FUEL CELLS IN SHIPPING: HIGHER CAPITAL COSTS AND REDUCED FLEXIBILITY

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1 FUE CE IN HIPPING: HIGHER CPIT COT ND REDUCED FEXIBIITY igbjøn ødal * This vesion: Febuay 28, 2003 bstact: The ae discusses some main economic chaacteistics of fuel cell owe oduction technology alied to shiing. Wheneve cometitive fuel cell systems ente the maket, they ae likely to have highe caital costs and lowe oeating costs than systems based on taditional combustion technology. Imlications of the diffeence ae investigated with esect to investment flexibility by the use of a eal otions model of shi investment, lay-u and scaing decisions unde feight ate uncetainty. highe caital shae of total exected costs can eesent a significant ootunity cost in uncetain makets. The ae highlights the significance of accounting oely fo value of flexibility io to investment in new technology. Keywods: fuel cells, maitime tansot, ice uncetainty, flexibility. JE classification: O33, R40, D Backgound and objectives Due to its intenational chaacte, the maitime tansot industy has avoided many envionmental egulations that othe enegy intensive tansot sevices ae usually faced with. Following this tadition, shiing is not included in the Kyoto tagets fo cuts in global CO 2 emissions even if the industy is esonsible fo aoximately 2% of such emissions. Most likely, some of these athe unique aangements fo maitime tansot will not suvive the steadily inceasing envionmental concens in intenational olitics Mæstad et al Occasional accidents most ecently the sinking of the oil tanke Pestige outside ain in Novembe 2002 also contibute to incease the olitical essue towads a moe stict envionmental egime fo all tyes of maitime tansot. Fuel cell technology 1 is often egaded as the ideal solution to the envionmental oblems that aise fom cabon based owe oduction in shiing and othe tansot industies. * gde Univesity College, chool of Management, eviceboks 422, 4604 Kistiansand, Noway. sigbjon.sodal@hia.no. This wok is at of a eseach oject at Cente fo Intenational Economics and hiing. Financial suot fom the Nowegian hiownes ssociation is acknowledged. 1 ee IE 2003 fo an infomative website on fuel cell technology. 1

2 Wide use of fuel cells is exected to educe local and global ollution fom combustion engines cuently dominating the makets, but any ediction on when fuel cell systems may take ove as a majo owe oduction souce is as uncetain as it is contovesial. This is tue even in oad tansotation, whee the technology is matuing aidly. ecent examle: The Geneal Motos Chaiman, Jack mith, foecasted ecently that it can take yeas befoe hybid and fuel cell cas ae fully commecialized due to thei excessively high ice tags. He said so even if his own comany, and othe ca manufactues, ae sending lage amounts on eseach in the field, and the fist fuel cell vehicles ae about to aea in the maketlace FT This is in line with IE ojections saying that fuel cells will not lay a significant ole in global enegy makets fo the next 25 yeas WEO 2002,. 30. ome efeences cited below ae fa moe otimistic. s fa as oulsion of shis is concened, no fuel cell system yet exists that is of inteest to any majo maket segment. Wheneve such systems become cometitive, the otential maket is vast Zvi et al This ae addesses some economic asects of using fuel cells in shiing. The intention is not to fulfil the immense task of edicting when a fuel cell evolution may take lace; no is it to esent a technical analysis of diffeent fuel cell systems and alications. The focus is entiely on the economic side of the issue. The objective of the ae is to oint at some main economic chaacteistics common to most fuel cell systems of inteest, and to investigate one secific asect that seems to be imotant, namely value of flexibility. ince shiing makets ae volatile, flexibility can have geat economic value. It is woth discussing whethe the amount and chaacte of flexibility could change by switching to fuel cell owe oduction. The emaining at of the ae is stuctued as follows: ection 2 descibes some main economic chaacteistics of fuel cell technology, emhasizing imlications fo maitime makets. Even if the futue of fuel cell technology is uncetain, many ossible consequences of using the technology can be discussed aametically, and in a shiing context, in ode to imove the basis fo investment and oeations. ection 3 contibutes to this discussion by investigating the value of flexibility in a maket with feight ate uncetainty and otions to lay u shis when ices ae low. The analysis is based on a eal otions aoach. It agues that significant amounts of flexibility could be lost by switching to fuel cell owe oduction. ection 4 concludes. 2

3 2. Fuel cell costs Geneal chaacteistics The chemical basis fo any fuel cell egime is that enegy is oduced fom hydogen and oxygen by the eaction 2H 2 +O 2 2H 2 O+enegy. eveal hydogen caies can be used, and the exact chemical ocess could be moe comlex. Yet, this chemical elationshi between two of the most common elements demonstates, in its simlicity, the otential economic owe of fuel cell owe oduction as oosed to moe taditional combustion engines. The main chaacteistics can be summed u as follows: Fuel cells ae enegy efficient because electic owe is oduced diectly fom a chemical eaction instead of indiectly though the themal and mechanical enegy of combustion engines. The efficiency of a combustion engine is tyically in the ange 25-30%, while the simila efficiency of a fuel cell system is 40-60%. This imlies a otential fo oeating cost savings. ince fuel cells have no moving ats, maintenance costs may also be lowe. Fuel cells ae much cleane than combustion engines, and excet fo technological beakthoughs, envionmental olicy can obably moe than anything else make fuel cells cometitive. Fuel cells ae cleane because highe efficiency imlies lowe emissions, and because some fuel candidates hydogen gas in aticula contain less ollutants than moe common fossil fuels. Fuel cells do oduce cabon monoxide CO and cabon dioxide CO 2, sulfu and othe ollutions as long as the enegy caie contains such substances, but usually in small amounts. ince no exlosion occus, noise is esticted to comessos, ums etc. This could be esecially valuable in shot-sea shiing, cuise taffic and militay alications. In a maketlace whee inceased taxation of extenal costs is exected, the low emission levels chaacteizing fuel cells eesent a otential fo futhe oeating cost savings. Most emission taxes, e.g. a cabon tax in the aftemath of the Kyoto Potocol, geneally favos fuel cells elative to othe technologies of inteest. Fuel cells can even moe easily outefom othe technologies in a close-to-zeo emission egime fo intenational shiing. uch a egime, which may soon be intoduced by the Euoean Union, could lead to moe aid changes than eviously exected, since the cost of installing cleaning equiment in existing shis could be vey high. 3

