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Uncertainty, Irreversibility, and Investment in Second-Generation Biofuels

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Abstract

The present study quantifies the importance of price risk and irreversibility for investment in a corn stover-based cellulosic biofuel plant. Using a real-option model, we recover prices of gasoline that would trigger entry into the market and compare it to breakeven price. Our analysis shows that the price premium (above breakeven) required by investors to enter the market due to risk is substantial. Managerial flexibility (embedded in the option of mothballing and reactivating the plant) does not sensibly reduce the entry premium. Results also show that price volatility may greatly reduce plants’ responsiveness to gasoline prices and decrease supply elasticity. In combination, results suggest that (1) policies supporting second-generation biofuels may have fell short of their targets because of their failure to alleviate price uncertainty and (2) the use of price-based instruments such as reverse auctions, either in isolation or in combination with mandates, may be warranted.

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Notes

  1. This assumption is consistent with statistical tests conducted with historical gasoline price data. Tests will be presented and discussed in detail in the Empirical Implementation section.

  2. The assumption of infinite horizon greatly simplifies the problem. On the other hand, this assumption may overestimate the entry trigger price. However, the upward bias generated by the infinite horizon assumptions has been found to become very small when time to maturity is 20 years [36]. Since cellulosic biofuel plants are typically assumed to operate for 20 years (e.g., [6]; [3]), we assume an infinite horizon.

  3. A note of caution is in place here. Kior’s primary feedstock is yellow pine, and previous studies suggest that there could be a yield reduction when converting from yellow pine to corn stover ([37]; [3]).

  4. This figure uses real-option entry and exit trigger prices without managerial flexibility so that the effects of such flexibility are not confounded with those of uncertainty and irreversibility. It is worth noting, however, that prices with and without managerial flexibility are virtually the same.

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Acknowledgments

The authors would like to thank Wallace Tyner and Benjamin Gramig for useful comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Agricultural Economics, Purdue University, KRAN 591A, West Lafayette, IN, 47907-2056, USA

    Tanner McCarty & Juan Sesmero

Authors
  1. Tanner McCarty
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  2. Juan Sesmero
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Correspondence to Juan Sesmero.

Appendices

Appendix A: Numerical Solution in MatLab

Code

First, we create an m.file with the following code

function F = ROA(x)

alpha = −2.0628;

beta = 2.2155;

delta = 0.1;

mu = .01854;

w = 2.56;

k = 9.91;

m = 0.25;

em = 0.25;

r = 0.50;

l = −2.48;

F = [x(7)*(x(1)^beta)-x(1)*((delta-mu)^-1) + w*(delta^-1)-x(5)*(x(1)^alpha) + k;

x(3)*((delta-mu)^-1)-w*((delta)^-1) + x(5)*(x(3)^alpha)-x(6)*(x(3)^alpha)-x(8)*(x(3)^beta) + m*(delta^-1) + em;

x(6)*(x(4)^alpha) + x(8)*(x(4)^beta)-m*(delta^-1)-x(4)*((delta-mu)^-1) + w*(delta^-1)-x(5)*(x(4)^alpha) + r;

x(6)*(x(2)^alpha) + x(8)*(x(2)^beta)-m*(delta^-1)-x(7)*(x(2)^beta) + l;

beta*x(7)*(x(1)^(beta-1))-((delta-mu)^-1)-alpha*x(5)*(x(1)^(alpha-1));

((delta-mu)^-1) + alpha*x(5)*(x(3)^(alpha-1))-alpha*x(6)*(x(3)^(alpha-1))-beta*x(8)*(x(3)^(beta-1));

alpha*x(6)*(x(4)^(alpha-1)) + beta*x(8)*(x(4)^(beta-1))-((delta-mu)^-1)-alpha*x(5)*(x(4)^(alpha-1));

alpha*x(6)*(x(2)^(alpha-1)) + beta*x(8)*(x(2)^(beta-1))-beta*x(7)*(x(2)^(beta-1))];

Second, we implement the following steps for solving the problem

Options = optimset ('MaxFunEvals',10000,'MaxIter',10000)

x0 = [5;1;1;2;1;1;1;1]; % Make a starting guess at the solution

[x,fval] = fsolve(@ROA,x0,options)

Appendix B: Equations defining value matching and smooth pasting conditions without the managerial flexibility to mothball or reactivate

Code

First, we create an m.file with the following code

function F = ROA2(x)

alpha = −2.0628;

beta = 2.2155;

delta = 0.1;

mu = .01854;

w = 2.2.56;

k = 9.91;

l = −2.48;

F = [x(4)*(x(1)^beta)-x(3)*(x(1)^alpha)-x(1)*((delta-mu)^-1) + w*(delta^-1) + k;

beta*x(4)*(x(1)^(beta-1))-alpha*x(3)*(x(1)^(alpha-1))-((delta-mu)^-1);

x(3)*(x(2)^alpha) + x(2)*((delta-mu)^-1)-w*((delta)^-1)-x(4)*(x(2)^(beta)) + l;

alpha*x(3)*(x(2)^(alpha-1)) + ((delta-mu)^-1)-beta*x(4)*(x(2)^(beta-1))];

Second, we implement the following steps for solving the problem

Options = optimset ('MaxFunEvals',10000,'MaxIter',10000)

x0 = [4;1;1;1]; % Make a starting guess at the solution

[x,fval] = fsolve(@ROA2,x0,options)

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McCarty, T., Sesmero, J. Uncertainty, Irreversibility, and Investment in Second-Generation Biofuels. Bioenerg. Res. 8, 675–687 (2015). https://doi.org/10.1007/s12155-014-9549-y

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  • DOI: https://doi.org/10.1007/s12155-014-9549-y

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