Rules of Thumb in Real Options Applications

George Y. WangNational Dong-Hwa University2004 NTU Conference on FinanceDecember 20, 2004

Capital Budgeting Practices

Capital Budgeting PracticesThe literature indicates that NPV, IRR, and payback are top-three frequently used valuation techniques.

Busby and Pitts (1997) and Graham and Harvey (2001) reveal that only a small percentage of firms have formal procedures to appraise real options.

MotivationCapital budgeting literature suggests two important facts: first, conventional capital budgeting techniques are shown to have various theoretical shortcomings, yet still have widespread applications in practice; second, real options techniques are considered as relatively sophisticated analysis tools, yet most firms do not make explicit use of real options techniques to evaluate capital investments. This paper aims to bridge the theory-practice gap by translating real options theory into existing capital budgeting practices.

Research PurposesExplore how real options decision criteria can be transformed into equivalent capital budgeting criteria such as NPV, profitability index, hurdle rate, and (discounted) payback. Propose heuristic investment rules in terms of capital budgeting practices to proxy for the inclusion of real options valuation.

Modified Capital Budgeting Rules under Real Options (Generalized Expressions)NPV

Profitability Index

Payback

Hurdle Rate

Cash Flow Trigger

Discounted Payback

The Comparison between the Modified Investment Rules and Conventional Rules

Stochastic Processes of Interest

Options, F(V*), and Investment Triggers, V*GBM

Mixed Diffusion-Jump

Mean ReversionwherewherewherePyndick (1991) and Dixit and Pindyck (1994)

Real Options in Capital Budgeting (GBM and Mixed Diffusion-Jump)Profitability Index

Cash Flow Trigger

Hurdle Rate

Payback

Discounted Payback

The Option Impact=Modified Rules = Conventional Rules + Option Impact(for PI, Hurdle Rate, and Cash Flow Rules)Modified Rules = Conventional Rules Option Impact(for Payback Rules)

Numerical Analysis of the Optimal Triggers under Alternative Processes

FindingsThe graph suggests that for a set of reasonable parameter values, both mean reversion and competitive arrivals have a significant influence on lowering optimal triggers, indicating that investment in both cases should be launched sooner than the normal GBM case. It seems that mean reversion has a stronger power to induce investment than the competitive arrival effect.

The Comparison between the Modified Investment Rules and Conventional Rules

The Cost of Suboptimal Investment Rules under a GBM

The Cost of Suboptimal Investment Rules under a Mixed Diffusion-Jump

The Cost of Suboptimal Investment Rules under a Mean Reversion

FindingsThe best investment rule under uncertainty is the optimal investment rule itself.

However, if a simple heuristic decision rule is used to approximate V*, the rule should be as near as possible in order to minimize the opportunity cost of adopting the suboptimal investment policy.

The Process of Developing HeuristicsIdentify a proper stochastic processConduct base-case analysis to determine target investment ruleConduct regression analysis and sensitivity analysis to identify key determinants and weightsFine-tuning the weightsDetermine heuristic rules

Optimal Hurdle Rate as a Function of and under a GBM

Optimal Hurdle Rate as a Function of and under a Mixed Diffusion-Jump

Optimal Hurdle Rate as a Function of and under a Mean Reversion

The Sensitivity of Other Capital Budgeting Criteria to and under a GBM

The Sensitivity of Other Capital Budgeting Criteria to and under a MX Process

Monte Carlo Simulation

Regression Analysis(GBM)

Regression Analysis(Mixed Diffusion-Jump)

Regression Analysis(Mean Reversion)

Heuristic Investment Rules

Sensitivity to Growth RateClassify five types of projectsProject A: high discount rate (=35%) and high volatility (=40%) Project B: high discount rate (=35%) and low volatility (=10%) Project C: middle discount rate (=25%) and middle volatility (=25%) Project D: low discount rate (=15%) and high volatility (=10%) Project E: low discount rate (=15%) and low volatility (=10%)

Sensitivity to Growth RateGBM Model

Sensitivity to Growth RateMixed Diffusion-Jump Model (= 20%)

Sensitivity to Growth RateMean Reversion Model

4-8 Rule under a GBMLow-Growth ProjectsMid-Growth ProjectsHigh-Growth Projects

3-9 Rule under a Mixed Diffusion-JumpLow-Growth ProjectsMid-Growth ProjectsHigh-Growth Projects

2-10 Rule and 2-10-(-2) Rule under a Mean Reversion2-10 RuleZero-Growth Projects2-10-(-2) RuleAll Projects

Testing the Heuristic Investment Rules

ImplicationsThe heuristic investment rules provide a seemingly accurate approximation to the optimal investment rules by a set of two parameters, volatility and discount rate, under managerial flexibility and uncertainty. Corporate practitioners can apply real options techniques without always carrying out complicated analysis.