equipment replacement in agriculture: the case of a 110-hp tractor with an overhauling option

Agricultural & Applied Economics Association

Equipment Replacement in Agriculture: The Case of a 110-hp Tractor with an OverhaulingOptionAuthor(s): Angelos Pagoulatos and Melanie BlackwellSource: Review of Agricultural Economics, Vol. 18, No. 1 (Jan., 1996), pp. 115-125Published by: Oxford University Press on behalf of Agricultural & Applied Economics AssociationStable URL: http://www.jstor.org/stable/1349671 .

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EQUIPMENT REPLACEMENT IN AGRICULTURE: THE CASE OF A 110-HP TRACTOR WITH AN OVERHAULING OPTION

Angelos Pagoulatos and Melanie Blackwell

Smith, and subsequently others, have argued that equipment replacement decisions concern the minimization of cost in producing a given output. Faris and Perrin were the first to delineate a point-input, point-continuous, output- replacement model for farm machinery. This model was later extended by incorporating specific expressions for taxes and inflation (Chisholm; Kay and Rister; Bates, Rayner, and Custance; Perry and Nixon; Perry, Bayaner, and Nixon). Reid and Bradford used a multiperiod, mixed- integer programming model to determine replacement intervals within the overall strategies for a farm. Chisholm; Leatham and Baker; and Perrin recast the replacement decision as one where the entrepreneur maximizes the present value of the future stream of residual earnings from the productive process associated with the asset.

Each of these earlier replacement models is prescriptive and fundamentally deterministic. Each attempts to find the "optimal" age at which equipment should be replaced and recommends a planned replacement policy. As an alternative, this study proposes a dynamic model that accounts for the possibility of necessitating an overhaul prior to a predetermined "optimal" replacement age. If overhaul is required, two viable options exist: trade the equipment or overhaul it. The owner needs to compare the present value of the effects of each action on the owning and operating cost of the equipment. Of course, the timing of equipment overhaul will affect the present value of each action. If, at a certain age, overhauling is determined to be the least costly alternative, the equipment owner

needs to know by how much. This cost differential will establish the maximum an owner would be willing to pay for the overhaul.

Considering the problem as one of piecemeal replacement of a single machine, demand considerations can be ignored since the output expansion effects are negligible. As a result, the cost-minimization procedure is adequate for the replacement problem. A dynamic programming framework is proposed to model the decision alternatives of overhauling and trading a 10-hp tractor. The dynamic programming model considers the relevant costs of owning and operating the tractor. Specifically, standard operating costs (repair, maintenance, and fuel costs) and depreciation are included. In addition, reliability (opportunity) costs that arise from operating an aging tractor are estimated. Losses or the number of tractor breakdowns in a specific time period are assumed to be greater as the machine ages; the value of these losses are the relevant opportunity costs. Shadow prices from a linear programming (LP) simulator of a Midwestern farm are used to estimate these opportunity costs. The implications of alternative tax strategies upon the costs of owning and operating the tractor over a period of time are also examined.

Opportunity Costs

Operational reliability is defined as the probability that a machine will function satisfactorily under specified conditions at any given time, and is computed as one minus the probability of failure. As a machine ages, the probability of a temporary breakdown or a loss in reliability increases, causing not only increased repair costs, but also costs resulting from a loss of timeliness.

For many operations during a cropping season, an optimal period exists when an

Angelos Pagoulatos is a Professor of Agricultural Economics at the University of Kentucky, Lexington, KY and Melanie Blackwell is an Associate Professor of Economics and Human Resources, Xavier University, Cincinnati, OH.

Review of Agricultural Economics 18(1996): 115-125 Copyright 1996 North Central Administrative Committee



116 REVIEW OF AGRICULTURAL ECONOMICS, Vol. 18, No.1, January 1996

operation should be completed. Timeliness costs approach zero for those operations that need not be finished quickly (Hunt). However, for operations where equipment reliability is essential, temporary breakdowns will result in delays that reduce yields, and hence returns.

