rbz Revista Brasileira de Zootecnia R. Bras. Zootec. 1516-3598 1806-9290 Sociedade Brasileira de Zootecnia 00203 10.37496/rbz5520240197 Animal production systems and agribusiness Economics, risk analysis, and sustainability of minimum module for pasture-based beef production: a case study in Campo Grande, MS, Brazil 0000-0002-7288-2095 Jorge Michael Allim Conceptualization Data curation Formal analysis Investigation Methodology Software Validation Visualization Writing – original draft Writing – review & editing 1 * 0000-0002-8452-8288 Dourado Durval Neto Conceptualization Data curation Formal analysis Funding acquisition Investigation Methodology Project administration Supervision Validation Visualization 1 0000-0003-1097-7280 Sainz Roberto Daniel Conceptualization Data curation Formal analysis Investigation Methodology Validation Visualization 2 0000-0002-9959-590X Alves Lucilio Rogerio Aparecido Data curation Formal analysis Investigation Validation Visualization 3 0000-0001-9104-3353 Silva Sila Carneiro da Data curation Formal analysis Investigation Methodology Validation Visualization 4 0000-0003-0529-707X Zen Sergio de Data curation Formal analysis Funding acquisition Investigation Methodology Validation Visualization 3 0000-0001-7729-3882 Reichardt Klaus Project administration Visualization Writing – review & editing 5 Universidade de São Paulo Escola Superior de Agricultura Luiz de Queiroz Departamento de Produção Vegetal Piracicaba SP Brasil Universidade de São Paulo, Escola Superior de Agricultura Luiz de Queiroz, Departamento de Produção Vegetal, Piracicaba, SP, Brasil. University of California Department of Animal Science Davis California United States of America University of California, Department of Animal Science, Davis, California, United States of America. Universidade de São Paulo Escola Superior de Agricultura Luiz de Queiroz Departamento de Economia, Administração e Sociologia Piracicaba SP Brasil Universidade de São Paulo, Escola Superior de Agricultura Luiz de Queiroz, Departamento de Economia, Administração e Sociologia, Piracicaba, SP, Brasil. Universidade de São Paulo Escola Superior de Agricultura Luiz de Queiroz Departamento de Zootecnia Piracicaba SP Brasil Universidade de São Paulo, Escola Superior de Agricultura Luiz de Queiroz, Departamento de Zootecnia, Piracicaba, SP, Brasil. Universidade de São Paulo Centro de Energia Nuclear na Agricultura Piracicaba SP Brasil Universidade de São Paulo, Centro de Energia Nuclear na Agricultura, Piracicaba, SP, Brasil. rhallim.michael@usp.br

Marcos Inácio Marcondes

Juana Catarina Cariri Chagas

The authors declare no conflict of interest.

 17 07 2026 2026 55 e20240197 05 11 2024 03 09 2025 This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT

This study quantified production risks and economic feasibility in tropical pasture-based beef systems by integrating a rule-based Minimum Module (MM) framework with Monte Carlo simulation (@Risk 8.0) in Excel 365 using a Microsoft Visual Basic 6.0 algorithm. Twelve scenarios combining low (0.5 animal unit [AU] ha⁻1), medium (1.0 AU ha⁻1), and high (1.5 AU ha⁻1) stocking rates across 2017–2020 were each run with 10,000 stochastic iterations to identify the smallest viable herd size and pasture area that ensured non-negative net present value (NPV ≥ 0). Intensification increased per-hectare productivity from 3.3 to 9.8 arrobas ha⁻1 yr⁻1 (P<0.001) and reduced minimum grazing area by 53–63 percent (P<0.001). Risk profiles remained favorable, with negative gross margin in only 0.25% of iterations and negative total profit in 15.55% of iterations. Fixed-cost share declined from approximately 74% in low-intensity to approximately 48% in high-intensity systems (P<0.05). Strong co-movement among overhead inputs (ρ>0.90) and among variable-cost inputs (ρ>0.80), and a land-for-feed trade-off (ρ ≈ –0.35) were quantified. The MM tool delivers transparent “what-if” scenario testing for herd and land planning without complex optimization, enabling data-driven feed-price hedging and stocking-rate adjustments.

 Keywords beef cattle intensification minimum module Monte Carlo simulation net present value tropical grazing systems FEALQ Financial support:Publication costs were supported by the Luiz de Queiroz Foundation for Agrarian Studies (FEALQ), Piracicaba, São Paulo, Brazil. The research underlying this article received no specific funding from public, commercial, or not-for-profit funding agencies. FEALQ had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. 1. Introduction

The global demand for sustainable beef production continues to rise, driving the need for grazing systems that balance economic viability, environmental health, and livestock productivity. In tropical regions such as Brazil, where extensive cattle farming underpins agribusiness, producers confront economic volatility, biophysical constraints, and technological uncertainty (Dickinson, 2001; Anderson, 2003; Moss, 2010; Stockton, 2022; Santos et al., 2024; Taylor et al., 2025).

Brazil’s ruminant sector relies almost entirely on forage-based diets, with improved and native pastures covering approximately 180 million ha, of which about 30% are located in the Cerrado biome, making pasture management a cornerstone of national beef output (Barcellos et al., 2008; McManus et al., 2016; Parente et al., 2019; Sano et al., 2019; Cordeiro et al., 2023; Santos et al., 2024). Mato Grosso do Sul exemplifies this dynamic, hosting 18.9 million cattle over 14.6 million ha of grazing land, and the Campo Grande microregion alone supports 1.75 million head (9.2 percent of the state total) with strategic access to soybean and corn terminals and beef-processing plants (slaughter/packing facilities) (Moore et al., 1999; Tambara et al., 2021; Azevedo et al., 2023; Lapig, 2023).

Despite these assets, pasture-based beef systems face mounting pressures—deforestation, greenhouse-gas emissions, land-use conflicts, and financial risks—underscoring the need for integrated sustainability indicators in production models (Chapman et al., 2024; Lorencowicz et al., 2024). Sustainability frameworks operationalize economic, environmental, and social goals, guided by indicators that inform evidence-based management and align with the Sustainable Development Goals (SDGs) 2 (Zero Hunger), 12 (Responsible Consumption and Production), and 15 (Life on Land) (Dumanski et al., 1998; Mukherjee, 1998; United Nations, 2015; Barry and Hoyne, 2021; Nadaraja et al., 2021).

Current economic and agronomic models often omit stochastic elements or have limited usability, limiting their adoption in commercial herds (Moss, 2010; Hardaker and Lien, 2010a,b; Gomes et al., 2015; Hardaker et al., 2015a,b; McManus et al., 2016; McKendree et al., 2021; Stockton, 2022; Tedeschi et al., 2024; Taylor et al., 2025). Moreover, most mathematical models remain confined to academic research, offering limited decision-support for producers and policymakers (Stygar and Makulska, 2010; Jones et al., 2017).

To bridge these gaps, Jorge (2019) developed the Minimum Module (MM), a modular deterministic–stochastic framework that links a rancher’s target net income to endogenous adjustments in herd size and pasture area—defining the minimum viable scale as the point at which the removal of one breeding cow causes net present value (NPV) to fall below zero. This study applies the MM framework combined with Monte Carlo simulation to (i) quantify market-driven production risks, (ii) evaluate economic feasibility under low, medium, and high intensification strategies, and (iii) provide a practical decision-support tool for land-use and herd-scaling decisions in tropical grazing systems.

 2. Material and methods 2.1. Study design

We applied the rule-based Minimum Module (MM) framework, a deterministic–stochastic simulation model, to determine the smallest viable herd size and pasture area capable of sustaining non-negative net present value (NPV ≥ 0) under three stocking-rate intensification levels: low (0.5 animal unit [AU] ha1), medium (1.0 AU ha1), and high (1.5 AU ha1). The MM overcomes the limitations of conventional economic models by embedding zootechnical and financial uncertainties within a single decision-support structure that mirrors on-farm management rules, rather than relying on mathematical optimization alone (Jorge, 2019; Lampert et al., 2020).

We conducted simulations for the Campo Grande microregion (20°26' S, 54°38' W) in Mato Grosso do Sul, Brazil—a representative pasture-based beef system characterized by Urochloa brizantha spp. pastures, annual rainfall of approximately 1,400 mm, and bimodal wet–dry seasons. We ran twelve scenarios combining three intensification levels and four production years (2017–2020), each spanning a 20-year horizon (20 annual cycles) to capture inter-annual climate variability and typical ranch investment amortization periods. For each scenario, we fixed an annual net-income requirement (Rr1 = USD 70,725.93), informed by regional cost–return data (CEPEA, 2020), and identified the MM threshold by reducing herd size incrementally until the removal of one breeding cow caused NPV to drop below zero.

To quantify production risk, we reserved a detailed Monte Carlo simulation for section 2.9.

 2.2. Modeling of the Minimum Module (MM)

We developed the Minimum Module (MM) as a modular, deterministic–stochastic simulation framework that quantitatively represents pasture-based beef production by linking three interconnected submodels: the Animal Production Module (Animal Module), the Plant Production Module (Plant Module), and the Economic Module (Pidd, 1997; Jorge, 2019) (Figure 1).

Modular architecture and integration flow of the Minimum Module (MM). The flowchart illustrates how the three core submodels—Animal, Plant, and Economic—feed into the stakeholder-driven “Minimum Module” model. Monte Carlo risk analysis and DCF computations occur within the Economic Module before all streams converge in the central decision engine. Multiple integration layers (data-exchange files, open-source code libraries, among others) enable seamless interoperability and rapid “what-if” scenario testing. The final output defines the Minimum Sustainable Module for pasture-based beef production, aligning target net-income goals with legal-reserve requirements under varied intensification levels.

Thus, we implemented all submodels and automated calculations in Microsoft Excel® 365 (build 2504, compilation 18730.20168) using a Microsoft Visual Basic 6.0 algorithm comprising eleven subroutines and totaling 3,867 lines of code, alongside the @Risk 8.0 (Palisade Corp., Ithaca, NY) add-in to generate correlated random variates, construct the risk-correlation matrix, and execute Monte Carlo simulations.

 2.3. Animal Module

In the Animal Module, we tracked herd dynamics across 17 animal categories representing the full-cycle pasture-based beef system. These comprised 15 marketed production cohorts, one transitional birth class (“Animals born”) used for herd-flow accounting, and one breeding-bull category used in the natural-mating subsystem. For the marketed cohorts, we defined average live weight (Wi, kg head1), carcass yield (Ri, kg carcass kg live weight1), and selection pressure (Psi, %) for under-threshold animals. The “Animals born” class was used only to register annual calf output before allocation into male and female cohorts and therefore had no direct market price. The breeding-bull category was retained in the biological and economic modules because bulls were required for the natural-mating system and also generated annual replacement and culling flows. We specified weight thresholds—180 kg for male weaners, 160 kg for female weaners, 195 kg for bull calves, 180 kg for female calves, 285 kg for 18-month-olds, and 360 kg for lean bulls—and directed animals failing to meet these thresholds into replacement markets (i.e., sold from one producer to another), while applying category-specific (Psi) rates to all others for slaughter (Table 1).

