**Richard Shaw provides an insight into the valuation of projects.**

The real options approach to the analysis of capital investment projects can be found in many areas, for example the development of natural oil fields, the valuation of high-tech companies, the valuation of manufacturing flexibility, and the valuation of entry to or exit from a market. The nature of the optionality may take a number of forms. Examples are:

- the option to make follow-on investments if an immediate project is successful;

- the option to abandon a project if the immediate project is not successful;

- the option to wait before investing, and;

- the option to vary a firm's output or production methods.

The first three of these are described further in this article.

Traditional NPV approach to the valuation of projects

The traditional net present value (NPV) approach to the valuation of capital investment projects is to calculate the expected present value of future cashflows (V) and then to subtract the present value of the cost of investment (I). The discounting is performed using a risk-adjusted discount rate, eg capital asset pricing model (CAPM).

Projects are treated as independent and an immediate accept or reject decision is often made based on the value of the NPV (= V-I).

This approach does not allow for the management flexibility that is often present. Management can add value by reacting to changing conditions, eg by expanding operations if the outlook seems attractive or reducing the scope of activities if the future outlook is unattractive. The traditional NPV approach also ignores the strategic value of projects, such as the opportunity to expand into a new market, to develop natural resources, or technology.

When considering uncertainty and managerial flexibility, NPV does not properly capture the non-linear nature of the cashflow distribution or the changing risk profile over time.

Many investment opportunities have options embedded in them and the traditional NPV misses this extra value because it treats investors as passive.

The real options approach to the valuation of projects

The real options approach to the capital investment decision provides a different insight into the valuation of projects. Real options can capture the value of managerial flexibility and strategic value, and provide intuition that may be contrary to popular thinking.

A simple example will illustrate the embedded options nature of a project.

Consider the development of a new personal computer (PC1) with an initial investment of £200m and an expected present value of future cashflows using the risk-adjusted discount rate equal to £175m. Using a traditional approach, the NPV = -£25m. Now consider the value of the option to make a follow-on investment in a superior PC (PC2) in three years' time (this investment in PC2 being too expensive unless an entry is made with PC1). This follow-on investment may either be a good investment or a bad one. This further investment also requires £600m in three years' time and will produce an expected present value of future cashflows equal to £500m at that time, which is equivalent to a value of £290m now. Using a traditional NPV approach, the value of this additional investment in three years' time is -£100m.

As these future cashflows are very uncertain, they have a high standard deviation of 40% pa. The value of the cashflows of £290m can be viewed as a stock that evolves over time with a standard deviation of 40% pa.

If the expected value of these future cashflows in three years' time is greater than £600m then the option to invest in PC2 proceeds. If it is less than £600m then no further investment will take place. This assumes that there are no further embedded options present, ie options on PC3 or PC4, as a result of developing PC2. This option to invest further has the features of a European call option, exercisable in three years' time with an exercise price of £600m.

The valuation of this option, using Black-Scholes (assuming the underlying conditions hold) turns out to be equal to £35m. This now produces an overall project NPV of -£30m plus £35m, which is equal to £5m. So entering the market to develop PC1 begins to look attractive, even though under a traditional approach the NPV is negative for PC1 on a stand-alone basis.

The real options approach implicitly assumes that each real investment opportunity has a 'double', a security or portfolio with identical risk characteristics to the capital investment being evaluated.

The real options valuation approach can be summarised as follows:

Real options NPV =

traditional NPV + real option value

Call options stock options v

real options

The valuation of options on stocks is a function of certain parameters; the analogous relationships in the valuation of real options are as follows:

- Stock price PV of expected project cashflows.

- Exercise price investment cost.

- Expiry date date until which the investment opportunity remains open.

- Stock return uncertainty project value uncertainty.

- Dividends operating cashflow or competitive erosion.

The riskless interest rate is the same for both stock and real options.

Different forms of optionallity

Option to expand (this is described above)

Sometimes there is a strategic value in taking on negative NPV projects, in that the project's payoff may contain call option features, as connected future project opportunities, in addition to the immediate negative NPV, the value of these call options being greater than the negative NPV.

Option to abandon

The option to abandon a project can be viewed as a put option against the failure of a project. The exercise price is equal to the value of the project's assets if sold or if used for alternative purposes. The exercise of this put option would occur if this were greater than the expected present value of future cashflows.

Option to wait

Sometimes it may be beneficial to defer the start of a project that currently has a positive NPV. This is because there is more value in waiting. This is analogous to the valuation of American call options (ie early exercise is allowable). Investing in a project immediately can be viewed as exercising an option, but sometimes it pays to wait and keep the option alive. The value of waiting is greatest when the cashflows forgone by waiting are small and there is greater volatility over future cashflows.

Real options approach complexities

Real options are more often complex in practice:

- Cost of further investment or the price of abandonment is likely to vary over time.

- Abandonment of a project may occur at any time in a project and the reinstatement of a project may be possible.

- Postponement of a project and missing out on the first year's cashflows in the anticipation of learning from them may sometimes provide no additional information.