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ANIMAL PRODUCTION |
* Departments of Animal Sciences and
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Agricultural and Consumer Economics, University of Illinois at Urbana-Champaign, Urbana 61801; and
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Carthage Veterinary Service, Ltd., Carthage, IL 62321
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Abstract |
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 Top Abstract INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
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Key Words: economic • net present value • sow longevity • swine • voluntary replacement
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INTRODUCTION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
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). Sows are replaced, on average, by the third or fourth parity (D’Allaire et al., 1987; Boyle et al., 1998) through involuntary and voluntary culling practices. Replacement decision making is a continual and complex process based on biological and economic considerations (Rajala-Schultz and Grohn, 2001). On the one hand, the longer a sow remains in a herd the greater opportunity to recuperate the initial cost and could result in larger and heavier litters, fewer nonproductive days, acquired immunity to diseases, greater salvage value, and lower replacements costs (D’Allaire and Drolet, 1999; Lucia et al., 2000; Stalder et al., 2003). On the other hand, the longer a sow remains in a herd the smaller the piglet revenues and sow salvage revenues relative to the initial sow replacement cost due to the discount rate.
It is important to economically assess the impact of replacing sows at different parities while the sow is subject to involuntary replacement. Burt (1965) proposed a model for optimal replacement of assets in an infinite planning horizon. Asset replacement was the only corrective action and net marginal productivity was a diminishing function with respect to age after some age. Schnitkey and Arbaugh (1989) applied this approach to evaluate replacement of dairy cattle. The objectives of this study were to identify the optimal average parity at replacement for 3 sow replacement-salvage value scenarios in US breed-to-wean herds using Burt’s approach (Burt, 1965), to characterize the optimal parity using multiple economic indicators, and to identify the biological and economic variables that influence the optimal parity at replacement and economic indicators using sensitivity analyses.
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MATERIALS AND METHODS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
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proposed to compute the capitalization of the weighted average of expected net revenues into perpetuity for an infinite planning horizon, V(T), using the formula:
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where T = planned replacement parity; pt = probability that a sow in parity t will survive to parity t+1 with normal productivity; ß = 1/(1+i), and i is the discount rate; CT = voluntary replacement cost of a sow after parity T; Rt = conditional expected value of net sow revenue in parity t = ptHt – (1 – pt)Dt; Ht = net revenue of a sow in absence of replacement costs due to involuntary culling in parity t; Dt = replacement cost of a sow due to involuntary culling in parity t; wt = weight at parity t determined by the discounting and survival probability
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pu = probability that a sow in parity u will survive to parity u+1 with normal productivity; and the product of pu is the Kaplan-Meier estimate of survival to time t.
Input Variable Values and Sensitivity Analysis
The input values for the biological variables in the Burt (1965) formula were based on the data and results reported by Rodriguez-Zas et al. (2003) using sow longevity records from 148,568 sows in 32 breed-to-wean herds from central Illinois obtained from January 1995 to May 2001. Accordingly, the calculations in this study target breed-to-wean swine operations. The biological inputs used in the model were removal rate per parity, litter size at weaning, and number of parities per year. The base number of parities per year value was 2.2 and the base litter sizes at weaning across parities are provided in Table 1. Records from the first 10 parities only were considered because only a small proportion of herds had records from parities greater than 10 (Rodriguez-Zas et al., 2003). Sensitivity of the results to these biological inputs was evaluated by augmenting the base litter size by 1.1- and 1.3-fold and by changing the base number of parities per year by 0.9- (2 parities per year) and 1.1- (2.4 parities per year) fold (Table 2).
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In this study, death rate accounted for 3.5% of the herd per parity or approximately 7.26% per year (Rodriguez-Zas et al., 2003). This value is consistent with the 7.99% mean sow death percentage per year for US operations reported for the second quarter of 2005 in the PigCHAMP benchmarking summary (Olson, 2005). Locomotion problems and old age accounted, on average, for 5.4 and 7.9% per parity or 11.9 and 17.4% per year, respectively (Rodriguez-Zas et al., 2003). Fertility, reproduction, and litter performance, and disease accounted for 17.5, 7.6, 4.6, and 11% of the herd per parity, respectively, and there was no recorded information on removal rate based on lifetime performance (Rodriguez-Zas et al., 2003). All previous removal rates are consistent with the review of removal rates across multiple studies reported by D’Allaire and Drolet (1999).
