discounting and divergence of opinion the objective of this paper is to adopt a general equilibrium model and determine the socially efficient discount factor risk free rate and discount rate when there are heterogeneous anticipations about the growth of the economy as well as heterogeneous time preference rates among others we tackle the following questions is the socially efficient discount factor an arithmetic average of the individual subjectively anticipated discount factors more generally can the arrow debreu prices the risk free rates the subjectively expected socially efficient discount factors and discount rates be obtained as an average of the individual subjectively anticipated ones can beliefs dispersion be analyzed as a sort of additional risk or uncertainty leading to possibly lower discount rates is it socially efficient when diversity of opinion is taken into account to reduce the discount rate per year for more distant horizons if so what is the trajectory of the decline

government incentive strategies and private capital participation in china s shale gas development abstractshale gas development investments are uncertain and irreversible in the initial stage in china flexible incentive strategy is needed for governments to guide private capital participation at different development stages this study aims to provide analysis governments can use to encourage private investment in shale gas projects according to its plans in an extended real options framework a social benefits variable is introduced to determine the threshold of social benefits that determine whether the government will choose a deferred or instant incentives strategy by considering the efficiency factor we show the optimal arrangements of two kinds of incentives tax cuts and production subsidies to implement incentive targets the results indicate that current market demand and social benefits are the key factors that affect the government s choice of incentive strategy we also find that the optimal level of incentives either tax cuts or production subsidies are independent of current market

investment uncertainty and liquidity we analyze the dynamic investment decision of a firm subject to an endogenous financing constraint the threat of future funding shortfalls lowers the value of the firm s timing options and encourages acceleration of investment beyond the first best optimal level as well as highlighting another way by which capital market frictions can distort investment behavior this result implies that 1 the sensitivity of investment to cash flow can be greatest for high liquidity firms and 2 greater uncertainty has an ambiguous effect on investment

the impact of the timing of patents on innovation performance abstract in the context of industry standard setting firms face the strategic decision of whether to move faster than competitors or wait for more information that reduces uncertainty these decisions are even more challenging if there are multiple standards and if there are benefits to belonging to more than one standard this paper examines the effect of the timing of patents on a firm s innovation performance the strategic logic of real options posits that patent timing is determined by the tension between the value of preemption and the value of waiting we analyze 680 dvd disc patents in dvd patent pools to test the effect of the timing of patents on innovation performance consistent with real options logic under high uncertainty the later the timing of the patent the higher the innovation performance while under low uncertainty there is an early mover advantage

the value of the option to wait and see abstract this note shows a very simple way to incorporate the effects of uncertainty about the accuracy of present value estimates into the firm s option to delay irreversible investment it is shown that if the firm s priors about the distribution of present value are sufficiently diffuse a reduction in the accuracy of present value estimates will increase the value of delay while learning will reduce its value

evaluating natural resource investments notwithstanding impressive advances in the theory of finance over the past 2 decades practical procedures for capital budgeting have evolved only slowly the standard technique which has remained unchanged in essentials since it was originally proposed see dean 1951 bierman and smidt 1960 derives from a simple adaptation of the fisher 1907 model of valuation under certainty under this technique expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk and the resulting present value is compared with the cost of the project this standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory but see brennan 1973 bogue and roll 1974 turnbull 1977 constantinides 1978 the inadequacy of this approach to capital budgeting is widely acknowledged although not widely discussed its obvious deficiency is its the evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices it is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing and abandoning them the approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern

valuing investment projects under interest rate risk empirical evidence from european firms abstractin this article we perform an empirical investigation of the effect of the interest rate uncertainty on the valuation of investment projects the analysis is carried out by employing a real option approach and by considering a set of firms that operate in various production sectors in the euro area in particular the revenues generated by the investment projects are modelled using a geometric brownian motion whereas the interest rate is specified as a stochastic process of vasicek type moreover using the volatility of the equity return as a proxy the volatility of the revenues is calibrated to real firm data while the parameters of the interest rate model are estimated by fitting the euribor time series to this aim an ad hoc calibration procedure is developed which is based on the maximum likelihood principle and thus has the merit of being simple fast and suitable for practical purposes our study reveals that the interest rate uncertainty reduces the valuation of investment projects h