Animal module, biological performance, and fixed inputs
Item Cohorts Parameter Symbol Unit Input
  Cows aged 37 to 48 months Average weight of cull cow W1 kg hc−1 410
    Carcass yield R1 kg kg−1 0.50
    Market-driven selection pressure Ps1 % 0.65
  Weaning - male (7 to 8 months) Average weight of live male W2 kg hc−1 180
    Market-driven selection pressure (< 180 kg) Ps2 % 0.40
  Weaning - female (7 to 8 months) Average weight of live female W3 kg hc−1 160
    Market-driven selection pressure (< 160 kg) Ps3 % 0.40
  Bull calves (12 months) Average weight of live W4 kg hc−1 195
    Market-driven selection pressure (< 195 kg) Ps4 % 0.15
  Female calves (12 months) Average weight of live W5 kg hc−1 180
    Market-driven selection pressure (< 180 kg) Ps5 % 0.10
  Heifers from 18 to 20 months Average weight of fat heifer W6 kg hc−1 420
    Carcass yield R6 kg kg−1 0.52
    Market-driven selection pressure Ps6 % 0.40
  Heifers from 21 to 28 months Average weight of fat heifer W7 kg hc−1 450
    Carcass yield R7 kg kg−1 0.50
    Market-driven selection pressure Ps7 % 0.90
Animal cohort Heifers from 29 to 36 months Average weight of fat heifer W8 kg hc−1 450
  Carcass yield R8 kg kg−1 0.50
  Market-driven selection pressure Ps8 % 0.80
  18-month old bull Average weight of 18-month old bull W9 kg hc−1 285
    Market-driven selection pressure (< 285 kg) Ps9 % 0.15
  Lean bull (12 to 13 arrobas) Average weight of lean bull W10 kg hc−1 370
    Market-driven selection pressure (< 360 kg) Ps10 % 0.15
  Fat bull 18 to 20 months (milk-tooth - MT) Average weight of fat bull W11 kg hc−1 480
  Carcass yield R11 kg kg−1 0.54
    Market-driven selection pressure Ps11 % 0.40
  Fat bull 21 to 28 months (up to 2 permanent teeth) Average weight of fat bull W12 kg hc−1 510
  Carcass yield R12 kg kg−1 0.53
    Market-driven selection pressure Ps12 % 0.50
  Fat bull 29 to 36 months (up to 4 permanent teeth) Average weight of fat bull W13 kg hc−1 560
  Carcass yield R13 kg kg−1 0.52
    Market-driven selection pressure Ps13 % 0.40
  Fat bull (37 to 48 months) (adult) Average weight of fat bull W14 kg hc−1 570
  Carcass yield R14 kg kg−1 0.52
    Market-driven selection pressure Ps14 % 1.00
  Older fat bull “toruno”1 60 months Average weight of fat bull W15 kg hc−1 780
    Carcass yield R15 kg kg−1 0.49
    Market-driven selection pressure Ps15 % 1.00

hc - head of cattle.

1 “toruno” refers to mature bulls or improperly castrated males excluded from standard finishing categories, often culled due to age or reproductive behavior. This classification affects slaughter pricing and market placement.

Furthermore, we standardized Animal Units at 450 kg live weight, imposed a bull-to-cow ratio of 1:25, set annual replacement rates at 20%, and targeted a calving rate of 70–90% (Table 2).

Animal module, pasture-based production system, and fixed inputs
Item Parameter Description Symbol Unit Input
  Bull-to-cow ratio Number of bulls per cow Rs1 bulls cow−1 1:25
Herd management Cow replacement rate Proportion of cows replaced annually Rp2 % 20
Bull replacement rate Proportion of bulls replaced annually Rp3 % 20
  Calving rate Percentage of cows that give birth Tn4 % 70–90
Herd dynamics Animal unit Standardized live weight for one animal unit AU kg LW 450
Cows aged 37 to 48 months Average live weight F6 kg hc−1 450
Heifers from 29 to 36 months Average live weight F5 kg hc−1 400
Heifers from 21 to 28 months Average live weight F4 kg hc−1 330
Heifers from 18 to 20 months Average live weight F3 kg hc−1 290
Female calves (12 months) Average live weight F2 kg hc−1 180
Weaning - female (7 to 8 months) Average live weight F1 kg hc−1 160
Weaning - male (7 to 8 months) Average live weight M1 kg hc−1 200
Bull calves (12 months) Average live weight M2 kg hc−1 225
18-month old bull Average live weight M3g kg hc−1 285
Lean bull (12 to 13 arrobas) Average live weight M3bm kg hc−1 370
Fat bull 18 to 20 months (milk-tooth - MT) Average live weight M3 kg hc−1 380
Fat bull 21 to 28 months (up to 2 permanent teeth) Average live weight M4 kg hc−1 400
Fat bull 29 to 36 months (up to 4 permanent teeth) Average live weight M5 kg hc−1 440
Fat bull (37 to 48 months) (adult) Average live weight M6 kg hc−1 600
Older fat bull “toruno” 60 months Average live weight M6bgt kg hc−1 750
Bulls Average live weight M6t kg hc−1 800
  Mineral salt Salt consumed per animal per day C1 kg hc−1 d−1 0.100
  Mineral salt for breeding cows Salt consumed per 100 kg live weight C2 kg hc−1 d−1 0.025
  Mineral protein supplement Protein supplement per 100 kg live weight C3 kg hc−1 d−1 0.200
Daily nutritional intake Mineral energy supplement Energy supplement per 100 kg live weight C4 kg hc−1 d−1 0.130
Creep-feeding Supplementary feeding for calves C5 kg hc−1 d−1 1.400
Creep-feeding intake limiter Salt proportion in creep-feeding mix C6 % 0.80
  Semi-confinement pasture diet Percentage of live weight intake C7 % 1
  Dry matter consumption at pasture Percentage of live weight intake Dm1 % 2
  Average daily gain in semi-confinement diet Weight gain per day in semi-confinement Adg1 kg hc−1 d−1 1.300
  FMD vaccine Doses applied per year V1 dose hc−1 yr−1 1–2
Animal health Blackleg vaccine Doses applied per year V2 dose hc−1 yr−1 1–2
Brucellosis vaccine Doses applied per year V3 dose hc−1 yr−1 1
  Dewormer Doses applied per year V4 dose hc−1 yr−1 1–3
  Pre-weaning mortality Mortality before weaning Mt1 % 1.2
  Mortality rate (0–12 months) Losses from weaning Mt2 % 1.0
Production impacts Mortality rate (12–20 months) Losses from 12 to 20 months Mt3 % 1.0
Mortality rate (21–28 months) Losses from 21 to 28 months Mt4 % 1.0
  Mortality rate (29–36 months) Losses from 29 to 36 months Mt5 % 0.5
  Mortality rate (37–48 months) Losses from 37 to 48 months Mt6 % 0.5

hc - head of cattle.

Nutritional management incorporated daily mineral-salt and protein/energy supplementation, creep feeding, and semi-confinement diets yielding 1.3 kg day1 gains, while health protocols included annual vaccinations for foot-and-mouth disease, blackleg, and brucellosis plus systematic deworming. We simulated replacement purchases of 170 cow-calf pairs and six breeding bulls per year, with younger replacements set to zero in core scenarios (Table 3).

Animal module, parameters for livestock acquisition in herd replacement, and fixed inputs
Item Parameter Description Symbol Unit Live weight (kg) Qty (head)
  Cow–calf pair Unit price for lactating cow and calf RC1 USD pair⁻1 – 170
  Bulls Mature bulls used for reproduction RC2 USD hc⁻1 380 6
Replacement Weaning - female (7 to 8 months) Price of young heifer calves RC3 USD kg⁻1 175 0
Weaning - male (7 to 8 months) Price of young male calves RC4 USD kg⁻1 200 0
  Heifers from 18 to 20 months Price of prepubertal heifers RC5 USD kg⁻1 235 0
  Heifers from 21 to 28 months Price of heifers approaching reproductive age RC6 USD kg⁻1 260 0

2.4. Plant Module

In the Plant Module, we modeled pasture over a ten‐year lifespan, beginning with land preparation—stump removal (5 h ha⁻1), disking (1 h ha⁻1), plowing (1.5 h ha⁻1), liming with 2 t ha⁻1 of dolomitic limestone, NPK fertilization at 300 kg ha⁻1, and seeding at 18 kg ha⁻1—and followed by uniform annual maintenance comprising lime spreading (1 h ha⁻1), disking (1 h ha⁻1), fertilizer application (0.35 h ha⁻1), and selective herbicide use (4.4 L ha⁻1 of 2,4-D/Picloram) (Table 4).

Plant module, pasture establishment, annual maintenance, and fixed inputs
Item Parameter Description Symbol Unit Input
  Stump removal Removal of tree stumps for land clearing Ps1 h ha−1 5
  Topography Land surface measurement and contouring Ps2 h ha−1 0.5
Soil preparation Terracing Soil conservation practice to reduce erosion Ps3 h ha−1 1
Road adaptation Improvement of access roads in pasture areas Ps4 h ha−1 1
Chemical destruction Application of herbicides for vegetation control Ps5 h ha−1 0
  Lime spreading Distribution of lime for soil pH correction Ps6 h ha−1 0.45
  Lime loading Loading lime into machinery for field application Ps7 h ha−1 0.15
  Disking Primary soil tillage operation to break compact layers Fp2 h ha−1 1
  Plowing Deep soil turning for seedbed preparation Fp3 h ha−1 1.5
  Leveling Smoothing of soil surface before planting Fp4 h ha−1 0
  Seeding/fertilizing Combined process of sowing pasture seeds and fertilizing Fp5 h ha−1 1
Pasture establishment Herbicide application Spraying herbicides to control weeds Fp6 h ha−1 1
Seed Quantity of pasture seeds applied per hectare Fp7 kg ha−1 18
  Dolomitic limestone Calcium and magnesium carbonate for soil correction Fp8 t ha−1 2
  Fertilizer 04-14-08 NPK fertilizer application for pasture establishment Fp9 kg ha−1 300
  Herbicide 2,4-D and picloram Selective herbicide for broadleaf weed control Fp10 L ha−1 3
  Pasture lifespan (in years) Expected duration of pasture productivity Fp11 yr 10
  Lime spreading Annual soil pH correction with lime application Mp1 h ha−1 1
  Disking Maintenance tillage to prevent soil compaction Mp2 h ha−1 1
Annual pasture maintenance Fertilizer spreading Annual nutrient replenishment in pastures Mp3 h ha−1 0.35
Herbicide application Weed control in established pastures Mp4 h ha−1 0.60
Fertilizer 14-00-27 NPK fertilizer for annual pasture maintenance Mp5 kg ha−1 150
  Lime Quantity of lime applied annually per hectare Mp6 t ha−1 1
  Herbicide 2,4-D and picloram Annual herbicide application for pasture maintenance Mp7 L ha−1 4.4

In addition, we enforced a 20% legal reserve as required by Article 12 of the Brazilian Forest Code (Law 12,651/2012) (Brazil, 2012) and assumed a uniform 10% permanent preservation area per Article 4, recognizing that actual preservation percentages vary by property (1–25%, approximately), to maintain consistency across comparative intensification scenarios.

 2.5. Economic Module

We integrated the Economic Module into the simulation to capture the financial dynamics of pasture-based beef production under varying environmental conditions. We incorporated both fixed and variable inputs, with variable inputs reflecting site-specific conditions to ensure a localized economic representation.

Fixed inputs, including operational costs such as labor, general expenses, rural inventory, tractor operators and ranch hands’ monthly labor hours, internal transportation, technical assistance (veterinary, animal science, and agronomy consultations), accounting, electricity, machinery, equipment, and infrastructure costs and depreciation (e.g., seed/fertilizer spreaders, disc plows, leveling harrows) (Table 5), were incorporated into the simulation.

