Net present value of the project with the put option is approximately $3.05m ($3.50m – $0.45m).

If Swan Co’s offer is not considered, then the project gives a marginal negative net present value, although the results of any sensitivity analysis need to be considered as well. It could be recommended that, if only these results are taken into consideration, the company should not proceed with the project. However, after taking account of Swan Co’s offer and the finance director’s assessment, the net present value of the project is positive. This would suggest that Duck Co should undertake the project.

### LIMITATIONS AND ASSUMPTIONS

Many of the limitations and assumptions discussed below stem from the fact that a model developed for financial products is used to assess flexibility and choice embedded within physical, long-term investments.

#### European-style options or American-style options

The BSOP model is a simplification of the binomial model and it assumes that the real option is a European-style option, which can only be exercised on the date that the option expires. An American-style option can be exercised at any time up to the expiry date. Most options, real or financial, would, in reality, be American-style options.

In many cases the value of a European-style option and an equivalent American-style option would be largely the same, because unless the underlying asset on which the option is based is due to receive some income before the option expires, there is no benefit in exercising the option early. An option prior to expiry will have a time-value attached to it and this means that the value of an option prior to expiry will be greater than any intrinsic value the option may have, if it were exercised.

However, if the underlying asset on which the option is based is due to receive some income before the option’s expiry; say for example, a dividend payment for an equity share, then an early exercise for an option on that share may be beneficial. With real options, a similar situation may occur when the possible actions of competitors may make an exercise of an option before expiry the better decision. In these situations the American-style option will have a value greater than the equivalent European-style option.

Because of these reasons, the BSOP model will either underestimate the value of an option or give a value close to its true value. Nevertheless, estimating and adding the value of real options embedded within a project, to a net present value computation will give a more accurate assessment of the true value of the project and reduce the propensity of organisations to under-invest.

#### Estimating volatility

The BSOP model assumes that the volatility or risk of the underlying asset can be determined accurately and readily. Whereas for traded financial assets this would most probably be the case, as there is likely to be sufficient historical data available to assess the underlying asset’s volatility, this is probably not going to be the case for real options. Real options would probably be available on large, one-off projects, for which there would be little or no historical data available.

Volatility in such situations would need to be estimated using simulations, such as the Monte-Carlo simulation model, with the need to ensure that the model is developed accurately and the data input used to generate the simulations reasonably reflects what is likely to happen in practice.

#### Other limitations of real options

The BSOP model requires further assumptions to be made involving the variables used in the model, the primary ones being:

**(a) **The BSOP model assumes that the underlying project or asset is traded within a situation of perfect markets where information on the asset is available freely and is reflected in the asset value correctly. Further it assumes that a market exists to trade the underlying project or asset without restrictions (that is, that the market is frictionless)

**(b) **The BSOP model assumes that interest rates and the underlying asset volatility remain constant until the expiry time ends. Further, it assumes that the time to expiry can be estimated accurately

**(c) **The BSOP model assumes that the project and the asset’s cash flows follow a lognormal distribution, similar to equity markets on which the model is based

**(d) **The BSOP model does not take account of behavioural anomalies which may be displayed by managers when making decisions, such as over- or under-optimism

**(e) **The BSOP model assumes that any contractual obligations involving future commitments made between parties, which are then used in constructing the option, will be binding and will be fulfilled. For example, in example three above, it is assumed that Swan Co will fulfil its commitment to purchase the project from Duck Co in two years’ time for $28m and there is therefore no risk of non-fulfilment of that commitment.

In any given situation, one or more of these assumptions may not apply. The BSOP model therefore does not provide a ‘correct’ value, but instead it provides an indicative value which can be attached to the flexibility of a choice of possible future actions that may be embedded within a project.

### CONCLUSION

This article discussed how real options thinking can add to investment appraisal decisions and in particular NPV estimations by considering the value which can be attached to flexibility which may be embedded within a project because of the choice managers may have when making investment decisions. It then worked through computations of three real options situations, using the BSOP model. The article then considered the limitations of, and assumptions made when, applying the BSOP model to real options computations. The value computed can therefore be considered indicative rather than conclusive or correct.

The second article will consider how managers can use real options to make strategic investment appraisal decisions.

**Written by a member of the ***Advanced Financial Management* examining team