4 Fuel cells need hydogen in one fom o anothe. Hydogen is an exlosive gas that is difficult to stoe, tansot o convet efom fom othe substances befoe it can go into a fuel cell. Fo cost and safety easons, hydogen caies othe than ue hydogen could be moe useful fo the shiing industy. The main challenge fo the develoes of fuel cells is to each feasible technical solutions that ae not too exensive. The ices of cuent fuel cell systems ae 5-20 times the ice of simila combustion engines. Five main fuel cell candidates ae cuently unde develoment: PEM oton exchange membane, DM diect methanol, P hoshoic acid, O solid oxide, and MC molten cabonate fuel cells. One imotant diffeence lies in the oeating temeatue, which sans fom below 100 C PEMDM to above 600 C MCO. The majo advantage of low temeatue fuel cells is a shot statu time. The majo disadvantage is a need fo exensive catalyzes and clean fuel. The latte is obtained by using hydogen o by efoming othe hydogen caies. High temeatue fuel cells could equie many hous fo statu, but as they ae less sensitive to ollution, moe fuel candidates exist. The chaacteistics above imly that vaious fuel cell systems aeal diffeently to diffeent makets. The level of matuity also vaies. ll fuel cell cas unde develoment seem to use the PEM technology. High temeatue fuel cells, which may be moe inteesting in maitime tansot, ae still at a moe exeimental stage Wüzig Most studies of maine alications of fuel cells, like attle 2000, llen et al and Bolind 2000, conside some diect cost asects, but they ay moe attention to technical issues. Kani et al esent a elatively detailed cost analysis of oulsion systems fo a eesentative shi, comaing two tyes of 5.5 Mw fuel cells with taditional diesel engines of simila size. The analysis indicates that the otimal choice of technology will be a tade-off between investment costs and oeating costs. Without ignoing the fact that many aametes ae uncetain, it is concluded that fuel cells can become cometitive fo easonable levels of fuel costs. Bingen et al focus on fuel cell oulsion in fey oeations in Noway, and conclude similaly. Wüzig et al ae moe sketical than the efeences above, emhasizing that all cost estimates ae simly taget values. Existing fuel cells ae fa moe exensive, and any cost 4

5 estimate long into the futue is highly seculative. s fa as oulsion in shiing is concened, the technology has hadly been tied out in a scale of inteest. Thee seems to a geneal consensus that fuel cells will not become a majo oulsion souce in long-haul shiing in the foeseeable futue, mainly fo two easons. Fist, much of this tade is fueled by cude oil. Cude oil is chea, and it cannot be efomed by existing technologies. No ae cleane fuels such as hydogen o methane satisfactoy altenatives due to cost and safety concens. Diesel is moe omising, but its content of sulfu may also ceate technical oblems and aise costs. econd, high temeatue fuel cells the most aealing tye in this case ae most effective when oeated at 20-40% of total caacity, while combustion engines ae most effective at 70-90% loads. Efficient long-haul shiing based on high temeatue fuel cells theefoe equies much caacity that aely would be needed. The situation is diffeent in shot-sea shiing, whee sae owe is in highe demand due to safety concens and need fo efficient habo oeations. Fom the comments above, it is clea that fuel cells make moe sense in shot-sea shiing. This agument is stengthened by the fact that low emission levels ae also moe valuable in shot-sea shiing. lthough much of the discussion below is geneal in natue, it is obably most elevant to shot-sea shiing with cago and assenge feies, shuttle tankes o shis sailing on inland wateways. New envionmental olicies may imove the ootunities in long-haul shiing, too, but thee is a long way to go befoe a new VCC is oelled by a fuel cell system. On the othe hand, fuel cells could be useful fo auxiliay owe oduction even if not being efficient fo oulsion. They could, fo examle, elace diesel geneatos in cuise taffic to educe noise and othe emissions. Investment costs Investment costs fo oulsion system using state-of-the-at fuel cell technology ae tyically estimated to $ kw, while edicted ices ange fom $100 to $1500 kw Hömandinge and ucas 1996, Bolind 2000, Kani et al Kani et al estimated the cost of a eesentative fuel cell system 5.5 Mw to $ kw in a comaative study of altenative oulsion systems fo shis. This was aoximately 50% highe than the estimate fo a simila IDE integated diesel system, and almost thee times the estimate fo a CODD conventional diesel system. Bolind 2000 is moe otimistic with esect to 5

