Development of a calculation model and production cost index for feedlot beef cattle

Sartorello, Gustavo Lineu; Bastos, João Paulo Sigolo Teixeira; Gameiro, Augusto Hauber

doi:10.1590/rbz4720170215

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Animal Production Systems and Agribusiness • R. Bras. Zootec. 47 • 2018 • https://doi.org/10.1590/rbz4720170215 copy

Development of a calculation model and production cost index for feedlot beef cattle

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The objective of this study was to develop a feedlot beef cattle calculation model and production cost analysis and, from the results obtained, devise a production cost index. A case study was conducted to understand the characteristics of the productive processes of a commercial feedlot. Then, based on the Economic Theory, cost items of the farm under analysis were identified and transferred to a spreadsheet. The survey included ten feedlot farmers from the state of São Paulo and other nine from the state of Goiás and was carried out to determine representative properties, and prices of items used were monitored. Production costs of each farm were calculated, and theoretical concepts of index numbers were used to devise the feedlot cattle production cost index. The cost allocation scheme was divided into four cost groups: variable, semi-fixed, fixed, and production remuneration factors. The developed model allowed a cost prognosis of the analyzed systems. Highest total costs for São Paulo State feedlots were R$ 9.17 kg⁻¹ and R$ 9.08 kg⁻¹ for average-sized and large farms, respectively, as contrasted to that of Goiás, of R$ 8.29 kg⁻¹. Between the months April and June, the cost of production for feedlot beef cattle showed reductions of 1.48 and 1.40% for the average and large feedlots in the State of São Paulo and 9.13% for the Goiás feedlot by the Konüs Exact Index, respectively. Studies available in literature were compared and it was concluded that the model can help feedlot cattle farmers take production decisions. The Konüs Index allows for a methodological advancement in relation to other studies carried out on the Brazilian livestock industry; besides, it can contribute to the sector organization.

Key Words
economic indicators; economy; livestock; mathematical model; production systems; survey

Equation	Equation number
$I C B C_{t} = \frac{C D B_{p^{t} q^{t}}}{C D B_{p^{b} q^{b}}}$	1
$C T_{t} = C V_{t} + C S F_{t} + C F_{t} + C O_{t}$	2
$C V_{t} = \sum_{i} C I_{i t}$	3
$C I_{i t} = Q I_{i t} \times P I_{i t}$	4
$C S F_{t} = γ \times \sum_{s} F I_{s t}$	5
$F I_{s t} = Q F_{s t} \times P F_{s t}$	6
$C F_{t} = C m a o_{t} + C d e p_{c t} + C m a n_{c t} + C o u t_{t}$	7
$C d e p_{c t} = \frac{V a q_{c t} - V r e s_{c t}}{ν u_{c}}$	8
$V r e s_{c t} = V a q_{c t} \times τ_{c}$	9
$C m a n_{c t} = V a q_{c t} \times σ_{c}$	10
$C O_{t} = C O G_{t} + C O I_{t} + C O A_{t}$	11
$C O G_{t} = C O G a n_{t} + C O G a l i_{t} + C O G o u t_{t}$	12
$C O G a n_{t} = C V a q a_{t} \times ({(1 + j)}^{δ} - 1)$	13
$C O G a l i_{t} = C V a l i_{t} \times ({(1 + j)}^{\frac{δ}{2}} - 1)$	14
$C O G o u t_{t} = C O E_{t} - C V a q a_{t} - C V a l i_{t} \times ({(1 + j)}^{\frac{δ}{2}} - 1)$	15
$C O E_{t} = C V_{t} + C S F_{t} + C m a o_{t}$	16
$C O I_{t} = \sum_{c} A F_{c t} \times {(1 + j)}^{φ} - 1$	17
$C O A_{t} = A \times P A_{t}$	18
$C O T_{t} = C V_{t} + C S F_{t} + C F_{t}$	19
$C O P_{t} = C T_{t} - C V a q a_{t} - C V a l i_{t} - C V i m p_{t} - C O G a n_{t} - C O G a l i_{t}$	20
$C O P d_{t} = \frac{C O P_{t}}{Q D B_{t}}$	21
$Q D B = N A C \times ((1 - ε) \times δ + ε \times θ)$	22
$C T M d b_{t} = \frac{C T_{t}}{Q D B_{t}}$	23
$C T M_{t} = C T M d b_{t} \times δ$	24
$C T M a r p_{t} = \frac{C T_{t}}{Q a r p}$	25
$Q a r p = N A C \times (1 - ε) \times P C A$	26
$P C A = \frac{P V F \times α}{15}$	27
$C T M q p_{t} = \frac{C T M a r p_{t}}{15}$	28
$C D B_{t} = \frac{C T_{t} - C V a q a_{t} - C O G a n_{t}}{Q D B}$	29
$R A V_{t} = Q a r p \times P a r_{t}$	30

