Application of Real Options Analysis in the Valuation of Investment in Biodiesel Production

Transcription

1 Applicaion of Real Opions Analysis in he Valuaion of Invesmen in Biodiesel Producion Frank E. Yeboah Abolghasem Shahbazi Osei A. Yeboah Harmohindar Singh Assisan Professor Professor Associae Professor Professor Norh Carolina A&T Sae Universiy Greensboro, NC Franklin H. Holcomb Chief, Energy Branch US Army Engineering Research & Developmen Cener, Consrucion Engineering Research Laboraory Champaign, IL ABSTRACT There are basically wo main mehods used in he valuaion of capial invesmens; he discouned cash flow (DCF) echniques, and he opion pricing valuaion (OPV) mehod. The DCF echniques and oher ne presen value (NPV) mehods when used o value invesmen projecs ha have flexibiliy in hem end o underesimae he values of he projecs, because hey fail o capure he value of he flexibiliy embedded in such projecs. For biodiesel producion, such flexibiliy may include he opion o defer, expand, conrac or abandon he projec, should he economic environmen necessiae ha. Mos biodiesel producion projecs have been valued using he DCF echniques. This paper evaluaes he economic feasibiliy of convering WVO from he Army Barracks as well as oher feedsock ino biodiesel, using he OPV mehod so as o incorporae managerial flexibiliy in he producion process. The log-ransformed binomial mehod (LTBM) is envisaged for he real opions analysis. INTRODUCTION Biodiesel is a renewable fuel produced from sources including virgin and wase vegeable oils, and animal fas. As a ransporaion fuel, i is increasingly being used in federal, sae, and oher ransi flees, privae rucking companies, and personal auomobiles. The US Miliary is one of he larges consumers of convenional diesel oil; a nonrenewable fossil fuel ha is known o conribue o he emissions of greenhouse gases as well as increases US dependence on impored peroleum. Forunaely, huge quaniies of wase vegeable oil (WVO) are disposed of a Miliary Caneens annually. The opporuniy, herefore, exiss for he US Deparmen of Defense (US DOD) o ge involved, one way or he oher, in he producion of biodiesel for use in heir ransporaion vehicles. Bu wih biodiesel producion cosing more han $3/gallon, i someimes begs he quesion wheher such an invesmen will be worh i? Cos is no, however, he only goal of he US Miliary in increasing is use of biodiesel as source of ransporaion fuel. In fac, improving is energy securiy and independence as well as environmenal susainabiliy is also an inegral par of is sraegic goals. Tha nowihsanding, i is of imporance o assess he economics of using biodiesel based on WVO and oher feedsock. There are basically wo mehods used in he valuaion of capial invesmens, he discouned cash flow (DCF) echniques and opion pricing valuaion (OPV) mehods. The DCF echniques and oher ne presen value (NPV) mehods when used o value invesmen projecs ha have flexibiliy in hem end o underesimae he values of he projecs, because hey fail o capure he value of he flexibiliy embedded in such projecs. Real capial invesmens enail several managerial and operaing flexibiliy [14]. In addiion, if invesmen projecs are irreversible hen hey should be valued using opion pricing echniques, since he radiional NPV echniques are based only on expeced fuure cash flows bu no on heir second momens i.e. heir variabiliy [7]. Convenional valuaion echniques, such as DCF, are difficul o apply when accouning for managerial flexibiliy and hence undervalue he values of projecs in capial budgeing [10]. Flexibiliy embedded in opion pricing models makes hem normally difficul o solve analyically, especially when he underlying asse (price of biodiesel) is a dividend-paying as well as a cash flow generaing asse. A numerical echnique will herefore be developed o analyze he problem. The log-ransformed binomial mehod (LTBM) is envisaged for his sudy, because of he ease wih which i incorporaes flexibiliy and oher opions. We will use he real opion valuaion approach o assess he economic value of biodiesel producion, including he opions o defer, and expand he projec should he economic environmen change. The oal Proceedings of he 011 Indusrial Energy Technology Conference New Orleans, Louisiana, May 17-19, 011

