Assessing the feasibility of cofiring wood pellets with coal for electricity generation:
A real option analysis
Hui Xian, Graduate Research Assistant, Department of Agricultural and Applied
Economics, University of Georgia;
Gregory Colson, Assistant Professor, Department of Agricultural and Applied
Economics, University of Georgia;
Bin Mei, Assistant Professor, Warnell School of Forestry and Natural Resources,
University of Georgia
Michael E. Wetzstein, Professor, Department of Agricultural and Applied Economics
University of Georgia
Selected Paper prepared for presentation at the Southern Agricultural Economics
Association Annual Meeting, Dallas, TX, February 1-4, 2014
Copyright 2014 by Hui Xian, Gregory Colson, Bin Mei, Michael E. Wetzstein. All rights reserved.
Readers may make verbatim copies of this document for non‐commercial purposes by any
means, provided that this copyright notice appears on all such copies
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Assessing the feasibility of cofiring wood pellets with coal for electricity generation:
A real option analysis
Abstract: Real options is employed for investigating the lack of incentives for U.S. coalpower plants to cofire wood pellets. Results indicate that despite a thriving U.S. woodpellet industry to supply EU demand, the price differential between wood pellets and coal
and the muted level of fuel volatility renders U.S. cofiring unsupportable.
Key Words: coal, electricity, real options, wood pellets
Introduction:
Energy production from biomass has the potential to reduce greenhouse gas (GHG)
emissions, reduce reliance on nonrenewable fuels, and increase domestic energy security.
Despite the promise, biomass waste and wood accounts for less than 2% of total U.S.
electricity generation (EIA 2013b). Coal has historically been the primary U.S. fuel for
generating electricity, accounting for well over a third of all electricity consumed in the
U.S. over the past two decades. However, with the advent of commercially viable
hydraulic fracturing technologies coupled with horizontal drilling methods allowing for
faster and more efficient extraction of oil and natural gas, the future dominance of coal
for U.S. electricity production is in question.
Recent estimates by the U.S. Energy Information Administration (EIA) project
that natural gas could supplant coal by 2035 as the primary fuel for U.S. electric power
generation (EIA 2013a). The effects of the rapid maturation of the U.S. shale-gas sector
are already being felt in the coal industry. Between 2008 and 2012 net generation by
electric utilities from natural gas increased from 320,190 thousand Megawatt hours to
504,958 while production from coal dropped from 1,466,395 to 1,146,480 (EIA 2012b).
Over the same time period 23 new natural gas electric utilities were brought online while
3
33 coal plants have gone offline (EIA 2012b). In contrast, this shift has not been
mirrored in the EU, which has realized an increase in coal usage for electricity generation
(EIA 2013d). Even with stricter environmental regulations including a 2007 directive for
Renewable Energy Sources (RES) targeting 20% of energy consumption from renewable
sources by 2020 among all EU-27 countries (Sikkema et al. 2011), there are a number of
market forces encouraging increased coal usage in Europe including (i) sharply lower
coal prices due to decreased U.S. demand and the global slowdown, (ii) lagging naturalgas infrastructure and pipelines, (iii) high regional natural-gas prices and unfavorable
existing contracts.
While the full environmental impacts of hydraulic fracturing are unknown and
hotly debated, particularly regarding methane emissions from new and existing wells, the
lower levels of carbon dioxide and nitrogen oxide released from burning natural gas
compared to coal is an important step in the fight against climate change. However, as
hypothesized and analyzed, the emergence of cheap and abundant natural gas may be
detrimental to the development and use of lower carbon-renewable fuels in the U.S.
including biomass.
Biomasses in general and wood pellets in particular, are a renewable resource
with lower GHG emissions that can be cofired in coal plants. Wood pellets are
constructed from woody biomass that undergoes a pelletization process that increases
wood density resulting in higher energy and lower moisture content as well as uniform
sizing, which facilitates hauling, handling, and usage (Spelter and Toth 2009).
Cofiring,in contrast to building a new stand-alone biomass plant, has a number of
advantages, the very low cost of modifying existing coal power plants to be able to cofire
4
small percentages of biomass such as wood pellets being the most prominent (Zhang et al.
2009).
