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 the P4 paper, 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 the P4 paper, 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 P4 paper 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 P4 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. In each of the three examples the N(d1) and N(d2) figures are determined using the Excel normal distribution formula: =NORMSDIST(d1 or d2 cell reference). Using the normal distribution tables that are provided in examinations to calculate the value of real options may result in small rounding differences, but are equally acceptable.
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 $35m.
The company has forecast the following end of year cash flows for the four-year project.
Year | 1 | 2 | 3 | 4 |
---|---|---|---|---|
Cash flows ($m) | 20 | 15 | 10 | 5 |
The relevant cost of capital for this project is 11% and the risk free rate is 4.5%. The likely volatility (standard deviation) of the cash flows is estimated to be 50%.
Solution:
NPV without any option to delay the decision
Year | Today | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|
Cash flows ($) | -35m | 20m | 15m | 10m | 5m |
PV (11%) ($) | -35m | 18.0m | 12.2m | 7.3m | 3.3m |
NPV = $5.8m
Supposing the company does not have to make the decision right now but can wait for two years before it needs to make the decision.
NPV with the option to delay the decision for two years
Year | 3 | 4 | 5 | 6 |
---|---|---|---|---|
Cash flows | 20m | 15m | 10m | 5m |
PV (11%) | 14.6m | 9.9m | 5.9m | 2.7m |
Variables to be used in the BSOP model
Asset value (Pa) = $14.6m + $9.9m + $5.9m + $2.7m = $33.1m
Exercise price (Pe) = $35m
Exercise date (t) = Two years
Risk free rate (r) = 4.5%
Volatility (s) = 50%
Using the BSOP model
d1 | 0.401899 |
d2 | -0.30521 |
N(d1) | 0.656121 |
N(d2) | 0.380103 |
Call value | $9.6m |
Based on the facts that the company can delay its decision by two years and a high volatility, it can bid as much as $9.6m instead of $5.8m for the exclusive rights to undertake the project. The increase in value reflects the time before the decision has to be made and the volatility of the cash flows.
Example 2: Exploiting a follow-on project
A company is considering a project with a small positive NPV of $3m but there is a possibility of further expansion using the technologies developed for the initial project. The expansion would involve undertaking a second project in four years’ time. Currently, the present values of the cash flows of the second project are estimated to be $90m and its estimated cost in four years is expected to be $140m. The standard deviation of the project’s cash flows is likely to be 40% and the risk free rate of return is currently 5%.
Solution:
The variables to be used in the BSOP model for the second (follow-on) project are as follows:
Asset Value (Pa) = $90m
Exercise price (Pe) = $140m
Exercise date (t) = Four years
Risk free rate (r) = 5%
Volatility (s) = 40%
Using the BSOP model
d1 | 0.097709 |
d2 | -0.70229 |
N(d1) | 0.538918 |
N(d2) | 0.241249 |
Call value | $20.85m |
The overall value to the company is $23.85m, when both the projects are considered together. At present the cost of $140m seems substantial compared to the present value of the cash flows arising from the second project. Conventional NPV would probably return a negative NPV for the second project and therefore the company would most likely not undertake the first project either. However, there are four years to go before a decision on whether or not to undertake the second project needs to be made. A lot could happen to the cash flows given the high volatility rate, in that time. The company can use the value of $23.85m to decide whether or not to invest in the first project or whether it should invest its funds in other activities. It could even consider the possibility that it may be able to sell the combined rights to both projects for $23.85m.
Example 3: The option to abandon a project
Duck Co is considering a five-year project with an initial cost of $37,500,000 and has estimated the present values of the project’s cash flows as follows:
Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Present values | 1,496.9 | 4,938.8 | 9,946.5 | 7,064.2 | 13,602.9 |
Swan Co has approached Duck Co and offered to buy the entire project for $28m at the start of year three. The risk free rate of return is 4%. Duck Co’s finance director is of the opinion that there are many uncertainties surrounding the project and has assessed that the cash flows can vary by a standard deviation of as much as 35% because of these uncertainties.
Solution:
Swan Co’s offer can be considered to be a real option for Duck Co. Since it is an offer to sell the project as an abandonment option, a put option value is calculated based on the finance director’s assessment of the standard deviation and using the Black-Scholes option pricing (BSOP) model, together with the put-call parity formula.
Although Duck Co will not actually obtain any immediate cash flow from Swan Co’s offer, the real option computation below, indicates that the project is worth pursuing because the volatility may result in increases in future cash flows.
Without the real option
Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Present values | 1,496.9 | 4,938.8 | 9,946.5 | 7,064.2 | 13,602.9 |
Present value of cash flows approx. = $37,049,300
Cost of initial investment = $37,500,000
NPV of project = $37,049,300 – $37,500,000 = $(450,700)
With the real option
The asset value of the real option is the sum of the PV of cash flows foregone in years three, four and five, if the option is exercised ($9.9m + $7.1m + $13.6m = $30.6m)
Asset value (Pa) | $30.6m |
Exercise Price (Pe) | $28m |
Risk-free rate (r) | 4% |
Time to exercise (t) | Two years |
Volatility (s) | 35% |
d1 | 0.588506 |
d2 | 0.093531 |
N(d1) | 0.721904 |
N(d2) | 0.537259 |
Call Value | 8.20 |
Put Value | $3.45m |
Net present value of the project with the put option is approximately $3m ($3.45m – $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 P4 examining team