• The effects of an uncertain abandonment value on the investment decision

      Adkins, Roger; Paxson, D. (2016)
      Using a three-factor stochastic real option model framework, this paper examines the effects of abandonment on the investment decision. Abandonment is classified according to whether the opportunity arises for an active operating asset post-investment, or for holding the project opportunity pre-investment. Separate analytical models are developed for the alternative forms of abandonment optionality. Numerical sensitivity analysis shows that the presence of a post-investment abandonment opportunity makes the investment opportunity appear to be more attractive because of the abandonment option value, but not by a considerable amount. Also, in contrast to the standard real option finding, an abandonment value volatility increase produces a project value threshold fall owing to the increase in the abandonment option value.
    • Investment decisions with finite-lived collars

      Adkins, Roger; Paxson, D.; Pereira, P.J.; Rodrigues, A. (2019-06)
      The duration of most collar arrangements provided by governments to encourage early investment in infrastructure, renewable energy facilities, or other projects with social objectives are finite, not perpetual. We extend the previous literature on collar-style arrangements by providing an analytical solution for the idle and active values, as well as the investment triggers, for projects where collars are either finite-lived or retractable. What is the difference between these types of arrangements with their perpetual counterpart? Lots, including different vega signs, and substantially different values for different current price levels. Often, finite and retractable collars justify earlier investment timing than perpetual collars. In general, we demonstrate that the finite-lived and retractable versions have a significant impact on optimal behavior, relative to the perpetual case. An important consideration when negotiating the floors, ceilings, and duration (or signalling the expected duration) of a finite or a retractable collar is the current price level of the output and its expected volatility over the life of the contract.
    • Real collars as alternative incentives for subsidizing energy facilities

      Adkins, Roger; Paxson, D. (2019-06)
      We suggest that real collars may be acceptable incentives for encouraging development of low (or no) carbon energy generating facilities as an alternative for high feed‐in‐tariffs. We provide novel analytical solutions for real collars and partial collars, plus floor and ceiling partial derivatives. The ‘gains/losses’ of the energy generator as perceived parameter values change are compared to those of the government providing the collar, and floor or ceiling only, viewing the arrangement as a real option game between principal and agent. A volatility increase first increases, then decreases the ‘gains’ of the generator.
    • Replacement decisions with multiple stochastic values and depreciation

      Adkins, Roger; Paxson, D. (2017-02-16)
      We develop an analytical real-option solution to the after-tax optimal timing boundary for a replaceable asset whose operating cost and salvage value deteriorate stochastically. We construct a general replacement model, from which seven other particular models can be derived, along with deterministic versions. We show that the presence of salvage value and tax depreciation significantly lowers the operating cost threshold that justifies (and thus hastens) replacement. Although operating cost volatility increases defer replacement, increases in the salvage value volatility hasten replacement, albeit modestly, while increases in the correlation between costs and salvage value defer replacement. Reducing the tax rate or depreciation lifetime, or allowing an investment tax credit, yield mixed results. These results are also compared with those of less complete models, and deterministic versions, showing that failure to consider several stochastic variables and taxation in the replacement process may lead to sub-optimal decisions.
    • Rescaling-contraction with a lower cost technology when revenue declines

      Adkins, Roger; Paxson, D. (2019-09)
      A mature oil field rescaled contraction describes a switch to a technological alternative more appropriate for the depleted state of an underlying resource. Off-shore oil rigs are an illustration, since the original technological scale designed for very large output flows becomes inappropriate as the operational efficiency declines later in life and facing a dwindling output flow, so a more appropriate extraction technology becomes economic. A real option representation is formulated on a stochastic oil price and deteriorating output volume. We consider investment/divestment decisions both separately, and jointly, which have different implications for government policies and also option values. The resulting model yields analytical (or semi-analytical) results indicating that immediate switching to the lower cost technology could sometimes be hastened as the price volatility increases, depending on the current revenue, if divestment and switching are considered jointly. However, greater volatility could also promote hysteresis.
    • Sequential investments with stage-specific risks and drifts

      Adkins, Roger; Paxson, D. (2017)
      We provide a generalized analytical methodology for evaluating a real sequential investment opportunity, which does not rely on a multivariate distribution function, but which allows for stage-specific risks and drifts. This model may be a useful capital budgeting and valuation tool for exploration and development projects, where risks change over the stages. We construct a stage threshold pattern whereby the final stage threshold exceeds the early stage threshold due to drift differentials between the project values at the various stages, value volatility differences, and correlation differentials, implying a rich menu of parameter values that may be suitable for a variety of projects. Governments seeking to motivate early final stage investments might lower final stage project volatility or specify project value decline over time, unless prospective owners are willing to pay the real option value (ROV) for concessions. In contrast, concession owners, more interested in ROV than thresholds that motivate early investments, may welcome final stage value escalation, or guarantees that reduce the correlation between project value and construction cost.
    • Stochastic equipment capital budgeting with technological progress

      Adkins, Roger; Paxson, D. (2014-11)
      We provide multi-factor real option models (and quasi-analytical solutions) for equipment capital budgeting under uncertainty, when there is either unexpected, or anticipated, or uncertain (volatile) technological progress. We calculate the threshold level of revenues and operating costs using the incumbent equipment that would justify replacement. Replacement is deferred for lower revenue thresholds. If progress is anticipated or highly uncertain, alert financial managers should wait longer before replacing equipment. Replacement deferral increases with decreases in the expected correlation between revenue and operating costs, and with increases in the revenue and/or operating cost volatility. Uncertain technological progress increases the real option value of waiting. The best approach for equipment suppliers is to reduce the expected revenue and/or cost volatility, and/or reduce the expected uncertainty of technological innovations, since then an incentive exists for the early replacement of old equipment when a technologically advanced version is launched.
    • Subsidies for Renewable Energy Facilities under Uncertainty

      Adkins, Roger; Paxson, D. (2016-02-23)
      We derive the optimal investment timing and real option value for a facility with price and quantity uncertainty, where there might be a government subsidy proportional to production quantity. Where the subsidy is proportional to the multiplication of the price and quantity, dimensionality can be reduced. Alternatively, we provide quasi-analytical solutions for different quantity subsidy arrangements: permanent (policy is certain); retractable; suddenly permanent; and suddenly retractable. Whether policy uncertainty acts as a disincentive for early investment depends on the type of subsidy arrangement. The greatest incentive for early investment is an actual retractable subsidy, a ‘flighty bird in hand’.