Roger Adkins

Renewing Assets with Uncertain Revenues and Operating Costs

We study optimal replacement and abandonment decisions for real assets, when both revenues and costs are uncertain and deteriorate with age. We develop an implicit representation of the renewal boundary as the solution to a set of simultaneous equations. This quasi-analytical method has the merit of computational ease and transparency. We show that the correlation between revenues and operating costs has a significant influence on the renewal boundary, and that the increase in revenue immediately following a renewal has a greater relative influence on the boundary than either operating cost or renewal cost. The quasi-analytical method is sufficiently flexible to deal with other real option models involving 2 variables.

Subsidies for Renewable Energy Facilities Under Uncertainty

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’.

Replacement decisions with multiple stochastic values and depreciation

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.

The effects of an uncertain abandonment value on the investment decision

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.

The effect of tax depreciation on the stochastic replacement policy

The optimal replacement policy for an asset subject to a stochastic deteriorating operating cost is determined for three different tax depreciation schedules and a known re-investment cost, as the solution to a two-factor model using a quasi-analytical method. We find that tax depreciation exerts a critical influence over the replacement policy by lowering the operating cost thresholds. Although typically a decline in the corporate tax rate, increase in any initial capital allowance, or decrease in the depreciation lifetime (increase in depreciation rate) results in a lower operating cost threshold which justifies replacing older equipment, these results are not universal, and indeed for younger age assets the result may be the opposite. An accelerating depreciation schedule may incentivize early replacement in a deterministic context, but not necessarily for an environment of uncertainty.

The Tourinho model: neglected nugget or a receding relic?

This article evaluates Tourinhos (1979b) work as one of the earliest contributors to the real options literature. His model pioneered the application of risk neutrality to uncertain investments, but his originality of introducing an option-holding cost albeit to overcome the extraction paradox is rarely imitated. We claim that the combination of a convenience yield and an option-holding cost produces a more satisfying representation. Moreover, variations in the holding cost give rise to a host of investment decisions ranging from the standard real option solution for a zero-holding cost to a net present value solution for an infinite-holding cost. Not only does the holding cost mediate between these two poles, but it provides the option seller (usually a landowner or a government) with a policy instrument for influencing the extraction timing and thus the extraction profit of the option buyer. We derive the holding cost that optimizes the landowners combined value of the option premium, holding costs and eventual royalties.

Stochastic Equipment Capital Budgeting with Technological Progress

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.

Sequential investments with stage-specific risks and drifts

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.