6 lage fuel cell installations suited fo shis, execting ices as low as $ kw befoe the end of the cuent decade. The sead in cost estimates eflect to some extent ice diffeences between vaious alications, but mainly it demonstates that eliable estimates cannot be obtained at the cuent stage of develoment. Investment cost comaisons must, in ode to be meaningful, take into account diffeences in exected lifetime, and degadation ove the life-cycle. Fuel cells contain some comonents that tend to degade ove time due to ai and fuel imuities. High-temeatue fuel cells degade each time the temeatue in the cell is changed. lso, it may take hous o days to cool down o wam u the cells, so the temeatue should be ket close to the oeating temeatue even when the cell is idle. This is of inteest with esect to maintenance, since some comlex tade-offs could aise between oeating efficiency, ovehaul and degadation. The technological otential is uncetain as fa as lifetimes ae concened. Initial maine MC molten-cabonate fuel cells may have to be elaced afte aoximately hous. Nomally this coves no moe than five yeas of sevice. uch a lifetime taget is eached most easily when the fuel is natual gas. tack elacement costs must be accounted fo along with othe maintenance equiements, but othewise, most fuel cell owe systems can obably live as long as othe engines, tyically yeas llen et al. 1998, Wüzig et al Oeating costs The main cost advantage of fuel cell owe oduction lies in a otential fo lowe oeating costs. The gains obviously deend on the choice of fuel, because the exected ice of diffeent fuels usually diffe in efficiency tems. Diffeences in ice uncetainty could also lay a ole due to switching otions, e.g. when slow steaming is ofitable at high fuel ices. In a comaative study of an MC molten-cabonate fuel cell system and an IDE integated diesel system, Kani et al eoted that the fuel cell system consumed 25% less fuel. Based on comaisons of vaious fuel cell and combustion systems, llen et al claim, moe geneally, that fuel cells could educe fuel costs by 50%. s fo absolute cost levels, Kani et al estimated total annual fuel costs to $80 kw fo the MC fuel cells vesus $110 fo the IDE system. This is based on meican data, and a 6

7 diesel ice of $270 e ton. The fuel cost eduction is not enough to comensate fo highe initial investment costs in a life-cycle esective. If the fuel cell wee to be cometitive ove a 25-yea life-cycle, the diesel ice would have to be close to $600. ince the latte is still below the ice level in many Euoean makets, the analysis by Kani et al. indicates that fuel cells could be cometitive fo some easonable combinations of facto ices. Infastuctue The need fo infastuctue is an obstacle to aid intoduction of fuel cells in tansotation. Thomas et al estimated long-un infastuctue costs to be lowe fo gasoline than fo hydogen as fa as oad tansotation in the United tates is concened. Ogden et al eoted simila esults. Total infastuctue costs do not amount to moe than aoximately $1000 e ca sold, so the imotance of diffeences in this egad should not be exaggeated. I am not awae of simila studies of shiing makets. Intuitively, lowe infastuctue costs can be exected in maitime makets due to fewe nodes in the tansot netwok. On-boad sace equiements could also ceate an infastuctue cost baie, but obably not a citical one. llen et al claim that the need fo sace is of simila magnitude as fo taditional engines 2.5 cubic ftkw fo a eesentative MC fuel cell. Most systems could obably also be designed to avoid conflicts with the nomal utilization of sace in a shi. Uncetainty hiing makets ae volatile due to the combined effect of inelastic and stochastic tansot demand, caacity constained suly, and fluctuating facto ices. Oil ice changes can have suising effects on feight ates and evenues because suly and demand shift in the same diection. Inceasing oil ices ae tyically elated to deceasing demand fo some tades oil in aticula, but also to deceasing suly as the otimal seed goes down tofod 1992, Wegeland and Wijnolst uch effects make the makets highly deendent on extenal shocks, many of which oiginate fom OPEC decisions and events in the Middle East. One question in this esect is whethe a hydogen-based owe oduction egime could change aggegate maket uncetainty. The answe is not evident as it could deend on the maket segment, and many economic foces could be involved. On the one hand, fuel cells 7

8 make shiing even moe caital intensive, and moe influenced by ievesible investment and caacity constaints than today. This tends to incease oveall isk and uncetainty. On the othe hand, lowe cost uncetainty may esult, as oeations become less deendent on the oil ice, which is usually the most volatile facto ice in shiing. Most cuent fuel cells ae fueled with hydogen, which is most easily develoed fom natual gas. ltenative hydocabon fuels such as methanol, alcohol o ammonia cannot be excluded in the futue, but natual gas, methanol and diesel ae obably the most imotant altenative fuels Bolind In a study of U enegy secuity, Geene 1999 claims that use of natual gas will educe OPEC maket owe, and make global fuel makets moe cometitive due to the availability and distibution of gas esouces. It is an issue fo futhe eseach whethe this could also educe the oveall fuel ice uncetainty by significant amounts. 3. Flexibility analysis Objectives and models The evious section descibed some economic chaacteistics that ae imotant when fuel cells ae to be valued u against taditional combustion engines in shiing. The coe of the matte seems to be the distibution of caital costs vesus oeating costs and othe costs sead ove time. The question is whethe some solutions ae moe flexible than othes, and what the imlications of the diffeence might be. This section uses a eal otions aoach to exemlify and quantify exeimentally the value of flexibility in a classical setting, with ootunities to lay u and to sca shis when feight ates ae low. I discuss the imlications fo otimal investment behavio and shi valuation aising fom: the distibution of caital costs vesus oeating costs execting that fuel cells will be moe costly to build, but less costly to oeate than combustion engines inceased oeating costs afte a lay-u eiod execting that a fuel cell system could degade by being shut down comletely estictions with esect to the numbe of lay-u eiods fo the same eason as above The analysis is aametic as it looks at altenative distibutions of caital costs vesus oeating costs, stating with a baseline technology. In the most exteme case, the caital cost 8