holding on for too long an experimental study on inertia in entrepreneurs and non entrepreneurs disinvestment choices abstract disinvestment in the sense of project termination and liquidation of assets including the cession of a venture is an important realm of entrepreneurial decision making this study presents the results of an experimental investigation modeling the choice to disinvest as a dynamic problem of optimal stopping in which the patterns of decisions are analyzed with entrepreneurs and non entrepreneurs our experimental results reject the standard net present value approach as an account of observed behavior instead most individuals seem to understand the value of waiting their choices are weakly related to the disinvestment triggers derived from a formal optimal stopping benchmark consistent with real options reasoning we also observe a pronounced psychological inertia i e most individuals hold on to a losing project for even longer than real options reasoning would predict the study provides evidence for entrepreneurs and non entrepreneurs being quite similar in their behavior

discounted utility and present value a close relation we introduce a new type of preference condition for intertemporal choice which requires present values to be independent of various other variables the new conditions are more concise and more transparent than traditional ones they are directly related to applications because present values are widely used tools in intertemporal choice our conditions give more general behavioral axiomatizations which facilitate normative debates and empirical tests of time inconsistencies and related phenomena like other preference conditions our conditions can be tested qualitatively unlike other preference conditions our conditions can also be directly tested quantitatively and we can verify the required independence of present values from predictors in regressions we show how similar types of preference conditions imposing independence conditions between directly observable quantities can be developed for decision contexts other than intertemporal choice and can simplify behavioral axiomatizations there o

geometric brownian motion and structural breaks in oil prices a quantitative analysis the purpose of this paper is to present a quantitative analyses of oil price s path we try to argue that despite its parsimony and simplicity geometric brownian motion can perform well as a proxy for the movement of oil prices and for a state variable to evaluate oil deposits we base our argument on evidences of very low speed of mean reverting or long half life since unit root tests only can reject its null hypothesis in a sample longer than 100 years on the other hand we reject the null hypothesis of unit root with two endogenous breaks showing that the usual rejection can be attributed to omitted structural breaks we conclude that the average half life of oil price between 4 and 8 years depending on the model chosen is long enough to allow a good approximation as a geometric brownian motion

an option pricing approach to evaluating petroleum projects abstract option pricing applications in capital budgeting decisions are still in the development stage this paper uses concepts and methods from option pricing theory to evaluate real projects rather than financial ones within a petroleum projects context such real options include development and operations of satellite fields break even values of incremental capacity and flexibility value with compound development and operations options the option pricing results may be quite different from those obtained by traditional capital budgeting and decision tree approaches some related papers on real options are also briefly noted

convertible bond design and capital investment the role of call provisions if firms issue convertible securities to facilitate sequential investment the securities should be engineered to give sufficient flexibility to accommodate timing of follow on investment we examine call provisions in convertible bonds and argue that firms with investment options expected to expire sooner later will offer weaker stronger call protection we find that issues with weak or no call protection are offered by firms that invest greater amounts soon after issuance than those issuing convertibles with strong protection moreover capital expenditure levels during the 5 year period following issuance are inversely related to the length of call protection periods most convertible bonds and notes have call provisions and most provisions have important qualifications or protection broadly speaking convertibles may have absolute protection not callable hard call protection noncallable for a specified period provisional or soft call protection callable if certain conditions on stock price are met or no protection callable anytime in this study we investigate the relations between the strength and length of call protection and firms subsequent investment behavior our hypothesis is a natural implication of the sequential financing motive for convertible debt financing for example in mayers 1998 firms finance their planned multistage investment programs with convertibles besides mayers sequential financing motive other explanations for convertible financing include theories based on post issuance risk shifting jensen and meckling 1976 green 1984 heterogeneous risk assessment brennan and schwartz 1988 and asymmetric information stein 1992 in a recent study lewis rogalski and seward 2001 offer an explanation based on equity market rationing stein s 1992 model has at least an implicit role for callability but we believe mayers explanation has direct implications for the nature of call provisions that we examine here he argues that convertible financing is well suited to