In addition to aiding coal based power plants’ reducing GHG emissions and
meeting environmental regulations, cofiring has an additional potential benefit: the
portfolio effect. By employing a portfolio of two fuels instead of just coal, power
generators can potentially benefit by reducing the volatility of fuel input costs. For
example, Vedenov et al. (2006) demonstrated the volatility of alternative fuels (gasoline
blended with ethanol) is lower than conventional gasoline and when considering both
price levels and volatilities, gasoline wholesalers may have an incentive to switch to the
use of ethanol blended gasoline despite the higher costs.
In this study, a real options framework is explored to assess the feasibility of
cofiring wood pellets with coal for electricity generation, considering the decline in
demand, prices, and volatility of coal resulting from an increasing supply of low-cost
natural gas, which has significantly reduced or eliminated incentives for U.S. based coal
power plants to cofire wood pellets. Results suggest that although the thriving woodpellet industry in the U.S. has emerged to supply EU demand particularly in the timber
regions of the Southeastern US (Anich, Burnston, and Gitlin 2012), the price differential
between wood pellets and coal and the muted levels of volatility in these markets renders
cofiring unsupportable. However, supporting the hypothesis that the natural-gas boom is
hindering U.S. adoption of biomass, evidence is presented that without the shifts in the
coal and natural gas markets that wood pellet cofiring would be economically
advantageous from the perspective of reducing fuel input price volatility.
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Methodology
The decision threshold of when to exercise the option and switch from total coal firing to
cofiring with supplemental wood pellets is based on real options analysis (Dixit and
Pindyck 1994). It is assumed an adoption option is exercised by an electric power utility
manager with the objective of minimizing expected future energy cost over a given
planning horizon. The manager has the option of adopting alternative fuels based on
differing percentages of cofiring wood pellets with coal. Consistent with the current
trend in existing European cofiring plants, a 10% to 25% wood pellet percentage is
considered (Sikkema et al. 2010)
The manager’s expected present value of cost saving resulting from switching to
an alternative fuel at current time t is
(1)
𝑡+𝑇
𝑉(𝑃𝐶 , 𝑃𝐴 ) = 𝐸 ∫𝑡
[𝑃𝑐 (𝑡) − 𝑃𝐴 (𝑡)]𝑒 −𝑟𝑡 𝑑𝑡 ,
where E is the expectation operator, T is the planned lifetime horizon for the power plant,
r is the continuous risk-adjusted discount rate (the overall average cost of capital in the
power plant), and PC (t) and PA(t) are the prices of coal, C, and alternative fuel, A,
respectively, at time t. Both the prices of coal and mixed fuels are allowed to fluctuate
randomly through the two correlated geometric Brownian motion processes
(2a)
𝑑𝑃𝐶 = µ𝐶 𝑃𝐶 𝑑𝑡 + 𝜎𝐶 𝑃𝐶 𝑑𝑧𝐶 ,
(2b)
𝑑𝑃𝐴 = µ𝐴 𝑃𝐴 𝑑𝑡 + 𝜎𝐴 𝑃𝐴 𝑑𝑧𝐴 ,
where dP refers to the change in the price, µ is the rate of change or drift rate, and σ is the
volatility. The increment of a Wiener process is dz with the properties that 𝐸(𝑑𝑧𝐶2 ) =
𝐸(𝑑𝑧𝐴2 ) = 𝑑𝑡 and 𝐸(𝑑𝑧𝐶 𝑑𝑧𝐴 ) = 𝜌𝑑𝑡, where ρ is the correlation coefficient between the
uncertainty incorporated in the change of the two prices. Taking the expected value of (2)
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and substituting it into (1), assuming the current time is t = 0, and the manager is
considering whether it is optimal to switch to an alternative fuel at this current time yields:
𝑇
𝑉(𝑃𝐶 , 𝑃𝐴 ) = ∫0 [𝑃𝐶 (0)exp(µ𝐶 𝑡) − 𝑃𝐴 (0)exp(µ𝐴 𝑡)]𝑒 −𝑟𝑡 𝑑𝑡 .
(3)
Integrating (3)
(4)
𝑉(𝑃𝐶 , 𝑃𝐴 ) =
𝑃𝐶 (exp[T(µ𝐶 −𝑟)]−1)
µ𝐶 −𝑟
−
𝑃𝐴 (exp[T(µ𝐴 −𝑟)]−1)
µ𝐴 −𝑟
.
