||The Valuation of Operating Leverage Option in Strategic Asset Allocation
||Graduate Institute of Finance & Banking
In this article we consider a two-period investment project in which we include the option to wait, option to expand, option mothball, and option to abandon. In addition we also specify the optimal inherent operating risk measured by the degree of operating leverage in an investment project for a more precise evaluation of the feasibility. We assume that the market uncertainty follows the geometric browning motion, and the managerial flexibility, or the operating leverage option, is the flexibility to optimally control the production inputs, capital and labor, for maximizing project NPV. We adopt the Numerical Calculus to solve the project value with and without the managerial flexibility to specify the value of the operating leverage option and the optimal degree of operating leverage of the firm.
We show that the operating leverage option can enhance the project value and diversify the inherent operating risk. Our numerical example also shows that lower initial capital investment would be suitable when the volatility is high, and the converse is also true. Moreover, overinvestment is more valuable than underinvestment in an investment project, but the overinvestment brings higher operating risk, while the underinvestment creates the potential enhancement on project NPV in the future. In addition, when a firm overinvests or underinvests an investment project, it should focus mainly on the accuracy of the initial capital investment when the volatility is low, while it also needs to focus on the expanding, mothballing, and abandoning strategies when the volatility is high.
TABLE OF CONTENTS V
LIST OF TABLES VIII
LIST OF FIGURES IX
CHAPTER 1 INTRODUCTION 1
1.1 Research Background and Motivation 1
1.2 Research Objectives 3
1.3 Structure of Thesis 4
CHAPTER 2 LITERATURE REVIEW 5
2.1 Financial Option 5
2.1.1 European Options 5
2.1.2 American Options 6
2.1.3 Analytic Solution 6
2.1.4 Numerical Approximation 7
2.2 Option to Delay 9
2.3 Option to Expand 11
2.4 Option to Abandon 13
2.5 Degree of Operating Leverage 15
CHAPTER 3 METHODOLOGY 17
3.1 Definition of Degree of the Operating Leverage 17
3.2 Basic Assumptions 18
3.3 Valuation of an One-Period Capital Budgeting 25
3.3.1 Valuation of the Project Given a Certain Capital Investment 26
3.3.2 Optimal Capital Investment and Net Present Value at the Time Point 0 28
3.4 Valuation of a Two-Period Project and the Operating Leverage Option 29
3.4.1 Valuation of the Project Given a Certain Capital at the Time Point 0 30
3.4.2 Optimal Capital Investment at the Time Point 0 39
3.4.3 Valuation of the Project When the Initial Capital Investment is Delayed 40
3.4.4 Investment Trigger of the Project at the Time Point 0 44
CHAPTER 4 NUMERICAL TEST 50
4.1 Project Value and Optimal Degree of the Operating Leverage 51
4.1.1 The Net Present Value of the Project 51
4.1.2 Degree of the Operating Leverage of the Project 54
4.2 The Strategies in the Project 57
4.2.1 Mothballing Strategy 57
4.2.2 Expanding Strategy 58
4.2.3 Overinvestment and Underinvestment in Initial Capital 61
4.3 Value of the Operating Leverage Option 63
4.3.1 Value of the Operating Leverage with the Flexibility to Choose the Optimal Initial Capital 63
4.3.2 Value of the Operating Leverage Option without the Flexibility to Choose the Optimal Initial Capital 65
CHAPTER 5 CONCLUSION AND FURTHER RESEARCH 68
5.1 Conclusions 68
5.2 Further Research 69
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