A model suitable for calculating timeliness (opportunity) costs due to temporary breakdowns of a tractor is the "Kash Profits" model. "Kash Profits" is a computerized linear programming model used at the University of Kentucky as an Extension tool to help Kentucky grain farmers better manage their crops (Debertin et al.). Five crops are considered in the model: corn, single- crop soybeans, wheat, double-crop soybeans, and silage based on a 10-year yield series. The crop plan is constrained by the availability of land, labor, machine time, and days available for work. There are a total of 185 activities and 116 constraints, where each activity carries a revenue or cost per unit of activity level.

Six planting periods combined with three harvesting periods are included in the model, thereby providing for different returns and input costs in each case. The model selects the crop combination and schedules planting, harvesting, and field operations to maximize net returns. Yields are reduced for delays arising from temporary tractor breakdowns in any of the above operations. According to engineering studies and assuming normal repairs and maintenance, accumulated breakdown hours for tractors

(ABx) are estimated as (American

Society of Agricultural Engineers):

ABx = (0.0003234)H 1.4173, (1)

where H is the accumulated hours of tractor use. In the base model, annual breakdown hours (Bx) are calculated for each age of the tractor (assuming 800 hours of annual tractor use). The annual breakdown hours are reported in Table 1. Annual breakdown hours increase as accumulated hours of tractor use increase.

The value of yield reductions is calculated from the optimal linear programming solution to "Kash Profits" in accordance with data collected from the Kentucky Agricultural Experiment Station field trials and farmer estimates collected by the Kentucky Crop Reporting Service

(Pagoulatos and Kontomichos). The model is solved under the assumption that no temporary breakdowns occur. From the solution, the optimal percentage of annual tractor use that occurs in each time period of critical farm operations is obtained and presented in Table 2. These percentages of annual tractor use also measure the probability of a temporary breakdown occurring during a critical time period, denoted p, (j = 1, ... , 10 critical time periods).

An estimate of losses in net returns for each critical time period arising from breakdown hours using an x-year-old tractor can be obtained by multiplying the tractor-hour shadow price in each critical time period (y) by the expected breakdown hours for that critical period (pjBx)

as long as the reduction in tractor-hours does not exceed the lower limit of the range of feasibility (Table 2). When the latter event occurs, a new solution to the linear programming models must be obtained to assess changes in net returns. As a result, the imputed value of the expected breakdown hours, or the expected annual timeliness costs (TCx) are estimated as:

10 TCx = BxyiPi,

(2) j--1

and are reported in Table 1. Annual opportunity costs of operating an

x-year-old tractor (OPx) are calculated as the

difference in annual timeliness cost associated with an x-year-old tractor and that associated with a tractor in its first year of operation. These annual opportunity costs for the base model (using 800 hours of operation annually) are reported in Table 3.

Tax Strategies

The estimation of the annual costs of owning and operating a I I 0-hp tractor are completed by including the effects of tax depreciation policies. Two methods of incorporating tax effects are used to determine deductions for a tractor which, for tax purposes, has a class life of seven years. For both methods, actual tax schedules are used rather than constant marginal tax rates (Perry and Nixon). The first method (referred to as method 1) uses the 200



EQUIPMENT REPLACEMENT IN AGRICULTURE: THE CASE OF A l10-hp TRACTOR Pagoulatos, Blackwell 117

Table 1. Salvage Values and Annual Costs of Owning and Operating an x-Year-Old Tractor

Year of Salvage Annual Expected Annual Tractor Use Value Breakdown Timeliness

(x) $ (sO) Hours (Bx) $ (TCx)

1 18,827 4.21 55.70 2 17,568 7.03 93.00 3 16,373 8.73 115.50 4 15,235 10.09 132.05 5 14,151 11.17 146.71 6 13,117 12.15 159.40 7 12,133 13.03 171.07 8 I1,196 13.83 181.65 9 10,305 14.57 191.71 10 9,460 15.27 200. 18

Source: Pagoulatos and Kontomichos.

