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OPTIMAL INVESTMENT STRATEGY IN LOW-CARBON ENERGY R&D WITH
UNCERTAIN PAYOFF
Emily Fertig, Carnegie Mellon University, +1 412 512 6656, [email protected]
Jay Apt, Carnegie Mellon University, +1 412 268 3003, [email protected]
Overview
Future development of low-carbon energy technologies is an important factor in determining the total cost to
society of greenhouse gas mitigation. In energy systems modeling, cost reductions of energy technologies over time
are almost always modeled as deterministic: either an exogenous rate of change is assumed, or cost is modeled as a
deterministic function of R&D spending or installed capacity (Riahi et al., 2004; Rao et al., 2006; Miketa and
Schrattenholzer, 2004; Shittu and Baker, 2010). Such models can inform R&D investment strategy under a set of
scenario assumptions or under non-technical uncertainty (in climate damages, for example), but they capture neither
the value of flexible decision making in R&D spending under uncertainty nor the hedging effect of initial investment
in multiple technologies.
This paper proposes a method based on real options (after Dixit and Pindyck, 1994) to value the opportunity to
develop and deploy an energy technology under uncertain cost, which is modeled as stochastic and decreasing in
expected value with R&D spending. The decision maker can stop or start R&D investment at any point prior to
deployment. Studies that use similar real option valuation methods to assess developmental energy technologies
include Siddiqui and Fleten (2010), Davis and Owens (2003), and Pindyck (1993). Our study is the first of which we
are aware to frame cost as both stochastic and continuously dependent on the rate of R&D spending.
Though the proposed method is widely applicable, we use solar photovoltaic (PV) as a case study for the
numerical example. Taking the perspective of an entity within the U.S. federal government that funds energy R&D,
we assume that a carbon price will enter in the year 2030 and that the objective is to maximize the value of the R&D
program until this date. In 2030, the technology is deployed only if it mitigates CO 2 emissions at lower cost than a
backstop technology whose cost is reflected in the carbon price. The real options approach explicitly values flexible
future decision making under uncertainty. The simplified framing of the problem, however, limits the utility of this
work as a decision support tool; its contribution is an exploration of the applicability of real options theory and
techniques to charting optimal R&D strategy. With further development, this method could help guide government
R&D strategies in energy technologies with different cost and risk characteristics.
Methods
A stochastic cost function for solar PV that decreases in expectation with respect to R&D investment is adapted
from previous work on industry learning and experience curves (Neij, 2008 and Drury et al., 2009). The cost
function is input into a real options valuation based on stochastic dynamic programming (SDP) to maximize the
value of the option to develop and deploy the technology, with R&D investment as a bounded, continuous control
input. The SDP problem yields a partial differential equation, which is solved numerically in MATLAB with a the
Crank-Nicolson method. The proposed method is much less computationally intensive than numerical SDP.
Results
The method is applied to analyze the optimal investment strategy in R&D of solar PV as a function of cost and
time. The structure of the problem yields a solution in which either zero or maximum R&D investment is optimal at
each point during the development period. The optimal investment strategy can therefore be expressed with two cost
thresholds that vary with time: if the cost of the technology is below the lower threshold, further R&D investment
will be ineffective at decreasing cost and is not warranted. If the cost is above the upper threshold, R&D investment
is unlikely to render the technology cost effective by the deployment time, so optimal R&D investment is again zero.
If the cost of the technology is between the two thresholds (which change with time), investment is optimal at the
maximum allowed rate. Cost can stochastically cross the thresholds multiple times during the investment period,
switching the rate of R&D spending.
Solving the problem with classical NPV analysis entails maximizing the discounted expected value of the
investment opportunity at the deployment time T less the discounted R&D costs incurred during the investment
period. This method neglects flexibility in adapting R&D investment levels to information on the current cost of the
technology and the value of exploratory investment in a high-cost technology with a small chance of substantial cost
reductions.
The real options valuation shows that under uncertainty, initial investment in a negative-NPV project could be
optimal: for the base case in the numerical example (with cost volatility of 5 % per year), the upper investment
threshold is initially 16 % higher than in the NPV analysis. As deployment time T nears, this effect diminishes, since
less time is available in which cost could stochastically decrease. For low initial costs, accounting for uncertainty
slightly reduces the value of the investment opportunity due to the possibility of stochastic cost increases. The
investment value is highly sensitive to the effectiveness of R&D spending and to the discount rate and less sensitive
to the maximum rate of R&D investment.
Conclusions
The majority of previous studies model technological change in the energy sector either as exogenous or as
endogenous and deterministic. This work develops a real options framework for explicitly incorporating uncertainty
in valuing energy R&D investment opportunities. Although the method does not account for other uncertainties or
complex relationships within the climate-economy system, it isolates the effect of cost uncertainty on optimal R&D
spending and captures the value of flexible future decision making in R&D investment. With further development it
could inform entities within the federal government seeking to minimize the cost of responding to anticipated largescale climate policy through energy technology development.
References
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