Laser Leveling and Federal Incentives

John Daubert and Harry Ayer

Our empirical analysis shows that federal tax and cost-sharing incentives signifi-cantly affect the profitability of laser leveling - a new irrigation technology whichsharply reduces gravity water applications. However, the structure of the incentives maymake slow rather than rapid adoption of the technology most profitable. Methodologyplus results for a wide range of physical and economic conditions are given.

Water policy in the West now stresseswater conservation in place of federal watersupply projects. To encourage water conser-vation in agriculture, the federal governmenthas introduced cost-sharing and tax deprecia-tion incentives that enhance private returnsto conservation investments. However, de-pending on how the incentives are struc-tured, they may also slow the rate at whichindividuals invest.

Laser leveling of gravity irrigated fields isan important new water-saving technology, 1

John Daubert is an Assistant Professor of AgriculturalEconomics, University of Arizona, and Harry Ayer is anAgricultural Economist, Natural Resource EconomicsDivision, ERS, USDA, and Adjunct Professor of Ag-ricultural Economics, University of Arizona.

The authors wish to acknowledge support from theNatural Resource Economics Division, Economic Re-search Service, U.S. Department of Agriculture and theUniversity of Arizona Agriculture Experiment Station,Department of Agricultural Economics, College of Agri-culture, Tucson, Arizona.

Review comments by David Barkley, William Martinand John Hostetler, plus anonymous journal reviewersare appreciated.

1The laser beam is transmitted from a rotating commandpost generating a light plane on the level or at predeter-mined grade. A receiver is mounted on a mast attachedto a scraper. The signal received keeps the scraperblade on the desired grade by operating hydrauliccontrol valves automatically. Results obtained havebeen within plus or minus five hundredths (.05) of afoot. This is greater accuracy than can be obtained with

which, in many instances, cuts water applica-tions by 30 percent or more. The analysisshows, both theoretically and empirically,how federal cost-share and tax incentive pro-grams, along with other factors, affect theprofitability and profit-maximizing rate of las-er leveling.

Setting

The analysis is based on Arizona data. Las-er leveling began in the mid-seventies, and isspreading rapidly in Arizona. Because Arizo-na has a wide range of water costs (the costper acre foot to divert or pump plus deliverwater), soil and field slope conditions, ex-pected changes in future pumping costs, andother factors, our sensitivity analysis coversconditions found in other regions of the Westwhere high-cost gravity irrigation water maymake lasering attractive.

Laser Leveling Benefits and Costs

Farmers can use laser technology to bringtheir irrigated fields to a zero slope, some-times referred to as dead or basin level.Laser leveled fields save water by reducing

traditional land leveling methods. Laser beam landleveling equipment includes: (1) tractor, (2) drag scrap-er, (3) laser command post, receiver control box, and (4)hydraulic valve pump, hose and connections [Hinz andHalderman].Laser technology can also be used to simply smooth asloping field, but here we consider only the case of lasertechnology used in conjunction with dead leveling.

173

Western Journal of Agricultural Economics

deep percolation beyond the root zone andrunoff associated with standard flood and fur-row gravity irrigation systems. Experts claimthat on-farm irrigation efficiencies of 50-65percent, typical of flood and furrow irriga-tion, can be increased to over 80 percent[Pachek]. The increase in field efficiencieslowers irrigation costs, reduces saline returnflows, and allows for acreage expansionwhere water is a limiting factor. In addition,the uniform distribution of water may pro-duce yield increases. While no physical cropproduction data on yield increases are availa-ble, estimates from irrigators, Soil Conserva-tion Service field specialists, and state exten-sion agents, all familiar with laser leveling,range from zero to over 20 percent [Parsons].