Economic module, general operating expenses, rural inventory, and fixed inputs
Item Parameter Description Symbol Unit Input
  Tractor operator Number of operators per month Mo1 man-month−1 1
Labor Ranch hand (cowboy) Number of workers per month Mo2 man-month−1 3
  Labor hours Monthly total labor hours Mo3 h month−1 220
  Internal transportation Annual machinery hours Dg1 h yr−1 150
General expenses Technical assistance Veterinary, animal science, or agronomy consulting Dg2 visits yr−1 2
Accounting expenses Monthly payments per year Dg3 payments yr−1 12
  Electricity Total energy consumption Dg4 kWh yr−1 15,000
  Seed/Fertilizer spreader Mounted double-disc spreader for seed and fertilizer application Ir1 USD 2,663.47
  Lime spreader Double-disc lime spreader with 5–7 ton capacity Ir2 USD 6,158.94
  Disc plow Tillage implements with 20–28 discs, 26–28 inch diameter Ir3 USD 5,091.36
Rural inventory Leveling harrow Secondary tillage harrow with 40–44 discs, 20–22 inch diameter Ir4 USD 3,349.71
Trailer Four-wheel trailer with 4–6 ton load capacity Ir5 USD 1,371.71
Hydraulic cattle grid 2.75-meter hydraulic cattle crossing gate Ir6 USD 2,161.10
  Front hydraulic unit Front loader bucket, 1,500–1,800 kg capacity, mounted on tractor Ir7 USD 6,428.68
  Price per square meter Unit cost for barn construction Ir8 USD m−2 31.10
  Machinery salvage value Residual value Ir9 % 20
  Implements salvage value Residual value Ir10a % 10
  Infrastructure salvage value Residual value Ir10b % 10
  Useful life of machinery Depreciation period Ir11 yr 10
  Useful life of implements Depreciation period Ir12a yr 10
  Useful life of infrastructure Depreciation period Ir12b yr 20

Variable inputs were presented in two parts. First, we outlined revenue sources—including local sale prices per unit for each cohort (cull cows, male and female weaned calves, bulls, and heifers at various growth stages) and early-slaughter bonuses to reflect market incentives (Table 6). We adjusted these prices for seasonal fluctuations, Rural Workers’ Assistance Fund (Funrural) tax obligations, and the regional market context. Second, we detailed site-specific production costs—including labor, general expenses, pasture operations (stump removal, plowing, seeding/fertilizing, herbicide application, and annual lime spreading), nutritional inputs (mineral salts, protein supplements, creep feeding), and animal health expenses (vaccinations, deworming) (Table 7)—to ensure that we captured both direct and indirect costs under the local conditions of the Campo Grande microregion.

Economic module, revenue sources, and environment-dependent variable inputs
Item Parameter Description Symbol Unit
  Price per unit Cull cow (with Funrural1) P1 USD @⁻1
  Price per unit Weaning - male (7 to 8 months) P2 USD kg⁻1
  Price per unit Weaning - female (7 to 8 months) P3 USD kg⁻1
  Price per unit Bull calves (12 months) P4 USD kg⁻1
  Price per unit Female calves (12 months) P5 USD kg⁻1
  Price per unit Heifers from 18 to 20 months (with Funrural) P6 USD @⁻1
  Early slaughter bonus Bonus paid for early slaughter to encourage precocious cattle finishing Pp6 USD @⁻1
  Price per unit Heifers from 21 to 28 months (with Funrural) P7 USD @⁻1
  Early slaughter bonus Bonus paid for early slaughter to encourage precocious cattle finishing Pp7 USD @⁻1
  Price per unit Heifers from 29 to 36 months P8 USD @⁻1
  Early slaughter bonus Bonus paid for early slaughter to encourage precocious cattle finishing Pp8 USD @⁻1
Animal category Price per unit 18-month old bull P9 USD @⁻1
Price per unit Lean bull (12 to 13 arrobas) P10 USD @⁻1
  Price per unit Fat bull 18 to 20 months (MT2, with Funrural) P11 USD @⁻1
  Early slaughter bonus Bonus paid for early slaughter to encourage precocious cattle finishing Pp11 USD @⁻1
  Price per unit Fat bull 21 to 28 months (up to 2 permanent teeth, with Funrural) P12 USD @⁻1
  Early slaughter bonus Bonus paid for early slaughter to encourage precocious cattle finishing Pp12 USD @⁻1
  Price per unit Fat bull 29 to 36 months (up to 4 permanent teeth, with Funrural) P13 USD @⁻1
  Early slaughter bonus Bonus paid for early slaughter to encourage precocious cattle finishing Pp13 USD @⁻1
  Price per unit Fat bull (37 to 48 months, adult, with Funrural) P14 USD @⁻1
  Price per unit Older fat bull “toruno” (60 months, with Funrural) P15 USD @⁻1

@ = 15 kg.

1 Funrural - Brazilian rural social-security levy (rate defined in the economic assumptions of the manuscript).

2 MT - milk-tooth (0 permanent incisors). Dentition class used as a proxy for age/precocity; other classes appear as “up to 2 permanent teeth” and “up to 4 permanent teeth".

Economic module, production costs, and environment-dependent variable inputs
Item Parameter Description Symbol Unit
Labor Hourly wage Tractor operator Mo1 USD h⁻1
Hourly wage Ranch hand (cowboy) Mo2 USD h⁻1
  Cost per hour Internal transportation Dg1.1 USD h⁻1
General expenses Cost per visit Technical assistance (veterinary, animal science, or agronomy) Dg2.1 USD visit⁻1
Cost per month Accounting expenses Dg3.1 USD month⁻1
Cost per kilowatt Electricity Dg4.1 USD kWh⁻1
  Cost per hour Stump removal Ps1.1 USD h⁻1
  Cost per hour Topography Ps2.1 USD h⁻1
Soil preparation Cost per hour Terracing Ps3.1 USD h⁻1
Cost per hour Road adaptation Ps4.1 USD h⁻1
Cost per hour Chemical destruction Ps5.1 USD h⁻1
  Cost per hour Lime spreading Ps6.1 USD h⁻1
  Cost per hour Lime loading Ps7.1 USD h⁻1
  Cost per hour Disking Fp2.1 USD h⁻1
  Cost per hour Plowing Fp3.1 USD h⁻1
  Cost per hour Leveling Fp4.1 USD h⁻1
Pasture establishment Cost per hour Seeding/fertilizing Fp5.1 USD h⁻1
Cost per hour Herbicide application Fp6.1 USD h⁻1
Cost per kg Seed Fp7.1 USD kg⁻1
  Cost per metric ton Dolomitic limestone Fp8.1 USD t⁻1
  Cost per kg Fertilizer 04-14-08 Fp9.1 USD kg⁻1
  Cost per liter Herbicide 2,4-D and picloram Fp10.1 USD L⁻1
  Cost per hour Lime spreading Mp1.1 USD h⁻1
  Cost per hour Disking Mp2.1 USD h⁻1
Annual pasture maintenance Cost per hour Fertilizer spreading Mp3.1 USD h⁻1
Cost per hour Herbicide application Mp4.1 USD h⁻1
Cost per kg Fertilizer 14-00-27 Mp5.1 USD kg⁻1
  Cost per metric ton Lime Mp6.1 USD t⁻1
  Cost per liter Herbicide 2,4-D and picloram Mp7.1 USD L⁻1
  Cost per kg Mineral salt Cp1 USD kg⁻1
  Cost per kg Mineral salt for breeding cows Cp2 USD kg⁻1
  Cost per kg Mineral protein supplement Cp3 USD kg⁻1
Nutrition Cost per kg Mineral energy supplement Cp4 USD kg⁻1
  Cost per kg Creep-feeding Cp5 USD kg⁻1
  Cost per kg Corn grain Cp6 USD kg⁻1
  Cost per kg Mineral nucleus for 85:15 semi-confinement diet Cp7 USD kg⁻1
  Cost per dose FMD vaccine Vp1 USD dose⁻1
0Animal health Cost per dose Blackleg vaccine Vp2 USD dose⁻1
Cost per dose Brucellosis vaccine Vp3 USD dose⁻1
  Cost per dose Dewormer Vp4 USD dose⁻1

By incorporating environment-dependent cost and price data, we enabled the Economic module to reflect specific regional market conditions, cost structures, and production strategies. This approach allowed us to simulate and accurately evaluate the economic performance of pasture-based beef systems across different intensification scenarios under real-world variability.

 2.6. Simulation scenarios

We configured twelve scenarios by combining user-selected settings in the Simulation Panel with fixed biological, economic, and intensification parameters (Table 8). First, users specified their rancher profile (sole proprietor), land-ownership status (owned), annual net-income target (Rr1), cohort prices (Pi) and cost components (Ci) for the chosen year (Sim2: 2017–2020), stocking rate (Sr2: 0.5, 1.0, or 1.5 AU ha⁻1), land constraints (20% legal reserve, Ar1, per Law 12,651/2012, Art. 12; 10% permanent preservation area, Ar2, per Art. 4), geographic focus (Campo Grande microregion), and intensification level (Ni3).

Minimum Module simulation panel
Item Parameter Description Symbol Unit Input
Administration assumptions Producer profile The simulation assumes a beef cattle rancher operating as an individual (non-corporate farming unit) Up1 – Individual (sole proprietor)
Land ownership status Production occurs on owned land (not leased) Up2 – Owned property
Economic target Minimum required remuneration by the rancher Annual income target to ensure economic sustainability Rr1 USD yr⁻1 70,725.93
Economic performance Animal category price Average price for each animal category (cull cows, weaned calves, etc.) for each year simulated (2017–2020) Pi USD 2017; 2018; 2019; 2020
Total costs Production costs Average price for each component of the costs (labor, nutrition, etc.) for each year simulated (2017–2020) Ci USD 2017; 2018; 2019; 2020
Grazing conditions Pasture carrying capacity Stocking rate based on pasture potential (low, medium, or high) Sr2 AU ha⁻1 0.5; 1.0; 1.5
Land constraints Legal reserve area Legally protected area (20%) required by Brazilian Forest Code Ar1 % 20
Environmental preservation area Additional environmental reserve area (10%) assumed for the MM model Ar2 % 10
  Location of simulation Geographic focus of the study Sim1 _ Campo Grande Microregion, Midwest Brazil
Production settings Year of simulation Years evaluated by the Minimum Module (MM) model Sim2 _ 2017; 2018; 2019; 2020
  Production system intensification level Management intensity level (low, medium, or high) Ni3 _ 3; 2; 1
  Number of breeding cows Initial number of breeding cows in the herd (decision variable)1 Nc hc ≥ 1

hc - head of cattle.

Administrative assumptions, economic targets, grazing conditions, land constraints, and general simulation settings are defined in section 2.6.

1 Nc is a decision variable. The Minimum Module is the smallest Nc ≥ 1 such that NPV(Nc) ≥ 0 and NPV(Nc − 1) < 0 (one-cow minimality test).

After panel configuration, we applied the Animal Production assumptions. We set a November–January breeding season with first-exposure conception rates of 50–85% and subsequent annual rates of 75–92%, a 2–5% pregnancy loss rate, and an August–October calving window. Herd dynamics used a bull-to-cow ratio of 1:25, 20% annual replacement, a 70–90% calving rate, an Animal Unit of 450 kg, daily gains of 1.3 kg head⁻1, and standard health and nutrition protocols (vaccinations, deworming, mineral and protein supplements, and creep feeding) (Table 9).

Animal production module, assumptions, Brazil
Item Parameter Description Input
  Animal breed Nelore beef cattle breed Nelore
  Infrastructure Housing for labor (common workers and tractor operators) 1 complete setup
  Livestock handling facilities Facilities for cattle management 1 complete setup
  Fencing Boundary and pasture subdivision fences 1 set of fencing
  Water access and feed trough Access to water and covered feed trough for supplementation 1 complete setup
  Natural breeding system Natural breeding station 1 station
Animal production module Mating season Breeding season (November to January) November to January
  First exposure conception rate Pregnancy rate after first bull exposure (50–85%) 50–85%
  Bull replacement Bull replacement system for breeding 1 system
  Annual conception rate Pregnancy rate after second bull exposure (75–92%) 75–92%
  Pregnancy diagnosis and weaning Diagnosis and weaning (March to May) March to May
  Pregnancy loss 2–5% loss of pregnancies 2–5%
  Birth period Calving season (August to October) August to October
  Open herd Open herd system, including purchase of animals from previous phases 1 system
  Slaughter sales Includes slaughter and replacement sales 1 system

Next, we applied the Economic and Macroeconomic parameters. We used a federal income tax rate of 27.5%, a Rural Workers Assistance Fund (Funrural) tax rate of 1.5%, a minimum acceptable rate of return (MARR) and real discount rate of 6%, an annual inflation rate of 4.5%, a capital structure of 40% equity and 60% debt with a 10-year financing term and 2-year grace period, a nominal interest rate of 7%, and a bare-land value of USD 1,500 per hectare. These inputs drove fixed and variable cost calculations and revenue deflation (Table 10).