The threshold for switching is when (4) is zero, where a manager would be indifferent to
adopting the alternative fuel. If r < μA or μA< r < μC, then the decision to switch to the
alternative fuel is deterministic, based on the length of the planned lifetime horizon for
the power plant, T. As T increases, (4) approaches zero from the left, leading to eventual
adoption regardless of the stochastic nature of the prices.
When r > max(μC, μA), the decision to switch to alternative fuel is not certain.
The volatility of the two price series could then be considered by applying a real options
approach. Intuitively, this option should be held when PC is low relative to PA and
exercised when it is relatively high.
Specifically, let F (PC, PA) be the value of this option with F = max (0, V). If there
is no cost saving, the value of this switching opportunity is zero, once the cost saving is
positive, the agent should adopt an alternative fuel and the value of this option is V.
Intuitively, this option should be held when PC is low relative to PA and exercised when it
is relatively high. Figure 1 illustrates the suggested regions in (PC, PA) space.
Within the waiting region, the only return of holding this option is its expected
capital appreciation, E(dF). By applying the Bellman equation, at the optimal threshold
PA*, this expected capital appreciation should equal to the return the investor could earn
on other investment opportunity with an equivalent risk, rFdt:
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(5)
𝐸(𝑑𝐹) = 𝑟𝐹𝑑𝑡,
Then the optimal threshold price by applying the real options approach is
where,
𝛽1
exp[T(µ𝐶 −𝑟)]−1
1
exp[T(µ𝐴
𝑃𝐴∗ = 𝛽
(6)
1
𝛽1 = 2 −
∗
−1
µ𝐴 −µ𝐶
𝜎2
µ −𝑟
∗ 𝐴 ∗ 𝑃𝐶 ,
−𝑟)]−1 µ −𝑟
1
+ √(2 −
𝐶
µ𝐴 −µ𝐶 2
𝜎2
) +
2(𝑟−µ𝐶 )
𝜎2
>1.
The optimal decision rule is: switch to an alternative (cofiring) when the price of mixed
energy PA is lower than this optimal threshold price.
Empirical Analysis
Data
Considering 10%, WP10, 15%, WP15, and 25%, WP25, mix of wood pellet cofiring, no
rebuilt or retrofit costs of the boilers or any additional costs are required. This enables a
direct comparison of stochastic energy prices. For this comparison, weekly coal and
wood-pellet price data are employed.
Coal prices ($/mmbtu) ranging from June 2008 to October 2013 are the average
weekly spot coal prices of Central Appalachian (CAPP) coal. They are obtained from
SNL Energy’s “Coal News and Market Report” (SNL Energy) available on the U.S.
Energy Information Administration website. The CAPP coal prices are used because this
region provides over 1/3 of the coal consumed by Georgia power plants.
The weekly wood pellet prices are the FOB (free on board) Southeast U.S. prices
collected from Argusmedia’s “Weekly Argus Biomass Market”(Argusmedia 2013).
Based on Argus’s specification on the energy density of wood pellet as 17GJ/ton, the
weight based price ($/ton) is transformed on energy base as $/mmbtu, making it
comparable with coal prices. This price series runs from July 2009 to November 2011.
8
These two nominal energy price series are adjusted using monthly Producer Price
Index (PPI) data for Crude Material (series WPSSOP1000) available from the U.S.
Department of Labor, Bureau Statistics website (U.S. Department of Labor 2013). The
PPI was normalized to 100 at January 2013, so the real prices for coal and wood pellets
are in terms of January, 2013 dollar. The FOB prices for wood pellets include
transportation costs, so a transportation fee for coal of $1.15/mmbtu was added to the real
coal price for direct comparison. This delivery cost for coal is the average railroad costs
in 2009 from CAPP to Georgia, adjusted to dollar value of January 2013 (EIA 2012c).
The overlap of the two series is from July 2009 to November 2011. For the purpose of
constructing weekly mixed energy prices, coal and wood-pellet prices from the same
week are compared, and after deleting some missing values in the overlap periods, the
full data sample has 121 coal and wood-pellet weekly-price pairs. Then the price of
mixed energy is calculated as the energy-weighted average of coal and wood pellet prices.
