## Real Options

The real options method represents a new technique for the valuation and management of strategic investments (capital budgeting decisions). American put option valuation techniques are used for abandonment options and contract options. American call option valuation techniques are used for upgrade options and unexcercise options.

## Abandonment option

It is not a derivative instrument, but an actual option (= business choice) to abandon project if the situtation is not favourable for a company. The exercise price for the abandonment option would be the salvage value or the cost savings for the company arising from abandoning the project.

## The use of abandonment options

**Example 1:** Lear Aircraft is interested in building a small passenger plane and approaches Airbus to create joint venture. Each company would invest $500 million for 30 years. Airbus, using traditional methods, calculates that expected cash flows would be $480 million and NPV would thus be negative. Airbus therefore rejects the proposal. However, Lear Aircrafts offers that it would buy out Airbus’s 50% share for $400 anytime over the next 5 years, thus creating abandonment real option.

**Example 2:** A pharmaceutical company PHARMA is developing a particular drug in 5-year project. The result is uncertain (development progress, human and animal testing, FDA approval, etc.) and company decides to enter into contractual agreement with another pharmaceutical company that in case the management decides to terminate the project, PHARMA will sell off its intellectual property (patents) to the other pharmaceutical company.

## Abandonment option valuation

There are 3 methods which could be used for the valuation of abandonment options:

• Black-Scholes type of closed form solution (Mun, 2002)

• Partial differential equation system (Jiao, 2006)

• Decision tree approach

**Black-Scholes type of closed form solution**

Follow-up of Example 1:

S - Present Value of the share of cash flows from the investment today = $480 million

K - Abandonment value = $400 million

T - Period for which abandonment option holds = 5 years

Standard deviation (measures volatility) is estimated using Monte Carlo simulation (for details see http://www.finint.ase.ro/materiale/manuale/investment%20valuation_damodaran/ch29.pdf , p.6) at the level of 25%

Dividend Yield = 3.33% (1/remaining life of the project = 1/30)

Value of abandonment option = 400e^{(-0.05)(5)}(1-0.5776)-480e^{(-0.033)(5)}(1-0.7748) = $40.09 million.

Since 480$ + $40.09 > $500 Airbus should accept the proposal for joint venture.

**Decision Tree approach**

Follow-up of Example 2:

S - Present Value of the future cash-flows (at appropriate risk-adjusted discount rate) = $150 million

Rf - risk-free rate = 5.0%

K - Abandonment or Salvage Value = $100 million

T - time of the option = 5 years

First step in the Decision Tree approach is the **Lattice evolution of the Underlying** (S), which includes calculation of the up factor, down factor, and risk-neutral probability. The next step is the **Option valuation lattice**, using the process called *backward induction* (i.e. the calculation proceeds in a backward manner, starting from the terminal nods).

For details, see: http://books.google.com/books?id=X47bm9Etd7IC&pg=PA55&dq=Real+Options+Analysis:+Tools+and+Techniques+for+Valuing+Strategic+Investment+and+Decisions&ei=N53pSKTsOoPqyATIitzbBw&sig=ACfU3U3ZSP6s7ooollb4DYFsxcmPEowQDA#PPA165,M1 , p.163. The resulting value of abandonment real option is $6.6412 million.

## Sources

[1] Mun, J., Real Options Analysis: Tools and Techniques for Valuing Strategic Investment and Decisions, John Wiley & Sons, Inc., Hoboken, 2006, p.26

[2] http://www.finint.ase.ro/materiale/manuale/investment%20valuation_damodaran/ch29.pdf

[3] http://www.real-options.org/

[4] http://www.entrepreneur.com/tradejournals/article/169383068_2.html