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K
BioBreak Model: Assumptions
for Willingness to Accept
T
his appendix provides detail on the assumptions and references used to calculate
Willingness to Accept (WTA) in the BioBreak model, discussed in Box 4-2 in Chapter
4.
EQUATION
WTA = {(CES + COpp)/YB + CHM + SF + CNR + CS + DFC + DVC*D} – G
The supplier’s WTA for 1 ton of delivered cellulosic material is equal to the total eco-
nomic costs the supplier incurs to deliver 1 unit of biomass to the biorefinery less the
government incentives received (G) (for example, tax credits and production subsidies).
Depending on the type of biomass feedstock, costs include establishment and seeding (CES),
land and biomass opportunity costs (COpp), harvest and maintenance (CHM), stumpage fees
(SF), nutrient replacement (CNR), biomass storage (CS), transportation fixed costs (DFC),
and variable transportation costs calculated as the variable cost per mile (DVC) multiplied
by the average hauling distance to the biorefinery (D). Establishment and seeding cost
and land and biomass opportunity cost are most commonly reported on a per acre scale.
Therefore, the biomass yield per acre (YB) is used to convert the per acre costs into per ton
costs, and the equation above provides the minimum amount the supplier can accept for
the last dry ton of biomass delivered to the biorefinery and still breakeven. The variables
in the equation are based on the following assumptions.
WTA PARAMETERS
Nutrient Replacement (CNR)
Uncollected cellulosic material adds value to the soil through enrichment and protec-
tion against rain, wind, and radiation, thereby limiting erosion that would cause the loss of
341
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342 APPENDIX K
vital soil nutrients like nitrogen, phosphorus, and potassium. Biomass suppliers will incor-
porate the costs of soil damage and nutrient loss from biomass collection into the minimum
price they are willing to accept. Nutrient replacement cost (CNR) varies by feedstock and
harvest technique. After adjusting for 2007 costs, estimates for nutrient replacement costs
range from $5 to $21 per ton. Based on the model’s baseline oil price ($111 per barrel) and
research estimates, nutrient replacement was assumed to have a mean (likeliest) value of
$14.20 ($15.20) per ton for stover, $16.20 ($17.20) per ton for switchgrass, $9 per ton for Mis-
canthus, and $6.20 per ton for wheat straw.1 Alfalfa was assumed to have a 2-year stand with
the first-year nutrient costs incorporated into the establishment costs discussed below and
a cost of $65 per acre for second-year nutrient application. Given the yield assumptions for
second-year alfalfa, this corresponds to approximately $16.25 per ton. Nutrient replacement
was assumed unnecessary for woody biomass. The cost of nutrient replacement depends
on the natural gas price and is therefore dependent on energy costs. EIA projected natural
gas to oil price factor for 2022 was used to scale fertilizer costs at varying oil price levels.
At the high oil price ($191 per barrel), nutrient replacement costs increase by about $1.35
per ton. At the low oil price ($52 per barrel), nutrient replacement costs decrease by about
$1.00 per ton.
Harvest and Maintenance Costs (CHM) and Stumpage Fees (SF)
Harvest and maintenance cost (CHM) estimates for cellulosic material have varied based
on harvest technique and feedstock. Noncustom harvest research estimates range from
$14 to $84 per ton for corn stover (McAloon et al., 2000; Aden et al., 2002; Sokhansanj and
Turhollow, 2002; Suzuki, 2006; Edwards, 2007; Hess et al., 2007; Perlack, 2007; Brechbill
and Tyner, 2008a; Khanna, 2008; Huang et al., 2009), $16 to $58 per ton for switchgrass
(Tiffany et al., 2006; Khanna and Dhungana, 2007; Kumar and Sokhansanj, 2007; Brechbill
and Tyner, 2008a; Duffy, 2008; Khanna, 2008; Khanna et al., 2008; Perrin et al., 2008; Huang
et al., 2009), and $19 to $54 per ton for Miscanthus (Khanna and Dhungana, 2007; Khanna,
2008; Khanna et al., 2008), after adjusting for 2007 costs.2 Estimates for nonspecific biomass
range between $15 and $38 per ton (Mapemba et al., 2007, 2008). Woody biomass collec-
tion costs up to roadside range between $17 and $50 per ton (USFS, 2003, 2005; BRDI, 2008;
Jenkins et al., 2009; Sohngen et al., 2010). Spelter and Toth (2009) find total delivered costs
(including transportation) around $58, $66, $75, and $86 per dry ton3 for woody residue in
the Northeast, South, North, and West regions, respectively.4
Using the timber harvesting cost simulator outlined in Fight et al. (2006), Sohngen et al.