The economic inputs used in the model were discount rate, revenue per piglet weaned, sow replacement cost, sow salvage value, building and equipment costs per sow, and yearly interest for buildings. The sow replacement cost assumes that gilts purchased for replacement are bred shortly after being purchased. Sows can be removed from the herd at any time between being purchased and parity 10. A single salvage value for all sows was assumed and represents an approximate average salvage value of light and heavy sows. An evaluation of the difference in salvage value between the few lightest and heaviest sows studied by Rodriguez-Zas et al. (2003) showed no effect of differential sow salvage value on optimal parity at replacement.
Two sow-related inputs, sow replacement cost and sow salvage value, were considered instead of a single net replacement value because the lapse of time between purchase and removal of the sow can have a substantial impact on the economic indicators, and also because of the flexibility to study divergent changes in both inputs. The base economic inputs values (in US$/sow), excluding taxation, were: 10% discount rate; $500 yearly costs per sow (e.g., veterinary treatment, insemination, feed); $40 revenue per piglet weaned; $250 replacement cost per sow; $150 salvage value per sow; $1,100 building and equipment costs per sow space; and $50 yearly interest for buildings. The base values for discount rate, net revenue per piglet, sow replacement cost, and sow salvage value are consistent with values used by Stalder et al. (2003) and Lacy et al. (2005).
Sensitivity analysis was performed for all economic input variables to characterize the impact of these inputs on the optimal parity at replacement. Table 2
summarizes the changes in the input values used for sensitivity analysis. The minimum and maximum discount rates considered were 5 and 15%. The minimum and maximum revenue per weaned piglet studied were $30 and $50. The minimum and maximum salvage values evaluated were $100 and $200 per sow. The minimum and maximum sow replacement costs considered were $150 and $350 per sow. The optimal parity at replacement was identified via a search over the 10 (1 to 10) possible parities. This search was performed for each combination of biological and economic input levels studied, excluding cases where sow salvage value exceeded sow replacement cost.
Economic Output Indicators
Economic indicators of profitability associated with the optimal parity of replacement were computed. A detailed description of the indicators is provided in Barry et al. (2000). Briefly, the net present value is defined as the difference between the present value of income and costs including depreciation. These computations encompass the initial cost of buying gilts and the discounted sales and costs per parity weighted by the probability of surviving that parity until the optimal parity was reached. The annuity equivalent was computed on the cumulative net present value of net returns adjusted for the number of parities per year. The internal rate of return and marginal or modified internal rate of return were computed on the net present value of the net returns, assuming that the finance discount rate was equal to the refinance discount rate. The internal rate of return is the interest rate that makes net present value of all cash generated and expended (including depreciation) equal to zero and assumes the cash flows from a project are reinvested at the internal rate of return. The modified internal rate of return assumes that all cash flows are reinvested at the enterprise cost of capital.
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RESULTS AND DISCUSSION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
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, 3, and 4). The optimal parity for the base situation was 5 parities in the LRNS scenario (Table 2) and 4 parities in the HRNS and HRYS scenarios with high replacement rates (Tables 3 and 4). The optimization results suggest that current culling practices result in maximum or close to maximum profit because sows in US breeding herds are on average replaced by the third or fourth parity (D’Allaire et al., 1987; Boyle et al., 1998).
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reported (based on 1996 to 2000 average production levels, segregated early weaning pig price, production costs, and equity values) that a replacement gilt must remain in the breeding herd for at least 3 parities before reaching a positive net present value. For base input values, Huirne et al. (1991) found that the average herd life (or sow life in the herd) was 5.5 and 6.5 parities with and without voluntary disposal, respectively. Kristensen and Søllested (2004b) reported average age at removal of 5.46 and 6.33 parities under optimal removal decisions based on data from 2 Danish herds. Dhuyvetter (2000) concluded that 8 or 9 are the most economical parities to cull a sow based on projected budgets. The difference in optimal parity reported by the different studies may be due to the approach used to identify the optimal parity and the assumed input values. A major advantage of Burt’s approach (Burt, 1965) over other approaches is the focus on a continuous operation and optimization of returns per fixed unit of time, thereby accounting for the opportunity cost of sow space.