Although the costs of using the laser beamare not extreme, the complete laser levelingoperation can be expensive [Daubert andAyer]. On many gravity irrigated farms, thefull operation requires replacing existingditch systems and moving sizeable quantitiesof soil from high to low areas. Initial invest-ment costs to laser level gravity irrigated landvary from $400 to $600 per acre in Arizona[Parsons]. Laser leveling also increases theannual operating costs, since basin fields areusually smaller than fields with furrow irriga-tion. The small field size, added ditches, androads reduce irrigated acreage by approxi-mately three percent, increase machineryturnaround costs by 10 to 15 percent and, inpump areas, raise labor irrigation costs by 50percent [Parsons]. In addition, added touch-up of lasered fields is necessary each 3-5years at a cost of about $50 per acre, and croprevenue is lost while the field is beingsmoothed.

Federal Incentive Programs

The Agricultural Stabilization and Conser-vation Service (ASCS) cost-share programpromotes laser leveling by lowering invest-ment costs of water conservation. The pro-gram reimburses the farmer for a percentageof investment costs, up to a total farm limit

per year. In most of Arizona, ASCS paymentscover 50 percent of investment costs up to$3500 per year.

Federal tax laws enacted in 1968 indirectlyencourage water conservation investment bylowering the farmer's tax liability [InternalRevenue Service]. The soil and water conser-vation depreciation allowance lets farmersdepreciate their laser leveling investment.This depreciation program is quite differentfrom others because the deduction dependson farm gross income rather than asset life.The law allows farmers to depreciate theirinvestment up to 25 percent of gross farmincome per year.

Modeling Laser LevelingInvestment Decisions

The cost-benefit criteria [Howe] which de-termines if federal water projects are worth-while can also apply, with minor modifica-tions, to private water conservation invest-ments. Criterion 1 requires that the presentvalue of the benefits (PVB) equals the pre-sent value of the costs (PVC) for the lastinvestment unit, or in this case acres lasered(L) - dPVB(L)=dPVC(L). Criterion 2 re-quires that the present value of the benefitsexceeds the present value of the costs -PVB>PVC at the optimal acres lasered fromCriterion (1).

The model of the private decision to in-vest, developed in this study, is, however,somewhat different from models of optimalpublic investment. Criteria (1) and (2) usemarket prices rather than shadow prices,value benefits and costs after taxes ratherthan before, and include tax and cost-sharetransfer payments.

The following analysis uses criterion (1)and (2) to determine conditions under whichlaser leveling is worthwhile without federalincentives. Following that, the impact of cur-rent tax incentives and the ASCS cost-sharing program on private profits and themost profitable rate to laser are determined.

174

December 1982

Daubert and Ayer

Private ProfitabilityWithout Federal Incentives

Without federal incentives, the farmerneeds to assess only criterion (2). Privatelaser leveling investments have constantmarginal benefits and costs with respect tothe amount lasered. Laser leveling the wholefarm immediately is profitable when the netpresent value per acre is positive:

PVB>PVC

or

T(1) E

t=l

[(P B+Y G)-(C+X)] (1-M)

(+ r)t

-N(1- M)>I

Private ProfitabilityWith Federal Incentives

Both federal incentive programs substan-tially change the per acre break-even analy-sis. With federal help, more farmers will findlaser leveling profitable, since the programsreduce net investment costs. The programsalso change the optimal number of acreslasered annually. Without the current soiland water conservation tax deduction (S) orthe ASCS cost-share payment (A), and if peracre net benefits are positive, laser levelingthe whole farm in the first year maximizesprofits. Without the federal programs, mar-ginal benefits and costs remain constant as afunction of acres lasered. With the programs,both the marginal benefits and marginal costsper acre per year vary as the farmer laserlevels more acres. The decision rule thefarmer should follow is:

where PVB and PVC are the per acre presentvalue of lasering benefits and costs, P is thefarm water cost per acre foot at the head ofthe field, B is the per acre water savings fromlaser leveling, Y is the per acre percentageincrease in yields, G is the per acre grosscrop revenue, C is the per acre maintenancecost, X is the added machinery, labor, andacreage loss costs per acre, I is the per acreinitial investment cost, M is the marginal taxrate, N is the per acre net crop revenue losswhile lasering, T is the planning horizon, andr is the after tax return on investment thefarmer desires. All prices, costs, net andgross revenues are in real 1980 dollars.

