The use of the Forstlicher Zinssatz * as an approximation approach in an uncertain world

Transcription

1 Meeting of the IUFRO, Octobe 8, Damstadt 9 The use of the Fostliche Zinssatz * as an appoximation appoach in an uncetain wold - a eal options pespective - of. D. Thomas Bukhadt * taditional inteest ate in foesty

2 Agenda Intoduction: Conceptual eal investment valuation appoaches N vs. eal options Example: The option to wait aluation and investment in foesty A simple eal options model in continuous time applied to foesty Analyze the decision to begin and abandon opeation Captue timing and opeational decisions simultaneously Conclusions

3 Fundamental popeties of eal investments Uncetainty» ices» Costs» Inventoy stock» olicy Ievesibility» Sunk costs, e.g. affoestation, tee species selection Timing options» Decisions may be delayed to gain infomation 3

4 aluation I: Net pesent value appoach Standad textbook appoach: Invest if N > N t zt i o N z t e t Does not account fo any of the issues above. Standad advice: In applications use expected payments o cude appoximations discount using isk adjusted discount ate In foesty: Use fostliche Zinssatz, below isk fee ate -ρt dt 4

5 aluation II: Real options appoach Manageial flexibility povides eal options Options give thei owne the ight, but not the obligation, to take a specified futue action Impotant eal options: Timing and staging investments, abandon/eopen poduction, alte scale, switch technology, change land use... Investment means execising the option Oppotunity costs theefoe compise option value The option value is often substantial aluation of eal eal options : abitage fee Othewise: Stochastic pogamming 5

6 Example: Option to wait I A simple pice pocess Conside an uncetain pice, whee uncetainty is esolved afte one time peiod ob q ob -q 3 The value of espective income steams is assumed to be given by the N N 3 3/i 33 N ob q ob -q N /i ee i %, q.5 and isk neutal valuation is assumed 6

7 Example: Option to wait II The eal investment option Assume an option C to invest K 6 to ealize the pojekt investment. Should one invest? N fo immediate investment: C maxn - K, max 6, 6 C >, indicating an advantageous investment! But is it the optimal investment stategy? N 33 C u max33-6, 7 N ob q C? ob q ob -q ob -q N C d max 6, 7

8 Example: Option to wait III Stochastic pogamming N fo delayed investment: C / i at i % Results: Invest in t, if pice goes up, else do not invest at all Tue oppotunity cost 373 >, the pice of the pofit steam The option value of 773 consist of» Intinsic value 6» Time value 73 Simple N calculation ignoes option value to delay investment, giving a suboptimal investment signal Note: Calculating the N fo the optimal stategy is the essence of stochastic dynamic pogamming. Essential disadvantage: An extenally given discount ate i is equied 8

9 Example: Option to wait I Abitage fee valuation Basic idea Nobel pice 997: Meton & Scholes Find a potfolio of tadable assets that duplicates the option in any futue state of the wold Then this potfolio is equivalent to the option fom an economic point of view: aw of one pice applies The option value must equal the known value of the potfolio Essential featues The option value is pefeence fee An exogenously defined discount ate is not equied aluation is based on abitage fee picing Expected values of futue pices ae not needed, just the stuctue and volatility of the pice pocess 9

10 Example: Option to wait Real option valuation Duplicating potfolio fo option C Buy.777 shaes of poject fo 7 Boow at the isk fee ate % assumed This costs today C This is the value of the duplicating potfolio and must equal the option value, as both will esult in the same futue value iespective of the futue state of the wold. N N 33 ob q ob -q N C 97.7 C u max33-6, ,73*. ob q ob -q C d max 6, ,73*.

11 aluation and investment in foesty Facts: foest management N standad Discount ates ae low, often % point below isk fee ate igh impotance of flexibility widely acknowledged Real options appoach Milestones:» Bennan/Schwatz 985» Dixit/indyck 994 Results show the value of flexibility as manageial options, especially of timing and closing/eopening poduction Many applications in envionmental- / esouce economics Applications in foesty: Optimization of optimal otation Changing land use Up- / downsizing opeations Timing options

12 Real options appoach I Coe model assumptions Costs ae assumed to be lump-sum costs: Investment: I to stat poduction» Constant vaiable cost C if poducing Abandonment: cost E to teminate poduction maybe negative, which would mean evenue Infinite time hoizon Output pice dynamics is given by geometic Bownian motion: d/ α dt σ dz, pefectly tadable in commodity makets Risk-fee inteest ate

13 Real options appoach II Begin and end of opeations Invest if > Remain in cuent state Abandon if < Thee must be theshold values to stat poduction and to abandon poduction t Stat: No poduction Conventional wisdom: Action if N > If idle, stat poduction: / δ C/ I > : >, N C/ I δ If poducing, abandon: C/ - / δ E > : <, N C/ - E δ Real Options: If idle, stat poduction: poducing poject > I idle poject : > If poducing, abandon: idle poject > poducing poject E: <, The state poducing / idle non poducing is theefoe path dependent t 3

14 Real options appoach III Deive valuation equations Constuct isk fee dynamic potfolio Φ, given no cuent poduction Φ with dφ shot position equies δ dt Detemine shot tem change in potfolio value, using Itô s lemma : dφ d d δ dt assuming no poduction fo the moment d α dt d if idle : if poducing : α σ σ δ σ dz σ σ dt This is isk fee and must equal Φ dt dt σ dz δ δ dt to avoid abitage C evenue fom poduction 4

15 5 and At lowe bounday : and At uppe bounday : alue matching and smooth pasting at boundaies : und / / / / / Solutions: : fo : fo ; E I C B A C < > ± σ σ δ σ δ δ δ σ δ σ Real options appoach I Solution of valuation equations

16 6 Real options appoach Calculate theshold values 4 equations fo A, B,, It can be shown that thee is a unique solution, with < < <, and A, B > Next we analyze the thesholds, and poject values: aametes ae I 3$/cod, E -77, $/cod, C 33,3 $/cod/yea, δ 4 %p.a, σ %p.a. and and A - alue matching and smooth pasting conditions yield : δ δ δ δ B A E C B A B A I C B

17 Thesholds N vs. eal options appoach Real options σ. Invest, if > 67,47 $/cod Abandon, if < 3,84 $/cod N Invest, if >,N 4,8 $/cod Abandon, if <,N 36, $/cod [$/cod] Theshold values,n,n Sigma σ Risk has a majo influence on the investment, often moe than inteest ates 7

18 oject value N vs. eal options appoach Real options values: : not opeating : opeating N: Opeating At isk fee ate dashed: at Fostliche Zinssatz [$/cod] N at the Fostliche Zinssatz povides an appoximation to the eal option values fo mean pice levels ice thesholds eflect the isk inheent in the decision to opeate Opeation will be continued, even if pices do not cove vaiable costs any moe Results value [$/cod] oject value N i3% N 8

19 Conclusion The application of financial valuation theoy might povide new and fuitful pespectives The consideation of eal options povides appoaches of explanation fo the use of a low Fostliche Zinssatz in pactice the high valuations compaed to N on the basis of appopiate isk adjusted etuns And helps to optimize the pepaation of decisions Relevant spans of time can be descibed stochastically Futue eseach must be intedisciplinay Appopiate modeling of foestal isks Development of appopiate hedging stategies 9