For a direct comparison of prices between mixed energy and coal, it is necessary
to adjust mixed energy prices for fuel efficiency difference. It is assumed the net
conversion efficiency of coal-to-electricity is 32.67% based on the average heat rate of a
coal power plant equal to 10,444 btu/kwh (EIA 2012a). This fuel-to-electricity efficiency
would be reduced when cofiring with wood pellets. The efficiency loss for low level
cofiring is roughly 0.5% for every 10% input of wood pellets (Robinson, Rhodes, and
Keith 2003), which is a small penalty due to lower level of moisture in wood pellets and
the small percentage of cofiring. This yields an efficiency-adjusted price for mixed
energy:
(7)
𝑃𝐴 = {(𝑘 ∗ 𝑃𝑤𝑝 ) + (1 − 𝑘) ∗ 𝑃𝑐𝑜𝑎𝑙 } ∗ 𝜂𝑘 ,
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where k is the percentage of energy input from wood pellets and η is the corresponding
efficiency-adjusted factor, which is calculated as the ratio of coal-only conversion
efficiency to the responding alternative fuel conversion efficiency. As an example,
considering 10% cofiring: k = 10%, η10 is 0.327/0.322 = 1.016. For the 10%, 15% and 25%
share of wood-pellet cofiring, the corresponding efficiency-adjusted factors are 1.016,
1.024, and 1.040, respectively. After adjusted by these parameters and weights, the
mixed-energy prices can be directly compared with coal and wood-pellet prices.
In the common time periods (called the Full Sample), when both price data are
available, wood pellets have a higher average price than coal, so as the percentage of
wood pellets increases, the average energy price increases. A simple comparison of price
levels may conclude burning coal is less costly. However, the stochastic nature of energy
prices considering the impacts of drift and volatility my lead to a counter conclusion.
From Table 1, the standard deviations for mixed energy prices are lower than pure energy
due to the portfolio effect.
Estimation Procedure
Following a geometric Brownian motion (2), the related parameters (drift and volatility)
as well as the correlation coefficient between the two corresponding increments of the
Wiener process (ρ) are estimated as the correlation coefficients of the changes in
logarithm of prices. The estimation process is the same for the two pure energies and the
three mixed, so the subscripts indicating fuel types are omitted for convenience.
Following Ito’s lemma, if the price variable follows a geometric Brownian motion
as in (2), then its logarithm is following a simple Brownian motion
(8)
1
𝑑(𝑙𝑛𝑃) = (µ − 2 𝜎 2 ) 𝑑𝑡 + 𝜎𝑑𝑧 = 𝛼𝑑𝑡 + 𝜎𝑑𝑧,
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where d(lnP) is from a normal distribution with mean αdt and variance σ2dt, so over a
finite time interval τ , the change in logarithm of P is normally distributed with mean ατ
and the variance σ2τ. Given weekly price series, τ is 1/52 year (it is one week). Set 𝛾𝑡 =
𝛥𝑃𝑡 /𝑃𝑡 and note that 𝛥𝑃𝑡 /𝑃𝑡 is the first difference of the logarithm of price at time t.
Applying maximum likelihood method to (8), the estimates for drift and volatility
can be found separately. Thus, for the ln(p) process, the weekly drift (ατ) and weekly
volatility (√𝜎 2 𝜏 ) are estimated as
1
𝛼̂τ = 𝛾̅ = 𝑛 ∑𝑛𝑡=1 𝛾𝑡 ,
̂2 𝜏 = 𝑠𝑡𝑑(𝛾𝑡 ) = √ 1 ∑𝑛 (𝛾𝑡 − 𝛼̂τ)2 ,
√𝜎
𝑛 𝑡=1
n is the number of observations. The drift estimates of the weekly stochastic prices are
1
̂2 τ .
𝜇̂ 𝑤𝑒𝑒𝑘 = µ̂τ = 𝛼̂τ + 2 𝜎
While the volatility estimates for the energy prices are the same as
̂2 𝑤𝑒𝑒𝑘 = 𝜎
̂2 𝜏 .