2 Repor Documenaion Page Form Approved OMB No Public reporing burden for he collecion of informaion is esimaed o average 1 hour per response, including he ime for reviewing insrucions, searching exising daa sources, gahering and mainaining he daa needed, and compleing and reviewing he collecion of informaion. Send commens regarding his burden esimae or any oher aspec of his collecion of informaion, including suggesions for reducing his burden, o Washingon Headquarers Services, Direcorae for Informaion Operaions and Repors, 115 Jefferson Davis Highway, Suie 104, Arlingon VA Respondens should be aware ha nowihsanding any oher provision of law, no person shall be subjec o a penaly for failing o comply wih a collecion of informaion if i does no display a currenly valid OMB conrol number. 1. REPORT DATE MAY 011. REPORT TYPE 3. DATES COVERED o TITLE AND SUBTITLE Applicaion of Real Opions Analysis in he Valuaion of Invesmen in Biodiesel Producion 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army Engineering Research & Developmen Cener,Consrucion Engineering Research Laboraory,Champaign,IL, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 1. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; disribuion unlimied 13. SUPPLEMENTARY NOTES 11. SPONSOR/MONITOR S REPORT NUMBER(S) 14. ABSTRACT There are basically wo main mehods used in he valuaion of capial invesmens; he discouned cash flow (DCF) echniques, and he opion pricing valuaion (OPV) mehod. The DCF echniques and oher ne presen value (NPV) mehods when used o value invesmen projecs ha have flexibiliy in hem end o underesimae he values of he projecs, because hey fail o capure he value of he flexibiliy embedded in such projecs. For biodiesel producion, such flexibiliy may include he opion o defer, expand, conrac or abandon he projec, should he economic environmen necessiae ha. Mos biodiesel producion projecs have been valued using he DCF echniques. This paper evaluaes he economic feasibiliy of convering WVO from he Army Barracks as well as oher feedsock ino biodiesel, using he OPV mehod so as o incorporae managerial flexibiliy in he producion process. The log-ransformed binomial mehod (LTBM) is envisaged for he real opions analysis. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Same as Repor (SAR) 18. NUMBER OF PAGES 6 19a. NAME OF RESPONSIBLE PERSON Sandard Form 98 (Rev. 8-98) Prescribed by ANSI Sd Z39-18

3 value of all he opions calculaed individually i.e. wihou ineracion, will be differen from when heir ineracions are incorporaed. Wihou ineracion he oal value of he individual opions will be overesimaed [1], [13]. However, incorporaing opions ineracion can also make he valuaion compuaionally very demanding. In such cases, some radiional opion valuaion mehods e.g. Black- Scholes may no be appropriae for he analysis wihou furher modificaions. This is no he case wih he Log-ransformed Binomial Mehod (LTBM), which can handle such ineracions wihou loss of compuaional efficiency. Consequenly, i is employed in his sudy. This paper uses he OPV mehod o evaluae he economic feasibiliy of convering WVO as well as oher feedsock ino biodiesel, so as o incorporae managerial flexibiliy in he producion process. The log-ransformed binomial mehod (LTBM) is envisaged for he real opions analysis. REAL S ANALYSIS Sochasic Process of he Price of Biodiesel Le he price of he oupu variable (price of biodiesel) a ime, P() be assumed o evolve as he sochasic process given by he geomeric Brownian moion (GBM). Then dp Pd PdW Equaion (1) Where dw is a sandard Wiener process, d is an incremen of ime, he insananeous sandard deviaion (volailiy) and he expeced reurn on he price of biodiesel P. Since here is a raded marke for biofuels or heir proxies, we will assume ha he biofuel price uncerainies can be spanned by he capial markes. Hence, coningen claims analysis could be used o find he value of he projec, V ( P, ). We assume V follows an Io s process i.e. i is wice differeniable wih respec o P and once wih respec o ime and consequenly also follows he sochasic process given in Equaion (1). Opion Pricing Valuaion (OPV) Mehod The ne presen value of biodiesel producion, including managerial flexibiliy, NPV can be given as NPV V I Equaion () V op Where V: Presen Value of Biodiesel Projec, $ I: Iniial capial invesmen, $ V op : Toal value of opions embedded in he projec, $ Numerical Approximaion of Real Opion Model Normally here exis no analyical soluions o opion pricing models, especially, when he underlying asse (price of fuel) is a dividend-paying as