Since water prices or costs vary widely fordifferent farm locations and water sources,the model determines the break-even waterprice per acre foot that just makes laseringprivately profitable. At the break-even pricethe PVB equal the PVC. Following this deci-sion rule, farmers should laser level theirfarmland immediately if water cost exceedsthe break-even water price.

Appendix A shows a cash-flow, and netpresent value and break-even calculations,for a hypothetical but somewhat typicalArizona lasering situation.

(2) Maximize PVB(L)- PVC(L);

= T Pt (1 -M) . L

- t = 1 (l + r)t

- N(1-M) Li+l Ll-(S ·M)

K i T+ I I

j=1 %t=jPt(-M) .

(l + r)t

K FNj(1-M) Lj . (L-(SM)

j = 1 L + r (l +r)- Jj=1 L (I+ri (I+rY JI

K+ E

t=l

At (1- M)

(1+ r)t

where 13 equals [ (P.B+Y YG-(C + X) ] fromequation 1, L1 is the number of acres laseredin the first year outside the ASCS cost-shareprogram, Lj is the number of acres laserleveled in year j under the ASCS program, Kis the number of years it takes to laser thewhole farm, and all other variables are aspreviously defined.

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Western Journal of Agricultural Economics

Soil and Water ConservationTax Depreciation Program

The current tax program enters the laserleveling decision via the second and forth setof terms in equation (2). If the farmer lasers

less than D acres per year, where D equalsI

25 percent of gross farm income, the profitmaximizing rule simplifies to a per acre netpresent value check, similar to equation (1),because the full investment can be subtract-ed from taxable income in the first year. Up

to D acres per year, total costs, includingI

the tax deduction, increase at a constant rate:only the investment costs change from I toI(1-M) as a result of the program. The taxdeduction, by lowering investment costs,will encourage more farmers to laser leveltheir entire farm at once.

Whenever the acres lasered annually ex-

ceeds I the farmer should continue laser

leveling until the dPVB(Lt) = dPVC(L),where Lt equals L1 + L2. While dPVB(Lt) isconstant, the marginal net investment costsper acre per year increase as Lt increases.Investment costs that exceed the yearly limitcan only be deducted from future tax liabili-ty, again subject to the 25 percent of grossfarm income rule. Deductions that the farm-er carries forward impose a real cost; thefarmer could have earned a return on themoney invested but not deducted from thisyear's taxes. Net farm investment costs inyear t (NIt) equal:

(3) NIt =(ILLt)-(St-M)

= (ILt,)

present value of the tax deduction(s) in-creases at a decreasing rate.2 Even thoughthe tax deduction enables more farmers toinvest by lowering net investment costs peryear, the farmers may laser more slowly ifdPVB(Lt) = dPVC(Lt) at a point less than farmsize.

ASCS Cost-Sharing Program

The ASCS cost-sharing program alsochanges the private lasering decision. Be-cause the ASCS payment reduces the break-even price, more farmers will find laser level-ing profitable. Like the tax program, cost-sharing programs having a maximum yearlypayment affect the most profitable rate tolaser. Laser leveling more acres per yearincreases the present value of total net bene-fits, the first and third term in equation (2),but decreases the present value of the ASCSpayments3 , the last term in equation (2). Asfarmers laser more, the number of futureASCS payments, K (farm size divided by Lt),falls. Farmers should continue to laser an

2 The first derivative of per year investment costs inequation 3, with respect to acres lasered per year (L), isthe constant I. Using a continuous formula, the first andsecond derivatives of the tax deduction show the deduc-tion increasing at a decreasing rate:

(1 -e -")Dr

=Ie- rw >0aL

a2S2 (-rI 2)e -rw

aL DW

w=1w=l

<0

[+r M

where W, the number of years it takes beforethe farm depreciates the investment costs in

