, the author would like to thank them for their continued support.
Contact details
Andrew Zull
Queensland Dept. of Agriculture, Fisheries and Forestry: Crop and Food Science
203 Tor St, Toowoomba, Qld. 4350
07 4688 1407
Andrew.Zull@daff.qld.gov.au
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