well as, a cash flow generaing asse. This sudy will herefore use numerical echniques o value he biodiesel invesmen projec. An opion is defined as he righ, bu no an obligaion, o buy (if a call) or sell (if a pu) a specified asse (e.g. common sock) by paying a pre-specified price (he exercise or srike price) on or before a specified dae (he expiraion or mauriy dae). If he opion can be exercised before mauriy, i is called an American opion; if only a mauriy, a European opion [14]. Several models are available for valuing opions. They range from analyical formulas o numerical echniques. Perhaps he mos famous analyical mehod is he model developed in [] and laer modified in [11]. Oher opion valuaion echniques include he binomial laice mehod developed in [6], he log-ransformed binomial mehod proposed in [1], he finie difference mehod proposed in [4], [5]. Furhermore, Mone Carlo simulaion mehod has been developed o value European opion in [3], which was laer improved in [9] o value American opions. The log-ransformed binomial mehod is envisaged for his sudy, because of he ease wih which i incorporaes flexibiliy and oher opions. i. Log-Transformed Binomial Mehod (LTBM) Numerical Technique The log-ransformed binomial mehod (LTBM) has been well described in [1]. I is summarized for he biodiesel projec as given below. If we le X lnv( P, ) Equaion (3) Then in any differenial ime inerval, d, dx follows an arihmeic Brownian moion, which under risk neural valuaion, will be given by he sochasic process given by [1] dx ( r 0.5 ) d dw Equaion (4) Where he incremens, dx are independen, idenical, and normally disribued wih mean ( r 0.5 )d, and variance d, while r is he risk-free ineres rae e.g. US Treasury Bonds. To approximae he coninuous process in equaion (4) he lifeime of he biodiesel projec T can be subdivided ino N equal discree subinervals of magniude so ha Proceedings of he 011 Indusrial Energy Technology Conference New Orleans, Louisiana, May 17-19, 011

4 T N Equaion (5) I can be shown ha wihin each discree subinerval, X follows a Markov random walk wih risk-neural probabiliy of moving up by an amoun X=H and down by an amoun X= H, p u and p d, given respecively, by [1] p u p d K 0.51 Equaion (6) H K 1 pu Equaion (7) H Where, K, H are also given by: K d Equaion (8) r 0.5 Equaion (9) H K ( K) Equaion (10) Once he sae and ime variables are ransformed, as given above, he discree-ime approximaion o he coninuous process will be assured sabiliy and consisency [1]. ii. LTBM Algorihm Using he LTBM echnique as described in [1], he ne presen value of he biodiesel projec ha incorporaes he opion value could be deermined by four main seps, as given in Figure 1. The opion o defer is an American call opion; he opion o abandon is a compound call opion; he opion o conrac is an European pu opion; he opion o swich use i.e. abandon for salvage value is an American pu opion [13]. Sep 1: Specify iniial parameers (V, r,, T, N, I), where I is iniial capial invesmen of he biodiesel projec. Addiional parameer specificaion include cash flow (amoun and iming), and real opion daa Sep : Calculae preliminary key variables Time sep (K), drif (m), sae-sep (H), and probabiliies (p u, p d ) Sep 3: Deermine he erminal boundary values (a j=n) Le j be he ineger number of ime-seps (each of lengh K) Le i be he ineger index of he sae variable X corresponding o he ne number of ups less downs (i.e. X(i) = X 0 +ih), and R(i) be he oal invesmen value (including embedded real opions e.g. defer, expand, conrac, abandon ec.) of he biodiesel projec A j=n, and for each i, projec value V(i)=exp(X 0 +ih), R(i)=max(V(i),0) Sep 4: Backward ieraive process For each ime sep j (j=n-1,.,1) and every second sae variable i, calculae (from sep j+1) R( i, j) e rk p u R( i 1, j 1) p A. Adjus for cash flows (dividends): d R( i 1, j 1), a new revised value for R(i), A each cash inflow (ex-dividend) ime, deermine downward exension of riangular pah and shif (e) for each sae variable index i: R (i)=r(i-e)+cf A each cash ouflow (exercise) ime: R (i)=r(i)-i B. Adjus for muliple real opions: Figure 1. Flow-char for LTBM Algorihm Proceedings of he 011 Indusrial Energy Technology Conference New Orleans, Louisiana, May 17-19, 011