9 shae is twice the simila shae of the baseline technology. With efeence to the cost estimates in the evious section, such a high caital cost shae could eflect fully fuel cell based owe oduction unde cetain assumtions. ome of the intemediate cases, whee caital costs incease less, moe likely eflect combined solutions whee fuel cells systems ae used fo auxiliay owe oduction. The fist at of the analysis is based on two standad eal otions models by vinash Dixit: the enty-exit model and enty-exit-scaing model. The second at also uses a modified vesion of the latte. 2 The enty exit model can be descibed as follows see endix 1 fo details: shi is eithe active oeating o inactive laid-u. No evenue o cost alies when the shi is laid-u. The annual cost of oeation, c, is constant. Then the net esent cost of continuous oeation equals c, whee is a fixed inteest ate. ifetime estictions ae disegaded. 3 The annual evenue fom oeation is stochastic, given by a geometic Bownian ocess with no dift. 4 It can be shown that the exected net esent evenue of continuous oeation equals, whee is the cuent value of the feight ate. fixed activation cost,, alies each time a shi stats to oeate, while a fixed lay-u cost,, alies wheneve a shi is laid u. Fom a standad net esent value ule, a laid-u shi should be set to oeate as soon as +c. Then the exected net esent value of a decision to ente the maket, and emain active, is non-negative. imilaly, an active shi should be laid u as soon as c +. Then the net esent cost of sustained oeations exceeds the total ootunity cost, which is the sum of the exit cost and the exected, net esent income loss. 2 The oiginal efeences ae Dixit 1988&1989, which daw on ioneeing wok by Mossin 1968 and Bennan and chwatz The models ae exloed numeically by Dixit and Pindyck 1994, ch. 7. The modified vesion of the enty-exit-scaing model is a mino extension of a model discussed by ødal Moe ealistic eesentations comlicate the model. The lifetime is usually so long that the eo fom this simlification is obably mino, unless the shi is vey old. 4 ee Dixit and Pindyck 1994 fo a discussion of stochastic ocesses of this kind. Oeating costs ae usually also uncetain, but since feight ates tend to be moe uncetain, I abstain fom modeling cost uncetainty. 9

10 Both decision ules above ae incoect because the investments ae atly ievesible, and the value of waiting fo infomation is ignoed. coect, otion based calculation will show that one should wait longe. shi cuently laid u should not stat to oeate befoe exceeds +c by a fixed magin. The magin could be lage if the feight ate is vey volatile. n active shi should not be laid u until is a fixed magin lowe than c. This magin is also inceasing in uncetainty. The otimal decision ules can be summed u as follows: If the shi is cuently inactive, it should stat to oeate when the feight ate hits a cetain value fom below whee >c+. If the shi is cuently active, it should be laid u when the feight ate hits a cetain value fom above whee <c. The shi should emain in the cuent state active o idle as long as the feight ate stays between and. The enty-exit-scaing model is an extended model that also consides shi investment and scaing see endix 2 fo details. If scaing is eve to be of inteest, we now have to add a small, but ositive unning cost duing lay-u; i.e., a mothballing cost. We also include the cost of a new shi, and the sca cost o value of an old one. Two additional investment thesholds will now encicle the two thesholds of the evious model, as follows: shi should be acquied, and stat oeations, when the feight ate hits a fixed value I fom below whee I. n existing shi should be scaed when the feight ate hits a fixed value fom above whee. The two inequality signs ae weak because lay-u is not always viable. If the mothballing cost is too high, it is bette eithe to kee the shi active o to sca ight away, so I = and =. Then the model collases to the simle enty-exit case with a diffeent inteetation of the switching costs; the enty cost eesents the total cost of acquiing and activating the shi, while the exit cost eesents the total cost of deactivation and scaing. s long as lay-u is viable, all fou investment thesholds aly, in the ode < < < I. In othe wods: a shi is acquied when the feight ate gets sufficiently high at I ; an active 10

11 shi is laid u when the feight ate gets sufficiently low at ; a laid-u shi is eithe activated at o scaed at, deending on which theshold is hit fist. Base case data The enty-exit-scaing model is exloed by Dixit and Pindyck 1994, ch. 7 fo a set of shiing data. The data, used hee as a base case scenaio, ae shown in Table 1. They contain eesentative costs fo a medium-sized dwt oil tanke fom 1992, based on industy infomation. Feight ate volatility is an emiical estimate fom quately data of the eiod The discount ate, set by Dixit and Pindyck, can be inteeted as a isk-adjusted inteest ate. The caital cost shae is not exteme, so even if the data ae fom oil tades, they may not be fa fom the tuth in many othe shiing segments whee fuel cells ae moe likely to be intoduced. The negative sca cost in Table 1 eflects a ositive sca value. Descition Value in mill. $ 1992 Initial shi cost, I 40 ca cost, 3.4 ctivation enty cost, ay-u exit cost, Oeating cost, c 4.4 Mothballing cost, m Feight ate volatility annual standad deviation, s 15 % Discount ate, 5 % Table 1. Base case data. The data in Table 1 lead to the following otimal investment thesholds: =2.99, =3.32, =4.62 and I =9.59. Thus, the shi is acquied when the aveage feight ate coesonds to $9.59 mill. in annual income. The equiement unde a standad net esent ule is $6.4 mill. i.e., the sum of oeating costs 4.4 mill. and annualized caital costs =2.0 mill.. The diffeence shows the imotance of consideing uncetainty uon investment. Pat 1: ltenative cost distibutions Table 1 is based on conventional technology fo owe oduction. Having in mind that fuel cells ae likely to incease the caital cost shae, we oceed by asking: How ae investment decisions and shi values affected by the distibution of costs ove time? Table 2 sums u an attemt to answe this question. 11

