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Partial Budget Model for Reproductive Programs of Dairy Farm Businesses
Partial BUdget Model for Reproductive Programs of Dairy Farm Businesses P. J. HADY end J. W. LLOYD Population Medicine Center and Department of Agricultural Economics
J. B. KANEENE Population Medicine Center A. L. SKIDMORE Department of Animal Science Michigan State University East Lansing 48824 ABSTRACT
A partial budget model was developed to investigate the economic impact of management changes for the reproductive program of dairy farm businesses. The model is unique because 1) the herd is split into groups for first lactation and second or greater lactation; 2) each group's days open distribution is employed; 3) a lactation curve simulation is used to estimate a weighted average daily milk production; 4) the current days open distribution is altered by estimating changes in days to first AI, efficiency of estrus detection, and conception rate for the two lactation groups to predict the altered distribution of days open; and 5) the model provides a structure to estimate changes in expenses for labor, feed, supplies and services, and replacement heifers that may occur with the suggested management plan. A microcomputer program was designed based on the partial budget model to support decision making on the dairy farm pertaining to suggested management changes in the reproductive program. When applied to specific case farms, the results of the model indicate that, with improved reproductive efficiency of the milking group, the replacement population increases, and strategies may be required to manage an increased
Received January 11. 1993. Accepted August 16. 1993. 1994 J Dairy Sci 77:482-491
number of replacements. Sensitivity analysis was performed on milk price, feed, and replacement expenses. The case study results indicate that milk price and expenses of raising replacements may have the greatest impact within the partial budget model. (Key words: reproduction, economics, partial budget model) INTRODUCTION
Reproductive performance affects profitability of the dairy farm business through its influence on milk produced per cow per day, number of replacements produced, and rate of voluntary and involuntary culling (2). A profit function was developed and used to describe the relationship of the dairy cow to economical return for the dairy farm (6). This function established that maximum profit per day of herd life was expected for cows with first calving at 25 rna of age and maintained 124 d open and 42 d dry. Cumulative net income curves produced via a dynamic model of the dairy herd were affected by days open and infertility (3). These models, along with those in earlier works (9, 12), have validated that increased days open affects the profitability of the dairy farm business. Studies have described the impact of decreased reproductive performance by estimating a monetary value of an open day for dairy cows. Estimates vary from negative dollars per day in high production cows (1), to cents per day (14), to dollars per day open (8). The differences in these values are related to the different assumptions in 482
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
methods of accounting for outputs and production input costs. Partial budget models can be used to evaluate individual reproductive programs by examining only those expenses and revenues that change with a proposed plan or change in management (7). Reproductive programs for dairy farm businesses have been analyzed using partial budget models (5, 15). Those models predict changes in milk production because of increased reproductive performance using a linear regression equation (10) and estimate milk and calf production using average days open. However, the resulting estimates used in these partial budgets may be imprecise because 1) the accuracy of the milk production prediction equations is limited, as measured by R2 values from .19 to .35 (10); 2) separate equations should be used for first lactation cows and second or greater lactation cows because of the different shape of their lactation curves; and 3) average days open assumes normal distribution in days open of the pregnant cows in a herd, but days open of pregnant cows is seldom normally distributed in ordinary dairy herds. Finally, the expense portion of these partial budgets was poorly developed, and estimates of the expenses employed to decrease the average days open are incomplete. The goal of this study was to develop a partial budget model that would address the aforementioned weaknesses in estimating the economic impact of management changes within the reproductive program of individual dairy farm businesses. MATERIALS AND METHODS
A management decision can affect the profitability of an individual dairy farm's reproductive program in four ways. The management change can increase revenues, decrease expenses, increase expenses, or decrease revenues (Figure 1). These four increases or decreases in revenues or expenses make up the structure of a partial budget model. The analysis compares the current situation and an alternative scenario without consideration of the transition period between the two management schemes (4). Although the model is simple, identification of the elements that change with each management change and estimation of the
483
PARTIAL BUDGET COMPONENTS 1. 2.
INCREASE REVENUES DECREASE EXPENSES
3. 4.
DECREASE REVENUES INCREASE EXPENSES
[(Component 1) + (Component 2)] - [(Component 3) + (Component 4)] = Net Change in Partial Budget Figure I. Structure for partial budget analysis.
economic impact of these modifications can be difficult. Presented are revenue and expense changes identified for this particular partial budget application, which considers an improvement in reproductive performance. Use of the model to address management changes in a different situation should be expected to include different changing budget elements. Specifically, decreased reproductive performance would likely lead to changes opposite in direction for revenues and expenses to those presented here. Increased Revenues
Increased revenues within the reproductive program relate to milk and calf production. In conjunction with the days open distribution, a modified Woods equation (Appendix) was used to simulate lactation curves both for cows in first lactation and for cows in second or greater lactation to estimate a weighted average daily milk yield (11). The herd's age distribution was assumed to be constant. Days in milk, days pregnant, and coefficient A (Appendix) were calculated from the days open distribution and rolling herd average. Coefficients b, c, and g are those estimated from Oltenacu et al. (11) and shown in the Appendix. The days open distribution started at 40 d open and split each lactational group into 20-d intervals ending at 180 d open. Cows with days open greater than 180 d were averaged to summarize this segment of the distribution of days open. The percentage of cows in each interval was linked to the lactation Journal of Dairy Science Vol. 77, No.2, 1994
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curve simulation that was initialized with the individual herd's rolling herd average and days dry. Changes in days to first AI, efficiency of estrus detection, and conception rate for both lactational groups were estimated from the suggested management change in the reproductive program. These estimates were used to alter the current days open distribution and to change average daily milk production through a modification of the percentage of cows in each interval of the days open distribution. Milk price was used to convert the predicted change in weighted average daily milk production to change in milk revenues. The number of calves produced in a year was dependent on the distribution of days open. The partial budget model computes the difference in the number of calves born per year between the two scenarios via differences in the current and altered days open distribution. The total number of calves produced per year was computed using the weighted average of cows in each interval of the distribution. This value is divided by 2 to estimate the number of male and female calves. Change in revenues was estimated for male calves using the price received for them (Appendix), and female calves were placed in the replacement inventory. If total milking herd size is assumed to be constant, an adjustment of current days open distribution will change the number of female calves in the replacement enterprise. The number of female calves was altered by the replacement death rate (which represents total losses, including stillborn and culled calves) to predict the number of replacements available to enter the milking group. The revenues gained from an increased number of replacement heifers could be obtained either by selling these heifers or by increasing revenues from culled cows (Appendix).