Acronym	Definition
ICBC_t	Feedlot cattle production cost index at moment t.
CDB_t	Cattle daily cost at moment t, in Reais (R$).
p^t	Prices p in period t (current).
t	Refers to the moment costs are being expressed, to be used on any date under analysis, in this case, current period (t).
p^b	Prices p in period b (basis).
b	Refers to the moment costs are being expressed, to be used on any date under analysis, in this case, basis period (b).
q^t	Quantity q consumed in current period (t) in units.
q^b	Quantity q consumed in base period (b) in units.
CT_t	Feedlot total annual cost regarding moment t, in Reais (R$).
CV_t	Feedlot activity variable annual costs regarding moment t, in Reais (R$).
CSF_t	Feedlot activity semi-fixed annual costs regarding moment t, in Reais (R$).
CF_t	Feedlot activity fixed annual costs regarding moment t, in Reais (R$).
CO_t	Feedlot activity annual opportunity costs regarding moment t, in Reais (R$).
i	Represents variable inputs: animals, animal feed, sanitary and identification managements, other variable costs, and variable taxes.
CI_it	Unit cost of input i used in feedlot activity regarding moment t, in Reais (R$).
QI_it	Amount of input i used in feedlot activity regarding moment t (in units or volume).
PI_it	Price of input unit i at moment t (per unit or volume in Reais – R$).
γ	Number of months a year when feedlot activities were held.
s	Represents semi-fixed factors: electricity, telephone and internet services, fuel, and other semi-fixed costs.
FI_st	Cost of semi-fixed input s used in feedlot activity regarding moment t, in Reais (R$).
QF_st	Amount of semi-fixed input s regarding moment t (in units or volume per month).
PF_st	Unit price of semi-fixed input s at moment t (in Reais – R$, monthly by unit or volume).
Cmao_t	Fixed labor annual costs, including wages, and labor benefits and charges regarding moment t, in Reais (R$).
Cdep_ct	Annual depreciation cost of capital asset c at moment t, in Reais (R$).
c	Represents all items of capital assets that are involved in the activity, such as machinery, vehicles, equipment, buildings, facilities, and others.
Cman_ct	Annual maintenance cost of capital asset c at moment t, in Reais (R$).
Cout_t	Other annual fixed costs involved in the productive system, such as fixed taxes, regarding moment t, in Reais (R$).
Vaq_ct	Acquisition value of capital asset c at moment t, in Reais (R$).
Vres_ct	Residual value of capital asset c at moment t, in Reais (R$).
vu_c	Useful life of capital asset c, in years.
τ_c	Percentage of capital asset c after depreciation period (scrap value).
σ_c	Maintenance rate of capital asset c in percentage terms.
COG_t	Working capital annual remuneration regarding moment t, in Reais (R$).
COI_t	Fixed capital annual remuneration regarding moment t, in Reais (R$).
COA_t	Land use (area) annual remuneration regarding moment t, in Reais (R$).
COGan_t	Annual cost of animal working capital regarding moment t, in Reais (R$).
COGali_t	Annual feed working capital opportunity cost regarding moment t, in Reais (R$).
COGout_t	Annual opportunity cost of other working capital items regarding moment t, in Reais (R$).
CVaqa_t	Annual cost of purchase of lean cattle for fattening regarding moment t, in Reais (R$).
j	Daily interest rate to remunerate business, in percentage terms.
δ	Average number of days on which animals of a given batch were kept under feedlot conditions until sent for slaughter, in days.
CVali_t	Annual feed costs regarding moment t, in Reais (R$).
COE_t	Effective operational cost regarding moment t, in Reais (R$) per year.
AF_ct	Asset value (fixed assets) of capital asset c at moment t, represented by the initial value paid in Reais (R$).
φ	One-year interval, 365 days.
A	Area needed for feedlot activity, in hectares.
PA_t	Land lease value per hectare per year, in Reais (R$).
COT_t	Total operational costs regarding moment t, in Reais (R$) per year.
COP_t	Activity operational costs regarding moment t, in Reais (R$) per year.
CVimp_t	Variable taxes annual cost regarding moment t, in Reais (R$).
COPd_t	Daily operational costs regarding moment t, in Reais (R$).
QDB_t	Amount of cattle daily rates produced along the year under feedlot conditions regarding moment t, in units.
NAC	Number of feedlot cattle along the yearly feedlot cycle, per head.
ε	Mortality rate, in percentage terms.
θ	Average period in which animal mortality occurs, in days.
CTMdb_t	Average cattle daily cost regarding moment t, in Reais (R$).
CTM_t	Average total cost per head of cattle, regarding moment t, in Reais (R$).
CTMarp_t	Total average cost per arroba produced regarding moment t, in Reais (R$).
Qarp	Number of arrobas produced yearly during the feedlot period, in units.
PCA	Carcass weight of slaughtered animals, in arrobas.
PVF	Final weight before slaughter, in kg.
α	Carcass yield rate at the slaughterhouse, in percentage terms.
15	One fat cattle arroba (corresponding to 15 kg).
CTMqp_t	Total average cost per kg produced regarding moment t, in Reais (R$).
RAV_t	Annual animal sale income regarding moment t, in Reais (R$).
Par_t	Marketed fat cattle arroba price regarding moment t, in Reais (R$).