Table 2. Optimal Solution Results of "Kash Profits"

Available Tractor Percentage Critical Time Good Tractor Hours Flours Used of Annual Shadow

Period Work Hours per Available (Optimal 800 Hr. Use Prices (j) Days Day (Original RHS) Solution) (pi) $ (y)

Apr 15 - May 4 4.3 12 52 52.00 .06500 $22.52 May 5 - May 13 3.4 12 41 41.00 .05125 19.24 May 14 - May 22 4.1 12 49 49.00 .06125 0.95 May 23 - May 31 4.6 12 55 11.48 .01435 0.00 June 1 - June 9 4. 1 12 49 6.87 .00859 0.00 June 10 - June 18 5.7 12 68 4.64 .00580 0.00 Sept 13 - Sept 26 9.0 10 90 20.33 .02541 0.00 Sept 27 - Oct 17 13.7 10 137 137.00 .17125 33.91 Oct 18 - Nov 7 12.0 10 120 120.00 .15000 17.25 Nov 7 - Nov 28 10.8 10 108 108.00 .13500 17.25

.68790

Source: Pagoulatos and Kontonmichos.

Table 3. Costs of Owning and Operating a 110-hp Tractor Operated an Average of 800 Hours Annually (m,n)

Year of Repair and Tractor Maintenance Opportunity Method I Tax Method 2 Tax Use Cost Depreciation Cost Deduction Deduction (x) $ (Rx) $ (Dx) $ (OPx) $ (T) $ (T)

I 156.8 16,173 0 3,928 1,805 2 470.4 1,259 37 4,096 4,490 3 784.0 1, 95 60 4,195 4,516 4 1,097.6 1,138 77 4,148 4,469 5 1,411.2 1,084 92 4,101 4,422 6 1,724.8 1,034 104 4,054 4,375 7 2,038.4 984 116 4,328 4,489 8 2,352.0 937 126 4,603 4,603 9 2,665.6 891 137 4,556 4,556

10 2,979.2 845 145 4,508 4,580

Source: Pagoulatos and Kontomichos.



118 REVIEW OF AGRICULTURAL ECONOMICS, Vol. 18, No.1, Januaiy 1996

percent declining balance method and a half-year convention with a change to the straight-line method. The percentages used from year one to year eight are: 10.71, 19.13, 15.03, 12.25, 12.25, 12.25, 12.25, and 6.13. The second method (method 2) uses the Section 179 Deduction whereby up to $17,500 can be deducted if certain provisions are met during the tax year in which the tractor is first placed in service. The declining balance/straight-line method also applies. Thus, assuming an initial cost of $35,000 in the base model, the tractor is depreciated using the two alternative methods in Table 3 (Master Federal Tax Manual).

Annual tax deductions (at the rate of 26 percent for Federal Income Tax; 15.3 percent for U.S. Social Security) are subtracted from the sum of the annual standard operating costs, depreciation, and opportunity cost to determine the annual cost of owning and operating an x- year-old tractor (mx). These costs are reported in Table 1, along with the salvage values of an x- year-old tractor (sx).

The Case of Tractor Replacement

For the base model, assume that a new 110-hp diesel tractor costs $35,000 (Shurley et al.). Such a tractor is operated 800 hours/year, and the costs of owning and operating an x-year old tractor in any year t include maintenance and repair costs (Rx), fuel costs (F,) and depreciation net of tax deductions (DX-Tx). In addition, opportunity costs

(OPx) become foregone profit

when the tractor breaks down and is temporarily away from productive services. Let

mx denote

the costs of owning and operating a tractor in its xth year of operation, where:'

mn = Fx + Rx + OPx + Dx -

TX. (3)

If a new tractor has been purchased, the goal is to determine a replacement policy that minimizes the net cost of owning and operating a tractor for a period of time. We choose to analyze this problem over a 10-year horizon, assumed to be the economic life of the tractor (Hunt and Shurley et al.).