(ILl t)any given year, equals .Marginal in-D

vestment costs in year t increase because anadditional acre lasered causes investmentcosts to rise at the constant rate I, while the

176

3 Using the continuous formula, the present value of totalASCS payments:

PVP =(1 - e-rF

L- )A,

decreases as the farmer lasers more per year:

aPVP = -AF e- rL-1

aL L2<0

December 1982

Daubert and Ayer

additional acre in the initial year if the pre-sent value of the extra water saving and yieldbenefit minus the operation cost exceeds thepresent value of the forgone extra ASCS pay-ment. As with tax incentives, the ASCS pro-gram makes lasering profitable for morefarmes, but may slow the rate some farmerslaser.

No Government Incentives:Break-even Results for Arizona

The price farmers pay for surface water atthe farm headgate, or the variable pumpingand delivery costs, are key determinants ofthe criterion 2 profitability check. Ratherthan estimate the net present value of laser-ing, the analysis focuses on the break-evenwater prices, the variable cost per acre foot topump or divert plus deliver water to thefield, necessary to just make lasering profit-able. Break-even prices are computed for awide range of possible Arizona farm condi-tions including different yield increases, mar-ginal tax brackets, investment costs, discountrates, time horizons, pumping cost increases,and farm sizes. The break-even analysis as-sumes that the farmer does not receive anycost-share payments or depreciation deduc-tion, thus eliminating any marginal or timingimpacts of federal incentives on the privatedecision.

The break-even costs, even without feder-al subsidies, are low relative to water costs onmany farms (Table 1). For a typical Arizonafarm having investment costs of $600 peracre, no anticipated increase in the real priceof pumping fuel, water savings of 20 acreinches per acre, a marginal tax bracket of 35percent, a yield increase of 10 percent, a realafter tax discount rate of 5 percent, mainte-nance costs of $50 per acre every 5 years, netcrop revenue loss while lasering of $150 peracre, farm size of 500 acres, gross farm in-come of $700 per acre, added machinery,labor and acreage costs of $37 per acre, and atime horizon of 25 years,4 the break-evenwater cost is $30 per acre foot. Many Arizonafarmers using groundwater will find laserleveling profitable, since pumping costs for

typical 300-600 foot lifts often exceed thebreak-even prices. A sensitivity analysis of allvariables shows that the potential yield in-crease, water savings, initial investmentcosts, real increase in pumping costs, and theplanning horizon significantly change thebreak-even water price.

Yield increases sharply lower break-evenprices whenever expected water savings arerelatively low (10 acre inches per acre), buthave much smaller effects when water sav-ings are great. For low water saving situa-tions, a 5 percent increase in yield oftenreduces the break-even water price by $30per acre foot.

Larger water savings also lower the break-even prices. Laser leveling can reduce waterapplications from 10 to 30 acre inches peracre by increasing field efficiency on floodirrigated fields. For any particular yield in-crease, the break-even water price is halvedas water savings go from 10 to 20 acre inchesper acre.

Initial investment costs in Arizona general-ly range from $400 to $600 per acre. Thehigher investment cost increases the break-even water price by $1 to $50 per acre foot,depending on water savings and yield in-crease combinations.

A real three percent fuel price increase, incomparison to a real zero percent increase,lowers the break-even price, especially atlow water savings (10 acre inches) and smallyield increases.

The planning horizon has a substantial im-pact. The break-even price difference oftenexceeds $30 per acre foot as the horizonincreases from 10 to 25 years.

4 Even though laser leveled fields have an infinite life ifmaintained properly, we use 10, 25 and 50 year hori-zons because at some point in time farmland may bechanged to urban or other uses not requiring leveledfields, or new technologies may make lasered fieldseconomically obsolete.