(2010) found harvest costs up to roadside about $25 per dry ton, with a high cost scenario
of $34 per dry ton. Based on an oil price of $111 per barrel, the model assumed harvest and
maintenance costs have mean (likeliest) values of $44.20 ($47.20), $37.20 ($39.20), $46.20
($49.20), $33.20 ($34.20), and $27.20 for stover, switchgrass, Miscanthus, wheat straw, and
1 For parameters with an assumed skewed distribution in Monte Carlo analysis, the “likeliest” value denotes the
value with the highest probability density.
2 Harvest and maintenance costs were updated using USDA-NASS agricultural fuel, machinery, and labor prices
from 1999-2007 (USDA-NASS, 2007a,b).
3 Based on a conversion rate of 0.59 dry tons per green tons.
4 Northeast includes Pennsylvania, New Jersey, New York, Connecticut, Massachusetts, Rhode Island, Vermont,
New Hampshire, and Maine. South refers to Delaware, Maryland, West Virginia, Virginia, North Carolina, South
Carolina, Kentucky, Tennessee, Florida, Georgia, Alabama, Mississippi, Louisiana, Arksansas, Texas, and Okla-
homa. States in the North region are Minnesota, Wisconsin, Michigan, Iowa, Missouri, Illinois, Indiana, and Ohio.
West includes South Dakota, Wyoming, Colorado, New Mexico, Arizona, Utah, Montana, Idaho, Washington,
Oregon, Nevada, and California.
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343
APPENDIX K
woody biomass. Alfalfa was assumed to be harvested once during the first year and three
times during the second year at a cost of $55 per acre per harvest. In addition to harvest
costs, suppliers of short-rotation woody crops (SRWC) incur a stumpage fee (SF) with an
assumed mean value of $20 per ton. Energy costs affect the cost of harvest through the
price of diesel. The relationship between diesel and oil prices was derived using data from
1988-2008. Harvest costs increase by approximately $2.70 per ton at the high oil price and
decreases by around $2.00 per ton at the low oil price.
Transportation Costs (DVC, DFC, and D)
Previous research on transportation of biomass has provided two distinct types of cost
estimates: (1) total transportation cost and (2) breakdown of variable and fixed transpor-
tation costs. Research estimates for total corn stover transportation costs range between
$3 per ton and $32 per ton (Aden et al., 2002; Perlack and Turhollow, 2002; Atchison and
Hettenhaus, 2003; English et al., 2006; Hess et al., 2007; Perlack, 2007; Brechbill and Tyner,
2008a; Mapemba et al., 2008; Vadas et al., 2008). Total switchgrass and Miscanthus trans-
portation costs have been estimated between $14 and $36 per ton (Tiffany et al., 2006; Ku-
mar and Sokhansanj, 2007; Mapemba et al., 2007; Brechbill and Tyner, 2008a; Duffy, 2008;
Khanna et al., 2008; Mapemba et al., 2008; Perrin et al., 2008; Vadas et al., 2008), adjusted to
2007 costs.5 Woody biomass transportation costs are expected to range between $11 and $30
per dry ton (Summit Ridge Investments, 2007; Sohngen et al., 2010). Based on the second
method, distance variable cost (DVC) estimates range between $0.09 and $0.60 per ton per
mile (Kaylen et al., 2000; Kumar et al., 2003; USFS, 2003; Kumar et al., 2005; USFS, 2005;
Searcy et al., 2007; Brechbill and Tyner, 2008a,b; Petrolia, 2008; Huang et al., 2009; Jenkins
et al., 2009; Sohngen et al., 2010), while distance fixed cost (DFC) estimates range between
$4.80 and $9.80 per ton (Kumar et al., 2003, 2005; Searcy et al., 2007; Petrolia, 2008; Huang
et al., 2009), depending on feedstock type. The BioBreak model utilized the latter method
of separating fixed and variable transportation costs.