This replacement model does not consider a farmer who owns and operates more than one tractor. In such a case, the physical and economic life of a tractor might be extended con- siderably; in part because of reduced annual use, and in part from its use in less demanding jobs. The tractor replacement and overhauling problem is then coupled with the management of two or more tractors and constrained by farm financial considerations. If timely farm operations can be continued with a second tractor when the other tractor temporarily breaks down, a different opportunity cost exists that depends on both the mix of crops and the timely requirements of farming activities. The results of this study will have to be interpreted by each farm operator according to his or her aversion to risk, capital constraints, etc.

The real discount rate chosen for the base study is six percent. Following Winston, a dynamic programming formulation of the equipment replacement model is chosen. Let the stage be the year t and the state at the beginning of any stage be the age of the tractor x. Define f,(x) as the minimum net cost (dollars in year t) incurred from year t to year 10, given that at the beginning of year t, the tractor is x years old.

'Hourly fuel consumption can be estimated as 6 percent of the maximum power-takeoff (max PTO hp) required by the implements and that, for a l10-hp diesel tractor, max PTO hp=70.67 (American Society of Agricultural Engineers). Annual fuel costs are obtained by multiplying the hourly fuel consumption of the tractor by the anticipated 800 hours of annual use and the cost of a gallon of diesel fuel (assumed to be $1). Total engine lubrication cost is estimated at 15 percent of fuel cost. Therefore, annual

fuel and engine lubrication cost, denoted Fx,

amounts to $3,901 and is given by: Fx=(0.06)(mnax PTO hp) (800)(1.15).

Repair and maintenance costs in the tractor's x"' year of operation, denoted

Rx, include the cost of labor associated

with maintaining and repairing the tractor (Table 3). Accumulated repair and maintenance costs, ARx,

are proportional to the use of the tractor (Rotz and Bowers):

ARx = P(0.007)[use(age+ 1)/1000]. Annual depreciation costs are calculated as the

difference in salvage cost net of the asset's salvage in that year, values at the beginning of each year and at the end of that year (Table 3). Salvage values

(sx) are calculated based

on the work by Perry, Bayaner, and Nixon using the following equation:

s, = Price [(0.9218 - 0.008 Use (0.41) - 0.0223 (age +1) 0.98)]2.439.



EQUIPMENT REPLACEMENT IN AGRICULTURE: THE CASE OF A I10-hp TRACTOR Pagoulatos, Blackwell 119

Since the problem is over at the beginning of year 10, the value of the tractor at the beginning of year 10 is the salvage value of an x-year-old tractor

(sx). Then:

flo(x) = sx (for x = 1, 2,..., 10). (4)

Operational reliability decreases and maintenance and repair costs increase with time. When a tractor breaks down necessitating an overhaul, a choice must be made with respect to keeping the tractor, trading the tractor (at a price that accounts for the cost of overhauling), or overhauling it. Breakdown of a tractor that necessitates an overhaul can be caused by abrupt breakdowns such as breaking of pistons, or severe loss of performance (hp hours/gallon) over a period of time. For a variety of reasons, a loss of performance caused by a loss of compression could be remedied with an overhaul. Because of manufacturer warranties that provide for repair or replacement when operational failure occurs early in the life of a tractor, we consider a model where overhauling is not an option before the tractor's fourth year of operation. The cost of an overhaul is denoted as Coh. Overhauling adds several years to the physical life of the tractor, but is assumed to add two years of economic life to the tractor. When a tractor is overhauled at age eight, the repair, maintenance, and opportunity costs are those associated with a tractor that is age six (and, hence, in its seventh year of operation). Depreciation and tax advantages other than the cost of the overhaul, which is considered a farm expense, are assumed to remain unchanged. This means that a tractor that is overhauled at age eight will still have a depreciation cost and tax deduction associated with a tractor in its ninth year of operation.

For tractors of overhauling age (3<x<10):

F, + R, + OP1 + D, - T1 +

(1 + i)-'ft+ (1), (TRADE)

Fx-2+1 + Rx-21 + OPx-21 +

Dx

- T, + (1 + i)'ft,(x + 1) (6)

+ Coh, (OVERHAUL)

ft(x) = min:

Fx-2I1 + Rx-2+1 + OPx2,I1 + Dx - Tx (7)

+ (1 + i)-' f,(x + 1), (KEEP/OH)

Fx+1 + Rx+I + OPx+1 + Dx+I - Tx(8 (8) + (1 + i)-'ftI (x + 1), (KEEP)

Equation (6) states that in any year after the third year of operation, the farmer can trade, overhaul or keep the tractor as it is. Since operating costs will differ for the keep option (depending upon whether the tractor was overhauled in a previous year or not), two keep options, KEEP/OH and KEEP, are delineated.