Item		Useful life (years)	Residual value (%)	Maintenance (%)
Machinery and vehicles
	Wheel loader	6-10	20	10
	Truck and tractor	10	20	10
	Feed distributor wagon and/or mixer wagon	10	20	10
	Cars and motorcycles	5	40	10
Equipment
	Stationary mixer	10	10	10
	Electronic balance	5	10	5
	Grain mill	5	20	20
	Converter	5	0	10
	Stationary generation	15	20	10
	Cattle chute	10	20	10
	Tools	5	0	0
	Traceability reader	5	0	5
Office material
	Computers and printers	5	0	10
	Air conditioning	5	0	10
	Radio communication system	5	0	10
	Tables, chairs, and refrigerators	5	0	5
	Fans	3	0	0
Buildings and facilities
	Pens	10	20	10
	Cattle handling facilities	10	20	10
	Animal feed factory and machinery shed	10	20	5
	Administrative office	20	20	10
	Employees’ housing	20	10	5
Others
	Working animals	10	0	0

	SPFa¹ 1 Representative average production capacity feedlot for the state of São Paulo (SP).	SPFl² 2 Representative large-production capacity feedlot for SP.	GOF³ 3 Representative feedlot for the state of Goiás.
Animals per pens (units)	150	120	160
Width (m)	48.00	36.00	49.60
Depth (m)	40.63	50.00	33.87
Pens (units)	12	118	66
Bunk line (units)	2	10	7
Treatment track width (m)	8.00	8.00	8.00
Distance between wedges (m)	2.00	2.00	2.00
Wedges (units)	720	6,401	3,924
Stretcher wedges (units)	48	472	264
Non-electrified fence wires (units)	5	5	5
Galvanized barbless wire (km)	5.30	50.20	26.90
Barbless wire, electrified wire (km)	1.10	10.00	5.40
Trough line wire rope (units)	2	2	2
Wire rope (km)	1.10	8.50	6.50
Bunk (m)	560.00	4,242.00	3,255.00
Water bunk (units)	12	118	66
Water reservoir (in thousands of L)	210	1,700	1,300
Concreted trough area (in thousands of m²)	1.400	10.605	8.137
Pen cleaning (yearly)	0	2	1

	SPFa¹ 1 Representative average production capacity feedlot for the state of São Paulo (SP).	SPFl² 2 Representative large-production capacity feedlot for SP.	GOF³ 3 Representative feedlot for the state of Goiás.
Yearly production capacity (animals)	3,000	27,000	16,500
Feedlot area (ha)	10	30	30
Initial age (months)	26.0	24.0	22.0
Initial live weight (kg)	390.0	353.9	353.3
Final live weight (kg)	537.0	520.3	509.0
Daily weight gain (g)	1,547	1,616	1,573
Daily ration offer (kg of dry matter)	10.56	10.40	10.00
Carcass yield (%)	55.80	55.46	55.29
Feedlot days	95	103	99
Mortality (%)	0.31	0.47	0.34
Mortality period (days)	32	33	32
Number of employees (units)	3	25	15
Employees’ housing (units)	0.75	4.00	3.00
Number of working animals (units)	3	40	20
Animal feed factory (m²)	750	2,350	1,800
Administrative office (m²)	20	242	184
Machinery shed (m²)	0	360	100
Other facilities (m²)	0	50	50

