Labor Cos and Sugarcane Mechanizaion in Florida: NPV and Real Opions Approach Nobuyuki Iwai Rober D. Emerson Inernaional Agriculural Trade and Policy Cener Deparmen of Food and Resource Economics Universiy of Florida
Background Foreign workers in US agriculure " 77% of farm workers in 2002-04 " A leas 50% of farm workers are undocumened in 2002-04 (16%( 1989-91, 38% in 1993-95) Wage gap Average prediced wages for auhorized, permanen residen, and ciizen worker are 10%, 18% and 14% higher han for unauhorized workers (Iwai e al. 2006).
Immigraion Policy Reform Increased border and domesic enforcemen, amnesy and gues worker programs Goal: legal labor force Concern ha he reform migh lead o labor cos increase in US ag. Need o sudy he impac of labor cos increase: Mechanizaion,, Terminaion (Emerson 2007)
Previous Sudies on Labor Cos and Sugarcane Mechanizaion Zepp and Clayon (1975) found cos advanage of mechanical harvesing operaion over hand- cu as early as 72-3 season. Reduced revenue due o large field losses wih mechanical harvesing, resuling in $40.70 lower ne reurns per acre in comparison o hand-cu. If projeced 74-5 machinery operaing raes had been used, he ne reurns per acre would have been abou equal (Zepp( 1975).
Problems Previous sudies calculaed and compared he cos and reurns from wo echnologies for a single individual season. Dynamic decision-making analysis ools ofen used in corporae finance: Ne presen value (NPV) approach, Real opions approach (ROA).
Objecive of Our Sudy Using NPV approach and ROA, we analyze he decision of he model sugarcane farmer (640 acres in oal and 408 acres harvesed) in Florida as o mechanizaion of harvesing for 72-3 season. Simulaion: We also compue he adopion hresholds for he labor cos ha should have riggered invesmen in mechanical harvesing for sugarcane in Florida. Implicaion for mechanical harvesing for cirus.
NPV Approach Compares discouned cash flow (DCF) less he invesmen cos of wo operaions. Imporan o forecas fuure free cash flow (FCF) given informaion when he decision is made. Also need o use appropriae discoun rae (Weighed Average Cos of Capial).
Esimaed FCF Esimaed FCF from growing and harvesing sugarcane for he model farm ($ per 404 acres harvesed) Season Revenue Labor cos Oher coss Operaing CF Depreciaion EBIT Tax on EBIT (29%) CAPEX FCF Hand cu harvesing 72-3 213,004.56 59,015.73 95,995.25 57,993.59 10,855.60 47,137.99 13,670.02 10,855.60 33,467.97 Mechanical harvesing 72-3 197,945.28 35,784.21 104,256.41 57,904.66 13,569.20 44,335.46 12,857.28 13,569.20 31,478.18 Calculaed from Zepp and Clayon (1975) and Walker (1972).
Forecasing Beyond 72-3 Season Previous sudies repored he revenue and cos esimae only for 72-3 season. Need o forecas for longer period for NPV and ROA. A common approach is he Mone Carlo simulaion in which all sochasic facors are generaed for fuure periods using he esimaed parameers and disribuions of hese series (Kobayashi 2003, Copeland and Anikarov 2003).
Esimaion of Sochasic Process We esimae sochasic process for yield, price, labor cos, and oher coss. We make saionary series by aking 1 s order difference of log of each series and subracing he mean of he 1 s order difference. Tes of independence beween yield and price and beween coss was rejeced.
Vecor Auoregressive Model Since independence hypohesis was rejeced, we esimae he VAR model for each combinaion. p is chosen ha minimizes he bias-correced version of he Akaike Informaion Crieria referred o as he AICC (Brockwell and Davis 2002): where L is likelihood funcion for bivariae normal disribuion, n is number of obs, and m=2 is number of variables.
