Standard Net Present Value (NPV) analysis, in which future cash flows are discounted to their present value implicitly assumes that firms hold real assets passively. In other words, standard NPV analysis of a firm or project does not reflect the value of management and does not work for projects that during their lifetime have imbedded options, hereafter called real options. The reason for this is that the risk of the imbedded real option changes continuously and therefore there is no fixed opportunity cost of capital at which to discount. In this section, we'll look at examples of real options in capital budgets, and how the ideas behind valuing financial options (such as puts and calls) can be applied to real financial business evaluations. While the underlying for a financial option is a security such as a share of common stock, the underlying for a real option is a tangible asset, for example a project or a business unit.

**Examples of real world options**

- Option to make follow-on investments if the project succeeds

e.g. buy neighboring land for possible factory expansion

- The option to abandon a project

e.g. buy equipment easy to sell-on or decommission

- The option to wait before investing

e.g. buy mineral rights to land where not economic to extract

- The option to vary the type of production or mix

e.g. purchase machine that can be programmed to make a variety of products

These real options allow managers to act in response to circumstances and new, additional information, the value of which is not captured in a traditional NPV analysis.

**How do we value real options?**

In their famous paper about option pricing, Cox et al (1979) presented a simple discrete-time model for valuing options. They concluded that the price of a financial option should always be equal to the expectation, in a risk-neutral world, of the discounted value of the payoff it will receive. However, it is important to note that this does not imply that the equilibrium expected rate of return on the call is the risk-free interest rate. Their conclusion comes however from a risk-neutral, no-arbitrage, argument that gives results equivalent to the famous Black-Scholes equation.

We can however use this conceptual model of a risk-free world, to construct a model to value a real option as follows:

We make a separate, parallel model to our standard NPV model:

Use the same projections except with inflation at the risk-free rate

Simulate the extra cashflows arising just from exercising the option

Discount these cashflows at the risk-free rate

Calculate the expected value of the resultant distribution

This expected value of the resultant distribution is equal to the value of the real option (Cox and Rubinstein, 1985). The real option value is then added to the expected value of the standard NPV to get the total project value.

Model Real Option provides an example.

The links to the Real Option software specific models are provided here:

In this example, we start with the same situation as in the model "NPV of a capital investment". However, in addition to this static NPV model, we added the option of production for large factories in California. We believe that fuel cells may take off in three years for these large factories. If we go ahead with our investment now, and if the price ever exceeds $63, we will enter this market for no extra capital or operating costs.

The question is now to calculate the total value of the project: the NPV value of our investment plus the revenue from the option (discounted at the risk free rate, rf, see above) to enter this new market in California.

The model shows the solution of this problem. It appears that the real options value of this expansion-option is considerable and ignoring this value would certainly underestimate the true value of this project.

**Further reading**

- Black F and Scholes M (1973). "The Pricing of Options and Corporate Liabilities", J Political Economy, 81 (May-June) 637-654.
- Brealey R A and Myers S C (2000). Principles of Corporate Finance, McGraw-Hill.
- Cox J, Ross S and Rubenstein M (1979). "Option pricing: a Simplified Approach." J Financial Economics 7 229-263.
- Hull J (1997). Options, futures and other derivatives. Prentice Hall.
- Merton R C (1973). "Theory of Rational Option Pricing", Bell J of Economics and Management science, 4 141-183.
- Wilmott P (1998). The Theory and Practice of Financial Engineering, John Wiley and Sons.