Subject:

## Robert Kiyosaki - 4 Assets that Make People Rich

Real options’ valuation methodology adds to the conventional net present value (NPV) estimations by taking account of real life flexibility and choice.

This is the first of two articles which considers how real options can be incorporated into investment appraisal decisions.

This article discusses real options and then considers the types of real options calculations which may be encountered in *Advanced Financial Management*, through three examples. The article then considers the limitations of the application of real options in practice and how some of these may be mitigated.

The second article considers a more complex scenario and examines how the results produced from using real options with NPV valuations can be used by managers when making strategic decisions.

### Net present value (NPV) and real options

The conventional NPV method assumes that a project commences immediately and proceeds until it finishes, as originally predicted.

Therefore it assumes that a decision has to be made on a now or never basis, and once made, it cannot be changed. It does not recognise that most investment appraisal decisions are flexible and give managers a choice of what actions to undertake.

The real options method estimates a value for this flexibility and choice, which is present when managers are making a decision on whether or not to undertake a project.

Real options build on net present value in situations where uncertainty exists and, for example: (i) when the decision does not have to be made on a now or never basis, but can be delayed, (ii) when a decision can be changed once it has been made, or (iii) when there are opportunities to exploit in the future contingent on an initial project being undertaken.

Therefore, where an organisation has some flexibility in the decision that has been, or is going to be made, an option exists for the organisation to alter its decision at a future date and this choice has a value.

With conventional NPV, risks and uncertainties related to the project are accounted for in the cost of capital, through attaching probabilities to discrete outcomes and/or conducting sensitivity analysis or stress tests.

Options, on the other hand, view risks and uncertainties as opportunities, where upside outcomes can be exploited, but the organisation has the option to disregard any downside impact.

Real options methodology takes into account the time available before a decision has to be made and the risks and uncertainties attached to a project. It uses these factors to estimate an additional value that can be attributable to the project.

### Estimating the value of real options

Although there are numerous types of real options, in *Advanced Financial Management*, candidates are only expected to explain and compute an estimate of the value attributable to three types of real options:

**(i) **The option to delay a decision to a future date (which is a type of call option)**(ii) **The option to abandon a project once it has commenced if circumstances no longer justify the continuation of the project (which is a type of put option), and**(iii) **The option to exploit follow-on opportunities which may arise from taking on an initial project (which is a type of call option).

In addition to this, candidates are expected to be able to explain (but not compute the value of) redeployment or switching options, where assets used in projects can be switched to other projects and activities.

For the *Advanced Financial Management* exam purposes, it can be assumed that real options are European-style options, which can be exercised at a particular time in the future and their value will be estimated using the Black-Scholes Option Pricing (BSOP) model and the put-call parity to estimate the option values.

However, assuming that the option is a European-style option and using the BSOP model may not provide the best estimate of the option’s value (see the section on limitations and assumptions below).

Five variables are used in calculating the value of real options using the BSOP model as follows:

- The underlying asset value (Pa), which is the present value of future cash flows arising from the project.
- The exercise price (Pe), which is the amount paid when the call option is exercised or amount received if the put option is exercised.
- The risk-free (r), which is normally given or taken from the return offered by a short-dated government bill.
Although this is normally the discrete annualised rate and the BSOP model uses the continuously compounded rate, for

*Advanced Financial Management*purposes the continuous and discrete rates can be assumed to be the same when estimating the value of real options. - The volatility (s), which is the risk attached to the project or underlying asset, measured by the standard deviation.
- The time (t), which is the time, in years, that is left before the opportunity to exercise ends.

The following three examples demonstrate how the BSOP model can be used to estimate the value of each of the three types of options.

**Example 1: Delaying the decision to undertake a project**A company is considering bidding for the exclusive rights to undertake a project, which will initially cost $35m.

The company has forecast the following end of year cash flows for the four-year project.