VAR Resuls VAR Resuls " # $ % & + " # $ % & " # $ % & ' ' + " # $ % & " # $ % & ' ' + " # $ % & = " # $ % & ' ' ' ' 2 1 2,2 2,1 1,2 1,1 2 1 0.40 0.60 0.077 0.45 0.17 0.67 0.077 0.66 0.00 0.00 U U X X X X X X -74.55 and AICC 0.042 0.0021 0.0021 0.0054, 0 0 ~ where 2 1 = " # $ $ % & ' ( ) * +, - - ' ( ) * +, ' ( ) * +, WN U U For yield and price " # $ % & + " # $ % & = " # $ % & 2 1 2 1 0.00 0.00 U U X X -38.65 and AICC 0.027 0.00052 0.00052 0.020, 0 0 ~ where 2 1 = " # $ $ % & ' ( ) * +, - - ' ( ) * +, ' ( ) * +, WN U U For labor and oher cos
Mone Carlo Simulaion Using he esimaion resuls, we can generae fuure series as X ˆ ìˆ + Öˆ X + Öˆ X + U = 1 1 2 2 whereu is a whie noise from esimaed disribuion. Since X is he change in he de-rended (mean-subraced) log of he original series, we can generae a sample of he original series by adding he rend, aking exponenial and muliply i o he previous value. Repeaing his nine imes for each vecor yields one sample of fuure nine-year pass for each variable. We generae 100,000 ses of he fuure pahs of sochasic facors wih which we calculae 100,000 ses of nine-year fuure FCF pahs for each operaion mode. The average of generaed FCF is given nex.
Mone Carlo Simulaion (coninued) Forecased FCF from growing and harvesing sugarcane afer 72-3 season ($) 73-4 74-5 75-6 76-7 77-8 Hand cu 32,880.05 32,882.90 25,847.06 20,299.64 20,848.51 Mechanical 36,505.76 42,991.52 37,478.13 33,386.73 35,036.43 78-9 79-80 80-1 81-2 Hand cu 17,011.08 9,449.28 4,457.93-470.85 Mechanical 32,698.77 26,970.87 23,726.29 20,617.16
Weighed Average Cos of Capial Since FCF are available for paymen o boh sources of capial, deb and equiy, he discoun rae mus comprise a weighed average of he marginal coss of boh sources of capial (Copeland 1994). WACC is given by WACC = k (1 T ) b B B + S where k b is he preax marke expeced yield o mauriy on deb, T is he marginal ax rae, B is he value of ineresbearing deb, and S is he value of equiy, and k s is he marke-deermined opporuniy cos of equiy capial. From marke daa we have k b =8%, T=29%, B/(B+S)=12%, and ks=10.84% from CAPM, so ha WACC=10.23%. + k s B S + S
NPV Calculaion PV for year for <1982 is given as PV ( FCF# ) ( 1+ g) E( FCF1982) + # ) (1 + WACC ( WACC g) E (1 + WACC 1982 = " 1982 # = + 1 ) where he second erm is coninuing value afer he explici forecas period in which g is he expeced growh rae in FCF in perpeuiy. NPV for year simply adds FCF of ha year o PV: NPV = FCT + PV
NPV Calculaion Resul NPV and iniial invesmen cos for each operaion for 1972-3 season ($) NPV Iniial invesmen cos NPV inv. cos Hand cu harvesing 181,013.87 181,013.87 Mechanical harvesing 319,815.40 63,431.21 256,384.19 NPV less iniial invesmen cos for mechanical operaion is more han NPV for hand cu operaion. NPV approach suggess ha he model farmer should have swiched o mechanical operaion even in 72-3 season.
NPV Calculaion Resul (coninued) NPV approach canno explain he fac ha only 15% of sugarcane was harvesed mechanically for 72-3 season. Esimaed % of mechanically harvesed sugarcane 120% 100% 80% % 60% 40% 20% 0% 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 Year
Real Opions Approach ROA assumes ha he producer has he opion o inves or wai, called invesmen flexibiliy. However, once he producer makes an irreversible invesmen, he exercises he opion o inves and gives up he opion value of invesmen. Hence he producer does no inves unil he NPV less invesmen cos and opion value of invesmen opporuniy is greaer han he NPV for he curren operaion.
Consolidaed Approach Our case sudy has four sochasic facors (yield, price, labor cos and oher coss). We use he consolidaed approach (Copeland and Anikarov 2003), which combines many sochasic facors ino one hrough he Mone Carlo simulaion. The approach is based on he following heorem by Samuelson (1973): Regardless of he paern of cash flows expeced in he fuure, change in asse value is a random process so ha reurn is iid process, as long all he informaion abou he expeced fuure cash flows is already backed ino he curren value.