For t > 0 and x < 3, the dynamic programming problem is:

F1 + R + OP1 + D1 - TI (9)

+ (1 + i) 'ft,+(1), (TRADE)

f,(x) = min:

Fx+I + Rx1 + OPx + Dx Il

- Tx+1 (10)

+ (1 + i)-'ft+i (x + 1), (KEEP)

and:

f0(O) = F1 +R + OP1 +?D -T (11) + (1 + i)-if(1). (KEEP)

An assumption is made that state 0 can be achieved only at time 0, implying the tractor must be kept in the year it is purchased (equation (11)).

Traditional Model Solution

Traditional replacement models attempt to find an "optimal" age for tractor overhaul and/or trade decisions. Using this traditional objective, the base dynamic programming problem in equations (5) through (8) is solved using method 2 (179 deduction) tax strategy over a 10-year horizon with no specified value assigned to

Cob. Method 2 is the cost-minimizing tax strategy (Table 4). The results of this traditional solution




are to keep the tractor and overhaul it at the beginning of year four if the cost of an overhaul is less than $3,873. If the cost of an overhaul is near this upper limit of $3,873, then a trade should be considered in year seven. For costs of overhauling that are significantly less than $3,873, trading only becomes an attractive option after year seven (with cost of $13,063-Coh). If no trade takes place, the discounted cost of the "optimal" policy is $53,923 plus the discounted cost of the overhaul, Cohx(1.06)3. These results are presented in Table 4.

To read the solution from Table 4, begin with year 1, where the only option available to the tractor owner is that of keeping the tractor without overhauling. (This action results in a discounted cost of $53,923 over the 10 years of the problem horizon). In year two, the tractor owner has a one-year-old tractor that can be kept (without overhauling) or traded. The minimum- cost option is to keep the tractor. (The keep option results in a discounted cost of $35,606 over the remaining nine years of the horizon problem versus $45,841 if the tractor is traded.) In year three, the tractor owner has a two-year- old tractor and faces the same options as in the previous year. The least cost option is to again keep the tractor without overhauling ($32,228 for keeping versus $40,808 for trading). By the beginning of year four, the owner has a three- year-old tractor that can be kept, traded, or overhauled. The least discounted cost of $28,331 is associated with overhauling the tractor. Note that this is true only if the cost of an overhaul (Col,) is less than the difference between the cost of keeping the tractor after overhauling it and the least costly strategy without an overhaul. (In this case, the least costly strategy without overhauling is to keep the tractor, resulting in a maximum overhaul cost of $32,204-$28,331= $3,873). Optimal strategies in subsequent years can be determined in a similar fashion.

The above solution reflects the traditional use of the dynamic programming model. But why use the model just to obtain the traditional prescriptive policy when the model's dynamic nature can be used? That is, let it guide the tractor owner to the least costly strategy if the tractor incurs a breakdown that requires an overhaul. This breakdown (or loss of perfor-

mance) can occur during any year (starting with year four), and then the trade-in value of the tractor will be reduced by the value of the overhaul.

Table 4 shows the discounted cost to year 10 of owning and operating tractors of varying ages in any given year of the planning horizon. Should a tractor fail before the 10'h year, an overhaul or a trade must occur. The maximum amount an owner of an x-year-old tractor would be willing to pay for an overhaul (Coh) is the difference between the cost of keeping the tractor after overhauling it and the least costly strategy without an overhaul. If the actual cost of the overhaul exceeds

Cob, the optimal strategy

is to trade the tractor. Note that in our example, the present value of the maximum amount an owner would be willing to spend on an overhaul (Coh) varies from $3,873 in year four for a three- year-old tractor to $681 for a nine-year-old tractor at the beginning of year 10.