The difference in economic indicators between the 3 involuntary replacement scenarios was partly due to the optimal number of parities and also to the net profit per parity. For example, the net present value of the LRNS scenario was nearly 8 times greater than the net present value of the HRNS scenario. The inclusion of salvage value for culled sows in the HRYS scenario (Table 4) did not change the optimal parity when compared with the HRNS scenario (Table 3); however, there was an improvement in the economic indicators and LRNS scenario still had greater economic indicators of all scenarios. For the base situation and LRNS scenario, the average net present value across the first 4 parities was $37 and $21 greater than the HRNS and HRYS scenarios, respectively. The additional difference amounted to $83 and was mainly due to the fifth parity that was unique to the LRNS scenario.
Discount Rate, Litter Size, and Parities Per Year.
The range of discount rates, litter sizes, and parities per year considered in this study did not influence the optimal parity at replacement within removal scenario when compared with the base situation (Tables 2, 3, and 4). However, these variables influenced the economic indicators and in general, the greatest impact occurred in the LRNS scenario. The discount rate had the smallest influence on the net present value of all 3 variables. High (low) discount rates reduced (increased) the economic indicators and the effect of changing discount rate was greater in the low replacement rate scenario than the high replacement rate scenarios (Tables 2, 3, and 4). The difference between the lowest and greatest discount rates resulted in a $56 increase in the net present value in the LRNS scenario and only $29 in the HRNS and HRYS scenarios. There was a nearly monotone and negative trend of net present value vs. the 3 discount rates values studied across all the replacement rate scenarios considered (Tables 2, 3, and 4). This trend was also observed in the annuity equivalent values.
Greater litter size values resulted in better economic indicators (net present value, annuity equivalent, internal rate of return, modified internal rate of return) than lower litter sizes due to the greater profitability from weaning more piglets for the same revenue per piglet. Improving litter size at weaning had the greatest impact on the HRNS scenario; a 10% increment in litter size at weaning from the base scenario corresponded to a 4-fold increase in the net present value. Litter size can compensate for the impact of replacement rate on profitability. For the range of input variables considered in this study, a similar absolute net present value (approximately $430) can be obtained with a 1.1 fold increase in litter size from the base case in the LRNS scenario and with a 1.3 fold increase in litter size in the HRYS scenario (Tables 2 and 4). Based on the high net present value, annuity equivalents, internal rate of return, and modified internal rate of return, the investment on a sow breeding enterprise with optimal average parity at removal is favored over other investments at 10% interest rate involving a similar risk profile, regardless of replacement-rate salvage value scenario when the litter size is approximately 1.1 times the base case and all other input variables are at the base level.
Increasing the number of parities per year increased the net revenue and consequently, all economic indicators (net present value, annuity equivalent, internal rate of return, modified internal rate of return). Reducing the number of parities per year from the base scenario reduced the economic indicators and a negative net present value occurred in the HRNS scenario. Increasing the number of parities per year from the base scenario improved the economic indicator by 32% in the LRNS scenario, 158% in the HRNS scenario, and 60% in the HRYS scenario. The main effect of increasing the number of parities per year was to increase the weighted net income from latter parities because the fixed costs per parity are reduced and future value from latter parities is discounted less when the number of parities per year is increased. Based on the high net present value, annuity equivalents, internal rate of return, and modified internal rate of return, the investment on a sow breeding enterprise with optimal average parity at removal is favored over other investments at 10% interest rate involving a similar risk profile, regardless of replacement-rate salvage value scenario when the number of parities per year is approximately 2.2 and all other input variables are at the base level. Stalder et al. (2003) observed that number of parities was sensitive to litter size at birth. Three parities were required to obtain a positive net present value with a base number of 10.1 piglets born alive per litter adjusted by parity (Stalder et al., 2003). A decrease of 0.5 piglets at birth increased the number of parities to 4 parities and an increase of 0.5 piglets resulted in zero net present value in the third parity (Stalder et al., 2003).
Revenue Per Piglet Weaned.