5 Model Parameers Esimaion Daa for he model consis, basically, of he curren and hisorical fuures prices of No. fuel oil i.e. convenional diesel, which is used as a proxy for biodiesel, and he risk-free ineres rae r (e.g. U.S. Treasury Bills). They are financial marke daa and could herefore be obained from, sources such as he New York Mercanile Exchange (NYMEX), US DOE-EIA (Energy Informaion Adminisraion) and he Wall Sree Journal. The main model parameer ha needs o be esimaed exogenously is he insananeous sandard deviaion (volailiy) of he price of biodiesel. Hisorical daa of biodiesel prices or is proxy (No. fuel oil) is used for he esimaion. For consisency wih he assumpions and convenions in opion valuaion, he volailiy of he underlying asse can be esimaed from he coninuously compounded reurn o he underlying asse (biodiesel or is proxy) [1], [8]. Le he coninuously compounded reurn on he price of biodiesel or is proxy be given as P u ln for = 1,,.,n+1 Equaion (11) P 1 Where u is he reurn beween -1 and, and P is he marke price of biodiesel or is proxy (No. fuel oil) a ime. Then he annual volailiy of he underlying asse (price of biodiesel) can be compued as [1], [8] s 1 n 1 n 1 u u 1 n 1 n 1 u 1 n( n 1) n 1 Equaion (1) Where n is he number of reurn daa poins (since he hisorical price daa are n+1) and u he mean of he u ' s Once he value for he insananeous sandard deviaion (volailiy) s has been esimaed i can be inpu ino he numerical model as proposed, o deermine he economic value of he biodiesel producion. MODEL RESULTS AND ANALYSIS A case sudy is presened in his secion o illusrae he applicaion of using he LTBM model o value biodiesel producion faciliy. We assume he following process and financial informaion for he analysis: Plan Capaciy = 1000 of wase vegeable oils Biodiesel Producion = 930 u Iniial Capial Invesmen, I 0 = $343/ or abou $30,000 (based on biodiesel produced) Presen Value of Projec, V = $300,000 Projec Lifeime = 15 yrs. Volailiy of Projec Value = 17%/yr. (based on price volailiy of # fuel oil) Risk-free Ineres Rae = 5%/yr. Managerial Flexibiliy (Real Opions o be incorporaed): i. Defer I 0 up o year ii. Expand producion capaciy by e=50% of V by invesing I E in year 5 Table 1: Sandard Opion Pricing Valuaion of Individual Opions (in $1000) TYPE Defer Invesmen for yrs. Expand Biodiesel Producion in Yr. 5 STRIKE PRICE OF ASSET Using he informaion as given in he case sudy above, i can be shown in Table 1, ha he opion o defer invesing $30,000 in he biodiesel projec by years has a value of $33,300, while he opion o expand producion in year 5, by invesing $140,000 addiional capial o obain 50% (or $150,000) addiional value of he projec has a value of abou $46,300, resuling in a oal combined real opion value of $79,600. This combined opion value is sufficien o make he NPV (-$0,000 wihou real opions) posiive value (i.e. -$0,000 + $79,600 = $59,600). Under his circumsance he projec will be acceped, since he NPV (afer incorporaing opion value) is posiive. The combined value of all hese opions if evaluaed individually would be subsanially oversaed, since hese opions may inerac negaively. In fac, cerain prior real opions may aler he underlying asse and value of subsequen opions. In addiion, he presence of subsequen opions would increase he effecive underlying asse for prior opions [1], [13]. The degree of ineracion is a funcion of he ype of opion and he degree o which he exercise price overlap [13]. Opions end o Proceedings of he 011 Indusrial Energy Technology Conference New Orleans, Louisiana, May 17-19, 011

6 be more addiive when hey are of opposie ypes e.g. call and pu opions; when he imes of possible exercise of he wo opions are closer; when he opions are more ou-of-he-money i.e. opion have relaively high exercise prices for calls and low exercise prices for pus [13]. The use of LTBM allows he ineracions of he various opions o be incorporaed. Table, illusraes he combined value of he opion in cases where he opions are in-hemoney, a-he-money and ou-of-he-money. When he opions are ou-of-he-money heir values are smaller han when hey are in-he-money or a-hemoney, as illusraed in Table. Table : Combined Opion Pricing Valuaion (in $1000) TYPE STRIKE PRICE (I) OF ASSET(V) In-he-money A-he-money Ou-of-hemoney The radiional NPV i.e. he difference beween V and I, is -$0, 000. This negaive number indicaes ha he invesmen projec should be rejeced, since NPV is negaive. Bu by incorporaing he opion o defer he projec by years and also o expand he projec in year 5, he combined opion value is $96,000 (based on he