| Written January, 1993 |  |
File B3-50 |
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Feeder Pig Pricing Formulas
John D. Lawrence, extension livestock economist, 515-294-6290, jdlaw@iastate.edu
Increasingly, feeder pigs are sold directly from producer to finisher and are not traded throughan organized market with centralized price determination. A variety of reasons support this trend; however, animal health concerns and marketing efficiency are two primary reasons. As a result, auction market receipts have declined to the point of concern over representative feeder pig quality and the resulting spot market price used in pricing direct trade pigs. While auction market prices may still serve as a base for direct trade price negotiations, state budget cuts have reduced or eliminated third-party federal or state price reporting of auction markets in Iowa and other states. Direct trade buyers and sellers are left on their own to find an alternative method for determining a transaction price for the feeder pigs. Formula prices based on early observable variables are one method for determining such a price.
Previous pricing formulas
Early feeder pig pricing formulas were often based on current cash hog prices rather than prices the feeder pig would sell for when it is ready for slaughter, and seldom accounted for important input costs such as corn price or overhead cost that also impact feeding profits. More recent formulas have used futures prices and have incorporated feed and overhead costs, but are often charged with being too complicated to be useful.
An inherent shortfall of formula prices is that the calculated formula price often does not match the observed spot market price. Although the buyer and seller know that the formula will likely differ from the spot market price in any one period, a formula that greatly under prices or overprices pigs relative to the spot market will strain a trading agreement. Thus, the question is whether a formula should reflect the actual auction market feeder pig price or what the price should be, considering available information. It may also be important for buyers and sellers to measure the formula's impact on profits rather than simply on price. This question is further complicated by requiring that the formula be simple enough to be practical.
Types of pricing formulas
Two types of feeder pig pricing formulas are examined. The first is a statistical analysis of past feeder pig auction prices, taking into account observed prices of other important variables (hog price, hog futures price, and corn price). The second is a partial budgeting procedure used to calculate what price buyers and sellers may accept, allowing for expected selling prices for barrows and gilts and observed input prices. The results of each procedure are compared with actual auction market prices. They are also compared by the impact each would have on returns to both the finisher and feeder pig producer.
Statistical analysis pricing procedure
The demand for feeder pigs depends on the profit the buyer expects to earn by finishing them. Expected profits are based on the expected selling price and the cost of inputs required to feed the pigs to slaughter weight. Although total cost must be covered in the long run, the decision to buy feeder pigs in the short run depends on only the variable costs of production. Expected returns to the finisher can be approximated by using the live hog futures contract price (HFP) that expires near the time hogs are to be marketed and adjusting it for expected basis; and input costs such as cash corn price (CCP), soybean meal price, and interest rates that are observed when the pigs are purchased.
The analysis uses weekly average price of:
1) U.S., 1-2, 40- to 50-pound feeder pigs at Iowa auctions;
2) U.S., 1-2, 230- to 250-pound barrows and gilts in Iowa -Southern Minnesota;
3) North Central Iowa corn;
4) Decatur, Illinois soybean meal (USDA Market News);
5) Chicago Mercantile Exchange live hog futures prices for the four month out contract; and
6) Monthly average interest rates.
Table 1. Key price variables, 1975-1990. |
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Variable |
Avg. |
Var.* |
Min. |
Max. |
Feeder pig (head) $ |
42.60 |
$ 10.20 |
$ 20.69 |
$ 67.67 |
Feeder pig (cwt.) |
94.66 |
22.67 |
45.98 |
150.38 |
Cash hog (cwt.) |
46.99 |
7.17 |
27.60 |
66.06 |
Hog futures (cwt.) |
46.55 |
6.22 |
30.20 |
60.50 |
N.C. Iowa corn (bu.) |
2.32 |
0.48 |
1.11 |
3.37 |
Soybean meal (ton) |
179 |
37 |
103 |
320 |
Interest rate (%) |
11.82% |
2.77% |
8.25% |
19.00 |
*Variability is measured as the standard deviation.
Coefficients of the equations were estimated using weekly data from January 1975 through December 1985 which encompasses two complete hog cycles. The equations were then used to estimate feeder pig prices over the January 1986 through December 1990 period, a third complete hog cycle. The estimated prices were then compared to actual prices. Upon analysis, it was found that soybean meal prices and interest rates did not significantly impact feeder pig prices and were removed from the equations. Comparisons to actual prices are shown in Table 2.
Table 2. Formula prices for 40-50 Ib. feeder pigs, 1986-1990 ($/cwt.) |
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Pricing method |
Avg. |
Var.* |
Min. |
Max. |
Actual price |
$102 |
$22 |
$56 |
$149 |
Equation 1 |
98 |
9 |
80 |
125 |
Equation 2 |
105 |
17 |
67 |
152 |
Should pay |
83 |
32 |
17 |
156 |
Cost plus |
101 |
6 |
90 |
120 |
Profit share |
86 |
15 |
58 |
117 |
*Variability is measured as the standard deviation.