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Laser Leveling

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Daubert and Ayer

Government Incentives: Break-evenResults and The Optimal Rate ofLaser Leveling in Arizona

Soil and Water Conservation Tax Incentive

Even for farmers who laser level the entirefarm immediately, the soil and water conser-vation tax deduction significantly reducesbreak-even water prices by lowering invest-ment costs. The break-even price on theexample farm falls from $30 to just $17 withthe depreciation allowance. Similarly, thebreak-even prices of Table 1, for farms with$600 per acre investment costs and timehorizons of 10, 25, and 50 years, declinebetween $50 and $4 per acre foot (Table 2).For farms with $400 per acre investmentcosts and time horizons of 10, 25 and 50years, break-even prices fall between $40and $3 per acre foot. Under the tax program,even more farms in Arizona will find laserleveling profitable.

With the program, a farmer with watercosts exceeding break-even prices may in-crease returns from laser leveling if only partof the farm is lasered each year, rather thanlasering the entire farm at once. On theArizona example farm, for each 145 acre in-crease in the number of acres lasered, thefarmer must wait another year before deduct-ing the additional investment costs from thefarm's tax liability. The optimal number ofacres to laser each year varies from 145 to 500depending on how much the farm water costper acre foot exceeds the break-even waterprices from Table 1 minus the $13 per acrefoot adjustment due to the program's ex-istence ($30- $13 = $17). The optimum num-ber of acres to level depends on farm watercosts, farm size, gross income, marginal taxrate, real discount rate, and investment cost(Table 3). Changes in yield from the assumed10 percent increase will change the $17 peracre foot break-even water price, but not theamount above the break-even water priceneeded before the farmer should laser more,as shown in Table 3. Different farm sizes orgross farm incomes will not change the deci-sion rule with respect to the difference be-

tween farm water cost and the break-evenwater price, but will change the optimalnumber of acres to laser each year. Differentmarginal tax or discount rates change thedecision rule governing the difference be-tween farm water cost and break-even prices,but not the acres lasered each year. Lower orhigher investment costs change both the wa-ter cost, break-even water price difference,and the acres lasered annually.

The results illustrate that with the tax pro-gram profit maximizing farmers, especiallythose with water costs approximately equal tothe break-even price, will laser more slowly.Specifically, if the example farm has a$31/acre foot water cost (PVB>PVC) withoutthe tax deduction the farmer lasers the wholefarm, while with the tax deduction the farmerlasers only 290 acres per year to maximizethe return from laser leveling.

Federal ASCS Cost-Sharing Programs

Similar to the Soil and Water ConservationTax program, ASCS cost-sharing enhancesthe profitability of laser leveling while sub-stantially changing the optimal acreage tolaser each year. Assuming that the programwill continue at least until the whole farm islasered, some farms will require ASCS pay-ments in order that the benefits from laseringoutweigh costs. Farms that require the ASCSpayment to make lasering profitable receivethe greatest net benefits by annually levelingthe number of acres which maximizes theirASCS payments. If the yearly maximumASCS payment is $3,500, there is a 50-50cost-sharing program, and leveling costs $600per acre, then the optimal number of acres tolaser each year is

$3500$3500 = 11.67 acres..5($600/ac)

Although additional lasering might be social-ly appropriate, lasering more is financiallyunattractive because for this farm benefitswithout the ASCS payments are less thancosts. Lasering less than the 11.67 acres peryear is uneconomic, since the farmer would

179

Laser Leveling

December 1982

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Daubert and Ayer

TABLE 3. Optimal Number of Acres to Laser per Year Under the Soil and Water ConservationTax Depreciation Program; Arizona, 1980/81.