The DFC for corn stover, switchgrass, Miscanthus, wheat straw, and second-year alfalfa
was assumed to range from $5 to $12 per ton with a mean value of $8.50 per ton. Besides
loading and unloading costs, woody biomass requires an on-site chipping fee. Therefore,
the DFC for woody biomass was assumed to have a mean value of $10 per ton. The DVC
was assumed to follow a skewed distribution to account for future technological progress in
transportation of biomass with a mean (likeliest) value of $0.38 ($0.41) per ton per mile for
stover, switchgrass, Miscanthus, wheat straw, and second-year alfalfa and $0.53 ($0.56) per
ton per mile for woody biomass. Energy costs affect the DVC through the price of diesel. The
1988-2008 relationship between diesel and oil prices was used to adjust DVC to each oil price
scenario. The DVC increases by approximately $0.07 per ton per mile at the high oil price
($191 per barrel) and decreases by approximately $0.05 per ton per mile at the low oil price
($52 per barrel).
One-way transportation distance (D) has been evaluated up to around 140 miles for
woody biomass (USFS, 2003, 2005; Miller and Bender, 2008; Spelter and Toth, 2009) and
between 5 and 75 miles (Perlack and Turhollow, 2002, 2003; Atchison and Hettenhaus, 2003;
English et al., 2006; Tiffany et al., 2006; Mapemba et al., 2007, 2008; BRDI, 2008; Brechbill and
Tyner, 2008a,b; Khanna, 2008; Taheripour and Tyner, 2008; Vadas et al., 2008) for all other
feedstocks. In the model, the average hauling distance was calculated using the formulation
by French (1960) for a circular supply area with a square road grid provided in Equation (3)
5 Transportation costs were updated using USDA-NASS agricultural fuel prices from 1999-2007 (USDA-NASS,
2007a,b).
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344 APPENDIX K
below. 6 Average distance (D) is a function of the annual biorefinery biomass demand (BD),
annual biomass yield (YB) and biomass density (B).
BD
D = 0.4789
640 * YB * B
(3)
Annual biomass demand was assumed to be consistent with the biorefinery outlined for
capital and operating cost distributions (772,000 tons per year). Biomass density was assumed
to follow a normal distribution with a mean value of 0.20 for all feedstocks except alfalfa,
which has a mean biomass density of 0.15 (McCarl et al., 2000; Perlack and Turhollow, 2002;
Popp and Hogan Jr., 2007; Brechbill and Tyner, 2008a,b; Petrolia, 2008; Huang et al., 2009).7
Storage Costs (CS)
Due to the low density of biomass compared to traditional cash crops such as corn and
soybean, biomass storage costs (CS) can vary greatly depending on the feedstock type, har-
vest technique, and type of storage area. Adjusted for 2007 costs, biomass storage estimates
ranged between $2 and $23 per ton. For simulation, BioBreak assumed storage costs follow
a skewed distribution for all feedstocks to allow for advancement in storage and densifica-
tion techniques. The mean (likeliest) cost for woody biomass storage was $11.50 ($12) per
ton, while corn stover, switchgrass, Miscanthus, wheat straw, and alfalfa storage costs were
assumed to have mean (likeliest) values of $10.50 ($11) per ton.