12 Oeating cost, c Initial shi cost, I I hi value loss 0.0 % 1.6 % 2.9 % 3.8 % 4.6 % 5.1 % Table 2. Investment with 15% feight ate volatility and altenative caital cost shaes. The fist column of esults is fo the base case scenaio. The $40 mill. ice tag coesonds to $2.0 mill. in annual caital costs. The vaiable hi value loss is set to zeo as it measues the total loss of shi value elative to the value of the baseline scenaio. 5 The second column eots the esults when the caital cost is inceased by $0.4 mill. which coesonds to inceasing the ice of the shi by $8 mill., and the oeating cost is deceased by the same amount. Thee ae two main effects of such a change. Fist, investment is discouaged as one should wait fo a highe feight ate befoe investing in a new shi I =9.76 vesus I =9.59. imilaly, lay-u and scaing ae discouaged as both and decease. The atio also inceases, so the amount of ievesibility inceases in all esects: one should wait longe befoe acquiing o scaing a shi, and also wait longe befoe laying u a shi o befoe activating one that is laid u. econd, the value of an active shi, o if investment has not yet taken lace the value of the otion to invest, deceases by 1.6%. The eduction of shi value is a measue of lost flexibility, caused by the fact that caital costs aly even when the shi is laid u. The geneal message is simle: investments should not, ceteis aibus, be made moe ievesible than necessay. In this maket thee is a value of flexibility in tems of an otion to lay u when the feight ate is low. cetain caital cost incease is not equivalent to an equal oeating cost decease. If the two technology choices wee to be equal when valued as altenative investment ojects, the oeating cost must be educed futhe fo the moe caital-intensive altenative. The est of Table 2 demonstates how decisions change, and moe flexibility is lost, fo highe caital cost shaes. t a cetain oint lay-u is no longe viable, so the otimal investment 5 The shi value is the exected, discounted net esent value of futue net evenues. Only the change is eoted as the absolute net esent value deends on the cuent feight ate, wheeas the ecentage change does not. 12

13 behavio changes qualitatively. With the assumtions of the two ightmost columns, the cost of lay-u elative to the cost of oeation is so high that the shi should be scaed diectly when the feight ate is low enough. In the most caital intensive case, when the cost of the shi is twice the baseline cost, the value of the shi deceases by 5.1% It can be shown that the oeating cost must be educed by anothe 10% fom $2.4 to $2.2 mill. to comensate fo the flexibility loss by choosing such a caital intensive fuel cell technology. Uncetainty is cucial fo these esults. The moe uncetainty, the highe ae the values of layu otions and sca otions. Table 3 eots simila esults when the feight ate uncetainty is inceased fom 15% to 25%. The latte aeas to be in the ue end of long un estimates even in many secialized maket segments. The value of flexibility inceases, and the lay-u otion now is valuable fo all data sets. With the data set of the ightmost column, the value of the investment otion is significantly loweed. It can be shown that the oeating cost must be educed by moe than 20 ecent fom $2.4 to $1.9 mill. e yea to comensate fo the loss of flexibility. This indicates that flexibility otions could be decisive fo the choice of technology when the uncetainty is high enough. Oeating cost, c Initial shi cost, I I hi value loss 0.0 % 1.7 % 3.1 % 4.3 % 5.3 % 6.2 % Table 3. Investment with 25% feight ate volatility. Pat 2: ay-u estictions ome fuel cells can be damaged, and lose efficiency, by being switched on and off. Possible imlications ae lost flexibility as the numbe of switches could be esticted o inceasing oeating costs ove time. ltenatively, low oeating costs could be sustained by keeing the fuel cell active even when the shi is idle. The model can be adjusted to handle seveal such otions. Hee I estict to a stylistic, stewise analysis of two altenatives. Fist it is shown how investment and valuation ae affected by esticting the numbe of lay-u eiods. Then the effect of inceasing the oeating cost is added to this. 13