ou-of-he-money opion i.e. he original daa from he case analysis). This, herefore, makes he expanded NPV i.e. he sum of he radiional NPV and he real opions value ogeher posiive ($96,000 - $0,000 = $76,000), and consequenly, make he invesmen raher aracive. Wihou incorporaing managerial flexibiliy (i.e. real opions) he projec would no have been underaken, given NPV o be negaive. I should also be noed ha he combined opions value are larger for in-hemoney and a-he-money opions i.e. $136,000 and $116,000, respecively, han for he ou-of-he-money opion value. CONCLUSION There are basically wo mehods used in he valuaion of capial invesmens, he discouned cash flow (DCF) echniques and he opion pricing valuaion (OPV) mehods. The DCF echniques and oher ne presen value (NPV) mehods when used o value invesmen projecs ha have flexibiliy in hem end o underesimae he values of he projecs, because hey fail o capure he value of he flexibiliy embedded in such projecs. Mos invesmens in biodiesel projecs have been evaluaed using he radiional discouned cash flow (DCF) echniques. These echniques normally underesimae he value of such projecs, because hey fail o capure he value of he flexibiliy embedded in hem. In fac, mos capial invesmen projecs can be deferred, conraced, abandoned or swiched for salvage value, as well as expanded. In his paper, we analyzed he case where a biodiesel projec can be deferred and also expanded. We used he log-ransformed binomial mehod o analyze he managerial flexibiliy embedded in he projec due o he opion o defer he projec by years and also he opion o expand he value of he projec by 50%, if addiional capial is invesed in he fifh year. The sudy shows ha even when he radiional NPV mehod suggess rejecing a projec because is value is negaive, incorporaing managerial flexibiliy could make such a projec value become posiive. I can also be shown ha he value of he combined opion, when calculaed individually could be oversaed because hese individual opions can inerac negaively. Finally, i should be noed ha he combined opions value is larger for in-he-money and a-he-money opions han for he ou-of-hemoney opion value. ACKNOWLEDGEMENT Funding from he US Deparmen of Defense (US DoD) under Conrac No. W911NF-08-R-0001, and US Deparmen of Agriculure (USDA) under Conrac No. A is acknowledged. REFERENCES 1. Amram, M. and N. Kulailaka, 1999, Real Opions: Managing Sraegic Invesmen in an Uncerain World. Boson, MA: Harvard Business School Press.. Black, F. and M. Scholes, 1973, The pricing of opions and corporae liabiliies, Journal of Poliical Economy 81 (May June), pp Boyle, P., 1977, Opions: a Mone Carlo approach, Journal of Financial Economics 4 (May), pp Brennan, M. and E. Schwarz, 1977, The valuaion of American pu opions, Journal of Finance 3 (May), pp Brennan, M. and E. Schwarz, 1978, Finie difference mehods and jump processes arising in he pricing of coningen claims: A synhesis, Proceedings of he 011 Indusrial Energy Technology Conference New Orleans, Louisiana, May 17-19, 011

7 Journal of Financial and Quaniaive Analysis 13, pp Cox, J., S. Ross and M. Rubinsein, 1979, "Opion pricing: A simplified approach," Journal of Financial Economics 7(3), pp Dixi, A. K. and R. S. Pindyck, 1994, Invesmen under uncerainy. Princeon, NJ: Princeon Universiy Press. 8. Hull, J. C., 000, Opions, Fuures and Oher Derivaives. Upper Saddle River, NJ: Prenice- Hall. 9. Longsaff, F.A. and E.S. Schwarz, 001, "Valuing American opions by simulaion: a simple leas-squares approach," The Review of Financial Sudies 14 (1), pp Mason, S. and C. Baldwin, 1988, Evaluaion of governmen subsidies o large scale energy projecs: a coningen claims approach, Advances in Fuures and Opions Research Vol. 3. Ed(s): F. Fabozzi.: JAI Press, p Meron, R.C., 1973), "Theory of raional opion pricing," Bell Journal of Economics and Managemen Science 4 (1), pp Trigeorgis, L., 1991, A log-ransformed binomial numerical analysis mehod for valuing complex muli-opion invesmens, Journal of Financial and Quaniaive Analysis 6(3), pp Trigeorgis, L., 1993, The Naure of Opion Ineracions and he Valuaion of Invesmens wih Muliple Real Opions, Journal of Financial and Quaniaive Analysis 8(1), pp Trigeorgis, L., 1996, Real Opions: Managerial flexibiliy and sraegy in resource allocaion. Cambridge, MA: MIT Press. Proceedings of he 011 Indusrial Energy Technology Conference New Orleans, Louisiana, May 17-19, 011