Optimal AcresParameter Farm Water Cost LaseredChange ($/af) (ac./year)

Example Farma FWC = 17b to 17 + 9 145FWC=17 +10to 17+19 290FWC=17 +20 to 17+29 435FWC =17 + 30 or greater 500

Farm Size = 700 ac. FWC = 17b to 17 + 9 204FWC=17 + 10to 17+19 408FWC=17 + 20 to 17+29 612FWC =17 + 30 or greater 700

Gross Income per FWC = 1 7b to 17 + 9 104Acre = $500/ac. FWC = 17 + 10 to 17 +19 208

FWC=17 +20to 17 +29 312FWC=17 +30to 17 +39 416FWC=17 +40 to 17 +49 500

Marginal Tax Rate = FWC = 17b to 17 + 14 14550% FWC=17 +15 to 17+30 290

FWC=17 +31 to 17+45 435FWC =17 + 46 or greater 500

Real Discount Rate FWC = 1 7b to 17 +19 145=10% FWC=17 +20 to 17+36 290

FWC= 17 +37 to 17 + 52 435FWC =17 + 53 or greater 500

Investment Cost = FWC= 7c to 7+7 219$400/ac. FWC= 7 +8 to 7+13 438

FWC= 7 +14 or greater 500

alnvestment Costs =$600/ac.; Marginal Tax Rate =35%; Real Discount Rate =5%; Gross Income =$700/ac.;Farm Size =500 ac.; yield increase = 10%; FWC = Farm Water Cost.

bThe break-even water price from Table 1 ($30/af) minus $13/af.The break-even water price from Table 1 ($18) minus $11/af.

fail to take full advantage of the maximum$3,500 annual payment.

Some Arizona farmers will find laseringprofitable even without the ASCS payment.For these farmers, laser leveling additionalacres in the first year is profitable until thepresent value of the future ASCS paymentgiven up by lasering more today equals thenet benefit of lasering one more acre. Theoptimal amount to laser in the first year willoccur somewhere between the number ofacres which just exhausts the maximum an-nual ASCS payment 5 and farm size, again

5In Arizona, farmers seldom laser level less than 25 acresdue to the production costs associted with small fields.

assuming that the program continues untilthe farmer lasers the whole farm. For illus-trative purposes, the example farmer lasers25 acres per year for 20 years if the farmwater cost just equals the break-even price.If the farm water cost exceeds the break-evenwater price by $5 per acre foot, the farmersshould laser 50 acres in the first year and 25acres per year for 18 years. Scheduling re-sults for different tax brackets and discountrates are shown in Table 4.

In Arizona, the ASCS cost-sharing pay-ment slows the rate at which profit maximiz-ing farmers laser level. Approximately350,000 acres with groundwater irrigationand 100 to 300 feet pumping lifts could have

181

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Western Journal of Agricultural Economics

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December 1982

Daubert and Ayer

pumping costs about equal to the break-evenwater price without the program. Farmers inthat situation will find laser leveling thewhole farm profitable even without the ASCSprogram, while with the program theyshould laser level only 10 percent of the farmeach year. On 200,000 acres where waterdepths exceed 300 feet the farm water costexceeds the typical break-even water priceby $10 to $20 per acre foot. Again, withoutthe program, those farmers will find laserleveling the whole farm profitable, but withthe program the farmer with 500 acres shouldlaser level 50 percent of the farm in the firstyear and 25 acres per year for 11 years. Thefarmer with 1000 acres should laser 75 per-cent in the first year and 25 acres per year for11 years.

Conclusions

Laser leveling can greatly reduce irrigationapplications, and is often a profitable privateinvestment in Arizona where farm watercosts often exceed break-even water prices.In other states where groundwater is cur-rently used to gravity irrigate and where liftdepths are relatively great, it appears thatlaser leveling will be profitable.

The results show that the federal tax andcost-sharing incentives significantly affect theprivate profitability of laser leveling. Otherfactors - investment costs, water savings,fuel prices, yield benefits, and the planninghorizon, also effect investment profitability.However, even without the federal incentiveprograms there are a wide variety of Arizonaconditions under which lasering would beprofitable.

The farmer participating in federal cost-sharing and tax programs must also choosehow many acres to laser per year. The type ofprogram, yield benefits, farm water costs,farm size, investment costs, gross farm in-come, and marginal tax rates affect the opti-mal number of acres to laser per year. Feder-al incentive programs that limit yearly taxdeductions or ASCS cost-share paymentswere shown to slow the rate at which land ismost profitably lasered. In fact, to maximize

profits the typical farmer in Arizona may takeapproximately 10 years to laser if the pro-gram is expected to continue.