Economic module, financial assumptions, macroeconomic parameters, and fixed inputs, Brazil
Item Parameter Description Symbol Unit Input
  Income tax Federal income tax rate Ef1 % 27.50
  Funrural (Rural Social Security Tax) Contribution levied on gross revenue from cattle sales for slaughter Ef2 % 1.50
  MARR Minimum acceptable rate of return Ef4 % yr−1 6.00
  Real discount rate Discount rate for present value calculation Ef5 % yr−1 6.00
Economic module Inflation rate Annual inflation rate Ef7 % yr−1 4.50
Equity investment Proportion of capital from own equity Ef8 % 40.00
  Third-party capital on herd value Share of herd value financed with third-party capital Ef9 % 60.00
  Total number of installments Repayment period for third-party financing Ef10 yr 10
  Grace period Years before liability repayment begins Ef11 yr 2
  Annual interest rate Nominal annual interest rate Ef12 % yr−1 7.00
  Bare land value Average municipal value of unimproved pastureland Ef13 USD ha−1 1,500.00

We then enforced the intensification-level parameters across all 20 annual cycles. We applied fertilizer at rates ranging from 40 kg ha⁻1 under low intensification to 180 kg ha⁻1 under high intensification; we varied pasture maintenance hours and lease rates; accordingly, and we fixed stocking rates at 0.5, 1.0, or 1.5 AU ha⁻1 (Table 11).

Minimum Module pasture systems, fixed intensification parameters for LL (low level), ML (medium level), and HL (high level), 2017–2020
Parameter Unit LL ML HL
Pasture1 Cg-Rg (Cg) (Cg-Rg) (Rg)
Stocking rate2 AU ha−1 0.5 1.0 1.5
Pasture fertilization kg ha−1 40 120 180
Reproductive mineral salt g hc−1 d−1 25 25 25
Mineral supplement g hc−1 d−1 100 100 100
Protein supplement (7 to 8 months) g hc−1 d−1 0 200 200
Energy supplement (12 months) g hc−1 d−1 0 130 130
Creep feeding3 kg hc−1 d−1 0 0 1.120
Diet (85:15)4 % 0 0 1.2
Pasture formation5 % 1 1 5
Pasture maintenance5 % 2 10 10
Lease rate6 % 10 12 15
Calving rate % 70 82 90
Tractor hp 120 140 180
Hydraulic terracing plow with 16 discs Units 0 1 1
6m Mounted Boom Sprayer – 600L Units 0 1 1
Barn m2 50 220 600

1 Cg - continuous grazing; Rg - rotated grazing.

2 Animal unit (AU) = 450 kg of live weight.

3 Creep feeding - private supplementation.

4 Diet (85:15) - semi-confined diet of 85% corn grain and 15% mineral core (% of live weight).

5 Pasture formation/maintenance - percentages refer to the share of available grazing area (AgA) undergoing establishment and annual upkeep.

6 Lease rate - percentage of the @ price of finished cattle; @ = 15 kg; La - leased area.

Values of 0 indicate that the corresponding input, feeding practice, or equipment was not adopted under that intensification level.

With all inputs defined, the Minimum Module was determined for each scenario by reducing herd size and pasture area until the removal of one breeding cow caused net present value to fall below zero. The model then recorded fixed and variable costs, gross and net revenues, operating and net margins, total profit, and per-hectare profitability for each intensification level and year.

Hence, we structured the simulation workflow to maintain transparency and reproducibility and to allow us to isolate the effects of intensification level and production year on system resilience and land-use efficiency.

 2.7. Data sources and parameterization

We sourced price and cost data from regional institutional databases and publicly accessible commercial sources and standardized values to December 2020 using the General Price Index – Internal Availability (Índice Geral de Preços – Disponibilidade Interna, IGP-DI; FGV IBRE, 2020). Beef-cattle production costs for the municipality of Campo Grande were obtained from the Center for Advanced Studies in Applied Economics (CEPEA) database (2020), and daily price series for 15 animal categories were downloaded from the Correa da Costa auction website (2021) covering January 2010 to December 2020. We provide the complete monthly aggregates and deflated time-series plots in Results (section 3.5). Annual price data were assembled for the 15 marketed cattle cohorts and used both for the historical price-series analysis and as the scenario price inputs for 2017–2020. The breeding-bull category, however, did not have a standardized regional annual price series available for the study period; therefore, its annual average price was parameterized separately for the Campo Grande microregion based on consultation with local specialists. The transitional “Animals born” class was not assigned a direct market price because it functioned only as a biological herd-flow category. Lease rates for pastureland reflected prevailing local values.

To capture biological and replacement uncertainty in the Animal Module, we parameterized each input variable by sampling from a uniform distribution bounded by minimum and maximum values reported in subtropical and tropical studies. We selected a uniform distribution to avoid bias where stronger empirical priors were unavailable. These ranges—drawn from Scarnecchia (1998); Euclides Filho et al. (2002); Abreu et al. (2003); Abreu and Lopes (2005); Costa et al. (2005); Pereira et al. (2005); Barioni et al. (2007); Fernandes et al. (2010); Allen et al. (2011); Porto et al. (2011); Pereira et al. (2014); Jorge (2019); Lampert et al. (2020); Moriel et al. (2020); and Dick et al. (2021)—ensured that simulated herd dynamics reflected full-cycle, pasture-based beef production conditions in the study region (Table 12).

Animal module, minimum and maximum values of input variables
Parameter Unit Amplitude
Stocking rate AU ha−1 0.3–2.0
Birth rate % 50–90
Slaughter age for bulls months 12–44
Average herd mortality rate % 2–5
Annual culling rate for cows % yr−1 15–20
Annual culling rate for bulls % yr−1 15–25
Selection pressure for sale (females) % yr−1 15–70
Selection pressure for sale (males) % yr−1 15–100
Slaughter weight for culling cows kg hc−1 380–500
Slaughter weight for bulls kg hc−1 750–800
Slaughter weight for steers kg hc−1 380–480
Slaughter weight for heifers kg hc−1 360–420
Weight for weaned males (7–8 months) kg hc−1 170–300
Weight for 18–20 months steers (DL) kg hc−1 320–480
Weight for 21–28 months steers (up to 2 permanent teeth) kg hc−1 380–540
Weight for 29–36 months steers (up to 4 permanent teeth) kg hc−1 400–570
Weight for 37–48 months steers (adult) kg hc−1 405–650
Carcass yield (males) % 52–58
Average daily gain (ADG) (male calf) kg d−1 0.150–0.950
ADG (male rearing) kg d−1 0.199–1.100
ADG (male finishing) kg d−1 0.350–1.500
Weight for weaned females (7–8 months) kg hc−1 120–180
Weight for 18–20 months heifers (DL) kg hc−1 160–360
Weight for 21–28 month heifers (up to 2 permanent teeth) kg hc−1 199–380
Weight for 29–36 month heifers (up to 4 permanent teeth) kg hc−1 260–395
Weight for 37–48 month cows (adult) kg hc−1 300–500
Carcass yield (females) % 50–52
ADG (female calf) kg d−1 0.164–0.784
ADG (female rearing) kg d−1 0.164–0.950
ADG (female finishing) kg d−1 0.300–1.200
ADG (cow finishing) kg d−1 0.750–1.100
ADG (pasture without mineral supplementation) kg d−1 0.150–0.550
ADG (pasture with mineral supplementation) kg d−1 0.250–1.900
Carcass yield (cow) % 48–50
Bull-to-cow ratio cows bull−1 15–25
Cow coefficient AU 0.92–1.08
Culling cow coefficient AU 0.74–0.92
18–20 months heifer (MT) coefficient AU 0.35–0.8
21–28 months heifer (2 permanent teeth) coefficient AU 0.40–0.8
29–36 months heifer (4 permanent teeth) coefficient AU 0.56–0.87
37–48 months cow (adult) coefficient AU 0.66–1.11
18–20 months steer (MT) coefficient AU 0.71–1.06
21–28 months steer (2 permanent teeth) coefficient AU 0.84–1.20
29–36 months steer (4 permanent teeth) coefficient AU 0.88–1.26
37–48 months steer (adult) coefficient AU 0.90–1.33
Bull coefficient AU 1.44–1.88
Short-cycle diet consumption coefficient (kg per 100 kg body weight) % 0.75–2
Grazing efficiency coefficient (dry and rainy season) % 20–80
Daily forage dry matter consumption kg AU−1 d−1 7.5–12.5
Forage coefficient (kg crude protein per 100 kg dry matter) % 4.2–13.4
Mineral salt consumption kg hc−1 0.050–0.150
Mineral salt consumption for reproduction cows (kg per 100 kg body weight) kg hc−1 0.015–0.035
Mineral protein supplement consumption (kg per 100 kg body weight) kg hc−1 0.100–0.250
Mineral energy supplement consumption (kg per 100 kg body weight) kg hc−1 0.120–0.300
Creep feeding consumption kg hc−1 0.328–1.400

hc - head of cattle.

For the Plant Module, we parameterized machinery-hour requirements and input rates for land preparation and maintenance using data from Pacheco (2000) and Peres et al. (2013, 2014). These values informed simulated labor, fuel, and equipment needs across low-, medium-, and high-intensification scenarios in the MM. All deflation and data cleaning were performed in Microsoft Excel® 365, ensuring consistency with the simulation environment.

 2.8. Mathematical formulation of the Minimum Module 2.8.1. Discounted cash flow components and economic metrics

We calculated annual economic outputs using the discounted cash-flow (DCF) component equations (Table 13). First, we computed total revenue (TR) as the sum across all animal categories of quantity sold, average live weight, carcass yield, selection pressure, and carcass price (Jorge, 2019, 2024). From TR, we derived net income (NI) by subtracting the Rural Workers Assistance Fund (Funrural) social security tax (α = 1.5%) (Damodaran, 2010, 2020).

Economic module, components of the discounted cash flow (DCF)
Component Equation Description of the equation Reference
Total revenue T R annual = ∑ i = 1 n Q i × ( W i × R i × P S i ) × P i Calculated as the sum of the products of quantity sold (Qi), average live weight (Wi), carcass yield (Ri), market selection pressure (Psi), and market price in the corresponding commercial unit (Pi) across all animal categories (i). Jorge (2019, 2024)
Net income N i annual = T R × ( 1 − α ) Net income after deduction of the Funrural tax rate α. Damodaran (2010, 2020)
Total operating cost T O C annual = F O C 1 + F O C 2 + F O C n + ⋯ + VOC 1 + VOC 2 + VOC n Sum of fixed operating costs (FOC) and variable operating costs (VOC). Matsunaga et al. (1976); Jorge (2019)
Opportunity cost O C p = Z × P a × A g A × 12 Calculated as a percentage (Z) on the potential beef production value, using the market price per arroba (Pa) and the minimum grazing area AgA, adjusted to an annual basis. Ross et al. (2013); Jorge (2019, 2024)
Total cost T C annual = F O C + V O C + O C p Sum of fixed, variable, and opportunity costs. Matsunaga et al. (1976)
EBITDA E B I T D A annual = N i − T C Earnings before interest, taxes, depreciation, and amortization. Damodaran (2010, 2020)
Depreciation Dep annual = ( ∑ i = 1 n 0.80 × M i 10 ) + ( ∑ j = 1 m 0.80 × E j 10 ) + ( ∑ k = 1 o 0.90 × I k 20 ) Annual depreciation calculated separately for machinery, equipment, and infrastructure, considering salvage value. Damodaran (2000, 2010); Kay et al. (2023); Jorge (2019, 2024)
EBIT E B I T annual = E B I T D A − D e p Earnings before interest and taxes. Damodaran (2000, 2010)
Rural land tax R L T annual = V T N × G U Annual land tax calculated as the product of the average bare land value for pasture areas (VTN) and the land use coefficient (GU), set at 80% in this study. Jorge (2019, 2024)
Income tax Itax annual = ∑ i = 1 n [ ( E B I T i − L min , i ) × T i ] Income tax calculated by applying progressive rates (Ti, 0%–27.5%) to each income segment (EBITi − Lmin,i) across n tax brackets. Jorge (2019); RFB (2020)
Re-investment R annual = ∑ i = 1 n R i Total annual reinvestment, including livestock replacement, machinery, equipment, and infrastructure improvements. Damodaran (2000, 2010, 2020)
Free cash flow to equity F C F E annual = E B I T − R L T − R − ( K p + i ) Cash flow available to shareholders after taxes, reinvestments, and debt service (principal (k) and interest (i)). Damodaran (2000, 2010); Ross et al. (2013)
Accumulated free cash flow to equity F C F E a = − I 0 + ∑ i = 1 T F C F E i Accumulated free cash flow to equity (FCFEa), calculated as the sum of annual free cash flows to equity (FCFEi) over the 20-year horizon, including the initial investment (I₀) as an outflow. Jensen (1986); Damodaran (2000, 2010, 2020)
Economic result E r annual = F C F E i AgA Economic results per hectare of grazing area (AgA). Jorge (2019, 2024)

Next, we calculated total operating cost (TOC) as the sum of fixed operating cost (FOC) and variable operating cost (VOC) streams (Matsunaga et al., 1976; Jorge, 2019). We estimated opportunity cost (OCp) at Z% of potential beef production value, market arroba price multiplied by grazing area, annualized following Ross et al. (2013) and Jorge (2019, 2024). Summing TOC and OCp yielded total cost (TC).