14 The comlexity of the investment oblem inceases by esticting the numbe of lay-u eiods, since the otimal investment thesholds now deend on the emaining numbe of switches. Howeve, with these data it tuns out to be sufficient to study the case with one layu eiod. s usual, the shi is built and set to oeate when the feight ate exceeds some value I. When the ate is down to, the shi is laid u. Then it is eithe scaed at o eactivated at, deending on what comes fist. ll this coincides with the evious model. When no lay-u otion is left, the shi must be scaed diectly when the feight ate gets sufficiently low. This theshold is denoted by X in Table 4. The table confims the basic intuition that one should not wait quite as long befoe scaing when the otions to lay-u and eactive have aleady been used i.e., X exceeds. Oeating cost, c Initial shi cost, I I X hi value loss 0.0 % 1.6 % 2.9 % 3.8 % 4.6 % 5.1 % Table 4. Investment with maximum one lay-u eiod. s obseved by comaison with Table 2, the lay-u estiction lays a mino ole. The initial theshold I inceases slightly, but the change is so small that it does not show u in the second decimal lace fo any data set. Thee ae thee easons fo this: fist, a ossible second oeating eiod is so long into the futue when the shi is acquied that the ofit effect is suessed by discounting; second, the oeating cost change is small; thid, the oeating cost eesents only a faction about 30 ecent of total costs. Othe changes in investment behavio ae also mino excet fo the new scaing theshold X. Note also that the estiction is ielevant in the two ightmost columns, whee lay-u is not viable. It follows fom the discussion above that lay-u is a ae event with these numbes. Most of the value of flexibility is catued by the otion to lay u once. One main eason fo this is that even the shi with taditional owe oduction is quite caital intensive. 14

15 The last case to be investigated focuses on the effect of inceasing the oeating cost afte the lay-u eiod. The oeating cost is assumed to incease by thee ecent. 6 Having been though the evious analysis, such a change cannot be exected to influence investment behavio geatly. This is confimed in Table 5. The inteetation of the last ow is new; this ow now eots the loss when comaing the oject value io to o shotly afte the initial shi ocuement with the simila value in Table 4, whee the oeating cost does not incease afte the lay-u eiod. Oeating cost befoe lay-u, c Oeating cost afte lay-u, αc Initial shi cost, I I X Value loss due to cost incease 0.03 % 0.02 % 0.01 % 0.00 % 0 % 0 % Table 5. Investment with one lay-u eiod followed by 3% oeating cost incease. Fo the data set closest to the base case data the fist column, the initial investment theshold I inceases maginally, fom 9.59 to This is due to highe exected costs. The change also imlies a gain fom ostoning lay-u, so deceases fom 3.32 to 3.18, slightly moe than the exta cost. The thee othe investment thesholds H, X, and all incease. The changes in and X ae easonable consequences of highe oeating costs. The incease in follows fom an otion agument: the cost of investing in a new shi has become elatively cheae as the value of a laid-u shi is lowe than befoe. Theefoe scaing should take lace ealie. Not unexectedly, the value loss fom the evious model is negligible 0.03 ecent at most. This is because of discounting, because the oeating cost incease is small, and because it eesents only a faction of total costs. Nonetheless, even this small cost change leads to a 6 uch a small oeating cost incease is sufficient to detect the chaacteistics of the model. lage incease easily makes lay-u ielevant fo all of the investigated distibutions of costs. 15

16 qualitative change in investment behavio fo one data set. ay-u is no longe viable in the middle column, wheeas lay-u was indeed viable with the elated data set in Table 4. Citicism The assumtions behind the analyses above intend to eflect maket chaacteistics of vaious owe oduction systems in shiing. Thei eesentativeness can obviously be questioned. In addition to the cost aametes, which may not be cedible, one might object to the choice of stochastic ocess. Feight ates ae clealy not geometic Bownian, since that imlies they could gow beyond all limits. ome kind of mean evesion is moe likely, by which the feight ate is evented fom deviating too much fom a long un mean. Tyically, the mean value will not be fa fom long un aveage costs. In the model of this ae, we might exect massive shi investment when the feight ate hits the tigge value I. That would incease aggegate suly, and event the feight ate fom inceasing futhe. imilaly, aggegate suly could shink as a esult of scaing if demand emains low enough fo a long eiod of time. This would ush the feight ate u again. When consideing the issues focused in this ae, such aguments may not be imotant in actice desite being coect in incile. It can be shown that the otimal investment ules need not change much by tuning to industy equilibium even if the undelying assumtions ae diffeent eahy Moeove, the objective of the numeical analysis is not to end u with secific investment ecommendations. Maitime fuel cell technology is fa fom being matue enough fo that. Yet, the analysis exemlifies the otential imotance of flexibility by numbes that ae hoefully in the ballak of coect values unde some elevant technological and economic conditions. When comaing system solutions, the oint of the matte is not shi values o ice levels in absolute tems, but diffeences and maginal values of change. I believe the analysis caies some tuth in this esect. It should also be mentioned that the models could be extended to moe comlex stochastic ocesses, which include meanevesion. When moe eliable data ae available, such extensions could be wothwhile. 4. Final emaks This ae has ointed out some economic chaacteistics of fuel cells alied to shiing. Possible imlications fo valuation and decision making have been investigated though 16