Consolidaed Approach (coninued) In consolidaed approach (Copeland and Anikarov 2003) annual rae of reurn (z( ) is an iid process. z = ( FCF + PV ) PV 1 PV Using he Mone Carlo simulaion resul, we calculae mean and volailiy (sandard deviaion) of z : mean=0.1023, volailiy=1.77. 1 Copeland and Anikarov sugges assuming less-han- 15 years unil expiraion of opion. We assume 10 years unil expiraion.
Binomial Tree 4,084,946 181,014 147,546 869,161 693,447 25,047 3,145,836 117,717 90,655 19,983 3,392 2,612 Binomial ree is build o approximae he PV ransiion (up o 81-2 season).
PV wih Opion Value The decision in each node for he final year is ( mech Max PV PV InvCos ), 1981, 1981 1981 which yields 1,621,856 and 157,297 in each node. Then we muliply hese by (1+FCF rae). 167,827 30,535 168,982 28,490 4,836 4,870
PV wih Opion Value (coninued) The calculaion of PV wih opion value is done by risk neural probabiliy (or( replicaed porfolio) approach : The farmer creaes a hedge porfolio composed of one share of he curren operaion and a shor posiion of m unis of he invesmen opion and he curren operaion. Making appropriae he hedge raio (m),( he hedge porfolio can be made risk free, he non-arbirage principle requires ha he farmer has o earn he risk free rae from his porfolio. The formula of PV wih opion value for he node for 1980: Max C 1980 ( mech C, PV " InvCos ), = 1980 1980 1980 where (1 + r ) " e [ u d ( ) ][ ]" 1 f qc1981 + 1" q C1981 1+ rf and q = " e " e "
PV wih Opion Value (coninued) We repea hese seps for oher nodes of season 81-2 and 80-1, and up o season 72-3, and resul in he NPV 1972 wih OpValue 1972 = $357,179.45. Then he opion value is simply calculaed as: (NPV 1972 wih OpValue 1972 ) - NPV 1972 = $ 357,179.45 - $181,013.87 = $176,165.58 = OpValue 1972.
Decision from ROA NPV, iniial invesmen cos and opion value for 1972-3 season ($) NPV Iniial Invesmen Cos Opion Value NPV Inv. Cos Op. Value Hand cu harvesing 181,013.87 181,013.87 Mechanical harvesing 319,815.40 63,431.21 176,165.58 80,218.60 NPV of mechanical operaion less iniial invesmen cos and opion value is less han NPV for hand cu operaion. ROA suggess ha he model farmer should no swich o mechanical operaion in 72-3 season.
Threshold Level Threshold labor cos assuming labor cos increases a he same rae for boh operaion ($) Labor cos Resuling NPV Iniial Invesmen Cos Resuling Opion Value Hand cu harvesing 90,152.43 (52.76% increase) -14,608.28 Mechanical harvesing 54,663.96 (52.76% increase) 181,107.56 63,431.21 132,284.63
Conclusions Previous sudies found cos advanage of mechanical harvesing operaion over hand-cu as early as 72-3 season. The NPV approach suppors he views of previous sudies: NPV less iniial invesmen cos of mechanical operaion ($319,815) exceeds he NPV for hand cu operaion ($181,014).
Conclusions (coninues) Conclusion from ROA is opposie: Due o a high volailiy, he opion value of holding invesmen opporuniy is high ($176,166) enough o overurn he conclusion of NPV. Threshold value analysis shows ha i akes more han 52% increase in labor cos for immediae mechanizaion in 72-3 season. ROA explains beer he hisorical fac ha large scale mechanizaion was delayed unil mid/lae 80s (only 15% in 72-3 season).
Similar Siuaion of Mechanical Harvesing for Cirus Currenly, mechanically harvesing Florida oranges resuls in abou 16% cos-savings (25( cen per 90 pound box) relaive o hand harvesing, under ypical condiions (Roka 2008). Cos-savings sugges only wo year payback period for he grower s s invesmen in preparing he grove. Ye he adopion rae remains relaively low a abou only 7.5% of he acreage.