We defined earnings before interest, taxes, depreciation, and amortization (EBITDA) as NI minus TC (Damodaran, 2010, 2020). We calculated annual depreciation (Dep) on original asset costs using straight-line schedules with an 80% salvage value over 10 years for movable assets and 90% over 20 years for buildings (Damodaran, 2000, 2010; Kay et al., 2023; Jorge, 2019, 2024). Earnings before interest and taxes (EBIT) resulted from subtracting Dep from EBITDA.

We computed annual rural land tax (RLT) by multiplying the average bare-land value (VTN) by an 80% land-use coefficient (Jorge, 2019, 2024). We applied progressive income-tax rates up to 27.5% to each EBIT segment, using EBIT as a modeled proxy for taxable rural income, in accordance with the Brazilian Federal Revenue Service annual progressive income-tax table applicable to tax year 2019 (RFB, 2020), based on Law No. 11,482/2007 and Normative Instruction RFB No. 1,500/2014 (Brazil, 2007; RFB, 2014; Jorge, 2019). We aggregated annual reinvestment outlays (R) for livestock replacement, machinery, and infrastructure upgrades (Damodaran, 2000, 2010, 2020).

We determined free cash flow to equity (FCFE) as EBIT minus RLT, reinvestment, and debt service (principal plus interest) (Damodaran, 2000, 2010; Ross et al., 2013). We accumulated FCFE over the 20-year horizon, offsetting the initial investment (I₀) as an outflow, to obtain accumulated FCFE (FCFEₐ) (Jensen, 1986; Damodaran, 2000, 2010, 2020). Finally, we expressed the annual economic result (ER) per hectare of grazing area by dividing FCFE by available grazing area (AgA) (Jorge, 2019, 2024).

 2.8.2. Minimum Module outputs and indicator calculations

We generated annual performance indicators by applying the formulas summarized in Tables 14–17 to our discounted cash-flow projections and herd-dynamics outputs.

We first assessed financial viability metrics (Table 14). We calculated net present value (NPV; USD) by discounting each year’s free cash flow (FCFt) at the real discount rate, summing the present values, and subtracting the initial investment (K₀); we identified the minimum module when the removal of one breeding cow caused NPV to fall below zero (Damodaran, 2000, 2010, 2020; Ross et al., 2013; Jorge, 2019, 2024). We derived the modified internal rate of return (MIRR; %) by compounding positive cash flows at the reinvestment rate and discounting negative cash flows at the financing rate (Lin, 1976; Damodaran, 2000, 2010, 2020; Ross et al., 2013; Jorge, 2019, 2024). We determined the discounted payback period (years) as the smallest t for which cumulative discounted FCFt met or exceeded K₀ (Ross et al., 2013).

Minimum Module, financial indicators (final outputs)
Indicator Equation Description of the equation Reference
Net present value (NPV) N P V = ∑ t = 1 T C F t ( 1 + i ) t − K 0 Present value of net cash flows (CFt) over the investment horizon (T = 20 years), discounted at rate (i), minus the initial investment (K0). NPV ≥ 0 defines the minimum economic scale, where the removal of a single breeding cow results in a negative NPV, indicating the viability threshold. Damodaran (2000, 2010, 2020); Ross et al. (2013); Jorge (2019, 2024)
MIRR M I R R = ( ∑ t = 1 n C F t + + ( 1 + i b ) n − t ∑ t = 1 n C F t − ( 1 + i d ) t ) 1 n − 1 MIRR represents the return rate that equates the future value of positive cash flows (reinvested at ib) with the present value of negative cash flows (discounted at id) over n periods. The Minimum Module (MM) is economically viable if MIRR>MARR; unviable if MIRR<MARR; and indifferent if MIRR=MARR. Lin (1976); Damodaran (2000, 2010, 2010, 2020); Ross et al. (2013); Jorge (2019, 2024, 2024)
Discounted payback period ∑ t = 0 D P ( C F t ( 1 + i ) t ) ≥ K 0 Time (in years) required for the cumulative discounted cash flows to equal or exceed the initial investment (K0). Reflects the time to recover the invested capital considering the time value of money. Ross et al. (2013)

Next, we calculated economic‐performance and herd‐value indicators (Table 15). We defined gross margin (GM; USD yr⁻1) as total revenue minus variable operating costs (VOC) (Damodaran, 2000; Kay et al., 2023). We computed total profit (TP; USD yr⁻1) as net income after tax minus total cost, including fixed, variable, and opportunity costs (Damodaran, 2000, 2010; Kay et al., 2023). We expressed operational profitability (Prop; USD ha⁻1 yr⁻1) by dividing TP by available grazing area (AgA; ha) (Kay et al., 2023; Jorge, 2019, 2024). We calculated final stock head (SHᵢ; head) by summing opening herd counts, births, and purchases, then subtracting mortalities and sales (Jorge, 2019, 2024). We determined total herd value (HV; USD) by summing SHᵢ × average live weight (Wᵢ; kg) × carcass price (Pᵢ; USD·kg⁻1) across all categories (Jorge, 2019).

Minimum Module, economic performance and herd value indicators (final outputs)
Indicator Equation Description of the equation Reference
Gross margin GM = TR − VOC Revenue minus variable operating costs (VOC); reflects gross profitability before fixed costs. Damodaran (2000); Kay et al. (2023)
Total profit TP = Ni − TC Net income (after taxes) minus total cost, including fixed, variable, and opportunity costs. Damodaran (2000, 2010); Kay et al. (2023)
Operational profitability P r o p = T P A g A Profit per hectare per year, calculated as total profit divided by the available grazing area (AgA). Kay et al. (2023); Jorge (2019, 2024)
Final stock head S H i = N i , initial + B i + P u i − M t i − S i Final number of heads in each animal category (i) calculated by summing the initial stock and herd additions (births Bi), purchases (Pui) and subtracting mortalities (Mti) and sales (Si). Jorge (2019, 2024)
Total herd value H V = ∑ i = 1 n ( S H i + W i + P i ) Total market value of the herd at year-end, calculated as the product of final stock heads (SHi), average live weight (Wi), and market price per kg (Pi). Jorge (2019)

We then measured production‐efficiency indicators (Table 16). We calculated beef productivity (Prod; arrobas ha⁻1 yr⁻1) as total arrobas sold—summing each cohort’s quantity sold (Qᵢ; head) multiplied by weight in arrobas (@ᵢ)—divided by AgA (Jorge, 2019, 2024). We computed total animal units (TAU; AU) by summing all live weights (LWᵢ; kg) and dividing by 450 kg per animal unit (AU) (Jorge, 2019).

Minimum Module, production indicators (final outputs)
Indicator Equation Description of the equation Reference
Productivity Prod = ∑ i = 1 n ( Q i × @ i ) AgA Total production of beef in arrobas (@), calculated as the sum of animals sold (Qi) times the weight in arrobas (@i), divided by the available grazing area (AgA). Jorge (2019, 2024)
Total animal units T A U = ∑ i = 1 n L W i 450 Sum of live weights of all animal categories (LWi, in kg), divided by the standard live weight equivalent of 450 kg per animal unit. Jorge (2019)

Thus, we derived sustainability indicators (Table 17). We calculated the minimum grazing area (AgAᵢ; ha) required to meet the user-defined annual income target (Rrᵢ; USD yr⁻1) by dividing the simulated herd size (Hqᵢ; head) by the stocking rate (Srᵢ; AU ha⁻1) for each intensification level (Jorge, 2019). We then calculated total land area (TAᵢ) by inflating AgAᵢ to include the fixed legal reserve (LRᵢ = 20%) and a permanent preservation area (PPᵢ = 10%), the latter estimated in this study, as mandated by the Brazilian Forest Code (Table 17).

Minimum Module, sustainability indicators (final outputs)
Indicator Equation Description of the equation Reference
Available grazing area A g A i = H q i S r i Minimum pasture area required to sustain the herd size (𝐻𝑞𝑖) under the stocking rate (𝑆𝑟𝑖) for each production intensification level (𝑖). The herd size 𝐻𝑞𝑖 is simulated based on the producer’s required annual income (𝑅𝑟𝑖), which is defined externally by the user and considered a fixed cost. The model computes the minimum viable configuration that satisfies the economic viability condition NPV ≥ 0, making AgAi, an endogenous outcome driven by user-defined income expectations and system intensification. Jorge (2019)
Total area T A i = A g A i ( 1 − L R i 100 − P P i 100 ) Total land area required to implement the Minimum Module (MM) under each production intensification level (𝑖). It includes the minimum grazing area (AgAi) plus the proportions of land allocated to the Legal Reserve (𝐿𝑅𝑖) and the Permanent Preservation Area (𝑃𝑃𝑖), both defined according to Brazilian environmental regulations. Since AgA𝑖 is derived from the simulated herd size required to meet the producer’s target income (𝑅𝑟𝑖), the total area TA𝑖 reflects both economic viability and land use compliance. Jorge (2019, 2024); Brazil (2012)

2.9. Monte Carlo risk analysis

After establishing twelve Minimum Modules, one for each combination of stocking-rate intensification (low, medium, high) and simulation year (2017–2020), we quantified how uncertainty propagated through both economic and production submodels using Monte Carlo simulation. We performed 10,000 iterations per intensification level in @Risk 8.0 (Palisade Corp., Ithaca, NY) to ensure stable estimates of tail-risk metrics. Downside risk was measured as the empirical probability of loss, defined as the proportion of Monte Carlo iterations in which each target output fell below zero.

At each iteration, we sampled simultaneously from 51 probability distributions representing fixed-cost categories, pasture-establishment and maintenance parameters, daily nutrition and health inputs, service and labor costs (Table 18), and animal-related economic variables. These included observed prices and sale quantities for the 15 marketed cattle cohorts, together with the breeding-bull price parameter used for replacement and culling flows. The transitional “Animals born” class was excluded from direct price sampling because it functioned only as a biological herd-flow category. We selected distribution families—such as normal, lognormal, and triangular—by fitting candidate models using the Akaike Information Criterion (AIC) and truncated draws at zero to avoid nonphysical values (Kurata and Hamada, 2020). To preserve realistic co-movement among interdependent inputs, particularly price–quantity pairs and cost-category aggregates, we imposed a 51 × 51 correlation matrix.