The formulas for estimating feeder pig price per hundredweight are shown below:
Equation 1:
2.10 x HFP
Equation 2:
32.85 + 2.73 x HFP - 27.90 x CCP
Equation 1 estimates feeder pig prices based only on the four-month-out hog futures prices. It is a simple formula. The feeder pig price per cwt. is 2.1 times the hog futures price per cwt. However, it explains only 44 percent of the variation in feeder pig prices. It has a lower average price and considerably less variability than the auction market (Table 2).
Equation 2 uses two variables, hog futures and cash corn prices. It explains 70 percent of the variation in feeder pig prices. On average, it slightly overestimates price relative to the auction market, and is less variable than cash (Table 2).
Partial budgeting pricing procedure
An alternative procedure is to develop a formula that is agreeable to both the buyer and seller based on their cost of production and profit objectives. Costs of production budgets for feeder pig producers and finishers were estimated from the ISU Swine Enterprise Records.
While the resulting formulas use the same variables as the statistical analysis, they focus on what prices should be given expected performance to meet profit objectives, rather than what prices actually have been.
Maximum should pay
The maximum price a finisher should be willing to pay for feeder pigs depends upon expected revenues, expected cost, and his or her profit objective. Multiplying the basis-adjusted hog futures price by 240 pounds serves as expected gross revenue. Costs depend on corn and supplement prices at the time the pig was bought. The profit objective is $5.00 per head. The resulting price a finisher should pay is $19.36/cwt. lower than the auction market price (Table 2) and more variable due to a lower minimum price. The budgeted maximum price is only slightly higher than the highest auction price, but the minimum is nearly $40/cwt. lower than the auction minimum.
Cost-plus
The cost-plus pricing formula represents a should receive price because it covers the seller's cost of production and includes a predetermined profit. It uses the budget in Table 3, corn and supplement prices when the pigs are sold, and adds a $5.00 per head profit. This price is $0.94/cwt. below the auction price, but is much more stable (Table 2). Prices vary less than $30/cwt. from high to low compared to the $92.22 range in auction prices.
Profit Sharing
A third formula involves sharing the actual profits determined after the hogs are sold. This procedure assumes a constant deathloss and animal performance. It assumes that actual profits are divided in proportion to the inputs supplied by each party (valued at pig purchase date) to finish the hog to market weight. Based upon the budgets in Table 3, the seller supplies 37 percent of the inputs and the buyer supplies 63 percent. Corn and supplement prices are the simple average of prices when the pig was bought and the hog was sold. This formula resulted in lower average and maximum prices, less variability, and a higher minimum price relative to actual prices.
Table 3. Budgets. |
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| Inputs per head to produce: | ||
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Feeder |
Finisher |
Corn (bu.) |
3.30 |
10.50 |
Supplement (Ibs.) |
53.00 |
125.00 |
Operating cost w/labor |
$17.00 |
$22.00 |
Overhead cost |
$8.00 |
$7.00 |
Variability is measured as the standard deviation. |
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Impact on buyer and seller returns
While average prices and variability are of concern, the more important question is how profits are affected under the different pricing arrangements. Returns to labor, overhead, and management for feeder pig producers and finishers using actual auction market prices were compared to those using the formulas over the 1986 to 1990 period as shown in Table 4.
While the budgets indicate similar labor and overhead costs for both buyer and seller, auction prices provided the buyer a 28 percent higher return and a 41 percent wider range of returns than they do the seller. Comparing the pricing methods on returns rather than feeder pig price puts the formulas in a different light, and may cause one to be preferred to the other.
Profit sharing and paying what the finisher should pay produced the greatest return to the buyer. The remaining formulas generated returns similar to auction prices for the buyer. The seller received the greatest returns from Equation 2, the formula that depends on hog futures and corn prices. The should pay formula produced the smallest and most variable returns to the seller. Cost-plus pricing generated a slightly lower return than did the auction market, but it had no variability. However, feeder pig producer returns under cost-plus pricing will vary due to changes in production efficiency and price changes in inputs other than corn and protein supplement. Profit sharing cut seller returns by more than 50 percent compared with the auction market.
Choosing a formula
It is doubtful that any one formula will satisfy both buyer and seller. These formulas represent starting points for negotiation, rather than a fixed rule to follow. The best formula depends on the objective of each party. Equation 1, the one variable equation based on hog futures prices, is the simplest formula, and provided the buyer a $1.75 per head higher return at only a slightly higher risk (downside risk increases by $2.16 per head). The seller forgoes $1.70 per head profit, but limits his or her downside risk to -$0.32 per head. If one of the seller's objectives is to reduce price risk, this simple formula does quite well. Other formulas that may also be feasible include the profit share and cost-plus formulas, provided the terms are negotiated to make it attractive enough to the other party. The two variable equations, using both hog futures and corn prices, generated feeder pig prices that were $2.55 per hundred higher than auction prices, but buyer returns that were $1.20 lower and more variable than the auction market. Seller returns were $1.15 per head higher, but with similar downside risk.