that change conception rates. The total number of cows in the milking group, conception rates, number of conceptions per year, and average service (or AI) price were used to estimate breeding expense differences that were due to management change (Appendix). Decreased Revenues
No decreased revenues were identified in this partial budget model for improving reproductive performance. Increased Expenses
Increased expenses expected because of a management change in the reproductive program included feed expenses, labor expenses, replacement expense, and supplies and services. Methods for estimating these changes in ex.penses between the two scenarios were included in the partial budget model to allow for a complete analysis of reproductive cost to the business. Feed Expenses. Changes in feed expenses were due to the change in weighted average daily milk production in the herd and the length of time each ration was fed. Feed expenses were determined from farm prices of components used by the dairy farm, and nutritional software (13) was used to estimate the cost of feed per day on a dry matter basis. The model used these values for different ration groups in the milking herd. Groups consisted of high production, low production, 2-yr-old, early dry, and late dry cows. The number of days a cow remained in each group was used to estimate a weighted average feed cost per day per cow. This value was used to compute difference in annual feed cost for competing scenarios within the partial budget model (Appendix). Labor Expenses. Labor expenses were associated with the number of hours of labor Decreased Expenses used within the reproductive program. An Decreased expenses in the partial budget hourly wage rate was computed based on the model structure were used to compare the number of hours worked per week and total breeding expenses between the current and compensation for hourly and salaried emalternative scenarios. In some scenarios, ad- ployees. A weighted average wage rate was justment of the conception rate or services or computed for each labor category, hired or AI per conception might increase expenses. salaried, to take into account the segregation of The logic for placing the conception rate anal- labor that may occur in the reproductive proysis in this section of the model was to allow gram. The labor expense difference between for the uncomplicated analysis of scenarios the two scenarios is computed from the estiJournal of Dairy Science Vol. 77, No.2. 1994
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
mated change in number of hours per day that will be spent in the reproductive program (Appendix). Replacement Expenses. The number of female calves in the replacement enterprise is a direct result of reproductive management in the cow herd. The population of replacements in the partial budget model changed with the number of calves produced between the current and alternative scenarios. Changes in expenses because of a change in the population of replacements were calculated by the model. The model estimated variable expenses of the replacement enterprise to estimate the daily expense to raise a replacement. Feed expenses were computed by dividing the replacement enterprise into four groups by age: preweaning, growing, breeding, or postbreeding. These four groups are typically used by dairy farm businesses because of the nutritional differences among these types of animals. Feed cost per pound of dry matter and months to first calving were used by the model to estimate the number of animals in each group and to compute total feed cost for a replacement. Labor expenses were associated with labor time spent for feeding, detection of estrus, and manure and facility management. Time spent in each activity and the hourly wage rate were used to estimate the labor cost to raise a replacement. Supplies and services expenses related to replacements included cost of semen, bedding, medicine, vaccinations, and veterinary services. The total variable cost to raise a replacement was divided by days to first calving to estimate cost per day to raise a replacement. This value was used, along with the change in heifer inventories between the two scenarios, to estimate increased or decreased expenses that were incurred by the replacement enterprise because of a change in reproductive efficiency of the milking group. A default value was entered into the reproductive partial budget if the cost per day for replacement services was not known by the dairy farm business (Appendix). Supplies and Services Expenses. Supplies that were used in the reproductive program included the following: prostaglandin, aids for detection of estrus, progesterone tests, and
485
other types of reproductive aids. Services that were used in the reproductive program involved veterinary and consulting services. Expenses were estimated in the partial budget model as those expenses per pregnancy. The change in supplies and services occurred because the number of pregnancies per year changed between the two scenarios. With an increase in reproductive efficiency, more cows became pregnant during a year, which increased the annual expense for supplies and services (Appendix). To summarize, the model simulated the effects of a change of reproductive efficiency through a change in the current days open distribution. The model used lactation curve simulations for first lactation and for second or greater lactations to estimate change in weighted average daily milk between the current situation and the alternative scenario. The model compared revenues (milk sales, bull calf sales, cull cow, or replacement sales) and expenses (feed, labor. replacement, supplies, and services) associated with a suggested management change in the reproductive program. These elements of the partial budget and their estimates were used in the structure of the partial budget to calculate the net outcome of the suggested management change. Sensitivity analysis was performed in the model to evaluate changes in milk price, feed cost, and replacement cost. A computer program was developed from this model and was designed to operate on a microcomputer with 560K random access memory and requiring .75 MB for storage. Case StUdy Farm
A Holstein dairy farm located in central Michigan, milking approximately 300 cows, used the model to investigate a management change in its reproductive program. Lactating cows averaged 39.8 kg/d of milk with a 305-d mature equivalent of 12,553 kg. Milk fat content was 4.2%, and mean cow DHI somatic cell counts varied from 80,000 to 100,000 cells/ml. First lactation cows remained in one group for the entire lactation, and cows in second or greater lactation were divided into two groups by production and days in milk. Days dry averaged 58.3, and dry cows were split into two groups, early dry and late dry, Journal of Dairy Science Vol. 77. No.2, 1994
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TABLE I. Herd input data for partial budget model for the case farm. Prices Milk, $Icwt Bull calf. $Icalf Cull cow, $lIb Cull cow, $/kg Veterinary service, $Ih Feed expenses ~). $Id Lactating cows, high yield Lactating cows, low yield Lactating 2 yr olds Early dry cows Late dry cows Labor expenses Time worked. h1wk Rate of pay, $Ih Salary. S Months Benefits. $ Actual wage. I $Ih IAverage for hired employees
12.50 125.00 .51 1.12 60 3.87 3.65 3.70 2.03 2.03 40 12
40 9
o
o
12 2500 10.20
12 2500 13.20
= $11.701h;
average for salaried employees
based on days to calving. Farm inputs for the model included the following: 1) days open distribution for cows in fIrst and second or greater lactation; 2) reproductive indexes, efficiency of detection of estrus, conception rate, and days to fIrst AI; 3) feed expenses; 4) labor expenses; 5) supplies and services expenses; and 6) replacement expenses (see details of these inputs and other assumptions in Tables I, 2, and 3). To demonstrate the model's applicability, four scenarios were evaluated (Table 3). Scenario 1 suggested decreasing days to fIrst AI and increasing estrus detection effIciency and conception rate through additional labor time in detection of estrus. Scenario 2 used the same amount of additional labor for reproduction as scenario I, but with less improvement in performance. Also, scenario 2 did not change days to first AI from the base level. This scenario was evaluated because management changes are often made when the expected improvements in performance exceed those actually achieved. Scenario 3 considered the possibility that, if nothing is changed from the base situation, reproductive performance might actually decrease. Scenario 4 evaluated the same changes and expected results as scenario I, but in a situation in which the herd's base milk production was 10% lower. To asJournal of Dairy Science Vol. 77, No.2. 1994
60
o
35,000 12
o
11.22
60
o
35,000 12
o
11.22
= $11.22/h.