𝜎
In (6), the optimal threshold price is in terms of annual drift, μ, volatility, σ, and discount
rate, r, thus, the drift and volatility estimates are adjusted as
µ̂ = 𝜇̂ 𝑤𝑒𝑒𝑘 /τ, 𝜎̂ = 𝜎̂𝑤𝑒𝑒𝑘 /√τ .
Results
Main Results
The parameter estimates for coal, wood pellets, and mixed energies (WP10, WP15, and
WP25) are list in Table 2. Coal prices have a larger drift relative to wood pellets, so as
the percentage of wood pellets for cofiring increases, the drift declines. Wood-pellet
prices have a larger volatility than coal, however, for the WP10 and WP15, the volatility
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of each energy price is lower than both pure energy prices due to the portfolio effect.
This portfolio effect decays as the percentage of wood pellets beyond 10% increases. At
WP25, the volatility is larger than coal. The portfolio effect is due to the low correlation
between the two price processes, ρ = 0.450. For the three mixed energies,this correlation
declines with mixing more wood pellets as the price series behaves less like coal.
These estimated parameters in Table 2 were used to compute converting
thresholds given (6). A manager should switch to cofiring if the price level for the
alternative fuel is lower than this threshold price, 𝑃𝐴∗ . Recall from (3), both the discount
rate and power-plant life are required. Also, the mean value of the coal price
($4.50/mmbtu) is used to estimate this threshold when compared with the corresponding
average prices of different mixed energy. Currently, over half of U.S. coal-fired power
plants are 30 years old or older (EIA 2013c), and the average age at retirement for coal
power plants is between 50 to 60 years. Thus, considering the advanced age of the plants
a 10-, 20-, and 30-year time horizon was assumed. In terms of the discount rate r, when r
is smaller than either of the drift rates (for coal and alternative fuels), it is deterministic to
adopt the alternative fuel once the life expectation, T, is large enough. For r greater than
the drifts, (6) yields the optimal switching threshold.
From Table 2, the coal-price series has the largest drift at 0.151, so the annual
risk-adjusted discount rates are assumed to be 16%, 18%, and 20%. Incorporating these
discount rates and life expectancies along with the estimated drift, volatility, and
correlation coefficient, the threshold prices 𝑃𝐴∗ are determined (Table 3). Recall that it is
only optimal for a manager to adopt cofiring when the mixed energy price is lower than
the threshold price. Results listed in Table 3 indicate across the three alternative fuels,
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the average energy prices are generally below the threshold price for low discount rates
and relatively long-life expectancy. For a power-utility manager to consider an
alternative wood-pellet fuel, a relatively long payback period at a low discount rate is
required. For a given discount rate and life expectancy, as the percentage of wood pellets
increases, the price to threshold ratio increases and it becomes increasingly difficult to
switch. This indicates a manager will first consider incorporating a small percentage of
wood pellets before a major shift into pellets. However, the optimal threshold is not very
sensitive to changes in both the discount rate and life expectancy, indicating the results
are robust for these parameter shifts.
These results follow from the interpretation of Bellman equation (5). Recall that
the switching threshold is determined as a price that equates the total expected return
from a switch to the expected capital appreciation. A longer life expectancy increases the
expected returns, so the switch is economically optimal even at higher prices for the
alternative fuels. On the other hand, higher discount rates result in higher capital
appreciation, which can be matched by the expected returns only when the switch occurs
at relatively low alternative-fuel prices. Thus, cofiring is more attractive for the younger
coal-power plants, given they have the potential to operate for a longer period. As
indicated in Table 3, it is always optimal to switch at 30 years of remaining life, while not
for 10 and 20 years. Further, there is lower incentive to switch when expected returns are
lower, as increased risk is considered. This is observed at a 20-year life expectancy, the
threshold ratio goes up when the discount rate increases, implying a manager is more
averse to switch at a high risk.
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The main result from this analysis is given the fuel-price pattern from July 2009
to November 2011, on average the mixed energy prices are around the threshold point, so
wood pellets have a strong potential to enter into U.S. electronic-power generation. If
similar behaviors of the two price series continue in the future, U.S. power plants
probably should consider switching to cofire. However, given the recent price trends in
natural gas prices, natural gas may trump wood-pellet adoption.