Establishment and Seeding Costs (CES)
Corn stover, wheat straw, and forest residue suppliers were assumed to not incur estab-
lishment and seeding costs (CES), while all other feedstock suppliers must be compensated
for their establishment and seeding costs. Costs vary by initial cost, stand length, years to
maturity, and interest rate. Stand length for switchgrass ranges between 10 and 20 years
with full yield maturity by the third year. Miscanthus stand length ranges from 10 to 25 years
with full maturity between the second and fifth year. Interest rates used for amortization
of establishment costs range between 4 and 8 percent. Amortized cost estimates for switch-
grass establishment and seeding, adjusted to 2007 costs, are between $30 and $200 per acre.
Miscanthus establishment and seeding cost estimates vary widely, based on the assumed
level of technology and rhizome costs. James et al. (2010) reported a total rhizome cost
(not including equipment and labor) of $8,194 per acre as representative of current costs
and $227.61 per acre for a projected cost estimate after technological advancement (2008$).
Lewandowski et al. (2003) provided a cost range of $1,206-$2,413 per acre (not updated).
Jain et al. (2010) pointed out the benefit of using rhizomes over plugs where the total cost
of establishment of rhizomes is about $1,200 per acre in Illinois and $1,215-$1,620 per acre
for plugs. Establishment costs for wood also vary by species and location. Cubbage et al.
(2010) reported establishment costs of $386-$430 and $520 per acre for yellow pine and
Douglas Fir, respectively (2008$).
6 Theauthors’ simplifying assumption of uniform density is maintained.
7 Although the biomass density for a corn-soybean rotation is assumed to be 0.20, the value used to calculate the
average hauling distance for stover from a corn-soybean rotation is 0.10 since only half of the acreage is in corn
at any given point in time.
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345
APPENDIX K
Given research estimates, switchgrass establishment and seeding costs were based on
a $250 per acre cost, amortized over 10 years at 10 percent to yield a mean value of $40 per
acre in all regions. Miscanthus was assumed to have a mean value of $150 per acre per year
mean establishment costs based on a total cost of $1,250 per acre amortized over 20 years at
10 percent. Establishment of alfalfa was assumed fixed at $165 per acre, including fertilizer
application. Finally, SRWC were assumed to cost $400 per acre to establish and amortized
over 15 years at 10 percent to yield a mean value of $52 per acre per year.
Opportunity Costs (COpp)
To provide a complete economic model, the opportunity costs of utilizing biomass for
ethanol production were included in BioBreak. Research estimates for the opportunity cost
of switchgrass and Miscanthus ranged between $70 and $318 per acre (Khanna and Dhun-
gana, 2007; Brechbill and Tyner, 2008a; Khanna et al., 2008; Jain et al., 2010), while estimates
for nonspecific biomass opportunity cost ranged between $10 and $76 per acre (Khanna
et al., 2008; Mapemba et al., 2008), depending on the harvest restrictions under the Con-
servation Reserve Program contracts. Opportunity cost of woody biomass was estimated
to range between $0 and $30 per ton (USFS, 2003, 2005; Summit Ridge Investments, 2007).