sess the sensItIvIty of the partial budget's results to input and output prices, scenario 1 was successively repeated with 10% increases and 10% decreases in the following variables: milk price, bull calf price, cull cow price, feed price (milking herd only), and heifer rearing costs. The effect that these different prices had on the initial scenario 1 estimation of changed net income was calculated as a percentage. RESULTS
The partial budget model was used to analyze several different reproductive management strategies employed by the dairy farm business. The results of the example farm analysis using the farm's suggested management change and data are summarized in Table 4. The following results summary pertains to those scenarios that improved reproductive performance (1, 2, and 4); scenario 3 involved decreased reproductive performance, and, as expected, budgetary changes occurred in the opposite directions. Revenue increases that were due to change in reproductive management were attributed to increase in milk sales, bull calf, and cull cow sales. The change in the days open distribution through decreasing days to first AI, increasing effIciency of estrus detection, and improving conception rate increased weighted average daily milk production. Bull calf sales increased
487
PARTIAL BUDGETING FOR DAIRY REPRODUCTION TABLE 2. Replacement expenses for the case farm. 1,2 Cost
Labor
($lib of DM) Preweaning Milk replacer Calf starter Forage Growing Grain Forage Breeding Grain Forage Postbreeding Grain Forage
($/kg of DM)
.326 .265 .028
.717 .583 .062
.215 .028
.473 .062
o
(h)
.25
o
.028
.25
.062
o
o .028
.25
.062
($)
Semen per replacement Detection of estrus Manure management Veterinary service
20 .5
2 2
lWeaning age = 1.5 mo; age at fIrSt calving = 28 mo; number of replacements sold = O. 2Total variable cost to raise replacement = $929; variable cost = $I.ll/d.
through production of more bull calves. The dairy farm did not plan to sell replacements, which allowed for increase in cull cow revenues because of increased number of replacements available to enter the milking group. Expenses decreased through an increase in conception rates for both lactational groups. The number of pregnancies per year increased, but the number of AI for each pregnancy was reduced. The balance of these two factors caused a positive impact in the partial budget model. Changed expenses relating to nutritional management, reproductive labor, the replacement enterprise, and supplies and services were associated with changes in the days open
distribution. Nutritional management involved increasing energy density of the rations to support milk production and to maintain body condition. The rations fed within the alternative scenario cost more per pound of dry matter than rations in the current feeding strategy. However, the change in the days open distribution caused a larger percentage of the cows to spend fewer days in the expensive lactating rations, thus actually decreasing total feed expense. Expenses increased for reproductive management because of the increase in labor time (.5 hid) in detection of estrus. The replacement enterprise had a large negative impact on the reproductive partial budget because of the increase in the number of replacements produced by the milking group.
TABLE 3. Reproduction and production indexes for projected scenarios for the case farm.
RHA,lb Days to first AI Efficiency of estrus detection, % Conception rate, % Days dry
Base
Scenario I
Scenario 2
Scenario 3
Scenario 4
21,750 80 50 35 60
21,750 60 60 50 60
21,750 80 50 40 60
21,750 80 40 35 60
19,575 60 60 50 60
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TABLE 4. Model output summary for the case farm. Estimated changes (Slyr)
Increased revenues Milk production Bull calf sales Cull cow sales Replacement sales Decreased expenses Nutritional management Breeding and conception rate analysis Replacement enterprise Decreased revenues Milk production Bull calf sales Cull cow sales Increased expenses Labor, reproduction Replacement enterprise Nutritional management Supplies and services Total change
Scenario 21,129 2061 9186 0
Scenario 2 3702 277 1234 0
Scenario 3 0 0 0 0
Scenario 4 19.101 2061 9186 0
3422 565 0
468 32 0
0 0 3233
3422 565 0
0 0 0
0 0 0
5864 431 1920
0 0 0
2409 15.469 0 0 18.485
2409 2077 0 0 1226
0 0 715 0 (5697)
2409 15,469 0 0 16,456
Change in net income estimated by the model is positive for scenarios 1, 2, and 4, but a negative change would be expected in scenario 3. Of the variables considered, sensitivity analysis indicates that the predicted benefit from improved reproductive performance in scenario I is the most sensitive to milk prices, followed by changes in heifer rearing costs (Table 5). DISCUSSION
As the results for the case study farm indicate, the management changes of interest can be expected to affect profitability. However, herd specificity of these results must be quickly emphasized. Herds with lower production or fewer cows (as is common in Michigan) could not expect benefits from improving reproductive performance as large as the case study farm. Also. herds of similar size and production apparently could expect increased benefits if heifer culling is possible. Finally, the sensitivity analysis results indicate the importance of time-specific evaluation because prices continuously fluctuate. Other major conclusions that can be drawn from the results of this partial budget model pertain to replacement and nutritional management. The increase in female calf production has a large impact on the replacement enterprise and Journal of Dairy Science Vol. 77, No.2. 1994
the model output. However. the structure of a partial budget model only allows comparison between two situations in a static state and does not take into account the transition period (4). In reality, a change in days open distribution causes the number of female calves entering the replacement enterprise to change continuously until they start to enter the milking group or are sold. Months to first calving determine when the alternative scenario becomes static for comparison in the model. The final effect is that the replacement population may enlarge or shrink dramatically with a change in days open distribution of the milking group. The model illustrates that, when a change in the reproductive program is planned,
TABLE 5. Percentage of differences in predicted benefits from improved reproductive performance (scenario 1) associated with 10% increases or decreases in prices for the case farm. Price
10% Decrease
10% Increase
Milk price
-11.4%
+11.4% +l.l% +5.0% +1.9% -8.4%
Bull calf price Cull cow price Feed price (milking herd) Heifer rearing costs
-1.1%
-5.0% -1.9% +8.4%
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
the dairy farm business should also plan for a change in the replacement enterprise. A change in reproductive performance has an effect on nutritional management of the milking group. Cows with shorter lactations may require increased nutritional support to maintain body condition or milk production as average milk production increases within nutritional groups. However, the increase in feed cost may be balanced by a decrease in the number of days spent on more expensive rations. Some important considerations in reproductive management are admittedly not captured in this model. As mentioned, the analysis is static and considers only one time period. Time lags between investment and payoff call for discounting procedures not possible in this analytical framework. Further, a constant age distribution in the milking herd is assumed. However, this assumption may well not be valid for all reproductive management changes; this limitation should be recognized, and the model output should be interpreted accordingly. Similarly, improved reproductive performance should allow accelerated genetic improvements. This potential is not captured in the current model. Limitations aside, this partial budget model was developed to analyze the reproductive programs of individual dairy farm businesses to assist with management decisions for the producer. This type of examination requires accurate, farm-specific biological and financial data for credible analysis. As these biological and financial data vary among farms and over time, the necessity of farrn- and time-specific analyses becomes obvious. The current model was designed to facilitate such analyses and is unique because 1) the herd is split into groups by first lactation and second or greater lactation; 2) each group's days open distribution is employed; 3) a lactation curve simulation is used to estimate a weighted average daily milk production; 4) the current days open distribution is altered by estimating changes in days to first AI, efficiency of detection of estrus, and conception rate for the two lactation groups to predict the altered days open distribution; and 5) the model provides a structure to estimate changes in expenses for labor, feed, supplies and services, and replacement raising that may occur with the suggested management plan.
