Inspiration of Valuing Strategic Option like Expansion

By Yafeng Liu

FIN 622, Fall, 2008, Bradley Univ

Advisor: Dr. Arlyn Rubash

(NOTE: For equations and figures details, please click the fourth button 'file' on the same row as the frist buttone 'edit' on the bottom of this page and you should be able to find a file with name of "Innovative Valuation of Expansion" in .doc for your reference.)

Abstract:

This short paper presents an innovative way of evaluating the value of one of the strategic options (expansion flexibility). Instead of calculating the present value twice for with and without expansion at year 1 from year 2 values back to year 0 and then using the difference between with and without expansion to find the value of the expansion at year 0, the method introduced here uses the value increase at year 2 for different economic scenarios and traces back to find the value at year 0 of the expansion at year 1.

Discussion:

First introduced are the assumptions:

1. All upward transition neutral risk probabilities are the same and equal to ,

2. No risk free interest rate difference from one year to year and risk free interest rate is

3. “One year up and one down” has the same value of “one year down and then one year up.” If one year up opens an strategic opportunity of expansion the facility with cost of C, it brings new added value at one year later from the expansion: value increase of dSuu to the original 2nd year Suu for one good year of year 2, and value increase of dSud to the original 2nd year Sud for one bad year of year 2. The value process is shown in Schematic as shown in Fig.1 below.

Due to the expansion at year 1, the present value increase at year 1, dSu, as shown in Fig.2, can be calculated using financial Binomial model and minus the cost or investment for expansion:

(Eq.1)

The present value increase at year 1 can be further converted to the present value increase at year 0, which is the creation of the facility or a project. Without the creation of the facility or the project at year 0, there is no strategic option available at year 1 for expansion. The present value increase at year 0 can be figured out as,

(Eq.2)

while,

dSd =0 since there is no value increase at year 1 when the economic situation is bad

Therefore, Eq.2 can be simplified as,

(Eq.3)

Combining Eq.1 and Eq.3, the present value increase at year 0 due to the expansion at year 1 is,

(Eq.4)

In Eq.4, dSuu and dSud can be percentage-wise increases from of Suu and Sud, respectively.

Fig.1 The expansion flexibility at Year 1 brings in Value from Year 2 to Year 1

Fig.2 The expansion flexibility at Year 1 relays Value from Year 1 to Year 0