Subsample Results
In an effort to mitigate greenhouse gas GHS) emissions, the EU demand for U.S.
produced word pellets for cofiring power plants increased sharply in 2008 (National
Renewable Energy Laboratory 2013). However, a corresponding demand within the U.S.
did not materialize. The advent of increased natural gas fracturing has led to reduced
natural gas prices and a shift toward natural gas as an energy source for remediating
electric power utilities’ GHS. The use of natural gas has reduced the price of coal, which
drives a larger wedge between the prices of coal and wood pellets. This will result in
lowering the threshold price for adoption of wood pellets and retarding adopting. For
determining the magnitude of this adoption failure, the recent coal-price series from
November 2011 to October 2013 (subsample) are compared with the historical woodprice series, November 2009 to 2011. This assumes wood-pellet prices are not affected
by the U.S. domestic fracturing for natural gases. For these price series, a declining coal
price trend is observed until July 2012, then followed by a relatively stable period. While
wood-pellet prices at first decline with coal prices and then experience an upward trend.
Compared with summary statistics for the full sample in Table 1, Table 4 lists the
statistics for this subsample. Coal prices have a slightly lower average price ($3.79 vs.
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$3.84) and lower standard deviation (0.203 vs. 0.416), implying for the subsample, coal
prices become relatively cheap and stable. While for wood-pellet prices these two
statistics in Tables 1 and 4 are similar; with the subsample exhibiting a slightly higher
mean and lower standard deviation.
Following the same procedure for calculating the parameter estimates (drift,
volatility, and correlation), the subsample parameters are list in Table 5. All the energy
prices have a negative drift, while coal prices exhibit a sharper decline relative to woodpellet prices. This coal-price decline is probably due to the appearance of cheap natural
gas. In contrast to the full sample, the volatility of coal prices is larger relative to woodpellet prices. This results in volatility declining as the percentage of wood pellets
increase. Further, the correlations between the two stochastic prices are much smaller,
0.02 relative to the full sample, 0.45, which strengthens the portfolio effect of cofiring.
Incorporating the parameters into (6) yields the threshold prices (Table 6). For
the subsample across all the scenarios, the price to threshold ratio is greater than one,
indicating a manager should stay with only coal-firing. In particular, this supports the
hypothesis of managers forgoing wood pellets and adopting natural gas. The results
indicate in 2008 wood pellets appear to be a competitive biomass and can feasibly be cofired with coal in coal-power plants. There indeed are benefits for a manager to adopt
cofirng in the U.S. However, with the advent of cheap natural gas, the price of coal
declined and stabilized, which weakened the competitiveness of wood pellets for cofirng
with coal. This crowding-out effect by natural gas results in wood pellets, a new
sustainable energy, losing its competitive advantage in the United States.
15
Conclusion and Implication
Natural gas is a nonrenewable fossil fuel based on hydraulic fracturing large amounts of
water, contaminating chemicals, and possible ground disruption leading to earthquakes
and water contamination (EIA 2012d). The research results empirically indicate that
besides the possible environmental degradation of natural gas hydraulic fracturing, the
increased supply of this nonrenewable resource within the United States is potentially
retarding the development of an alternative renewable fuel. This empirical result is based
on a real options analysis measuring the substitution possibilities between a more
expensive but stationary biomass fuel (wood pellets) with a cheaper but more volatile
fuel (coal). Prior to the abundance of natural gas from new extraction technologies, real
options analysis indicates cofiring wood pellets with coal is feasible. However, with the
development of improved natural gas extraction technologies, the option of adopting
cofiring is no longer feasible. U.S. power plants have cheap natural gas as a fuel
alternative, which lowers domestic coal demand as well as coal prices. Thus, the relative
advantage of wood pellets over coal declines to the point where it is no longer a viable
option.