489
REFERENCES 1 Bar-Anan, R., and M. Soller. 1979. The effects of days open on milk yield and on breeding policy postpartum. Anim. Prod. 29:109. 2 Britt, 1. H. 1985. Enhanced reproduction and its economic implications. I. Dairy Sci. 68:1585. 3 Congleton, W. R., and C. A. Roberts. 1987. Cumulative net income curve of the dairy cow. 1. Dairy Sci. 70:345. 4 Eleveld, B. 1989. Partial budgeting: looking at the small picture. 1989 Yearbook of Agriculture-Farm Management. Publ. 89-6321. USDA Washington, DC. 5 Fetrow, I., B. Harrington, E. T. Henry. and K. L. Anderson. 1988. Herd Health Monitoring. Part 11. Computer spreadsheet for dairy herd monitoring. Compend. Contino Educ. Practicing Vet. 10(1):75. 6 Gill, G. S., and F. R. Allaire. 1975. Relationship of age at first calving, days open, days dry. and herdlife to a profit function for dairy cattle. I. Dairy Sci. 59: 1131. 7 Harsh, S. B., L. I. Connor, and G. D. Schwab. 1981. Managing the Farm Business. Prentice-Hall Inc., Englewood Cliffs, NI. 8 Lineweaver, I. A. 1975. Potential income for increased reproductive efficiency. I. Dairy Sci. 58:780. 9 Louca, A., and I. E. Legates. 1967. Production losses in dairy cattle due to days open. 1. Dairy Sci. 51 :573. 10 OIds, D., T. Cooper, and T. R. Thrift. 1979. Effects of days open on economic aspects of current lactation. 1. Dairy Sci. 62:1171. 11 Oltenacu, P. A., R. A. Milligan, T. R. Rounsaville. and R. H. Foote. 1980. Relationship between days open and cumulative milk yields at various intervals from parturition for high and low producing cows. I. Dairy Sci. 63:1317. 12 Schaeffer, L. R., and C. R. Henderson. 1971. Effects of days dry and days open on Holstein milk production. I. Dairy Sci. 55:107. 13 Spartan Dairy Ration Balancer, Version 2. 1992. Michigan State Univ., East Lansing. 14 Speicher, I. A., and C. Meadows. 1967. Milk production and cost associated with length of calving interval of Holstein cows. 1. Dairy Sci. 50:975. 15 Willamson, N. B. 1986. The economics of reproductive herd health programs for dairy herds. Page 410 in Current Therapy in Theriogenology 2. W. B. Saunders Co., Philadelphia, PA.
APPENDIX Modified Woods Equation
where MP A
= daily milk production, = normally distributed random variate, the mean of which scales the lactation curve to the target average production,
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DP e b, c, g
= days pregnant, = the base of natural logarithm, and = constants that determine shape of the lactation curves.
Cull Cow Revenue Difference 365 L (CPG lx x CI x .5 x CCP Ix n
NRD CC -
x=1
x CCW x (l - RDR»
- Ln
Calculation of Coefficient A, the Scaler Constant In Woods Equation
For lactation A
for lactation
=~
2x
.5 x CCP
x CCW x (1 - RDR» - «NHSI - NHS2) x CCP)
x .0Il - 20)12.96; where
2
= ([RHA x .01] RHA = rolling herd A
where
365
CI x
x=1
=1
= ([RHA
(CPG2x x
NRDcc
+ 14)12.96 averge in pounds.
The b, c, g, Coefficients in Woods Equation
CCP CCW RDR
NHS .5
Lactation 1
b
c
g
.08
~2
.14
-.002 -.0045
-.001 -.002
= net revenue difference from cull cows, = cull cow price, = cull cow weight, = replacement death rate, = number of heifers sold, and = constant to represent the proportion of calves born that are heifers; other variables are as defined previously.
Helfer Revenue Difference Bull Calf Revenue Difference
NRDBC
n ( 365 ) ~ \ CPG lx x C1lx x .5 x BCP
- Ln (\CPG2x x.1
x
365
CI x 2x
.5 x BCP
where )
NRDH
HP
= net revenue difference from heifers, and = heifer price; other variables are as defined previously.
where NRDBc = net revenue difference from bull calves, CPO = number of cows per group, CI = calving interval, BCP = bull calf price, x = subscript to denote groups from the days open distribution (x = 1 to n), .5 = constant to represent the proportion of calves born that are bulls, and 1,2 = subscripts to denote current (best estimate) and alternative (projected) scenarios, respectively. Journal of Dairy Science Vol. 77. No.2, 1994
Breeding Expense Difference
NEDB
n
(365
~ CPGlx x C1lx x SPCl x CPSI
-i (
CPG2X x
x=1
~:5
2x
)
x SPC2 x CPS2)
where NEDB SPC CPS
= net expense difference from breeding, = services or AI per conception, = cost per service or AI; other variables are as defined previously.
491
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
Feed Expense Difference
n
L
NEDF
z
= subscript to denote labor class
=
(z 1 to j) and other variables are as defined previously.
m
(CPGIx x
.=1
L
(FCPDly
Replacement Expense Difference
y=1
365
x D1Glxy) x C1IX) n
m
.=1
y=1
- L (CPG2x x L
(FCPD2y
where where NEDR
NEDp FCPD
DIG y
= net expense difference from feeding, = feed cost per cow per day. = number of days a cow spends in a group, = subscript to denote feeding groups (y = 1 to m); other variables are as defined previously.
DPDH DIP DFC AHI w
bles are as defined previously.
Labor Expense Difference
±({CWRz x HWz>+ FBz>} ~) (z:1 HWZ TOTHW
= net expense difference for replacements, = dollars per day per heifer by phase. = number of days a heifer spends in a phase, = days of age at first calving, = average heifer inventory, = subscript to denote heifer growth phases (w = 1 to k); other varia-
Supplies Expense Difference
x «DFTI - DFT2) + (DRTI - DRT2» x 365
NEDs
n
=[~
365)
(
CPGlx X C1lx
where
NEDr.
WR HW FB TOTHW DFT DRT
= net expense difference for labor, wage rate, = = hours worked per labor class per year, = total fringe benefits, = total hours worked on the farm per year, = number of hours spent daily in feeding, = number of hours spent daily in
reproductive management, and
~ n
-
(
365)~ ~
CPG2x X CI2x
where NEDs SPPC
= net expense difference for supplies, and = supplies per conception; other variables are as defined previously.