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

investment under uncertainty in information technology acquisition and development projects in this paper we develop two models for the valuation of information technology it investment projects using the real options approach the it investment projects discussed in this paper are categorized into development and acquisition projects depending upon the time it takes to start benefiting from the it asset once the decision to invest has been taken the models account for uncertainty both in the costs and benefits associated with the investment opportunity our stochastic cost function for it development projects incorporates the technical and input cost uncertainties of pindyck s model 1993 but also considers the fact that the investment costs of some it projects might change even if no investment takes place in contrast to other models in the real options literature in which benefits are summarized in the underlying asset value our model for it acquisition projects represents these benefits as a stream of stochastic cash flows

a fuzzy design of the willingness to invest in sweden abstract this paper uses a non linear fuzzy logic procedure to empirically investigate the links between the real interest rate and aggregate investments in sweden from 1950 to 1990 the economic environment is characterized by multivalued logic and an indicator for the economy wide investment climate is derived strictly from the interest rate it turns out that the fuzzy logic approach may reveal some empirical regularities that are not recognized by conventional linear regressions

wicksellian theory of forest rotation under interest rate variability abstract we apply the wicksellian single rotation framework to cover the unexplored case of variable and stochastic interest rate we provide a mathematical characterization of the two dimensional optimal stopping problem and show in the presence of amenity valuation that increased interest rate volatility lengthens the optimal rotation period and increases the value of the optimal policy by modelling the interest rate as a mean reverting process and forest value as a geometric brownian motion and abstracting from amenity valuation we present an explicit solution for the problem numerical illustrations indicate that interest rate volatility has a significant and non linear impact on optimal rotation

measuring the effectiveness of voluntary emission reduction programmes this paper examines the evaluation of state environmental policies aimed at reducing ground level ozone in order to meet air quality standards set by the us environmental protection agency several states with metropolitan areas that violate federal air quality regulations have adopted voluntary emission reduction programmes these programmes focus on emissions from mobile sources with the chief source being the automobile states are allowed to claim credit towards bringing their metro areas closer to compliance with regulations only if they can provide credible evidence that these voluntary programmes are successful in reducing emissions a model is developed to forecast aggregate traffic volumes so that one can assess the impact of the programme in reducing traffic flows during ozone action days background information on the difficulties of measuring the ozone problem and on the recent policies adopted by the us epa is provided using data from the atlanta georgia metropolitan area the accuracy o

irreversible investment under interest rate variability some generalizations we study the impact of interest rate and revenue variability on the decision to carry out irreversible investment we provide a mathematical characterization of the two dimensional optimal stopping problem and show that interest rate variability has a decelerating or accelerating impact on investment depending on whether the current interest rate is below or above the long run steady state allowing for interest rate volatility decelerates investment by raising both the required exercise premium of the investment opportunity and the value of waiting finally increased revenue volatility is shown to strengthen the negative impact of interest rate volatility and vice versa

political uncertainty and asset valuation evidence from business relocations in canada abstract quebec s drive for sovereignty from canada has been the source of political uncertainty for decades in canada this paper studies empirically stock market s reaction to the announcements of business relocations from the province of quebec to other provinces within canada similar announcements about toronto are used for control empirical results show that the market s reaction to the announcements of business relocations a from quebec is positive b from toronto is negative and c to toronto is positive the difference in abnormal returns between the quebec and toronto samples is positive and significant

the investment strategies for a dynamic supply chain under stochastic demands abstract a successful supply chain management scm should aim to maximize the net present value of joint profits along the supply chain however the volatile market conditions cause the future cash flows along the supply chain more difficult to anticipate to obtain higher supply chain value the supplier and the retailer should cooperatively determine the optimal entry time this paper proposes a two stage dynamic optimization model by using a real option approach and then performs the sensitivity analyses for the option value and the investment threshold the impacts of some critical factors including the growth rate and the volatility of demand shock sunk cost and relating operational costs cost rates fix costs holding costs of inventory and shipping costs are investigated

does inflation targeting anchor long run inflation expectations evidence from the u s uk and sweden we investigate the extent to which inflation expectations have been more firmly anchored in the united kingdom a country with an explicit inflation target than in the united states a country with no such target using the difference between far ahead forward rates on nominal and inflation indexed bonds as a measure of compensation for expected inflation and inflation risk at long horizons we show that far ahead forward inflation compensation in the u s exhibits substantial volatility especially at low frequencies and displays a highly significant degree of sensitivity to economic news similar patterns are evident in the uk prior to 1997 when the bank of england was not independent but have been strikingly absent since the bank of england gained independence in 1997 our findings are further supported by comparisons of dispersion in longer run inflation expectations of professional forecasters and by evidence from sweden another inflation targeting country with a relatively long history of inflation indexed bonds our results support the view that an explicit and credible inflation target helps to anchor the private sector s views regarding the distribution of long run inflation outcomes jel e31 e52 e58