Sensitivity analysis of the replacement model is obtained by varying those parameters that are associated with the greatest uncertainty. Thus, tractor price, annual hours of use, age of tractor at which overhaul may be required, years of added life to the tractor after overhaul, and real discount rates reflecting different levels of inflation and risk are varied. Table 5 presents a summary of the results obtained when using tax method 2 (179 deduction). For a $35,000 tractor with 800 hours of annual use, cost-effective overhauling at the beginning of year four decreases from $4,109 to $3,349 as the real discount rate increases from 3 to 12 percent. As hours of use increase from 600 to 1,000 and the value of the tractor increases from $30,000 to $40,000, the maximum an owner would be willing to spend for a cost-effective overhaul increases from $2,055 (for a $30,000 tractor with 600 hours of annual use) to $5,645 (for a $40,000 tractor with 1,000 hours of annual use). Cost-effective overhaul decreases in value as the real discount rate increases and as a lower priced tractor is considered, all else being equal. Decreasing the age at which an overhaul may be required from four to two raises the cost of an overhaul by about $1,000 in years two and three (about $4,800). Increasing the number of years of life after overhauling reflects an average



Table 4. Base Run Cost Results (Tax Method 2, 179 Deductions)'

Tractor Age 9 8 7 6 5 4 3 2 1

Beginning Keep w/o OH 1,499 2,527 3,598 4,872 6,190 7,394 8,645 9,946 11,372 of Year 10 Keep w/o OH 681 681 681 681 681 681 681 681 681

Coh <646 <647 <649 <651 <654 <659 <667 -- --

Keep w OH 2,145 3,175 4,247 5,524 6,845 8,053 -- --

Trade w OH (681-Coh) (681-Coh) (681-Coh) (681-Coh) (681-Coh) (681-Coh) -- -- --

Year 9 Keep w/o OH -- 5,779 4,579 3,179 1,587 1,151 1,248 3,285 4,181 Trade w/o OH -- 6,351 6,351 6,351 6,351 6,351 6,351 6,351 6,351 Coh -- <1,257 <1,260 <1,264.4 <1,269.7 <1,277.2 <1,289.3 --

Keep w OH -- 4,522 3,319 1,914 317 1,162 -- --

Trade w OH -- (6,351-Coh) (6,351-Coh) (6,351-Coh) (6,351-Coh) (6,351-Coh) -- -- --

Year 8 Keep w/o OH -- -- 12,416 10,894 3,183 7,453 5,836 3,106 2,102 Trade w/o OH -- -- 13,135 13,135 13,135 13,135 13,135 13,135 13,135 Coh -- -- <1,835 <1,840 <1,847 <1,857 <1,872 -- --

Keep w OH -- -- 10,581 9,053 7,335 5,595 -- -- --

Trade w OH -- -- (13,135-Coh) (13,135-Coh) (13,135-Coh) (13,135-Coh) -- -- --

Year 7 Keep w/o OH -- -- -- 18,287 16,461 14,619 12,759 9,240 8,132 Trade w/o OH -- -- -- 19,063 19,063 19,063 19,063 19,063 19,063 Coh -- -- -- <2,383 <2,391 <2,402 <2,419 -- --

Keep w OH -- -- -- 15,904 14,070 12,216 -- -- --

Trade w OH -- -- -- (19,063-Coh) (19,063-Coh) (19,063-Coh) -- -- --

Year 6 Keep w/o OH -- -- -- -- 23,436 21,485 19,519 15,255 13,919 Trade w/o OH -- -- -- -- 24,752 24,752 24,752 24,752 24,752 Coh -- -- -- -- <2,903 <2,915 <2,933 --

Keep w OH -- -- -- -- 20,533 18,569 -- -- --

Trade w OH -- -- -- -- (24,752-Coh) (24,752-Coh) -- --

aThe base sum is for a $35,000 tractor operating 800 hours per year and an assumed discount rate of 6 percent.