Journal of Dairy Science Vol. 77. No.2, 1994
J. B. KANEENE Population Medicine Center A. L. SKIDMORE Department of Animal Science Michigan State University East Lansing 48824 ABSTRACT
A partial budget model was developed to investigate the economic impact of management changes for the reproductive program of dairy farm businesses. The model is unique because 1) the herd is split into groups for first lactation and second or greater lactation; 2) each group's days open distribution is employed; 3) a lactation curve simulation is used to estimate a weighted average daily milk production; 4) the current days open distribution is altered by estimating changes in days to first AI, efficiency of estrus detection, and conception rate for the two lactation groups to predict the altered distribution of days open; and 5) the model provides a structure to estimate changes in expenses for labor, feed, supplies and services, and replacement heifers that may occur with the suggested management plan. A microcomputer program was designed based on the partial budget model to support decision making on the dairy farm pertaining to suggested management changes in the reproductive program. When applied to specific case farms, the results of the model indicate that, with improved reproductive efficiency of the milking group, the replacement population increases, and strategies may be required to manage an increased
Received January 11. 1993. Accepted August 16. 1993. 1994 J Dairy Sci 77:482-491
number of replacements. Sensitivity analysis was performed on milk price, feed, and replacement expenses. The case study results indicate that milk price and expenses of raising replacements may have the greatest impact within the partial budget model. (Key words: reproduction, economics, partial budget model) INTRODUCTION
Reproductive performance affects profitability of the dairy farm business through its influence on milk produced per cow per day, number of replacements produced, and rate of voluntary and involuntary culling (2). A profit function was developed and used to describe the relationship of the dairy cow to economical return for the dairy farm (6). This function established that maximum profit per day of herd life was expected for cows with first calving at 25 rna of age and maintained 124 d open and 42 d dry. Cumulative net income curves produced via a dynamic model of the dairy herd were affected by days open and infertility (3). These models, along with those in earlier works (9, 12), have validated that increased days open affects the profitability of the dairy farm business. Studies have described the impact of decreased reproductive performance by estimating a monetary value of an open day for dairy cows. Estimates vary from negative dollars per day in high production cows (1), to cents per day (14), to dollars per day open (8). The differences in these values are related to the different assumptions in 482
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
methods of accounting for outputs and production input costs. Partial budget models can be used to evaluate individual reproductive programs by examining only those expenses and revenues that change with a proposed plan or change in management (7). Reproductive programs for dairy farm businesses have been analyzed using partial budget models (5, 15). Those models predict changes in milk production because of increased reproductive performance using a linear regression equation (10) and estimate milk and calf production using average days open. However, the resulting estimates used in these partial budgets may be imprecise because 1) the accuracy of the milk production prediction equations is limited, as measured by R2 values from .19 to .35 (10); 2) separate equations should be used for first lactation cows and second or greater lactation cows because of the different shape of their lactation curves; and 3) average days open assumes normal distribution in days open of the pregnant cows in a herd, but days open of pregnant cows is seldom normally distributed in ordinary dairy herds. Finally, the expense portion of these partial budgets was poorly developed, and estimates of the expenses employed to decrease the average days open are incomplete. The goal of this study was to develop a partial budget model that would address the aforementioned weaknesses in estimating the economic impact of management changes within the reproductive program of individual dairy farm businesses. MATERIALS AND METHODS
A management decision can affect the profitability of an individual dairy farm's reproductive program in four ways. The management change can increase revenues, decrease expenses, increase expenses, or decrease revenues (Figure 1). These four increases or decreases in revenues or expenses make up the structure of a partial budget model. The analysis compares the current situation and an alternative scenario without consideration of the transition period between the two management schemes (4). Although the model is simple, identification of the elements that change with each management change and estimation of the
483
PARTIAL BUDGET COMPONENTS 1. 2.
INCREASE REVENUES DECREASE EXPENSES
3. 4.
DECREASE REVENUES INCREASE EXPENSES
[(Component 1) + (Component 2)] - [(Component 3) + (Component 4)] = Net Change in Partial Budget Figure I. Structure for partial budget analysis.
economic impact of these modifications can be difficult. Presented are revenue and expense changes identified for this particular partial budget application, which considers an improvement in reproductive performance. Use of the model to address management changes in a different situation should be expected to include different changing budget elements. Specifically, decreased reproductive performance would likely lead to changes opposite in direction for revenues and expenses to those presented here. Increased Revenues
Increased revenues within the reproductive program relate to milk and calf production. In conjunction with the days open distribution, a modified Woods equation (Appendix) was used to simulate lactation curves both for cows in first lactation and for cows in second or greater lactation to estimate a weighted average daily milk yield (11). The herd's age distribution was assumed to be constant. Days in milk, days pregnant, and coefficient A (Appendix) were calculated from the days open distribution and rolling herd average. Coefficients b, c, and g are those estimated from Oltenacu et al. (11) and shown in the Appendix. The days open distribution started at 40 d open and split each lactational group into 20-d intervals ending at 180 d open. Cows with days open greater than 180 d were averaged to summarize this segment of the distribution of days open. The percentage of cows in each interval was linked to the lactation Journal of Dairy Science Vol. 77, No.2, 1994
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curve simulation that was initialized with the individual herd's rolling herd average and days dry. Changes in days to first AI, efficiency of estrus detection, and conception rate for both lactational groups were estimated from the suggested management change in the reproductive program. These estimates were used to alter the current days open distribution and to change average daily milk production through a modification of the percentage of cows in each interval of the days open distribution. Milk price was used to convert the predicted change in weighted average daily milk production to change in milk revenues. The number of calves produced in a year was dependent on the distribution of days open. The partial budget model computes the difference in the number of calves born per year between the two scenarios via differences in the current and altered days open distribution. The total number of calves produced per year was computed using the weighted average of cows in each interval of the distribution. This value is divided by 2 to estimate the number of male and female calves. Change in revenues was estimated for male calves using the price received for them (Appendix), and female calves were placed in the replacement inventory. If total milking herd size is assumed to be constant, an adjustment of current days open distribution will change the number of female calves in the replacement enterprise. The number of female calves was altered by the replacement death rate (which represents total losses, including stillborn and culled calves) to predict the number of replacements available to enter the milking group. The revenues gained from an increased number of replacement heifers could be obtained either by selling these heifers or by increasing revenues from culled cows (Appendix).