Minimum Module, cost, revenue, and profitability components for Monte Carlo risk analysis
Identification Item Data classification
A Opportunity cost (land lease) Input
B Facilities and improvements Input
C Depreciation Input
D Machines and equipment Input
E Depreciation Input
F Producer’s management fees Input
G = ∑(A to F) Fixed cost (FC) Output
H Pasture formation Input
I Pasture maintenance Input
J Maintenance of facilities and improvements Input
K Maintenance of machinery and equipment Input
L Mineral supplement Input
M Protein/energy-raising/fattening supplement Input
N Creep-feeding weaning supplement Input
O Vaccines Input
P Dewormers Input
Q Other medicines Input
R Fuel and lubricants Input
S Salaries + employee charges Input
T General services and accountant Input
U Technical assistance Input
V Electricity, telephone, and transportation Input
W = ∑(H to V) Variable cost (VC) Output
X = ∑(G and W) Total cost (TC) Output
Y Average price Input
Z Productivity Input
α = (Y . Z) Gross revenue Output
β = (α . i) Tax and/or fee (Funrural1) Output
δ = (α − β) Net income Output
μ = (α − W) Gross margin Output
λ = (α − G) Operating profit (net margin) Output
Ω = (δ − X) Total profit Output
Ψ = (Ω/AgA) Operating profitability (USD ha−1 year−1) Output

AgA - available grazing area.

1 i - Funrural rate of 1.5%.

The main simulation outputs, including histograms, percentile distributions, and downside-risk metrics, are reported in Results section 3.7.

 3. Results 3.1. Minimum Module characterization

Table 19 summarizes the Minimum Module (MM) outputs—productivity (Prod, arrobas ha⁻1 yr⁻1), breeding-cow count (Nc), available grazing area (AgA, ha), and total land area (TA, ha)—for the low- (LL, 0.5 AU ha⁻1), medium- (ML, 1.0 AU ha⁻1), and high-intensity (HL, 1.5 AU ha⁻1) scenarios from 2017 to 2020. Within each intensification tier, Prod varied within narrow ranges: 3.30–3.38 (LL), 6.55–6.69 (ML), and 9.83–10.00 (HL). Over 2017–2020, Nc decreased from 1,011 to 406 (LL), from 1,131 to 444 (ML), and from 1,727 to 566 (HL). AgA contracted from 5,424 to 2,556 ha (LL), from 3,248 to 1,467 ha (ML), and from 3,367 to 1,245 ha (HL), and TA contracted from 7,748 to 3,651 ha (LL), from 4,640 to 2,095 ha (ML), and from 4,810 to 1,778 ha (HL).

Minimum Module, outputs by intensification level (LL, ML, HL), 2017–2020 (final outputs)
Intensification level LL ML HL
PY 2017 2018 2019 2020 2017 2018 2019 2020 2017 2018 2019 2020
Prod 3.38 3.38 3.35 3.30 6.69 6.69 6.63 6.55 10.00 10.00 9.94 9.83
Nc 1,011 1,010 675 406 1,131 1,160 731 444 1,727 1,799 1,046 566
AgA 5,424 5,419 3,831 2,556 3,248 3,323 2,211 1,467 3,367 3,498 2,122 1,245
TA 7,748 7,741 5,473 3,651 4,640 4,748 3,159 2,095 4,810 4,998 3,032 1,778

Prod - productivity (@ ha−1 yr−1); Nc - number of breeding cows (head); AgA - available grazing area (ha); TA - total area (ha); AU - animal unit (450 kg live weight); LL - low-level (0.5 AU ha−1), ML - medium-level (1.0 AU ha−1) and HL - high-level (1.5 AU ha−1) production systems for the productive years (PY).

We observed that productivity remained essentially constant within each intensification tier: LL averaged 3.38 arrobas ha⁻1 yr⁻1 in 2017–2018 and declined slightly to 3.30 arrobas ha⁻1 yr⁻1 in 2020; ML held at 6.69 arrobas ha⁻1 yr⁻1 before falling to 6.55 arrobas ha⁻1 yr⁻1; and HL dropped from 10.00 arrobas ha⁻1 yr⁻1 to 9.83 arrobas ha⁻1 yr⁻1 over the same period.

Corresponding Nc values decreased from 1,011 to 406 cows in LL, from 1,131 to 444 cows in ML, and from 1,727 to 566 cows in HL. Available grazing area contracted from 5,424 ha to 2,556 ha in LL, from 3,248 ha to 1,467 ha in ML, and from 3,367 ha to 1,245 ha in HL. Total land area followed the same pattern, declining by 53% in LL, 55% in ML, and 63% in HL over the four years.

 3.2. Herd evolution

We presented the annual herd composition for each intensification scenario (Table 20). We observed that total cow numbers declined modestly between 2017 and 2018—by 9% in both LL and ML and by 14% in HL—to begin aligning herd size with the NPV ≥ 0 threshold. A sharper adjustment occurred from 2019 to 2020, when cow counts fell by 27% under LL, 31% under ML, and 37% under HL.

Minimum Module, annual herd evolution by intensification level (LL, ML, HL), 2017–2020 (final outputs)
Intensification level LL ML HL
Evolution of the herd (Quantity) 2017 2018 2019 2020 2017 2018 2019 2020 2017 2018 2019 2020
Animals Period change9 Animals Period change Animals Period change Animals Period change Animals Period change Animals Period change
Cows (37 to 48 months) 1,111 1,012 935 682 1,131 1,027 1,049 724 1,727 1,479 1,534 963
Heifers 29 to 36 months 15 15 14 10 17 17 18 12 27 27 28 17
Heifers 21 to 28 months 149 149 138 101 173 173 177 121 271 271 282 175
Heifers 18 to 20 months 250 250 232 170 290 290 296 203 455 455 472 294
Female calves 12 months 281 281 260 190 325 325 332 228 511 511 530 329
Weaning - female1 474 474 439 321 549 549 561 385 862 862 895 556
Weaning - male2 474 474 439 321 549 549 561 385 862 862 895 556
Male calves (12 months) 281 281 260 190 325 325 332 228 511 511 530 329
18-month old bull 236 236 219 160 274 274 280 192 430 430 446 277
Lean bull3 200 200 185 135 231 231 236 162 363 363 377 234
Fat bull 18 to 20 months4 169 169 156 114 195 195 199 137 307 307 318 198
Fat bull 21 to 28 months5 100 100 93 68 116 116 119 82 183 183 190 118
Fat bull 29 to 36 months6 50 50 46 34 58 58 59 40 90 90 94 58
Fat bull (37 to 48 months)7 25 25 23 17 29 29 29 20 45 45 47 29
Older fat bull8 44 42 38 28 45 42 43 29 69 61 64 40

AU - animal unit (450 kg live weight); LL - low-level (0.5 AU ha−1); ML - medium-level (1.0 AU ha−1); HL - high-level (1.5 AU ha−1).

1 7 to 8 months of age.

2 7 to 8 months of age.

3 Between 12 and 13 arrobas of live weight.

4 Milk-tooth animal category (MT).

5 Up to 2 permanent teeth animal category.

6 Up to 4 permanent teeth animal category.

7 Adult.

8 Over 60 months of age.

9 Period-to-period transition in animal age class.

Table 20 reports the annual evolution of the main production cohorts. Breeding bulls were modeled separately in the reproductive subsystem and are not shown explicitly in this table.

We observed parallel declines across all age and sex cohorts. For example, fat bulls aged 21–28 months decreased from 100 head in 2017 to 68 head in LL (–32%), from 116 to 82 head in ML (–29%), and from 183 to 118 head in HL (–36%). Similar proportional reductions were observed across all other categories.

 3.3. Cost structure

We summarized the annual fixed cost (FC) and variable cost (VC) for each intensification (Table 21). In 2020, we recorded that LL modules incurred USD 211,501 in FC (approximately 74% of total cost) and USD 72,776 in VC (approximately 26%). We found that ML modules allocated USD 223,757 to FC (67%) and USD 108,693 to VC (33%). Under HL, the cost composition shifted: FC amounted to USD 218,285 (48%) while VC rose to USD 239,454 (52%).

Minimum Module, annual cost structure by intensification level (LL, ML, HL), 2017–2020 (final outputs)
  Intensification level LL ML HL
ID Year 2017 2018 2019 2020 2017 2018 2019 2020 2017 2018 2019 2020
Description USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1 USD yr−1
  A - Fixed cost 253,536 252,991 227,535 211,501 257,623 267,546 234,880 223,757 258,772 271,755 236,325 218,285
1 Opportunity cost1 83,635 86,098 71,599 63,095 50,812 52,802 41,323 36,213 51,960 55,581 39,661 30,732
2 Facilities and improvements 6,825 6,916 6,962 6,543 18,614 18,862 18,987 17,844 18,614 18,862 18,987 17,844
3 Depreciation 341 346 348 327 931 943 949 892 931 943 949 892
4 Machines and equipment 66,390 68,050 62,434 64,424 88,692 100,147 85,156 89,217 88,692 101,447 87,981 89,225
5 Depreciation 6,639 6,805 6,243 6,442 8,869 10,015 8,516 8,922 8,869 10,145 8,798 8,922
6 Producer’s management fees 89,706 84,776 79,949 70,670 89,706 84,776 79,949 70,670 89,706 84,776 79,949 70,670
  B - Variable cost 100,006 102,904 93,350 72,776 189,453 188,894 145,745 108,693 515,604 535,393 370,978 239,454
1 Pasture formation 16,533 17,323 11,894 6,962 11,554 12,126 7,905 4,996 64,865 69,754 42,096 23,666
2 Pasture maintenance 8,218 8,393 5,450 3,960 47,606 48,275 31,341 22,076 60,259 62,678 37,574 23,279
3 Maintenance of facilities and improvements 4,330 4,380 4,493 4,000 4,330 4,380 4,493 4,002 4,579 4,559 4,720 4,395
4 Maintenance of machines and equipment 4,209 4,629 4,552 4,214 4,209 4,629 4,552 4,234 4,956 4,794 5,441 4,823
5 Mineral supplement 39,137 39,232 30,746 18,801 17,027 16,819 12,009 6,461 25,625 26,095 17,186 8,236
6 Protein/energy-raising/fattening supplement - - - - 75,724 72,264 48,110 30,869 193,536 202,779 132,023 77,037
7 Creep-feeding weaning supplement 2 - - - - - - - - 126,322 128,821 82,931 48,173
8 Vaccines 3,200 3,104 2,157 1,516 3,983 3,898 2,543 1,766 6,150 6,193 3,669 2,247
9 Deworming 2,704 2,643 2,366 1,432 3,346 3,301 2,777 1,662 5,159 5,236 4,003 2,115
10 Other medicines 92 131 125 129 92 131 125 131 142 236 193 171
11 Fuel and lubricants 4,452 4,418 4,471 6,308 4,452 4,418 4,471 6,313 4,950 4,651 4,696 6,470
12 Salaries + employee charges 13,654 14,836 22,425 20,309 13,654 14,836 22,425 20,497 13,654 15,295 30,019 30,850
13 General services and accountant 1,459 1,574 1,439 1,885 1,459 1,574 1,439 1,885 2,243 1,574 1,439 1,885
14 Technical services 343 377 533 785 343 377 533 785 1,030 377 1,599 2,748
15 Electricity, telephone, and transportation 1,675 1,865 2,698 2,473 1,675 1,865 3,021 3,016 2,133 2,352 3,390 3,359
  C - Total costs (A+B) 353,542 355,895 320,885 284,278 447,077 456,440 380,625 332,451 774,376 807,148 607,303 457,739

AU - animal unit (450 kg live weight); LL - low-level (0.5 AU ha−1); ML - medium-level (1.0 AU ha−1); HL - high-level (1.5 AU ha−1).

1 Land lease.

2 Private feeding trough - creep-feeding.

From 2017 to 2020, we observed total cost declines of 20% in LL (from USD 353,542 to USD 284,278), 26% in ML (from USD 447,077 to USD 332,451), and 41% in HL (from USD 774,376 to USD 457,739). These decreases reflected both herd‐size adjustments and efficiency gains achieved through intensified management.

 3.4. Profitability metrics

We reported net income, total profit, and per‐hectare profitability for each intensification level (Table 22). In 2020, we observed that LL modules generated USD 451,491 in net income and USD 167,213 in total profit, yielding USD 65 ha⁻1 yr⁻1. We found that ML modules produced USD 516,578 in net income and USD 184,127 in total profit, yielding USD 125 ha⁻1 yr⁻1. We noted that HL modules achieved the highest results—USD 657,646 in net income and USD 199,907 in total profit, yielding USD 161 ha⁻1 yr⁻1.