The corn stover harvest activity was developed for a corn-soybean rotation alterna-
tive and has no opportunity cost beyond the nutrient replacement cost. A continuous corn
alternative, used by 10-20 percent of Corn Belt producers, was developed for corn stover
harvest but not included in the BioBreak results presented in this report. The continuous
corn production budgets, developed by state extension specialists, are always less profit-
able than corn-soybean rotation budgets with or without stover harvest. Continuous corn
has an associated yield penalty or forgone profit (opportunity costs) relative to the corn-
soybean rotation that occurs irrespective of stover harvest. Thus, a comparative analysis of
stover harvest with corn-soybean and continuous corn may be misinterpreted.8
Given the research estimates for perennial grass opportunity cost, switchgrass, and
Miscanthus grown on Midwest land were assumed to have mean opportunity costs of $150
per acre on high-quality and $100 per acre on low-quality land. Perennial grasses grown in
the Appalachian and South-Central regions were assumed to have lower mean opportu-
nity costs of $75 and $50 per acre. Wheat straw opportunity cost was assumed to follow a
distribution with likeliest value of $0 per acre with a range of –$10 to $30 per acre. Negative
values for the opportunity costs of wheat straw were based on the potential nuisance cost
of wheat straw. Occasionally, straw is burned at harvest to avoid grain planting problems
during the following crop season. Forest residue was assumed to have no value in an
alternative use and therefore no opportunity cost, and the stumpage fee was assumed to
account for the opportunity cost of SRWC. Finally, alfalfa is assumed to have a 2-year stand
with first-year harvest sold for hay at a value of $140 per ton while second-year alfalfa was
assumed to have 50-percent leaf mass sold for protein value at $160 per ton and the remain-
ing 50 percent used as a biofuel feedstock. Alfalfa opportunity cost (that is, land cost) was
assumed fixed at $175 per acre for both years.
8 From the rotation calculator provided by the Iowa State University extension services with a corn price of $4 per
bushel, a soybean price of $10 per bushel, and a yield penalty of 7 bushels per acre, the lost net returns to switching
from a corn-soybean rotation to continuous corn is about $62 per acre (http:/www.extension.iastate.edu/agdm/
crops/html/al-20.html). Previous literature that has attributed an opportunity cost to stover based on lost profits
from switching from a corn-soybean rotation to continuous corn production has assumed an opportunity cost
between $22 and $140 per acre (Khanna and Dhungana, 2007; Duffy, 2010).
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346 APPENDIX K
Biomass Yield (YB)
The final parameter in the BioBreak model is biomass yield per acre of land. Biomass
yield is variable in the near and distant future due to technological advancements and
environmental uncertainties. Corn-stover yield per acre will vary based on the amount
of corn stover that is removable, which depends on soil quality and other topographical
characteristics. Harvested corn-stover yield has been estimated between 0.7 to 3.8 tons per
acre (Duffy and Nanhou, 2002; Lang, 2002; Perlack and Turhollow, 2002; Sokhansanj and
Turhollow, 2002; Atchison and Hettenhaus, 2003; Quick, 2003; Schechinger and Hetten-
haus, 2004; Edwards, 2007; Khanna and Dhungana, 2007; Prewitt et al., 2007; BRDI, 2008;
Brechbill and Tyner, 2008a; Khanna, 2008; Vadas et al., 2008; Huang et al., 2009; Chen et al.,
2010). Potential switchgrass yields range between 0.89 and 17.8 tons per acre (Reynolds et
al., 2000; Muir et al., 2001; Bouton, 2002; Kszos et al., 2002; McLaughlin et al., 2002; Talia-
ferro, 2002; Vogel et al., 2002; Lewandowski et al., 2003; Ocumpaugh et al., 2003; Parrish et
al., 2003; Heaton et al., 2004b; Berdahl et al., 2005; Cassida et al., 2005; Kiniry et al., 2005;
McLaughlin and Kszos, 2005; Thomason et al., 2005; Comis, 2006; Fike et al., 2006a,b; Nel-
son et al., 2006; Schmer et al., 2006; Shinners et al., 2006; Tiffany et al., 2006; Gibson and
Barnhart, 2007; Khanna and Dhungana, 2007; Popp and Hogan, 2007; BRDI, 2008; Brechbill