that change conception rates. The total number of cows in the milking group, conception rates, number of conceptions per year, and average service (or AI) price were used to estimate breeding expense differences that were due to management change (Appendix). Decreased Revenues
No decreased revenues were identified in this partial budget model for improving reproductive performance. Increased Expenses
Increased expenses expected because of a management change in the reproductive program included feed expenses, labor expenses, replacement expense, and supplies and services. Methods for estimating these changes in ex.penses between the two scenarios were included in the partial budget model to allow for a complete analysis of reproductive cost to the business. Feed Expenses. Changes in feed expenses were due to the change in weighted average daily milk production in the herd and the length of time each ration was fed. Feed expenses were determined from farm prices of components used by the dairy farm, and nutritional software (13) was used to estimate the cost of feed per day on a dry matter basis. The model used these values for different ration groups in the milking herd. Groups consisted of high production, low production, 2-yr-old, early dry, and late dry cows. The number of days a cow remained in each group was used to estimate a weighted average feed cost per day per cow. This value was used to compute difference in annual feed cost for competing scenarios within the partial budget model (Appendix). Labor Expenses. Labor expenses were associated with the number of hours of labor Decreased Expenses used within the reproductive program. An Decreased expenses in the partial budget hourly wage rate was computed based on the model structure were used to compare the number of hours worked per week and total breeding expenses between the current and compensation for hourly and salaried emalternative scenarios. In some scenarios, ad- ployees. A weighted average wage rate was justment of the conception rate or services or computed for each labor category, hired or AI per conception might increase expenses. salaried, to take into account the segregation of The logic for placing the conception rate anal- labor that may occur in the reproductive proysis in this section of the model was to allow gram. The labor expense difference between for the uncomplicated analysis of scenarios the two scenarios is computed from the estiJournal of Dairy Science Vol. 77, No.2. 1994
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
mated change in number of hours per day that will be spent in the reproductive program (Appendix). Replacement Expenses. The number of female calves in the replacement enterprise is a direct result of reproductive management in the cow herd. The population of replacements in the partial budget model changed with the number of calves produced between the current and alternative scenarios. Changes in expenses because of a change in the population of replacements were calculated by the model. The model estimated variable expenses of the replacement enterprise to estimate the daily expense to raise a replacement. Feed expenses were computed by dividing the replacement enterprise into four groups by age: preweaning, growing, breeding, or postbreeding. These four groups are typically used by dairy farm businesses because of the nutritional differences among these types of animals. Feed cost per pound of dry matter and months to first calving were used by the model to estimate the number of animals in each group and to compute total feed cost for a replacement. Labor expenses were associated with labor time spent for feeding, detection of estrus, and manure and facility management. Time spent in each activity and the hourly wage rate were used to estimate the labor cost to raise a replacement. Supplies and services expenses related to replacements included cost of semen, bedding, medicine, vaccinations, and veterinary services. The total variable cost to raise a replacement was divided by days to first calving to estimate cost per day to raise a replacement. This value was used, along with the change in heifer inventories between the two scenarios, to estimate increased or decreased expenses that were incurred by the replacement enterprise because of a change in reproductive efficiency of the milking group. A default value was entered into the reproductive partial budget if the cost per day for replacement services was not known by the dairy farm business (Appendix). Supplies and Services Expenses. Supplies that were used in the reproductive program included the following: prostaglandin, aids for detection of estrus, progesterone tests, and
485
other types of reproductive aids. Services that were used in the reproductive program involved veterinary and consulting services. Expenses were estimated in the partial budget model as those expenses per pregnancy. The change in supplies and services occurred because the number of pregnancies per year changed between the two scenarios. With an increase in reproductive efficiency, more cows became pregnant during a year, which increased the annual expense for supplies and services (Appendix). To summarize, the model simulated the effects of a change of reproductive efficiency through a change in the current days open distribution. The model used lactation curve simulations for first lactation and for second or greater lactations to estimate change in weighted average daily milk between the current situation and the alternative scenario. The model compared revenues (milk sales, bull calf sales, cull cow, or replacement sales) and expenses (feed, labor. replacement, supplies, and services) associated with a suggested management change in the reproductive program. These elements of the partial budget and their estimates were used in the structure of the partial budget to calculate the net outcome of the suggested management change. Sensitivity analysis was performed in the model to evaluate changes in milk price, feed cost, and replacement cost. A computer program was developed from this model and was designed to operate on a microcomputer with 560K random access memory and requiring .75 MB for storage. Case StUdy Farm
A Holstein dairy farm located in central Michigan, milking approximately 300 cows, used the model to investigate a management change in its reproductive program. Lactating cows averaged 39.8 kg/d of milk with a 305-d mature equivalent of 12,553 kg. Milk fat content was 4.2%, and mean cow DHI somatic cell counts varied from 80,000 to 100,000 cells/ml. First lactation cows remained in one group for the entire lactation, and cows in second or greater lactation were divided into two groups by production and days in milk. Days dry averaged 58.3, and dry cows were split into two groups, early dry and late dry, Journal of Dairy Science Vol. 77. No.2, 1994
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TABLE I. Herd input data for partial budget model for the case farm. Prices Milk, $Icwt Bull calf. $Icalf Cull cow, $lIb Cull cow, $/kg Veterinary service, $Ih Feed expenses ~). $Id Lactating cows, high yield Lactating cows, low yield Lactating 2 yr olds Early dry cows Late dry cows Labor expenses Time worked. h1wk Rate of pay, $Ih Salary. S Months Benefits. $ Actual wage. I $Ih IAverage for hired employees
12.50 125.00 .51 1.12 60 3.87 3.65 3.70 2.03 2.03 40 12
40 9
o
o
12 2500 10.20
12 2500 13.20
= $11.701h;
average for salaried employees
based on days to calving. Farm inputs for the model included the following: 1) days open distribution for cows in fIrst and second or greater lactation; 2) reproductive indexes, efficiency of detection of estrus, conception rate, and days to fIrst AI; 3) feed expenses; 4) labor expenses; 5) supplies and services expenses; and 6) replacement expenses (see details of these inputs and other assumptions in Tables I, 2, and 3). To demonstrate the model's applicability, four scenarios were evaluated (Table 3). Scenario 1 suggested decreasing days to fIrst AI and increasing estrus detection effIciency and conception rate through additional labor time in detection of estrus. Scenario 2 used the same amount of additional labor for reproduction as scenario I, but with less improvement in performance. Also, scenario 2 did not change days to first AI from the base level. This scenario was evaluated because management changes are often made when the expected improvements in performance exceed those actually achieved. Scenario 3 considered the possibility that, if nothing is changed from the base situation, reproductive performance might actually decrease. Scenario 4 evaluated the same changes and expected results as scenario I, but in a situation in which the herd's base milk production was 10% lower. To asJournal of Dairy Science Vol. 77, No.2. 1994
60
o
35,000 12
o
11.22
60
o
35,000 12
o
11.22
= $11.22/h.