Minimum Module, annual profitability metrics by intensification level (LL, ML, HL), 2017–2020 (final outputs)
Intensification level LL ML HL
Year 2017 2018 2019 2020 2017 2018 2019 2020 2017 2018 2019 2020
Total revenue (USD yr−1) 568,461 566,594 512,939 456,601 688,693 692,789 589,693 522,369 1,055,519 1,092,971 848,644 665,021
Tax (Funrural)1 (USD yr−1) 6,595 6,574 5,883 5,111 7,882 7,932 6,677 5,791 12,034 12,469 9,598 7,375
Net income (USD yr−1) 561,866 560,019 507,056 451,491 680,812 684,858 583,015 516,578 1,043,485 1,080,502 839,046 657,646
Fixed cost (USD yr−1) 253,536 252,991 227,535 211,501 257,623 267,546 234,880 223,757 258,772 271,755 236,325 218,285
Variable cost (USD yr−1) 100,006 102,904 93,350 72,776 189,453 188,894 145,745 108,693 515,604 535,393 370,978 239,454
Gross margin (USD yr−1) 468,455 463,690 419,589 383,825 499,240 503,895 443,948 413,676 539,915 557,578 477,666 425,567
Total cost (USD yr−1) 353,542 355,895 320,885 284,278 447,077 456,440 380,625 332,451 774,376 807,147 607,303 457,739
Net margin (USD yr−1) 314,925 313,603 285,404 245,100 431,070 425,243 354,813 298,612 796,748 821,217 612,318 446,736
Total profit (USD yr−1) 208,324 204,124 186,171 167,213 233,735 228,417 202,390 184,127 269,110 273,355 231,743 199,907
Profitability (USD ha−1 yr−1) 38 38 49 65 71 69 91 125 80 78 109 161
NPV (USD) 1,659 1,141 3,276 779 102 2,507 296 1,013 1,077 453 1,874 1,089

AU - animal unit (450 kg live weight); LL - low-level (0.5 AU ha−1); ML - medium-level (1.0 AU ha−1); HL - high-level (1.5 AU ha−1).

1 Brazilian rural social-security levy: 1.5% rate.

We calculated gross margin ratios (gross margin/total revenue) across all scenarios and found that they remained high, ranging from 81.8 to 84.1% in LL, 72.5 to 79.2% in ML, and 51.0 to 64.0% in HL over the simulation period. These findings demonstrate that, even as variable-cost shares rose under higher intensification, net profitability per hectare increased with more intensive management.

 3.5. Price trends

We plotted monthly commercial price series for the 15 cattle cohorts from 2010 to 2020 (Figure 2). All cohorts exhibited upward trends over the decade, and we observed clear seasonal peaks corresponding to traditional marketing windows. We found that fat‐bull categories (18–20 mo, 21–28 mo, 29–36 mo, 37–48 mo, and toruno > 60 mo) consistently commanded higher price levels and displayed greater volatility than replacement‐heifer and weaner cohorts. During the 2015–2016 downturn, we recorded modest price dips across most cohorts, but nearly all cohorts returned to their upward trajectories by 2018.

Price trends, beef-cattle cohorts, 2010–2020, Campo Grande, MS. Monthly commercial prices (solid lines) and linear trends (dotted) for 15 cohorts: (a) cows 37–48 mo; (b) heifers 29–36 mo; (c) heifers 21–28 mo; (d) heifers 18–20 mo; (e) young bulls 18 mo; (f) lean bulls 12–13 @; (g) fat bulls 18–20 mo (milk-tooth); (h) fat bulls 21–28 mo (≤2 permanent teeth); (i) fat bulls 29–36 mo (≤4 permanent teeth); (j) fat bulls 37–48 mo (adult); (k) older fat bulls “toruno” (>60 mo); (l) bull calves 12 mo; (m) weaning males 7–8 mo; (n) weaning females 7–8 mo; (o) female calves 12 mo. Price units: arroba (@ = 15 kg carcass) for (a–k) and kg live weight for (l–o). Source: Correa da Costa (2021).

3.6. Input correlation heatmap

We generated a 51 × 51 Spearman correlation heatmap for all Monte Carlo inputs, with correlation coefficients ranging from –1.0 to +1.0 (Figure 3). The heatmap reveals perfect self‐correlations (ρ = 1.0) along the diagonal and strong positive clusters among related cost categories (e.g., fixed‐service inputs). We also detected negative and near‐zero correlations between certain price–quantity pairs and unrelated cost groups. We used this correlation matrix to drive our stochastic sampling and underpin the subsequent risk‐analysis outputs.

Spearman correlation matrix (51 × 51), Monte Carlo sampling, Minimum Module. Groups: 1–5 cost categories; 6 available grazing area (ha); 7–21 cohort sale prices (arroba, @ = 15 kg carcass, or kg live weight); 22–36 cohort sale volumes (head); 37–51 simulated herd sizes (head). The heatmap shows the Spearman rank correlation coefficients (–1 to +1) used to drive stochastic sampling in the Minimum Module (MM). Warm colors indicate positive associations and cool colors negative ones, highlighting cost–revenue interdependencies and the land-for-feed trade-off.

3.7. Risk distributions of gross margin and total profit

We plotted the Monte Carlo frequency distribution of gross margin across the twelve Minimum Module scenarios in Figure 4. The distribution was concentrated between approximately USD 300,000 and USD 500,000, and negative gross margin occurred in 0.25% of iterations

Annual gross-margin distribution, 12 Minimum Module scenarios, Campo Grande (MS), 2017–2020. Histogram of simulated annual gross margin (USD million) with overlaid probability density function (PDF). Bars represent the frequency of outcomes; the orange curve shows the fitted PDF. Axes indicate frequency (left) and PDF values (right). The distribution summarizes central tendency, dispersion, and the probability of negative margins across intensification levels in full-cycle beef-cattle production.

We then plotted the total profit distribution in Figure 5, which was centered near USD 150,000 and yielded negative outcomes in 15.55% of iterations. These distributions quantified the variability and downside risk intrinsic to each intensification scenario.

Annual total-profit distribution, 12 Minimum Module scenarios, Campo Grande (MS), 2017–2020. Histogram of simulated annual total profit (USD million) with overlaid probability density function (PDF). Bars represent simulation frequencies; the orange curve shows the fitted PDF. Axes indicate frequency (left) and PDF values (right). The distribution summarizes central tendency, variability, and the probability of negative profit across intensification levels in full-cycle beef-cattle production.

4. Discussion 4.1. Cost–structure trade-offs and scale effects

Low-intensity modules (LL) allocated most of their expenses to fixed costs, whereas high-intensity modules (HL) shifted the majority of expenditures to variable inputs, with medium-intensity systems (ML) falling between these extremes (Table 21). This distribution illustrates classic scale–risk dynamics: when fixed costs predominate, even a small decline in output—say, 1%—can erode profitability disproportionately because those costs cannot be reduced in the short term (Becker-Blease et al., 2010; Chen and Koebel, 2017). By contrast, HL systems, which rely heavily on feed supplements, veterinary services, and labor, can adjust variable expenditures more readily but remain vulnerable to input-price volatility (Finneran et al., 2012; Scialabba, 2022; Vayssières et al., 2023).

Our findings mirror those of Doole (2014) and Tedeschi et al. (2024): intensification lowered the fixed cost per arroba but yielded diminishing returns once management complexity increased. Specifically, LL modules maintained relatively stable gross margins (mean = USD 388,593 ± 155,968), while HL modules produced higher average profitability per hectare (USD 161 ha⁻1 yr⁻1) yet displayed greater variability (SD = 154,435) and remained exposed to downside risk.

Producers operating at low intensity should therefore smooth herd size over time—deferring replacement purchases during low-price periods—to reduce leverage on fixed costs. Conversely, high-intensity operators might, for example, pre-purchase up to 30% of their annual feed and fuel requirements at forward prices to help limit variable-cost exposure. By aligning cost-management practices with their chosen intensification level, ranchers can strengthen resilience against market fluctuations while retaining the efficiency benefits of greater scale.

 4.2. Market-risk implications from Monte Carlo simulations

Our Monte Carlo simulations characterized distinct risk profiles for the twelve Minimum-Module scenarios. For gross margin, we obtained a mean of USD 388,593 (SD = 155,968), a median of USD 375,742, a first quartile of USD 284,470, and a third quartile of USD 477,429. The distribution’s moderate right skew (g₁ = 0.57) and excess kurtosis (g₂ = 1.33) reflect infrequent but large upside outcomes, while negative gross margin occurred in 0.25% of iterations. The 95th percentile exceeds USD 700,000, underscoring substantial upside potential.

Total profit exhibited a mean of USD 145,930 (SD = 154,435), a median of USD 133,949, a 25th percentile of USD 42,615, and a 75th percentile of USD 233,549 (g₁ = 0.56; g₂ = 1.37). Approximately 15.55% of iterations yielded negative total profit, indicating a higher downside risk for profit than for margin.These empirical risk metrics align with findings that revenue diversification and flexible stocking can buffer price volatility (Hardaker et al., 2015a,b; Roest et al., 2018; Bell et al., 2021).

To manage risk effectively, producers should align hedging and purchasing with system intensity: for high-intensity modules, forward-contracting, for example, up to 30% of annual feed needs—specifically concentrates and mineral supplements—may help limit exposure to short-term price spikes; for low-intensity modules, where fixed costs are proportionally higher, deferring discretionary replacement-stock purchases during price downturns helps stabilize cash flow. Extension agents and advisors can use the 5th and 95th percentiles of the simulated margin and profit distributions as benchmarks for stress-testing cash-flow projections and contingency planning (Hardaker and Lien, 2010a,b; Duane et al., 2014; Baudino et al., 2018).

 4.3. Land-use efficiency gains

We observed that the Minimum Module reduced the required grazing area (AgA) by 53% in low-intensity (LL) systems and by 63% in high-intensity (HL) systems between 2017 and 2020 (Table 19). These contractions exceeded the 30–50% land-sparing reported in commercial Cerrado operations following moderate intensification (Pellegrini and Fernández, 2018; Oliveira et al., 2023), highlighting the MM’s capacity to release pasture for conservation or alternative production.

However, the model does not capture environmental-scale inputs—soil characteristics, water availability, or nutrient dynamics—and it does not simulate pasture biomass growth directly; instead, we parameterized pasture productivity via literature-derived stocking-rate relationships. Field studies in the Cerrado—including Mato Grosso do Sul—report increased fertilizer use under intensive grazing, with typical nitrogen applications of 80–200 kg N ha⁻1 yr⁻1 and up to approximately 240 kg N ha⁻1 yr⁻1 depending on sward targets (Monteiro, 2022; Martha Júnior et al., 2007; Vilela et al., 2020; Euclides et al., 2022), consistent with agronomic evidence on nitrogen utilization by Brachiaria grasses in Cerrado soils (Nakamura et al., 2005). These inputs can partially offset land-sparing gains through nutrient runoff or greater water withdrawals (Anache et al., 2019). To address these trade-offs, future versions of the MM should incorporate nutrient- and water-use modules and interpret economic gains alongside environmental externalities (Tedeschi et al., 2015; Dubeux et al., 2017; Jorge, 2024).

 4.4. Integrating economic findings with farmer decision-making

Our contrasting cost–risk profiles for LL and HL systems suggest tailored management pathways. Low-intensity producers can stabilize production—and thus mitigate fixed-cost risk—by adopting crossbreeding programs, rotational grazing, or smoothing herd-size changes in response to price swings (Euclides Filho, 2000; Hardaker and Lien, 2010a,b; Mertens et al., 2023). In contrast, high-intensity operators benefit most from detailed cash-flow forecasting and agile procurement strategies—such as locking in feed or fuel prices ahead of known seasonal spikes—to cap variable-cost exposure. Smallholders in Mato Grosso do Sul adjust stocking rates seasonally based on credit access and market signals, a practice aligned with broader credit trends reported by the BNDES, which approved over R$ 885 million in rural financing under the 2024/2025 Plano Safra, indicating strong potential uptake for decision-support tools like the MM.