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Table 4, Cont'd. Base Run Cost Results (Tax Method 2, 179 Deductions)a

Tractor Age 8 7 6 5 4 3 2 1 0

Beginning Keep w/o OH -- -- -- -- 28,065 25,997 21,147 19,592 of Year 5 Trade w/o OH -- -- -- -- 30,211 30,211 30,211 30,211 --

Coh -- -- -- -- <3,398 <3,417 -- -- -- Keep w OH -- -- -- -- 24,667 -- -- -- -- Trade w OH -- -- -- -- (30,211-Coh) -- -- --

Year 4 Keep w/o OH -- -- -- -- -- 32,204 26,801 25,152 -- Trade w/o OH -- -- -- -- -- 35,564 35,564 35,564 -- Coh -- -- -- -- -- <3,873 -- --

Keep w OH -- -- -- -- -- 28,331 -- -- --

Year 3 Keep w/o OH -- -- -- -- -- -- 32,228 30,486 -- Trade w/o OH -- -- -- -- -- -- 40,808 40,808 --

Year 2 Keep w/o OH -- -- -- -- -- -- -- 35,606 -- Trade w/o OH -- -- -- -- -- -- -- 45,841 --

Year I Keep w/o OH -- -- -- -- -- -- -- -- 53,923

aThe base sum is for a $35,000 tractor operating 800 hours per year and an assumed discount rate of 6 percent.

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Table 5. Results with Alternative Assumptions

600 Hours 800 Hours 1,000 Hours Real Value of Coh at Age at Cost at Coh at Age at Cost at Coh at Age at Cost at Discount Tractor Year 4 Trade Trade Year 4 Trade Trade Year 4 Trade Trade Rate $(000) $ Yrs $ $ Yrs $ $ Yrs $

3% 30 <2,055 10 41,445 <3,497 7 55,188 <2,956 6 67,796 35 <2,379 10 43,984 <4,109 7 58,600 <3,498 6 71,863 40 <2,702 10 46,524 <4,721 7 62,012 <4,040 6 75,931

6% 30 <1,875 10 38,513 <3,343 10 50,659 <3,603 7 62,372 35 <2,195 10 41,056 <3,873 10 53,923 <4,236 7 66,338 40 <2,493 10 43,599 <4,403 10 57,186 <4,869 7 70,304

12% 30 <1,641 10 33,814 <2,891 10 43,451 <4,201 7 53,520 35 <1,898 10 36,311 <3,349 10 46,498 <4,923 7 57,227 40 <2,156 10 38,808 <3,807 10 49,546 <5,645 7 60,933

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savings of $400 for early-age overhauls and $200 for late-age overhauls. Neither change altered the basic decisions between overhauling and trading.

With 800 hours of use and a 3 percent real discount rate, the replacement age is seven years. For a 12 percent real discount rate, the optimal replacement age becomes six years for a tractor valued between $30,000 and $40,000. The discounted cost of trading a tractor at the optimal replacement age decreases with higher real discount rates, higher priced tractors, and higher annual use, all else being equal (Table 5). When tax method I is used, there is a higher discounted cost of trading or keeping a tractor at any age. The discounted cost of trading a tractor at replacement age is approximately $400 to $1,368 higher than the cost obtained using tax method 2 (reported in Table 5).

Conclusions

A methodology for addressing the optimal tractor replacement problem that incorporates estimated relevant opportunity costs and allows for the option to overhaul has been specified. Since actions in one time period have an impact on costs in future time periods, a dynamic framework for depicting the relevant strategies at each stage of the decision process is formulated. The base model centers on a 110-hp tractor ($35,000) with an estimated life of 10 years, and operated an average of 800 hours annually.

The results of the model indicate that the owner of such a tractor taking advantage of tax method 2, should trade the tractor in year seven. However, the model is expanded to consider a breakdown requiring an overhaul. The net benefit of an overhaul is derived from its discounted future savings. If the actual cost of overhauling the tractor exceeds the derived one, then the optimal solution is to trade the tractor. Allowing for the possibility of overhauling adds a new dimension to the optimal replacement problem and provides the maximum amount of expendi- ture that would make overhauling an optimal strategy.