sess the sensItIvIty of the partial budget's results to input and output prices, scenario 1 was successively repeated with 10% increases and 10% decreases in the following variables: milk price, bull calf price, cull cow price, feed price (milking herd only), and heifer rearing costs. The effect that these different prices had on the initial scenario 1 estimation of changed net income was calculated as a percentage. RESULTS
The partial budget model was used to analyze several different reproductive management strategies employed by the dairy farm business. The results of the example farm analysis using the farm's suggested management change and data are summarized in Table 4. The following results summary pertains to those scenarios that improved reproductive performance (1, 2, and 4); scenario 3 involved decreased reproductive performance, and, as expected, budgetary changes occurred in the opposite directions. Revenue increases that were due to change in reproductive management were attributed to increase in milk sales, bull calf, and cull cow sales. The change in the days open distribution through decreasing days to first AI, increasing effIciency of estrus detection, and improving conception rate increased weighted average daily milk production. Bull calf sales increased
487
PARTIAL BUDGETING FOR DAIRY REPRODUCTION TABLE 2. Replacement expenses for the case farm. 1,2 Cost
Labor
($lib of DM) Preweaning Milk replacer Calf starter Forage Growing Grain Forage Breeding Grain Forage Postbreeding Grain Forage
($/kg of DM)
.326 .265 .028
.717 .583 .062
.215 .028
.473 .062
o
(h)
.25
o
.028
.25
.062
o
o .028
.25
.062
($)
Semen per replacement Detection of estrus Manure management Veterinary service
20 .5
2 2
lWeaning age = 1.5 mo; age at fIrSt calving = 28 mo; number of replacements sold = O. 2Total variable cost to raise replacement = $929; variable cost = $I.ll/d.
through production of more bull calves. The dairy farm did not plan to sell replacements, which allowed for increase in cull cow revenues because of increased number of replacements available to enter the milking group. Expenses decreased through an increase in conception rates for both lactational groups. The number of pregnancies per year increased, but the number of AI for each pregnancy was reduced. The balance of these two factors caused a positive impact in the partial budget model. Changed expenses relating to nutritional management, reproductive labor, the replacement enterprise, and supplies and services were associated with changes in the days open
distribution. Nutritional management involved increasing energy density of the rations to support milk production and to maintain body condition. The rations fed within the alternative scenario cost more per pound of dry matter than rations in the current feeding strategy. However, the change in the days open distribution caused a larger percentage of the cows to spend fewer days in the expensive lactating rations, thus actually decreasing total feed expense. Expenses increased for reproductive management because of the increase in labor time (.5 hid) in detection of estrus. The replacement enterprise had a large negative impact on the reproductive partial budget because of the increase in the number of replacements produced by the milking group.
TABLE 3. Reproduction and production indexes for projected scenarios for the case farm.
RHA,lb Days to first AI Efficiency of estrus detection, % Conception rate, % Days dry
Base
Scenario I
Scenario 2
Scenario 3
Scenario 4
21,750 80 50 35 60
21,750 60 60 50 60
21,750 80 50 40 60
21,750 80 40 35 60
19,575 60 60 50 60
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TABLE 4. Model output summary for the case farm. Estimated changes (Slyr)
Increased revenues Milk production Bull calf sales Cull cow sales Replacement sales Decreased expenses Nutritional management Breeding and conception rate analysis Replacement enterprise Decreased revenues Milk production Bull calf sales Cull cow sales Increased expenses Labor, reproduction Replacement enterprise Nutritional management Supplies and services Total change
Scenario 21,129 2061 9186 0
Scenario 2 3702 277 1234 0
Scenario 3 0 0 0 0
Scenario 4 19.101 2061 9186 0
3422 565 0
468 32 0
0 0 3233
3422 565 0
0 0 0
0 0 0
5864 431 1920
0 0 0
2409 15.469 0 0 18.485
2409 2077 0 0 1226
0 0 715 0 (5697)
2409 15,469 0 0 16,456
Change in net income estimated by the model is positive for scenarios 1, 2, and 4, but a negative change would be expected in scenario 3. Of the variables considered, sensitivity analysis indicates that the predicted benefit from improved reproductive performance in scenario I is the most sensitive to milk prices, followed by changes in heifer rearing costs (Table 5). DISCUSSION
As the results for the case study farm indicate, the management changes of interest can be expected to affect profitability. However, herd specificity of these results must be quickly emphasized. Herds with lower production or fewer cows (as is common in Michigan) could not expect benefits from improving reproductive performance as large as the case study farm. Also. herds of similar size and production apparently could expect increased benefits if heifer culling is possible. Finally, the sensitivity analysis results indicate the importance of time-specific evaluation because prices continuously fluctuate. Other major conclusions that can be drawn from the results of this partial budget model pertain to replacement and nutritional management. The increase in female calf production has a large impact on the replacement enterprise and Journal of Dairy Science Vol. 77, No.2. 1994
the model output. However. the structure of a partial budget model only allows comparison between two situations in a static state and does not take into account the transition period (4). In reality, a change in days open distribution causes the number of female calves entering the replacement enterprise to change continuously until they start to enter the milking group or are sold. Months to first calving determine when the alternative scenario becomes static for comparison in the model. The final effect is that the replacement population may enlarge or shrink dramatically with a change in days open distribution of the milking group. The model illustrates that, when a change in the reproductive program is planned,
TABLE 5. Percentage of differences in predicted benefits from improved reproductive performance (scenario 1) associated with 10% increases or decreases in prices for the case farm. Price
10% Decrease
10% Increase
Milk price
-11.4%
+11.4% +l.l% +5.0% +1.9% -8.4%
Bull calf price Cull cow price Feed price (milking herd) Heifer rearing costs
-1.1%
-5.0% -1.9% +8.4%
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
the dairy farm business should also plan for a change in the replacement enterprise. A change in reproductive performance has an effect on nutritional management of the milking group. Cows with shorter lactations may require increased nutritional support to maintain body condition or milk production as average milk production increases within nutritional groups. However, the increase in feed cost may be balanced by a decrease in the number of days spent on more expensive rations. Some important considerations in reproductive management are admittedly not captured in this model. As mentioned, the analysis is static and considers only one time period. Time lags between investment and payoff call for discounting procedures not possible in this analytical framework. Further, a constant age distribution in the milking herd is assumed. However, this assumption may well not be valid for all reproductive management changes; this limitation should be recognized, and the model output should be interpreted accordingly. Similarly, improved reproductive performance should allow accelerated genetic improvements. This potential is not captured in the current model. Limitations aside, this partial budget model was developed to analyze the reproductive programs of individual dairy farm businesses to assist with management decisions for the producer. This type of examination requires accurate, farm-specific biological and financial data for credible analysis. As these biological and financial data vary among farms and over time, the necessity of farrn- and time-specific analyses becomes obvious. The current model was designed to facilitate such analyses and is unique because 1) the herd is split into groups by first lactation and second or greater lactation; 2) each group's days open distribution is employed; 3) a lactation curve simulation is used to estimate a weighted average daily milk production; 4) the current days open distribution is altered by estimating changes in days to first AI, efficiency of detection of estrus, and conception rate for the two lactation groups to predict the altered days open distribution; and 5) the model provides a structure to estimate changes in expenses for labor, feed, supplies and services, and replacement raising that may occur with the suggested management plan.