option value uncertainty and the investment decision the options based approach to studying irreversible investment under uncertainty emphasizes that the opportunity cost of investment includes the value of the option to wait that is extinguished when an investment is undertaken thus the investment decision is affected by the determinants of the value of this option we extend and generalize a standard model of irreversible investment by introducing a second fully reversible technology and also incorporate partial reversibility by allowing capital to be abandoned at a cost as in the existing literature we find that the threshold value of the underlying asset in our case demand at which investment takes place is increasing in the uncertainty of demand we also find that the value of the option and thus the threshold value of the option value multiple at which investment takes place may be either increasing or decreasing in the uncertainty of demand in addition we find that for the case in which capital is used to replace the reversible technology the threshold value of the option value multiple is insensitive to the degree of reversibility of capital

discounting the distant future how much do uncertain rates increase valuations abstract we demonstrate that when the future path of the discount rate is uncertain and highly correlated the distant future should be discounted at significantly lower rates than suggested by the current rate we then use two centuries of us interest rate data to quantify this effect using both random walk and mean reverting models we compute the certainty equivalent rate that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future under the random walk model we find that the certainty equivalent rate falls continuously from 4 to 2 after 100 years 1 after 200 years and 0 5 after 300 years at horizons of 400 years the discounted value increases by a factor of over 40 000 relative to conventional discounting applied to climate change mitigation we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits

equilibrium with new investment opportunities abstract we develop a general equilibrium model where there are opportunities to abandon existing technologies and adopt new technologies we study how technologies change endogenously in an equilibrium and the effect of technological changes on the equilibrium we find that locally the equilibrium resembles that from cox et al 1985 econometrica 53 363 384 globally the equilibrium can be viewed as the equilibria from cir economies pasted together we also find that while the equilibrium consumption and security price processes are continuous the equilibrium return processes experience jumps at the time of technological changes

a compound option model of production and intermediate inventories this article extends the option approach to valuing real assets by modeling the firm as a two stage process with bounded output rates in which the output of the first stage may be held as work in process in this setting the real asset becomes a compound option which if exercised gives the option to finish the work in process and sell the output as its final payoff the existence of intermediate inventories may arise as an optimal investment strategy for exploiting possible future price increases the framework allows us to analyze the effect of uncertainty on output rates and the effect of interest rates changes on inventory levels copyright 1993 by university of chicago press

waiting to invest investment and uncertainty the textbook analysis that accepts all projections with positive net present values as positive is quite generally wrong the ability to delay a project means that almost every project competes with itself postponed with uncertain interest rates even the simplest of projects has an option value the effect of interest rate uncertainty on the optimal delay of investment is sizable this implies that the rate of aggregate investment will depend on both the level of the real interest rate and the degree of interest rate uncertainty furthermore it is not necessarily true that investment rises with a fall in interest rates copyright 1992 by university of chicago press

a duration model of irreversible oil investment theory and empirical evidence the aim of this paper is to analyse the implications of the theory of irreversible investment under uncertainty for investment in oil fields on the united kingdom continental shelf ukcs we consider the problem of an operator who owns a licence to develop and extract oil from a field of known capacity an intertemporal optimization model in discrete time is developed to derive decision rules for the timing of the irreversible development investment and for the optimal rate of extraction model simulation is then used to describe the properties of the numerical solutions the predictions of the theory on the determinants of the irreversible investment decision are then examined using statistical duration analysis data on the length of the time period between discovery and development are available for individual fields on the ukcs we measure the duration of the irreversible investment gestation lag for each field and test the model by assessing the significance of the theoretical variables in explaining the significance of such a lag both our theoretical model and our empirical results suggest the importance of a nonlinear interaction of the level of oil prices and the volatility of oil prices in determining the development lag the simulation of our theoretical model shows a nonlinear impact of oil price volatility on the trigger level of oil prices our empirical results suggest that the effect of price volatility is a function of the expected price level with increased price volatility having a positive impact on the duration of investment appraisal when expected prices are low and a negative impact when they are high

managerial incentives investment and aggregate implications scale effects we explore a managerial model of investment behaviour in which an incentive problem arises because one input factor managerial effort is not publicly observed we show that an optimal incentive contract leads to investment levels which are below first best in low states and that this phenomenon can account for greater cyclical variability in aggregate production and investment from the perspective of incentive scheme design a special feature of the model is that screening takes place over two variables investment and output rather than one as is customary