From a policy standpoint, the results indi-cate that the current structure of federal taxincentives and ASCS cost-share programs toconserve irrigation water has mixed effectson conservation goals. While these programsmake lasering profitable on more farms, theymay also slow the rate at which each farmlasers.

References

Arizona Groundwater Management Act. June, 1980.

Bierman, Harold Jr., and Seymour Smidt. The CapitalBudgeting Decision. New York: Macmillan, Inc.,1975.

Chisholm, A. H. "Effects of Tax Depreciation Policy andInvestment Incentives on Optimal Equipment Re-placement Decisions" American Journal of Agricul-tural Economics, 56(1974):776-83.

Ciriacy-Wantrip, S. V. "Water Policy and Economic Op-timization: Some Conceptual Problems in Water Re-search", American Economic Review, 57(1967):179-89.

Data Resources, Inc., "U.S. Long-Term Review, Winter1980-81", 1981.

Daubert, John and Harry Ayer, "Laser Leveling andFarm Profits", Technical Bulletin No. 244, Agricultur-al Experiment Station, University of Arizona, June,1982.

Erie, L. J., Orrin F. French and Karl Harris, "Con-sumptive Use of Water by Crops in Arizona", Techni-cal Bulletin 169, Agricultural Experiment Station,University of Arizona, September, 1965.

Hinz, Walter W. and Allan D. Halderman, "Laser BeamLand Leveing Costs and Benefits", Bulletin Q114,Cooperative Extension Service, University of Arizona,November, 1978.

Howe, Charles. Benefit-Cost Analysis of Water SystemPlanning. Washington, D.C.: American GeophysicalUnion, 1971.

Internal Revenue Service. Farmers' Tax Guide, Pub-lication 225, Revised October, 1980.

183

Laser Leveling

Western Journal of Agricultural Economics

Marglin, S. A. Approaches to Dynamic Investment Plan-ning, Amsterdam: North Holland Publishing Co.,1963.

Pachek, Carl E., Conservation Agronomist, Soil andWater Conservation Service, Phoenix, Arizona, per-sonal communications, March 1981.

Parsons, Walter, Agricultural Water Conservation Spe-cialist, Office of Water Conservation, Department ofWater Resources, Phoenix, Arizona, personal com-munication, December, 1981.

Statutes at Large, 90th Congress, 2nd Session, Volume82, U.S. G.P.O., Washington, D.C. 1969, p. 1328.

Statutes of the United States of America, 74th Congress2nd Session, 1936, U.S. G.P.O., Washington, D.C.,1936, p. 1148.

Equation 1 is expanded and set equal tozero to solve for the break-even water price:

25 (P-20.65)0= E

n = 1 (1 + .05)n

252 5 (10% $700.65)n= (1.05)n = 1 (1 +.05)n

202E

n=5

($50.65)(1+.05)n

25

n=l($37.65)

(1+.05)n

-($150.65)- ($600)

Substituting the discounted present valuesfrom Table A into the equation:

0 25 P-20.650= I

n=l (1 +.05) n

+ $648 - $78 - $338 - $98 - $600.

Simplifying and solving for P:

Appendix

Cash Flow, Plus Calculations for Present-Values and Break-Even Water Prices

A table of cash flows (Table A) may be usedto show how the present values and break-even water prices of equation (1) in the textare computed. Assume a hypothetical farmwhere water savings from dead leveling (B)are 20 acre inches/acre/year; the yield in-crease (Y) is 10 percent; gross crop revenuebefore lasering (G) is $700/acre/year; mainte-nance costs (C) are $50/acre every five years;added machinery, labor, and acreage losscosts (X) are $37/acre/year; initial investmentcosts (I) are $600/acre; the marginal tax rate(M) is 35 percent; net revenue crop loss whilelasering (N) is $150/acre; the planning hori-zon (T) is 25 years, 1 and the inflation-free,after-tax return on investment that the farm-er desires (r) is 5 percent.