Changes in the revenues per weaned piglet had a variable influence on the optimal parity; however, this input consistently had high influence on the economic indicators. For the range of input values considered, only the increase in revenues per piglet from $30 to $40 lowered the optimal parity by 1 in the LRNS and HRYS scenarios (Tables 2 and 4). The $30 revenue per piglet resulted in negative net present value and annuity equivalent across all scenarios (Tables 2, 3, and 4). Increasing the revenues per piglet from $40 to $50 (and keeping all other variables at base level) resulted in no change in optimal parity within involuntary replacement scenario; however, the net present value increased by approximately $278 in both high replacement scenarios and by $381 in the low replacement rate scenario (Tables 2, 3, and 4). In the $40 and $50 revenue per piglet levels, the increase in net present value (Tables 3 and 4) in the HRYS (– $241 and $381 for the $40 and $50 levels, respectively) compared with the HRNS (– $173 and $3,161 for the $40 and $50 levels, respectively) was approximately $66. The $278 increase in net present value associated with increase in revenues per piglet from $40 to $50 in the HRNS scenario was due to the additional $10 per piglet spread across the expected 27.8 piglets from all first 4 parities in the base scenario. The additional $64 in net present value received in the HRYS scenario compared with the HRNS scenario (both at revenues of $40 and $50 per piglet) were due to the sow salvage value received in the first scenario (Tables 3 and 4). Based on high net present value, annuity equivalents and levels of internal rate of return and modified internal rate of return, investment on a sow breeding enterprise with optimal average parity at removal is favored over other investments at 10% interest rate involving a similar risk profile, regardless of replacement-rate salvage value scenario when the revenue per weaned piglet is approximately $50 (or greater) and all other input variables are at the base level.
Sow Replacement Cost and Salvage Value.
Sow replacement cost and salvage value had a substantial impact on the average optimal parity of replacement (Tables 2, 3, and 4). For the LRNS and HRNS scenarios, the range in salvage value considered was associated with a decrease in optimal parity by 2 parities and for the HRYS scenario with a decrease in optimal parity by 1. The 1-parity reduction in the HRYS scenario was due to applying the same increase in salvage value to both the involuntary and voluntary removal; meanwhile, in the other 2 scenarios only the voluntary removals estimated using Burt’s formula (Burt, 1965) receive salvage value. Thus, the impact of increasing salvage value for all voluntary replacements (and involuntary replacements in HRYS scenario) was greater in the scenarios with no salvage value for involuntary removals. The benefit from an increase in salvage value from $150 to $200 was greater in the LRNS scenario than in the HRNS scenario because of the additional revenues per piglet resulting from the additional parity in the first scenario.
The impact of increasing the sow replacement cost was opposite to that of increasing the sow salvage value (Tables 2, 3, and 4). For the high involuntary replacement scenarios, the increase in optimal parity with sow cost had a nonlinear trend. The greatest increase in optimal parity (3 parities) was associated with increases in sow cost from $150 to $250 (base case). This trend plateaued as the increase in optimal parity was only 1 parity with a further increase in sow cost from $250 to $350. For the low involuntary replacement scenario, the increase in optimal parity was linear for the range of sow costs considered. The difference in correlation between optimal parity and sow cost among involuntary replacement scenarios is linked to the absolute optimal parity values because the low replacement scenario has greater optimal parities; thus, the cost of replacing a sow is distributed among more parities and a longer interval than the high replacement scenarios.
Sow salvage value and sow cost had the largest influence on the optimal parity, but had typically minor effects on the economic indicators. The greatest changes in the economic indicators were linked to changes in the sow replacement cost. All the sow costs for the low replacement rate scenario and the base sow cost for the high involuntary replacement scenarios resulted in positive net present value. For the low replacement scenario, the net present value at replacement costs of $250 and $350 per sow cost were similar; however, the optimal parity differed by 2 parities. The lowest and greatest sow cost considered in this study resulted in negative net present value in the high replacement scenarios. A $200 increase in sow cost was associated with an increment of the optimal parity by 4 parities in all scenarios (Tables 2, 3, and 4). However, this change had a relatively small influence on the economic indicators and the greater optimal parity associated with high sow replacement costs resulted in negative net present value in the high involuntary replacement scenarios. Even though the situations with the greater optimal parity generally had greater economic indicators reflecting the extra benefit of increased number of parities, the greater optimal parity associated with high sow replacement costs was associated with negative net present value because this cost could not be absorbed by the additional parity in the 2 high involuntary replacement scenarios. The lowest and greatest sow cost considered in this study resulted in negative net present value in the high replacement scenarios due to the extremely low and high optimal parity in these scenarios. For the low involuntary replacement scenario, the similarity in net present value between the $250 and $350 sow cost cases is due to compensation in the increase in sow cost by an increase in the optimal parity, and associated returns per piglet adjusted by the discount rate.