Cost item		SPFa¹ 1 Representative average production capacity feedlot for the state of São Paulo (SP); feedlot days = 95.	SPFl² 2 Representative large-production capacity feedlot for SP; feedlot days = 103.	GOF³ 3 Representative feedlot for the state of Goiás; feedlot days = 99.
A - Variable costs
	1 Animal purchase	R$ 6.21	R$ 5.85	R$ 5.80
	2 Animal feed	R$ 1.95	R$ 2.04	R$ 1.52
	3 Sanitary management	R$ 0.01	R$ 0.03	R$ 0.04
	4 Identification management	R$ 0.02	R$ 0.02	R$ 0.02
	5 Other variable costs	R$ 0.02	R$ 0.06	R$ 0.03
	6 Variable taxes	R$ 0.20	R$ 0.36	R$ 0.18
	Subtotal A - Variable costs	R$ 8.41	R$ 8.36	R$ 7.59
B - Semi-fixed costs
	7 Electricity	R$ 0.01	R$ 0.01	R$ 0.01
	8 Telephone and internet services	R$ 0.00	R$ 0.00	R$ 0.00
	9 Fuel	R$ 0.03	R$ 0.04	R$ 0.04
	10 Other semi-fixed costs	R$ 0.01	R$ 0.01	R$ 0.01
	Subtotal B - Semi-fixed costs	R$ 0.05	R$ 0.06	R$ 0.06
C - Fixed costs
	11 Labor	R$ 0.04	R$ 0.10	R$ 0.09
	12 Depreciation	R$ 0.15	R$ 0.11	R$ 0.10
	13 Maintenance	R$ 0.19	R$ 0.14	R$ 0.14
	14 Other fixed costs	–	–	–
	Subtotal C - Fixed costs	R$ 0.38	R$ 0.35	R$ 0.33
D - Cost of remuneration factors
	15 Working capital remuneration	R$ 0.25	R$ 0.27	R$ 0.24
	16 Fixed capital remuneration	R$ 0.07	R$ 0.05	R$ 0.05
	17 Land remuneration	R$ 0.01	R$ 0.00	R$ 0.00
	Subtotal D - Factor income	R$ 0.33	R$ 0.32	R$ 0.29
E - Effective operational cost		R$ 8.50	R$ 8.52	R$ 7.75
F - Total operational cost		R$ 8.84	R$ 8.63	R$ 7.99
G - Total costs		R$ 9.17	R$ 9.08	R$ 8.29
H - Daily operational cost⁴ 4 R$ day−1.		R$ 1.71	R$ 1.52	R$ 1.52
I - Cattle daily cost⁴ 4 R$ day−1.		R$ 8.67	R$ 8.44	R$ 6.47
Amount received⁵ 5 R$ kg−1.		R$ 8.57	R$ 8.57	R$ 7.77

Farm	April⁴ 4 Base month.	May	June
SPFa¹ 1 Representative average production capacity feedlot for the state of São Paulo (SP).	100.00	100.00	98.52
SPFl² 2 Representative large-production capacity feedlot for SP.	100.00	99.88	98.60
GOF³ 3 Representative feedlot for the state of Goiás.	100.00	96.21	90.87

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[1] * Corresponding author: gameiro@usp.br

A - Variable costs (CV)
	1 Animal purchase
	2 Animal feed
	3 Sanitary management
	4 Identification management
	5 Other variable costs
	6 Variable taxes
B - Semi-fixed costs (CSF)
	7 Electricity
	8 Telephone and internet services
	9 Fuel
	10 Other semi-fixed costs
C - Fixed costs (CF)
	11 Labor
	12 Depreciation
	13 Maintenance
	14 Other fixed costs
D - Remuneration factors (CO)
	15 Working capital remuneration with:
		15.1 Animals
		15.2 Animal feed
		15.3 Other items
	16 Fixed capital remuneration
	17 Land remuneration
E - Effective operational cost - COE (A + B + 11)
F - Total operational cost - COT (A + B + C)
G - Total costs - CT (A + B + C + D)
H - Daily operational cost - COPd (CT − 1 − 2 − 6 − 15.1 − 15.2)
I - Cattle daily cost - CDB (CT − 1 − 15.1)