and Tyner, 2008a; Duffy, 2008; Khanna, 2008; Khanna et al., 2008; Perrin et al., 2008; Sand-
erson, 2008; Vadas et al., 2008; Walsh, 2008; Huang et al., 2009; Chen et al., 2010; Jain et al.,
2010), depending on region, land quality, switchgrass variety, field versus plot trial stud-
ies, and harvest technique. On average, Miscanthus has significantly higher yield estimates
that range between 3.4 and 19.6 tons per acre when yield estimates from both the United
States and the European Union are considered (Lewandowski et al., 2000; Clifton-Brown
et al., 2001, 2004; Kahle et al., 2001; Clifton-Brown and Lewandowski, 2002; Vargas et al.,
2002; Heaton et al., 2004a,b; Khanna and Dhungana, 2007; Stampfl et al., 2007; Christian et
al., 2008; Khanna, 2008; Khanna et al., 2008; Smeets et al., 2009). Estimated U.S. Miscanthus
yields range between 9 and 28 tons per acre (Heaton et al., 2004a,b; Khanna and Dhungana,
2007; Khanna, 2008; Khanna et al., 2008; Chen et al., 2010; Jain et al., 2010). A wheat straw
yield of 1 ton per acre was assumed by the Biomass Research and Development Initiative
study (BRDI, 2008). For woody biomass, Huang et al. (2009) estimated Aspen wood yield
of 0.446 dry tons per acre from a densely forested area in Minnesota, while the BRDI (2008)
study assumed short-rotation woody crops yield 5 to 12 tons per acre. Using USDA Forest
Service data for Mississippi, the average removal rate of wood residue in 2006 was around
1.1 tons per acre.9 In a recent study on 2008 wood production costs, Cubbage et al. (2010)
estimated an annual yield of 3.6 and 4.3 tons per acre in North Carolina and the Southern
United States, respectively. In the same analysis, Douglas Fir was estimated to provide 4
and 5.1 tons per acre annually in Oregon and North Carolina, respectively.
For simulation, the mean yield of corn stover was approximately 2 tons per acre.
Switchgrass grown in the Midwest was assumed to have a distribution with a mean (like-
liest) value around 4 (3.4) tons per acre on high quality land and 3.1 tons per acre on low
quality land.10 Miscanthus grown in the Midwest was assumed to have a mean (likeliest)
value of 8.6 (8) tons per acre on high quality land and 7.1 (6) tons per acre on low quality
land.11 Switchgrass grown in the South-Central region has a higher mean yield of about 5.7
tons per acre. For the regions analyzed, the Appalachian region provides the best climatic
9 This value is a lower bound because forestry still had positive net growth over this period.
10 Plottrials were evaluated at 80 percent of their estimated yield.
11 This is a significantly lower assumed yield than previous research has assumed or simulated (Khanna and
Dhungana, 2007; Khanna et al., 2008; Khanna, 2008; Heaton et al., 2004).
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347
APPENDIX K
conditions for switchgrass and Miscanthus with assumed mean (likeliest) yields of 6 (5) and
8.8 (8) tons per acre, respectively. Wheat straw, forest residues, and SRWC were assumed
to be normally distributed with mean yields of 1, 0.5, and 5 tons per acre. First-year alfalfa
yield was fixed at 1.25 tons per acre (sold for hay value), while second-year yield was fixed
at 4 tons per acre (50-percent leaf mass sold for protein value), resulting in 2 tons per acre
of alfalfa for biomass feedstock during the second year.
Biomass Supplier Government Incentives (G)
For biomass supplier government incentives (G), the dollar for dollar matching pay-
ments provided in the Food, Conservation, and Energy Act of 2008 (that is, the 2008 Farm
Bill) up to $45 per ton of feedstock for collection, harvest, storage, and transportation is
used, and it is denoted as “CHST.” The CHST payment was considered in the sensitivity
analysis rather than the baseline scenario since the payment is a temporary (2-year) pro-
gram and might not be considered in the supplier’s long-run analysis. Although the Bio-
Break model is flexible enough to account for any additional biomass supply incentives, the
establishment assistance program outlined in the 2008 Farm Bill is not considered because
the implementation details were not finalized at the time of the model run.
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