17 exeiments, using maket data and altenative fuel cell cost ojections. The numeical analysis in the evious section demonstated, quantitatively and fomally, some tyical effects of changing the caital cost shae and vaious othe cost aametes that ae likely to be diffeent fo a fuel cell owe egime. On geneal conclusion stands out fom this analysis: valuation of fuel cell investments must account fo ossible losses of flexibility. The analysis also showed that the otimal investment behavio could change qualitatively by switching to fuel cell owe oduction. Hee this occued when lay-u tuned out to be ielevant with high caital cost shaes, but the investment olicy could also change as a esult of otions to switch between maket segments, o otions to incease efficiency by altenating between fuels, adjusting seed etc. Real otions models is the oe tool to imove the undestanding of all such otions fo both economic eseaches and technical innovatos. This statement will be even moe valid when the fuel cell technology matues, and moe eliable data aea. Refeences llen,., E. shey, D. Goe and M. Cevi Maine lications of Fuel Cells. Naval Enginees Jounal Januay. Bingen, K., J. Byknes,. Kingstad, C. tubø, M. Thomasssen, P. Valnikka and. Ødegåd Benselcelle i fege. Poject Reot in Nowegian, Nowegian Univesity of cience and Technology. Bolind,.M n Evaluation of Fuel Cells fo Commecial hi lications. Technical and Reseach Reot 55, The ociety of Naval chitects and Maine Enginees. Bennan, M. J. and E.. chwaz Evaluating Natual Resouce Investments, Jounal of Business 58, Dixit,. K Otimal ay-u and caing Decisions. Unublished July, Pinceton Univesity. Dixit,. K Enty and Exit Decisions unde Uncetainty. Jounal of Political Economy 97 June, Dixit,. K. and Pindyck, Robet Investment Unde Uncetainty. Pinceton Univesity Pess. Dixit,.; R.. Pindyck and. ødal Maku Inteetation of Otimal Investment Rules. Economic Jounal, , Eken, teina Enty and Exit Decisions with Resticted witching. Woking Pae no. 8, The Nowegian chool of Economics and Business dministation, Deatment of Finance and Management cience. FT Financial Times Infomation imited, sia fica Intellegence Wie, Januay 8, Intenet: htt:hoovnews.hooves.comf.as?layout=dislaynews&doc_id=nr _c54e000c28377af7 17

18 Geene, D n ssessment of Enegy and Envionmental Issues Related to the Use of Gas-to-Oil- iquid Fuels in Tansotation. Cente fo Tansotation nalysis Oak Ridge National aboatoy ORNTM IE htt: Hömandinge, G. and N. J. D. ucas Is Clean Enough? The Influence of Envionmental Extenalities on Makets fo Fuel Cells in Tansot. Tansotation Reseach: Pat D: Tansot and Envionment, vol. 1, issue 1, Kani, Z., R. Willigan, C. tze, M. Badal, W. Godon, J. Haide, R. evesque and W. Fosyth Comaative ife Cycle Costs of Fuel Cells and Othe Poulsion ystems. U Coast Guad Reseach & Develoment Cente, Reot CG-D eahy, J Investment in Cometitive Equilibium: The Otimality of Myoic Behaviou. Quately Jounal of Economics 1084, Mæstad, O.,.J. Evensen,. Mathisen and K. Olsen Intenational Climate Policy Consequences fo hiing. NF Reot no. 82. Foundation fo Reseach in Economics and Business dministation, Begen. Ogden, J.M., M.M. teinbugle and T. G. Keutz Comaison of Hydogen, Methanol and Gasoline as Fuels fo Fuel Cell Vehicles: Imlications fo Vehicle Design and Infastuctue Develoment. Jounal of Powe ouces 79, attle, G Fuel Cells Going On-Boad. Jounal of Powe ouces 86, tofod, M., Maitime Economics. Routledge. ødal, Enty and Exit Decisions Based on a Discount Facto oach. Woking Pae 2, gde Univesity College, Deatment of Economics and Business dministation. Thomas, C.E., J.P. Readon, F.D. omax, J. Pinyan and I.F. Kuhn Distibuted Hydogen Fuel ystems nalysis. Poceedings of the 2001 DOE Hydogen Powe Review. NRECP WEO Wold Enegy Outlook The Intenational Enegy gency OECDIE. Wegeland, T. and N. Wijnolst, hiing. Delft Univesity Pess. Wüzig, G.-M., R. Ka and H. Pauli Using Fuel Cell Technology in the Maine Maket. Gemanische loyd G, Hambug. Zvi, K., N. eavitt, T. Costa and R. Gijalva Maine Fuel Cell Maket nalysis. U Coast Guad Resach & Develoment Cente, Reot CG-D endix 1: The enty-exit model This aendix and endix 2 sulement the text in deiving the otimal olicy of the vaious models in section 3. The esentation does not use stochastic calculus which is needed to obtain fomal oofs, but moe details and efeences can be found in ødal The objectives ae mainly to document the models sufficiently that the analysis can be elicated, and to enable the eade to undetake simila investigations using othe numbes. 18

19 The otimal enty olicy in the enty-exit model is to activate a shi u when the evenue fom oeation the feight ate hits a cetain theshold fom below. imilaly, the otimal exit olicy is to lay u when the feight ate hits a cetain theshold fom above. The stochastic ocess fo the feight ate is a geometic Bownian motion with constant volatility, s. omewhat simlified, the ecentage feight ate change fom this yea to next yea is given by a nomal distibution with standad deviation s. The mean value is the cuent ate, so the exectation of the change is zeo even if the feight ate indeed will fluctuate due to uncetainty. dift tem on to of the uncetainty can easily be included. The otimal olicy can be deived by assuming that the shi is cuently idle, and by stating fom a fixed, low feight ate 0. Define a decision olicy by two abitay feight ates, and <, at which activation enty and lay-u exit take lace, esectively. The value of the olicy at the initial oint when the feight ate equals 0 is defined as the exected net esent value of all futue net benefits. Define this net esent value by W 0, and the simila values when and ae eached by W and W, esectively. The following elations hold: T 1.1 W E [ 0 e ] 0 = W T 1.2 W = E[ e ] c + W W [ ] T 1.3 = E e c W In Eq. 1.1, E[ ] is the exectations oeato, is the inteest ate, and T 0 is the stochastic time it takes fo the feight ate to hit. Technically, T 0 is the fist hitting time o fist assage time fom 0 to, while E[e T 0 ] is the exected discount facto. The equation says that W 0 is the exected and discounted value of W, which is tue as nothing but waiting, takes lace when the feight ate moves fom 0 to. Eq. 1.2 contains a simila exected and discounted value fo W. Enty occus as soon as is hit, so if the shi emains active foeve, the exected futue net benefits equal the exected and discounted net evenues, c, subtacted by the activation cost,. Thee is also an otion to switch again afte activation, W, so the net gain is c+w. This is discounted by the facto E[e T ], whose inteetation follows fom the aagah above. 19