Table 4. Returns per head to labor, overhead, and management by pricing method. |
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Buyer |
Avg. |
Var.* |
Min. |
Max. |
Actual market |
$18.55 |
$16.82 |
$-20.69 |
$62.39 |
Equation 1 |
20.30 |
20.29 |
-22.85 |
65.72 |
Equation 2 |
17.35 |
18.70 |
-20.68 |
67.33 |
Should pay |
27.59 |
15.88 |
-7.55 |
73.95 |
Cost plus |
18.97 |
23.40 |
-31.96 |
64.67 |
Profit share |
25.84 |
14.60 |
-6.03 |
54.41 |
Seller |
Avg. |
Var.* |
Min. |
Max. |
Actual market |
$13.42 |
$11.87 |
$-11.14 |
$37.41 |
Equation 1 |
11.72 |
5.26 |
-0.32 |
24.42 |
Equation 2 |
14.57 |
9.81 |
-11.01 |
39.25 |
Should pay |
4.71 |
16.24 |
-31.52 |
39.54 |
Cost plus |
13.00 |
0.00 |
13.00 |
13.00 |
Profit share |
6.39 |
8.47 |
-12.05 |
22.90 |
*Variability is measured as the standard deviation. |
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The formula of choice will differ between buyer and seller, and across buyers and sellers, depending on their cost of production and profit objectives. The two parties must decide which pricing method to use, the size of coefficients in the formula, and which prices to use (weekly average futures price or Friday closing price, local elevator corn price, etc.). Although they may wish to periodically renegotiate the coefficients in the model, once a buyer and seller agree upon a formula, they should stick with it for a specified time. Due to the nature of feeder pig prices, the formula may go through extended periods of under pricing or overpricing relative to auction prices, but adjustments should not be made hastily as the formulas are based on long-run relationships.
Adjusting for weight difference
The formulas discussed above are based on a 45pound feeder pig (prices for the 40- to 50-pound weight class). However, pigs trade in a wide range of weights and buyers and sellers should adjust their formula to reflect the actual weight of each lot of pigs traded. Sioux Falls, South Dakota, terminal market prices for feeder pigs in three weight classes (30-40, 40-50, and 50-60) were compared weekly for a three year period (1988-1990) to establish the price relationship.
Weight range |
Average |
Difference |
30 - 40 |
37.31 |
|
40 - 50 |
44.29 |
6.98 |
50 - 60 |
49.40 |
5.11 |
The prices were highly correlated, but significantly different from each other. The differences were not significantly related to hog, corn, or soybean meal prices. Thus, the simple average difference captures the value of pigs at various weights reasonably well.
Buyers and sellers can adjust their formula price to reflect the relative value of pigs weighing other than 45 pounds by using the following formula. The pig is worth 69.8¢ less per head for each pound less than 45 pounds. The pig is worth 51.1 ¢ per head more for each pound over 45 pounds.
As with the initial formulas, buyers and sellers must negotiate the price adjustment that is satisfactory to both parties. The accompanying example illustrates how to use the formulas to estimate prices and make the weight adjustment for pigs weighing more or less than 45 pounds.
Problems of formula pricing
The formulas described here and their comparison to actual spot market prices has two inherent problems.
Differences in pig quality
First, the statistical analysis and comparisons are based on auction market prices that represent pigs that may be different from direct trade pigs. In fact, buyers and sellers trade directly because they believe that their pigs are of higher quality (less stress, higher health status, etc.) than auction market pigs. Thus, the price derived by the statistical formulas may need to be adjusted upward, because direct trade pigs often sell at a premium to auction pigs.
The partial budget formulas are based on specific estimated production parameters. The production track record of the pigs on an individual's farm should be incorporated into the price negotiation process to more accurately reflect the value of the pigs to the buyer.
Declining access to auction prices
The second problem is that auction reporting by third-party state and federal government agencies are declining. This lack of reporting is one of the reasons why producers may find formulas attractive as they are based on readily observable data. However, if feeder pig prices are no longer reported, it will not be possible to update the formulas estimated here. Thus, formulas based on reported prices are only a short-term substitute for reported prices. Without a dependable feeder pig price series, formula updating will not be possible.
Summary
Feeder pig buyers and sellers seeking an alternative to the increasingly thinly traded spot market has many alternatives from which to choose. The formulas discussed here are neither exhaustive nor perfect solutions, but serve as starting points for negotiation. Buyers and sellers should examine the impact the various pricing formulas have on their operation and cost of production. The appropriate formula will depend on the needs of the two parties and whether it is a one-time sale or an ongoing agreement. The formulas appear to work better in ongoing agreements where the impact of a too high or too low price estimate will be offset on a later time.