investment under uncertainty the case of replacement investment decisions we analyze the determinants of replacement investment decisions in a contingent claims model with maintenance and operation cost uncertainty we find that the optimal time between replacements is increasing in the volatility of cost the purchase price of a new asset and the corporate tax rate and is decreasing in the systematic risk of cost the salvage value of the asset and the investment tax credit the optimal time between replacements can either increase or decrease with an increase in the depreciation rate extensions of the model to examine the effects of technological and tax policy uncertainty on replacement investment decisions give intuitive but striking results uncertainty about the arrival of a technological innovation that would decrease maintenance and operation cost results in a significant decrease in replacement investment uncertainty in a tax law change that would encourage investment decreases current investment and uncertainty in a tax law change that would discourage investment increases current investment

small firm investment and financing decisions an option value approach this paper reviews and discusses recent developments undergone by investment theory and tries to address both financial and real decisions within an uncertain environment here the italian economy according to the recent option value approach to investment if differing degrees of reversibility characterize the accumulation process by groups of firms small and larger firms we should expect their investment decisions to differ under uncertainty on the other hand asset reversibility has an influence on firm financing policy given the observed relationship between asset and liability composition assuming a different degree of investment reversibility for small and larger firms we explore how they react to interest rate uncertainty using the italian experience during the 1980s as a benchmark the main result of this paper is that interest rate uncertainty exerts a negative influence on firms investment demand the relationship is stronger for large firms than for small firms another result is that firm leverage also shows a negative relationship with interest rate uncertainty

understanding the relation between accruals and volatility a real options based investment approach abstract accruals are fundamental to financial reporting and are the underlying innovation of accounting despite this accounting research has provided little understanding of how economic forces affect a firm s level of accruals and limited guidance for forming expectations of accruals based on ex ante firm characteristics we consider accruals as a form of investment and examine whether theoretical predictions from a real options based investment framework provide insight into the relation between accruals and the ex ante expected volatility faced by the firm specifically the theory predicts that higher volatility dampens investment because firms prefer to wait and see instead of investing immediately consistent with this theory we document a robust negative relation between year ahead net working capital accruals and expected volatility we also predict and find that the negative association between year ahead net working capital accruals and expected volatility is less pronounced for distressed firms and more pronounced for firms with a longer operating cycle and that current asset accruals are more sensitive to volatility than current liability accruals finally we find that the residuals from an investment based expected accrual model outperform those from the widely used performance adjusted modified jones model in identifying companies that just meet or beat analysts earnings forecasts collectively our findings suggest that the investment perspective of accruals and in particular the real options based investment framework provide useful insights for forming expectations of accruals

information and the equity premium we determine how better information aects the average equity premium in a standard representative agent exchange economy perfect information obviously eliminates the equity premium and we show that a particular kind of information about the level of future consumption always lowers the average equity premium surprisingly information must sometimes raise the average equity premium no matter what the preferences of the representative agent information purely about the volatility either of consumption or the marginal utility of consumption raises the equity premium for a wide class of preferences moreover information can raise the average equity premium by an arbitrarily large percentage while still matching important magnitudes such as average growth and the risk free rate we consider two dierent economies a two period economy with arbitrary preferences for the representative agent and an infinite horizon economy with standard additive separable ces utility with independent growth rates through time

capital rationing and organizational slack in capital budgeting this paper reconciles three stylized facts about capital budgeting in firms and shows that they are tied to the presence of asymmetric information among the several members of the firm each with his or her own objectives and decisions the facts of interest are 1 the existence of organizational slack 2 the rationing of resources within organizations 3 the stated cut off rate for accepting capital projects in firms is often greater than the market rate of interest organizational slack is defined as the excess of resources allocated over the minimum necessary to accomplish the tasks assigned resource rationing is defined as the under allocation of resources i e an increase in the amount allocated would generate revenues in excess of its costs rationing and slack are both manifestations of ex post inefficiencies an lp model is used to show that these inefficiencies can occur in ex ante efficient organizational designs when asymmetric information is present the optimal allocation policy involves a hurdle rate criterion in which the hurdle rate is strictly in excess of the cost of capital thus inducing rationing in some states of the world typically resources are optimally allocated such that slack exists in other states the optimal allocation policy trades off these two inefficiencies