The apparent contradiction in greatest salvage values associated with lowest net present value seen in all replacement scenarios was due to a low optimal parity at replacement. A similar contradiction was observed between greatest sow costs and greatest net present value in the LRNS and HRYS scenarios and was also due to an elevated optimal parity at replacement. This contradiction was not observed in the HRNS scenario because the increase in optimal parity at replacement was insufficient to compensate the high sow replacement cost. The difference in the relationships between optimal number of parities and net present value in the high and low involuntary replacement scenarios was due to the relative contribution of revenue per piglet and net sow costs (replacement cost – salvage value) such that net present value increases in situations when litter returns have a greater contribution to the net present value than the net sow cost.
Based on high net present value, annuity equivalents, internal rate of return, and modified internal rate of return, the investment on a sow breeding enterprise with optimal average parity at removal was favored over other investments at 10% interest rate involving a similar risk profile. This result was observed for all the sow salvage value and replacement cost cases studied in the low involuntary replacement scenario, for all the salvage value and base replacement cost in the high replacement with salvage value scenario, and for the lowest salvage value in the high replacement with no salvage value scenario with all other input variables at the base level. Overall, the trends in internal rate of return and modified internal rate of return indicated that the swine enterprise would be favored over alternative investment with a 10% interest rate involving a similar risk profile for the vast majority of the LRNS scenario cases (Table 2) followed by the majority of the HRYS scenario cases (Table 4) followed by many of the HRNS cases (Table 3). The only unfavorable scenario in the LRNS scenario was when the revenue per piglet was $30 at the optimal parity and all the other inputs were set to the base case. Unfavorable cases with the HRYS scenario were 5% discount rate, 2 parities per year, and sow costs of $150 and $350 at the respectively optimal parity, and all the other inputs were set to the base case. The internal rate of return and modified internal rate of return of the base moderate sow costs ($250) were more favorable than the low sow cost ($150) because the optimal parity dropped from 4 parities to 1 parity.
Multiple Input Changes
Some biological and economic inputs are able to compensate limitations in other determinants of profit; however, the relationship among all the components is complex. Simultaneous changes in revenue per piglet weaned, sow replacement cost, and sow salvage value had dramatic influences on the optimal parity (Table 5) and net present value (Table 6).
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). This high involuntary optimal parity also resulted in the most negative net present value values within this replacement scenario.
The lowest optimal parity was 1 parity and occurred in the high involuntary replacement scenarios when the net replacement value (sow salvage value minus sow cost) was zero at sow costs of $150 or $250 (Table 5). For the LRNS scenario, the minimum optimal parity also occurred at zero net replacement value, however the optimal parity varied between 2 and 3 parities. The salvage value has a similar effect to sow cost in that reducing the salvage value typically increased the optimal parity. Decreasing the net replacement value by $100 (by increasing the sow cost by $100 or decreasing the sow replacement by $100) caused the optimal parity to increase by 2 to 4 parities in all the replacement rate scenarios. The latter increases in optimal parity associated with a less favorable net replacement value could be reduced by 1 parity, by increasing the revenue per piglet from $30 to $40. Revenue of $50 per piglet did not offer additional benefits in terms of reducing the optimal parity; however, the extra revenue increased the net present value and annuity equivalent.
A revenue of approximately $40 per piglet or greater was necessary for the enterprise to remain profitable for the range of sow costs considered. Increases in the revenues per piglet weaned helped overcome the high optimal parity associated with the nonpositive net replacement values in the LRNS scenario. This did not have a major impact on the optimal parity on the high involuntary replacement scenarios (Table 5). When the difference between sow cost and salvage values was zero, changes in revenues per piglet had no influence on the optimal parity.
Low revenues per piglet resulted in negative net present value except for low sow cost in the LRNS scenario. Not even particularly high (>$200 per sow) salvage values were able to result in positive net present value for the HRYS scenario. High sow costs typically resulted in negative net present value especially for the high involuntary replacement scenarios and were partly mitigated by high revenues per piglet. The influence of high sow costs in high replacement rate situations was mitigated when salvage value was obtained for the culled sows.