489
REFERENCES 1 Bar-Anan, R., and M. Soller. 1979. The effects of days open on milk yield and on breeding policy postpartum. Anim. Prod. 29:109. 2 Britt, 1. H. 1985. Enhanced reproduction and its economic implications. I. Dairy Sci. 68:1585. 3 Congleton, W. R., and C. A. Roberts. 1987. Cumulative net income curve of the dairy cow. 1. Dairy Sci. 70:345. 4 Eleveld, B. 1989. Partial budgeting: looking at the small picture. 1989 Yearbook of Agriculture-Farm Management. Publ. 89-6321. USDA Washington, DC. 5 Fetrow, I., B. Harrington, E. T. Henry. and K. L. Anderson. 1988. Herd Health Monitoring. Part 11. Computer spreadsheet for dairy herd monitoring. Compend. Contino Educ. Practicing Vet. 10(1):75. 6 Gill, G. S., and F. R. Allaire. 1975. Relationship of age at first calving, days open, days dry. and herdlife to a profit function for dairy cattle. I. Dairy Sci. 59: 1131. 7 Harsh, S. B., L. I. Connor, and G. D. Schwab. 1981. Managing the Farm Business. Prentice-Hall Inc., Englewood Cliffs, NI. 8 Lineweaver, I. A. 1975. Potential income for increased reproductive efficiency. I. Dairy Sci. 58:780. 9 Louca, A., and I. E. Legates. 1967. Production losses in dairy cattle due to days open. 1. Dairy Sci. 51 :573. 10 OIds, D., T. Cooper, and T. R. Thrift. 1979. Effects of days open on economic aspects of current lactation. 1. Dairy Sci. 62:1171. 11 Oltenacu, P. A., R. A. Milligan, T. R. Rounsaville. and R. H. Foote. 1980. Relationship between days open and cumulative milk yields at various intervals from parturition for high and low producing cows. I. Dairy Sci. 63:1317. 12 Schaeffer, L. R., and C. R. Henderson. 1971. Effects of days dry and days open on Holstein milk production. I. Dairy Sci. 55:107. 13 Spartan Dairy Ration Balancer, Version 2. 1992. Michigan State Univ., East Lansing. 14 Speicher, I. A., and C. Meadows. 1967. Milk production and cost associated with length of calving interval of Holstein cows. 1. Dairy Sci. 50:975. 15 Willamson, N. B. 1986. The economics of reproductive herd health programs for dairy herds. Page 410 in Current Therapy in Theriogenology 2. W. B. Saunders Co., Philadelphia, PA.
APPENDIX Modified Woods Equation
where MP A
= daily milk production, = normally distributed random variate, the mean of which scales the lactation curve to the target average production,
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DP e b, c, g
= days pregnant, = the base of natural logarithm, and = constants that determine shape of the lactation curves.
Cull Cow Revenue Difference 365 L (CPG lx x CI x .5 x CCP Ix n
NRD CC -
x=1
x CCW x (l - RDR»
- Ln
Calculation of Coefficient A, the Scaler Constant In Woods Equation
For lactation A
for lactation
=~
2x
.5 x CCP
x CCW x (1 - RDR» - «NHSI - NHS2) x CCP)
x .0Il - 20)12.96; where
2
= ([RHA x .01] RHA = rolling herd A
where
365
CI x
x=1
=1
= ([RHA
(CPG2x x
NRDcc
+ 14)12.96 averge in pounds.
The b, c, g, Coefficients in Woods Equation
CCP CCW RDR
NHS .5
Lactation 1
b
c
g
.08
~2
.14
-.002 -.0045
-.001 -.002
= net revenue difference from cull cows, = cull cow price, = cull cow weight, = replacement death rate, = number of heifers sold, and = constant to represent the proportion of calves born that are heifers; other variables are as defined previously.
Helfer Revenue Difference Bull Calf Revenue Difference
NRDBC
n ( 365 ) ~ \ CPG lx x C1lx x .5 x BCP
- Ln (\CPG2x x.1
x
365
CI x 2x
.5 x BCP
where )
NRDH
HP
= net revenue difference from heifers, and = heifer price; other variables are as defined previously.
where NRDBc = net revenue difference from bull calves, CPO = number of cows per group, CI = calving interval, BCP = bull calf price, x = subscript to denote groups from the days open distribution (x = 1 to n), .5 = constant to represent the proportion of calves born that are bulls, and 1,2 = subscripts to denote current (best estimate) and alternative (projected) scenarios, respectively. Journal of Dairy Science Vol. 77. No.2, 1994
Breeding Expense Difference
NEDB
n
(365
~ CPGlx x C1lx x SPCl x CPSI
-i (
CPG2X x
x=1
~:5
2x
)
x SPC2 x CPS2)
where NEDB SPC CPS
= net expense difference from breeding, = services or AI per conception, = cost per service or AI; other variables are as defined previously.
491
PARTIAL BUDGETING FOR DAIRY REPRODUCTION
Feed Expense Difference
n
L
NEDF
z
= subscript to denote labor class
=
(z 1 to j) and other variables are as defined previously.
m
(CPGIx x
.=1
L
(FCPDly
Replacement Expense Difference
y=1
365
x D1Glxy) x C1IX) n
m
.=1
y=1
- L (CPG2x x L
(FCPD2y
where where NEDR
NEDp FCPD
DIG y
= net expense difference from feeding, = feed cost per cow per day. = number of days a cow spends in a group, = subscript to denote feeding groups (y = 1 to m); other variables are as defined previously.
DPDH DIP DFC AHI w
bles are as defined previously.
Labor Expense Difference
±({CWRz x HWz>+ FBz>} ~) (z:1 HWZ TOTHW
= net expense difference for replacements, = dollars per day per heifer by phase. = number of days a heifer spends in a phase, = days of age at first calving, = average heifer inventory, = subscript to denote heifer growth phases (w = 1 to k); other varia-
Supplies Expense Difference
x «DFTI - DFT2) + (DRTI - DRT2» x 365
NEDs
n
=[~
365)
(
CPGlx X C1lx
where
NEDr.
WR HW FB TOTHW DFT DRT
= net expense difference for labor, wage rate, = = hours worked per labor class per year, = total fringe benefits, = total hours worked on the farm per year, = number of hours spent daily in feeding, = number of hours spent daily in
reproductive management, and
~ n
-
(
365)~ ~
CPG2x X CI2x
where NEDs SPPC
= net expense difference for supplies, and = supplies per conception; other variables are as defined previously.
Journal of Dairy Science Vol. 77. No.2, 1994