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Table1. Descriptive statistics for energy price series (full sample)
Fuel
Sampl
e Size
Minimum
($/mmbtu)
Maxmum
($/mmbtu)
Mean
Standard
($/mmbtu) Deviation
Coal
121
3.127
4.497
3.840
0.416
WoodPellets
121
7.737
10.102
9.096
0.492
WP10
121
3.645
5.103
4.436
0.395
WP15
121
3.910
5.412
4.740
0.386
WP25
121
4.451
6.043
5.360
0.375
Note: 1) All the prices are normalized to January 2013 dollars. 2) Coal prices are from
July 3, 2009 to November 11, 2011; Wood pellet prices are from July 1, 2009 to
November 9, 2011. The two prices are recorded at exactly the same week 3) WP10,
WP15 and WP25 denotes 10%, 15%, and 25% wood pellet cofiring, respectively.
Table 2. Estimated parameters of geometric Brownian motion (full sample)
Fuel
Mean($/mmbtu)
Drift
(μ)
Volatility
(σ)
correlation with
coal prices (ρ)
Coal
3.840
0.151
0.109
1.000
Wood Pellets
9.096
0.111
0.167
0.450
WP10
4.436
0.139
0.106
0.954
WP15
4.740
0.134
0.108
0.909
WP25
5.360
0.128
0.115
0.813
Note: full sample, 121 observations. WP10, WP15, and WP25 denoting 10%, 15%, and
25% wood pellet cofiring, respectively.
19
Table 3. Switching threshold prices for mixed energy (full sample)
Full Sample121 observations
Discount Rate
Year
16%
Energy
prices ($/mmbtu)
WP10
Average mixed price $4.44
WP15
WP25
10
18%
20
30
20
20
Threshold
4.25
4.49
4.73
4.44
4.40
Price /Threshold
1.04
0.99
0.94
1.00
1.01
Average mixed price $4.74
Threshold
4.42
4.76
5.10
4.69
4.63
Price/Threshold
1.07
1.00
0.93
1.01
1.02
Average mixed price $5.36
Threshold
4.71
5.22
5.74
5.11
5.02
Price /Threshold
1.14
1.03
0.93
1.05
1.07
WP10, WP15, and WP25 denoting 10%, 15%, and 25% wood pellet cofiring,
respectively.
.
20%
20
Table 4. Descriptive statistics for energy price series (subsample): Coal, November18,
2011 - Oct. 25, 2013; wood pellet, November18, 2009 - November 9, 2011
Fuel
Sample
Minimum
Maxmum
Mean
Standard
Size
($/mmbtu)
($/mmbtu)
($/mmbtu)
Deviation
Coal
101
3.329
4.320
3.791
0.203
Wood Pellets
101
8.223
10.147
9.271
0.394
WP10
101
3.898
4.962
4.409
0.219
WP15
101
4.189
5.290
4.724
0.228
WP25
101
4.783
5.967
5.368
0.248
WP10, WP15, and WP25 denoting 10%, 15%, and 25% wood pellet cofiring,
respectively.
Table 5. Estimated parameters of geometric Brownian motion for subsample: Coal,
November18, 2011 - Oct. 25, 2013; wood pellet, November18, 2009 - November 9, 2011
Fuel
Mean($/mmbtu)
Drift
Volatility
Correlation with
(μ)
(σ)
Coal Prices (ρ)
Coal
3.791
-0.053
0.117
1.000
Wood Pellets
9.271
-0.024
0.076
0.020
WP10
4.409
-0.050
0.093
0.985
WP15
4.724
-0.048
0.084
0.963
WP25
5.368
-0.045
0.073
0.883
WP10, WP15, and WP25 denoting 10%, 15%, and 25% wood pellet cofiring,
respectively.
21
Table 6. Switching threshold prices for mixed energy (subsample)
Subsample 101 observations
Discount Rate
Year
16%
Energy
prices ($/mmbtu)
WP10
Average mixed price $4.41
WP15
WP25
10
20
18%
30
20
20%
20
Threshold
3.96
3.95
3.94
3.94
3.93
Price /Threshold
1.11
1.12
1.12
1.12
1.12
Average mixed price $4.72
Threshold
4.03
4.01
4.00
4.00
3.99
Price /Threshold
1.17
1.18
1.18
1.18
1.18
Average mixed price $5.37
Threshold
4.15
4.11
4.10
4.09
4.08
Price /Threshold
1.29
1.30
1.31
1.31
1.31
WP10, WP15, and WP25 denoting 10%, 15%, and 25% wood pellet cofiring,
respectively.
Figure 1. Boundary between switching and not switching