Annual opportunity costs, as calculated from an LP model that simulates a typical

Midwestern farm, contribute only a small proportion to total costs in the base model (less than 2 percent for most years). Varying the annual usage of the tractor had a small impact on the LP solution, and thus on the dynamic programming results. Therefore, opportunity costs as calculated in this study, did not have an appreciable impact on the optimal replacement policy.

The results presented in this article are based on a set of assumptions regarding present and future costs, discount rates, hours of use, and the planning horizon. The usefulness of the analytical framework presented here is in the use of farmer-specific information in its solution. The model developed and used in this study is limited to the replacement of a single tractor and the results can be interpreted differently by farm managers, depending on their risk aversion. Parameters and alternative assumptions can be used to generate additional solutions. Additional work is needed to consider the overhauling option when a farm has more than one tractor available for different tasks.

[Received July 1993. Final version received October 1995.]

References

American Society of Agricultural Engineers. ASAE Standards. St. Joseph, MI, 1988.

Bates, J.M., A.J. Rayner, and P.R. Custance. "Inflation and Farm Tractor Replacement in the U.S.: A Simulation Model." American Journal ofAgricultural Economics 61(1979):331-34.

Chisholm, A.H. "Effects of Tax Depreciation Policy and Investment Incentives on Optimal Equipment Replacement Decisions." American Journal of Agricultural Economics 56(1974):776-83.

Debertin, D., C. Moore, L. Jones, and A. Pagoulatos. "Impacts on Farmers of a Computerized Management Decision-Making Model." American Journal of Agricultural Economics 63(1981):270-74.

Faris, J.E. "Analytical Techniques Used in Determining the Optimal Replacement Pattern." Journal of Farm Economics 42(1960):755-66.

Hunt, D. Farm Power and Machinery Management. Ames, IA: Iowa State University Press, 1983.

Kay, R.D. and E. Rister. "Effects of Tax Depreciation Policy and Investment Incentives on Optimal Equipment



EQUIPMENT REPLACEMENT IN AGRICULTURE: THE CASE OF A I10-hp TRACTOR Pagoulatos, Blackwell 125

Replacement Decision: Comment." American Journal of Agricultural Economics 58(1976):355-58.

Leatham, D. and T.G. Baker. "Empirical Estimates of the Effects of Inflation on Salvage Value, Cost, and Optimal Replacement of Tractors and Combines." North Central Journal of Agricultural Economics 3(1981):109-17.

Master Federal Tax Manual. New York, NY: The Research Institute of America, Inc., 1990.

Pagoulatos, A. and N. Kontomichos. "Estimation of Agricultural Estimation of Agricultural Tractor Reliability Costs." Agricultural Economics Research Report 36 Lexington, KY: University of Kentucky, February, 1982.

Perrin, R.K. "Asset Replacement Principles." American Journal of Agricultural Economics 54(1972):60-67.

Perry, G.M. and G.J. Nixon, "Optimal Tractor Replacement: What Matters?" Review of Agricultural Economics 13(1991): 119-28.

Perry, G.M., A. Bayaner, and C.J. Nixon. "The Effect of Usage and Size on Tractor Depreciation." American Journal ofAgricultural Economics 72(1990):3 17-25.

Reid, D.W. and G.L. Bradford. "On Optimal Replacement of Farm Tractors." American Journal of Agricultural Economics 65(1983):326-3 1.

Rotz, C.A. and W. Bowers "Repair and Maintenance Cost Data for Agricultural Equipment." Paper 91-1531, American Society of Agricultural Engineers, 1991.

Shurley, D., D.B. Peters, F.J. Benson, and L.D. Swetnam. "Farm Machinery and Equipment Cost Estimates for 1990." University of Kentucky Department of Agricultural Economics, Lexington, KY, 1990.

Smith, V.L. "The Theory of Investment and Production." Quarterly Journal of Economics 73(1959):61-87.

Winston, W.L., Operations Research: Applications and Algorithms. Boston, MA: Duxbury Press, 1987.



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