20 Eq. 1.3 contains the simila elationshi fo W. The shi is laid u when is hit. If it wee to emain laid-u, the gain would be c as the net esent oeating cost c is saved, the exit cost is aid, and the exected, discounted feight income is also lost. Right afte exit, the situation of Eq. 1.2 has etuned, so the value of futhe switching otions equals W. The total gain, c +W, is discounted by E[e T ] fo the same eason as above. Two chaacteistics of the geometic Bownian ocess and many simila ocesses ove to be convenient: it is a continuous ocess with no memoy in the sense that the distibution of futue values feight ates is detemined entiely by the cuent value. This imlies that the discount factos can be witten as functions of the statoint and endoint, so E[e T 0 ], E[e T ] and E[eT ] can be witten as Q 0,, Q, and Q,, whee Q is secific function. The model as visualized in Fig. 1. Decision Cost Feight ate Value Discount factos ctivation W Q, Q, ay-u W Q 0, Initial situation - 0 W 0 Fig. 1. The enty-exit model. The discount factos fo the geometic Bownian ocess of this ae can be shown to be: 1.4 0, = 0 Q b 1.5 Q, = b 1.6 Q, = b1 20

21 1 2 whee b = s. imila fomulas holds fo all ositive endoints: the atio of 2 the endoints is oweed to b if the motion is uwad, and to b1 if the motion is downwad. The initial value of the decision olicy, W 0, is found by solving the system with esect to W 0, W and W, and inseting The following exession is obtained: b1 b c + c 1.7 W0 = 0 2b1 1 The maximum of W0 with esect to and give the otimal olicy. No closed-fom solution exists, but numeical analysis can be used to detemine the otimal thesholds as well as the otimal W 0. The latte is used in the text when quantifying losses of flexibility. endix 2: The enty-exit-scaing model The otimal olicy of the enty-exit-scaing model can be deived by simila ocedues as in endix 1. The model with no switching estictions is illustated in Fig. 2. Decision Cost Feight ate Value Discount factos Investment in shi I I W I Q I, ctivation W Q *, Q, ay-u W Q, I Q *, caing W Q 0, Initial situation - 0 W 0 Fig. 2. The enty-exit-scaing model. Fou investment thesholds,, H, I chaacteize a decision olicy, whose value is detemined by the following equations: 2.1 W = Q, W W = Q, c I + W I I I 21

22 I I W m c Q W + =, 2.4 W m Q W m c Q W =,, * * 2.5 W m c Q W + =, This equation system is simila to that of endix 1, and need not be exlained in deth. Fo examle, Eq. 2.3 states the value of the olicy ight afte the shi has been acquied at feight ate I. This is simila to Eq. 1.2, excet fo the mothballing cost, m, which is subtacted wheeas lay-u was fee in the evious model. The main new element is Eq. 2.4, which states the value ight afte lay-u at. It is not clea whethe the feight ate then deceases to imlying scaing befoe o afte it hits imlying activation. The conditional discount factos Q *, and Q *, account fo this. The fist one is the exected discount facto when moving fom to conditional on not hitting. The second one is the simila discount facto when moving fom to conditional on not hitting. These discount factos can be shown to be: * 1, = b H b b b Q * 1, = b b b b Q whee 0, and <. By solving the system and inseting , an analytical exession fo W 0 is obtained. The otimal olicy and the value of the shi follow fom maximization of W 0 with esect to,, and I. The fomula fo W 0 is omitted as it is lengthy, and as a softwae ackage is needed anyway to detemine the maximum. When lay-u is esticted, the investment decisions ae the same as without the estiction u until the end of the lay-u eiod. The equations emain, but the following equations elace 2.4-5: 2.8 W m Q W m c Q W =,, * * α 2.9 X X W c Q W + =, α

23 2.10 W = Q, c I + W X X I I I Eq. 2.8 coincides with Eq. 2.4 excet fo the aamete α, which accounts fo a ossible oeating cost incease afte lay-u. The numbes used ae α=1.00 and α=1.03. Eq. 2.9 alies ight afte the lay-u eiod, so scaing when the feight ate hits X must be the next event. t that time the oeating cost αc is saved, and the evenue flow stating at X is lost. The net gain is discounted and educed by the sca cost,, while the emaining otion value, W X, is added. The latte, given by Eq. 2.9, coincides with Eq. 2.2 excet fo the initial ice. The otimal olicy is detemined as usual, by solving 2.1-3; fo W 0, W, W I, W, W, W X, and then maximizing with esect to, X,, and I. 23