1The planning horizon assumes that the costs accrue atthe beginning of each year and benefits at the end ofeach year.

184

25 10= E - 1 (P 20.65)-$466

n = 1 (1 + .05)n

0 = (14.0939)1 (P-20.65)- $466

P= $2.54/acre inch

= $30/acre foot (break-even water price fordead leveling example farm).

2n = 5, n = 10, n = 15, and n = 20.

3 25 1 1- (1+.05)- 25E = = 14.0939

n=1 (1+.05)n .05

is the discount factor determining the present value of$1 received annually at the end of each year for 25years. For additional information concerning discount-ing, present values, and tables of discount factors, seeAlpin, et. al.

December 1982

Daubert and Ayer Laser Leveling

TABLE A. Cash Flow and Present Value of the Annual Benefits and Costs of Dead Levelingfor Hypothetical Farm.

P-B(1 - M) + Y-G(1 - M) - C(1 - M) - X(1 - M) -N(1 -M) -IYear P-20.65 +(.1 700..65) -50(.65) -37(.65) -150(.65) -(600)

---------------------. ..-. . ................................ .............------------------------------------. .

P20-.65 46 24(1.05)1 (1.05)1 (1.05)1 98 600

2 P-20-.65 46 24(1.05)2 (1.05)2 (1.05)2

3 P20-.65 46 24(1.05) 3 (1.05) 3

(1.05) 3

4 P20.65 46 24(1.05)4 (1.05)4

(1.05)4

P20-.65 46 33 24(1.05) 5 ( (1.0 55) (1.05)5

P20.65 46 24(1.05) 6 (1.05) 6

(1.05)6

P20-.65 46 24(1.05)7 (1.05)7 (1.05)7

P20-.65 46 24(1.05) 8 (1.(1. 8

(1.05) 8

P20-.65 46 24(1.05) 9

(1.05) 9(1.05) 9

10 P-20-.65 46 33 24(1.05) 10 (1.05) 10 ((1-5) 10 (1.05) 10

11 P20-.65 46 24(1.05) 11 (1.05)(1.05)

12 P20.65 46 24(1.05)12 (1.05)12 (1.05)12

13 P-20.65 46 24(1.05) 13 (1 (1.5 13

(1.05) 13

14 P20.65 46 24(1.05) 13 (1.05) 13 (1.05) 14

15 P-20.65 463 24(1.05)14 (1.05)14 (1.05)14

1 P-20-.65 46 24(1.05)15 (1.05)15

(1.05)15

1 P-20-.65 46 24(1.05)16 (1.05)16

(1.05)16

1 P-20.65 46 24(1.05) 18 (1.05)18

(1.05) 18

1 P-20-.65 46 24(1.05) 19 (1.05) 19 (1.05) 19

20 P-20-.65 46 33 24(1.05) 20

(1.05) 20(1.05)2 0

(1.05)20

21 P-20-.65 46 24(1.05)21 (1.05)21 (1.05)21

P-20.65 46 24185185

Western Journal of Agricultural Economics

TABLE A. (Continued)

P.B(1 - M) + YG(1 - M) - C(1 - M) - X(1 - M) - N(1 - M) -IYear P-20.65 +(.1 700..65) -50(65) -37(.65) -150(.65) -(600)

22......... . . ..... --------- .......... ..................----------------------------------------22

(1.05)22 (1.05)22 (1.05)22

23 P20-.65 46 24(1.05)23 (1.05)23 (1.05)23

P-20-.65 46 2424(1.05)24 (1.05)24 (1.05)24

P-20-.65 46 2425(1.05)25 (1.05)25 (1.05)25

25 (P.20 .65)Total I )n + 648 - 78 -338 -98 - 600

n = 1 (1.05)n

186

December 1982