The impact of revenue per piglet on profitability found in this study was also observed by Huirne et al. (1991), Jalvingh et al. (1992), and Stalder et al. (2003). However, this factor had a smaller impact on the optimal parity at removal compared with sow replacement cost and salvage value in this study. Huirne et al. (1991) found that a 20% reduction in feeder pig price reduced the average herd life by 0.1 parities and that a 20% increase had no effect on average herd life. Jalvingh et al. (1992) reported that a 20% reduction or increase in feeder pig price changed the average culling rate by 0.9 and 0.8% respectively. In this study, greater revenues per piglet were able to offset high replacement costs (sow cost – salvage value) such that optimal parity decreased with greater revenues.
Increments in the sow cost increased the optimal parity; however, this increase in optimal parity (Table 5) did not always translate into increased net present value at the optimal parity (Table 6). The actual relationship between optimal parity and net present value depended on the replacement scenario and revenue per piglet considered. In the low replacement rate scenario and for revenue per piglet of $40 or $50, increments in optimal parity at replacement resulted in increased net present value in general. In contrast, for the high involuntary replacement scenarios, high sow costs resulted in greater optimal parity, but lower net present value in general.
The complex relationships among the economic indicators stem from the different impacts of revenue per weaned piglet, sow cost, salvage value, and optimal parity. In high involuntary replacement scenarios, the general trend was to favor investments with low sow replacement costs when the same optimal parity was obtained except when the net replacement value was zero. For the low involuntary replacement scenario, the increases in sow cost considered always resulted in increases in optimal parity and consequently in net present value.
Replacement costs constitute one of the greatest costs of a herd, increase the capital requirements for the operation, and thus reduce profitability. Plá et al. (2003) also noted that sow cost and salvage value were a major difference when performances of operations were compared with simulated values. Faust et al. (1993) reported that the cost of replacements had a large effect on different swine breeding structures, and structures with low replacement rates could absorb greater replacement costs than those with high replacement rates. Thus, improving sow longevity would reduce the costs associated with raising or purchasing and acclimatization of replacement gilts, resulting in increased profitability (Stalder et al., 2004).
Results from this study confirmed the importance of sow replacement cost and sow salvage value on parity at optimum replacement and profitability. Huirne et al. (1991) and Jalvingh et al. (1992) reported that sow cost and salvage value impacted the optimal parity at removal. Huirne et al. (1991) also reported that increasing the salvage value by 20% or decreasing the sow cost by 20% reduced the average by 0.9 and 1.2 parities, respectively. In contrast, decreasing the salvage value by 20% or increasing the sow cost by 20% increased the average by 0.6 and 0.5 parities, respectively (Huirne et al., 1991). Jalvingh et al. (1992) reported that if the salvage value was increased by 20% or the sow cost was decreased by 20%, the optimal culling rate of 47.4% reduced to 45.8 and 45.6%, respectively. If the salvage value was decreased by 20% or the sow cost was increased by 20%, then the culling rate increased to 50.7 and 51.5%, respectively (Jalvingh et al., 1992). Stalder et al. (2003) observed that an increase of 25% in gilt replacement cost from the base cost required an additional parity to obtain a positive net present value using a 9% discount rate. Similarly, a 25% decrease in replacement cost resulted in a drop of 1 parity to obtain a positive net present value, although a 12.5% decrease resulted in almost zero net present value (Stalder et al., 2003).
Replacement Decisions
Producers exercise control over sow replacement rates excluding the involuntary removal cases. Culling decisions are based on economic considerations (Rajala-Schultz and Grohn, 2001) and can have a profound effect on the profitability of the farm (Plá et al., 2003). Further challenges are long-term genetic and management goals, intensification of production, rapid fluctuations of the national and international markets and production methods, increase of competitiveness, and the reduction of marginal profits. The biological and economic responses to changing production conditions, and in particular the potential impact of replacement practices, must be considered to maximize the profit-ability of the enterprise (Plá et al., 2003).