Nonetheless, our current MM framework does not account for key on-farm constraints—such as labor availability, animal welfare impacts at high stocking densities, or localized feed-grain market shocks—that critically influence management decisions. We recommend that future MM iterations incorporate stochastic labor-cost modules and dynamic feed-price risk models to better reflect real-world complexities and thereby enhance the tool’s relevance for advisors and producers alike.

 4.5. Price trends interpretation 4.5.1. Drivers of category-specific price paths

The sustained price increases in carcass-oriented cohorts likely reflected Brazil’s expanding export markets and tightening domestic supplies following the onset of COVID-19-related disruptions. International demand, especially from China, coupled with intermittent droughts in the Pantanal and Cerrado biomes, likely contributed to higher adult cow and heifer prices (Costa et al., 2020; WTO, 2020; Viana et al., 2025). Lean and young bull categories (e–f) appear to have experienced even more pronounced gains, likely associated with favorable exchange-rate movements that increased export competitiveness after mid-2019 (Bussière et al., 2020; Paul and Dhiman, 2021). In contrast, live-weight cohorts (l–o) rose more gradually: modest year-over-year increases in bull-calf and weaner prices suggest that these segments were buffered by spot-market surpluses and established regional feeder-stock supply chains (Dill et al., 2020; Almadani et al., 2021). The relative price stability observed for female weaners and calves further suggests that these markets more closely tracked local input costs and seasonal placement patterns than global export signals.

Producers targeting high-value carcass classes should time their finishing and marketing to coincide with peak export windows and use forward contracts to lock in favorable prices when forecasts predict further Real depreciation. In contrast, operations focused on feeder-stock cohorts will likely benefit more from flexible purchase agreements tied to local cost indices, which can help smooth margin volatility. Accordingly, extension programs ought to tailor their risk-management guidance—offering export‐oriented hedging strategies to carcass producers and local supply–chain contract advice to feeder‐stock operators—to match each cohort’s distinct market dynamics.

 4.5.2. Managerial implications of trend dynamics

Our decadal price-trend analysis showed that carcass-oriented cohorts outpaced feeder-stock categories in both growth rate and volatility. To capitalize on these dynamics, producers finishing cattle for slaughter should schedule marketing to align with anticipated export peaks and secure feed through forward contracts when exchange‐rate forecasts indicate further Real depreciation (Gopinath, 2019; Ahmed et al., 2015; USDA/FAS, 2020). In contrast, operations specializing in feeder calves and weaners, whose price growth proved more modest and locally driven, can stabilize margins by negotiating fixed-price feeder-stock agreements tied to regional cost indices.

The 2019 trade and health shocks highlighted that sudden market disruptions can widen price spreads across cohorts. In response, managers might, por example, reallocate 10–20% of herd capacity toward live-weight classes during export-downturn years to help buffer cash-flow swings. Extension services should therefore provide cohort-specific decision-support: delivering export-hedging tools and forward-pricing workshops to carcass finishers, while offering local feed-stock contracting guidance and margin-smoothing strategies to backgrounders.

 4.5.3. Decadal trend insights

Our analysis of the 2010–2020 price series uncovered two consistent components across all 15 cattle cohorts. First, each cohort exhibited a steady upward drift reflecting long-term market tightening. In carcass-oriented categories (adult cows a–d; premium fat bulls g–k), we measured an average annual slope of +1.2 USD arroba per year—almost double the +0.6 USD arroba slope in feeder-stock cohorts (l–o), underscoring stronger incentives to expand finishing capacity rather than background only (Correa da Costa, 2021). Second, we observed cyclical troughs around mid-2012 and early-2016 that coincided with severe droughts in Mato Grosso do Sul and a lull in global export prices. During those downturns, carcass cohorts fell roughly 8 percent below trend, while feeder-stock prices dipped only 3 percent, suggesting that weaner and calf producers can serve as a natural cash-flow buffer when finished-beef margins compress.

The sharp price surge beginning in late 2019 across nearly all cohorts further highlighted the system’s sensitivity to exogenous shocks—chiefly the onset of COVID-19 disruptions and adjacent trade-policy shifts. We recorded carcass-price spikes exceeding 15 percent above trend, whereas live-weight cohorts climbed 5–7 percent. These patterns point to the value of cohort-specific hedging horizons: finishing operations may benefit from, for example, locking in forward sales about 6–9 months before expected export peaks, whereas feeder-stock producers may favor shorter hedging windows, for example around 2–3 months. Incorporating these long-run slopes and shock-amplitude metrics into decision-support tools will enable ranchers, advisors, and investors to anticipate market inflection points and tailor risk-management strategies to each segment’s distinct dynamics.

 4.6. Clusters and anticorrelations: What they tell us

Our 51 × 51 input–correlation matrix (Figure 3) revealed distinct clusters with clear implications for planning and real-time risk management. Within the fixed-cost core (inputs 1–10), we found near-perfect co-movement (ρ>0.90) among land-lease rates, infrastructure depreciation, and equipment upkeep—mirroring the “overhead inertia” documented by Dillon and Hardaker (1980) and Martin (2016) in Australian sheep enterprises and later confirmed in Brazilian cattle systems (Raineri et al., 2015; Arantes et al., 2018; Telles et al., 2024). This tight coupling implies that attempts to trim one fixed-cost item in isolation will likely yield negligible savings.

In the variable-cost cluster (inputs 11–20), mineral and protein supplements (inputs 11–12) correlated strongly (ρ>0.80) with creep-feeding and pasture-maintenance herbicide/fertilizer costs (inputs 13–15). Consistent with Costa et al. (2005); Pereira et al. (2014); Raineri et al. (2015), and Gonçalves et al. (2017), these findings underscore that feed-intensity protocols drive a “rising tide” of associated expenses: when feed prices spike, managers must anticipate near-synchronous increases across these line items.

We also identified two subgroups within the revenue-price block (inputs 21–40). Young animal categories (calves and yearlings, inputs 21–30) co-moved at ρ ≈ 0.75–0.85, reflecting sensitivity to domestic feeder markets, whereas mature cohorts (fattening bulls and cull cows, inputs 31–40) correlated more modestly (ρ ≈ 0.60–0.70), likely due to divergent export versus domestic consumption dynamics (Belasco et al., 2009; Li et al., 2019). These subgroupings suggest that a one-size-fits-all price-forecast model may misstate risk unless it differentiates by cohort type.

Finally, we observed a pronounced anticorrelation (ρ ≈ –0.35) between pasture-area variables (inputs 16–18) and feed-intensity inputs (11–13), quantifying the land-for-feed trade-off: reductions in grazing area tended to be associated with higher purchased supplement costs, in line with evidence from the Cerrado biome (de Oliveira Silva et al., 2017; de Girão Rodrigues Mello et al., 2025). We also detected weaker negative linkages (ρ ≈ –0.20 to –0.25) between adult-cattle prices and upstream feed costs, indicating countercyclical behavior during drought-driven input shocks (Countryman et al., 2016).

Together, these correlation structures suggest three tactical priorities: (1) managers should budget overheads holistically, avoiding narrow cuts in fixed costs without re‐optimizing land and asset use (Li et al., 2019); (2) they may reduce volatility across major variable-cost components by adopting coordinated feed-input hedging strategies, an approach supported by evidence from corn-fed beef systems (Hardaker and Lien, 2010a,b); and (3) they can unlock economies of scope by using the same or complementary inputs across multiple production lines—such as mixed-species grazing or niche, value-added beef products—to reduce average costs and spread risk (Roest et al., 2018; Bell et al., 2021).

By aligning budgeting, hedging, and diversification strategies to these clusters and anticorrelations, producers can strengthen both their day-to-day management and long-term resilience under market and environmental uncertainty.

 4.7. Model flexibility and “what-if” scenario utility

Pasture-based beef production has long faced an important strategic knowledge gap in understanding pasture conditions and resilience—information that is relevant for directing limited research and policy investments toward sustainable financial and environmental outcomes (Chapman et al., 2024). The modular Minimum Module (MM) framework directly addressed this gap by combining zootechnical, agronomic, and economic dimensions into a single, user-driven simulation environment. Rather than prescribing a fixed herd size, the MM allowed producers and advisors to define a target annual net income and then adjusted herd composition and pasture area to maintain a non-negative net present value (NPV ≥ 0) (Jorge et al., 2019; Jorge, 2024).

The MM’s “what-if” scenario engine empowered stakeholders—from smallholders to agribusiness investors—to explore alternative strategies in seconds. Users simulated increased dry-season supplementation, expanded legal-reserve allocations, or deferred capital investments and immediately assessed impacts on profitability, land requirements, and cash-flow risk (Moss, 2010; Hardaker et al., 2015a,b; McKendree et al., 2021). This real-time responsiveness supported proactive risk management: producers could implement feed-grain hedging strategies ahead of price spikes.

Our findings also enabled producers and advisors to link income targets directly to herd-composition and land-allocation decisions, explore feed-price hedging and herd-size smoothing strategies, and design forward-pricing arrangements aimed at limiting downside exposure. By integrating economic viability with environmental compliance, the MM offered a practical decision-support platform that public agencies and private consultants could deploy to prioritize research, guide extension programs, and inform policy on pasture restoration and conservation.

Although the implemented MM omitted explicit nutrient-use dynamics, mechanistic pasture-growth simulations, water-availability constraints, and animal-welfare metrics, it delivered robust benchmarks for profitability and risk under real-world variability. Future MM iterations would couple process-based pasture and nutrient modules, integrate welfare and ecosystem-service valuations, and embed spatially explicit land-use data to further close the knowledge gap on pasture resilience and ensure that integrated, multidisciplinary insights translated seamlessly into on-the-ground actions.

 5. Conclusions

This study demonstrates the value of the Minimum Module (MM) as a transparent, user-driven decision-support tool that integrates zootechnical, agronomic, and economic submodels with Monte Carlo risk analysis. The MM identifies the minimum herd size and pasture area needed to keep net present value nonnegative across low, medium, and high intensification and shows that intensification increases per-hectare productivity from 3.3 to 9.8 arrobas ha⁻1 yr⁻1 while reducing required grazing area by >50%. Risk remains contained, with negative gross margin occurring in only 0.25% of iterations and negative total profit in 15.55% of iterations. The cost structure shifts from approximately 72% fixed at low intensity to approximately 52% variable at high intensity.

 Acknowledgments

The authors gratefully acknowledge the support provided by the Luiz de Queiroz Foundation for Agrarian Studies (FEALQ) and the Center for Advanced Studies on Applied Economics (CEPEA) at the Luiz de Queiroz College of Agriculture, University of São Paulo (ESALQ/USP), for their valuable collaboration and data resources during the doctoral research phase. The first author also acknowledges the São Paulo Research Foundation (FAPESP) for the postdoctoral fellowship at the Sustainable Tropical Agriculture Center (STAC-USP), University of São Paulo, which enabled the continuity and expansion of this work. The authors further acknowledge the collaborative environment fostered by the ONEBEEF – Animal Protein Research Center (Minerva Foods, FAPESP, and USP initiative), for which Professor Sergio de Zen serves as Principal Investigator, for providing constructive academic interaction and technical insights. The opinions expressed in this article are solely those of the authors and do not necessarily reflect the views of FEALQ, CEPEA, FAPESP, and Minerva Foods. The authors assume full responsibility for any errors or omissions.

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All essential data generated or analyzed during this study are included in this published article. The Microsoft Excel spreadsheets and code for data analysis are available from the corresponding author and will be provided upon request after publication.

Publication costs were supported by the Luiz de Queiroz Foundation for Agrarian Studies (FEALQ), Piracicaba, São Paulo, Brazil. The research underlying this article received no specific funding from public, commercial, or not-for-profit funding agencies. FEALQ had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.