1 Rules of Thumb in Real Options Applications George Y. Wang National Dong-Hwa University 2004 NTU Conference on Finance December 20, 2004

2 Capital Budgeting Practices

3 The 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.

4 Motivation Capital 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.

5 Research Purposes Explore 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.

6 Modified Capital Budgeting Rules under Real Options (Generalized Expressions) NPV Profitability Index Payback Hurdle Rate Cash Flow Trigger Discounted Payback

7 The Comparison between the Modified Investment Rules and Conventional Rules

8 Stochastic Processes of Interest

9 Options, F(V*), and Investment Triggers, V* GBM Mixed Diffusion-Jump Mean Reversion where Pyndick (1991) and Dixit and Pindyck (1994)

10 Real Options in Capital Budgeting (GBM and Mixed Diffusion-Jump) Profitability Index Cash Flow Trigger Hurdle Rate Payback Discounted Payback

11 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)

12 Numerical Analysis of the Optimal Triggers under Alternative Processes

13 Findings The 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.

14 The Comparison between the Modified Investment Rules and Conventional Rules

15 The Cost of Suboptimal Investment Rules under a GBM

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

17 The Cost of Suboptimal Investment Rules under a Mean Reversion

18 Findings The 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.

19 The Process of Developing Heuristics Identify a proper stochastic process Conduct base-case analysis to determine target investment rule Conduct regression analysis and sensitivity analysis to identify key determinants and weights Fine-tuning the weights Determine heuristic rules

20 Optimal Hurdle Rate as a Function of σ and μ under a GBM

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

22 Optimal Hurdle Rate as a Function of σ and μ under a Mean Reversion

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

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

25 Monte Carlo Simulation

26 Regression Analysis (GBM)

27 Regression Analysis (Mixed Diffusion-Jump)

28 Regression Analysis (Mean Reversion)

29 Heuristic Investment Rules

30 Sensitivity to Growth Rate Classify five types of projects Project A: high discount rate (μ=35%) and high volatility (σ=40%) Project B: high discount rate (μ=35%) and low volatility (σ=10%) Project C: middle discount rate (μ=25%) and middle volatility (σ=25%) Project D: low discount rate (μ=15%) and high volatility (σ=10%) Project E: low discount rate (μ=15%) and low volatility (σ=10%)

31 Sensitivity to Growth Rate GBM Model

32 Sensitivity to Growth Rate Mixed Diffusion-Jump Model ( λ= 20%)

33 Sensitivity to Growth Rate Mean Reversion Model

Rule under a GBM Low-Growth ProjectsMid-Growth Projects High-Growth Projects

Rule under a Mixed Diffusion-Jump Low-Growth ProjectsMid-Growth Projects High-Growth Projects

Rule and 2-10-(-2) Rule under a Mean Reversion 2-10 Rule Zero-Growth Projects 2-10-(-2) Rule All Projects

37 Testing the Heuristic Investment Rules

38 Implications The 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.