Voluntary culling rates influence profits, and both voluntary culling rates and profits are influenced by the amount of involuntary culling (Allaire and Cunningham, 1980). The replacement rate including voluntary and involuntary culling of breeding herd females in US commercial swine herds was approximately 50% and the average herd parity of culled sows ranged from 3.1 to 3.7 parities (Stalder et al., 2003). Likewise, Dijkhuizen et al. (1989) found that the annual culling rate in Dutch farms was 50%. Early culling practices reduce the opportunity of an average sow to produce returns that are greater than the replacement cost, thus reducing the profit from the investment in breed-to-wean operations. Late culling practices, although less common, can affect profitability when the revenue from the additional parities cannot compensate the decrease in production and discount rate.
Optimal Parity at Replacement Formula
The optimal parity approach employed in this study is based on dynamic modeling and includes the effects of biological and economic variables on the optimal average parity of replacement and associated profit (Burt, 1965). Dynamic modeling is based on the hypothesis that a sow should be kept in the herd as long as the marginal profit is greater than the expected average profit of a young replacement sow (Lehenbauer and Oltjen, 1998; Vargas et al., 2001). Dijkhuizen et al. (1986, 1990) used a dynamic programming model to compute the parity at which the average sow should be removed. Dynamic modeling approaches are suited to consider herd dynamics while accounting for different economic and biological inputs. Several mathematical models representing sow herd dynamics have been developed (e.g., Huirne et al., 1991; Jalvingh et al., 1992; Plá et al., 2003; Kristensen and Søllested, 2004a,b). The objective of these models is to maximize the net present value from current and replacement sows over a given decision horizon (Rajala-Schultz and Grohn, 2001). Most of these models were validated subjectively by comparing simulated results to observed data (Plá et al., 2003; Kristensen and Søllested, 2004a,b).
The formula used in this study to identify the optimal parity at replacement was suitable for the data and scenarios considered. However, the formula could be extended to accommodate other situations. For example, the formula used in this study assumed a single salvage value regardless of weight because market differences did not have a substantial impact on the optimal parity or net present value. The proposed approach can be easily extrapolated to incorporate multiple sow salvage values that depend on weight. In addition, Burt’s formula (Burt, 1965) does not model the potential gains due to genetic progress. No other published mathematical models representing sow herd dynamics (Huirne et al., 1991; Jalvingh et al., 1992; Plá et al., 2003; Kristensen and Søllested, 2004a,b) have accounted for genetic gains. The economic impact of failing to account for genetic progress on the total net present value estimates is expected to be very small considering the time horizon of 10 parities studied here. The approach considered in this study assumed no limitation in the number of gilts available for replacement; however, replacement availability may be a limiting factor. Although the availability of replacement gilts may be difficult to quantify, Burt’s formula (Burt, 1965) could incorporate a cap in the percentage of sows available for voluntary replacement in the calculation of the net present value.
The replacement model used is a simplification of real breeding herd decisions. The model of Burt (1965) assumes that revenues and costs occur at the beginning of the parity and replacement occurs at the end of the parity. A model that partitions the parity into states (e.g., from conception to farrowing or abortion, from farrowing to weaning, from weaning to first service, interval between services) may offer a more detailed economic modeling of the sow breeding herd and help with specific voluntary replacement decisions including number of rebreeding attempts before culling. Plá et al. (2003) and Kristensen and Søllested (2004a,b) developed dynamic models that addressed these components of sow herd dynamics for a small number of European sow herds and scenarios. Based on the results from the sensitivity analyses in this study, the subdivision of the parity is unlikely to have a major impact on the optimal parity and may have minor influence on all the economic indicators of profitability.
The calculation of the net present value approach used by Stalder et al. (2003) and in this study considers the purchase of a gilt and the associated projected value of cash flows (revenues and expenses) to a predetermined stopping point. The difference in the optimal parity between our approach and that of Stalder et al. (2003) is the definition of the stopping point. The stopping point used by Stalder et al. (2003) was the occurrence of positive net present value. In this study, the stopping point was the optimum parity determined by Burt’s model (Burt, 1965) that considers an infinite planning horizon and assuming that a sow already exists and the purchase of the sow occurs only when the sow was culled after the optimal parity. The net present value approach to find an optimal parity requires the specification of a stopping rule because net present value will always increase with time until future returns have zero value.
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2 Corresponding author: rodrgzzs{at}uiuc.edu
Received for publication November 3, 2005. Accepted for publication April 9, 2006.
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