Abstract
The option pricing theory has wide applicability in corporate finance, but it is also increasingly used to analyze the effectiveness of non-financial (material) investments. In traditional investment analysis, a project or a new investment should be accepted only if the returns on the project exceed the hurdle rate; in the context of cash flows and discount rates, this translates into projects with positive net present values (NPV). There is no doubt that it does not take full account of the numerous options that usually relate to developer investment. However, in many cases, the valuation of real options is more difficult than the valuation of options for financial assets. In this paper, we will analyze one of the options, which isembedded in capital budgeting projects - the option to delay a project, especially when a the company has exclusive rights to the project. The value of the option is largely derived from the variance in cash flows – the higher the variance, the higher the value of the project delay option. The variance in the present value of cash flows from the project can be estimated in different ways, however, in the case of non-financial investment projects, these methods are very limited. We are analyzing the possibility of estimating this volatility, taking into account the fact that the forecasted cash flows may show varying volatility in individual years. The paper shows, that by using a probability-based valuation model (using the Crystal Ball techniques) it is possible to incorporate uncertainty into the analysis. The method of presented volatility estimation can be applied by taking into account the randomness of many input data to the project.
Highlights
Projects are typically analyzed based upon their expected cash flows and discount rates at the time of the analysis; the net present value calculated on that basis is a measure of its value and acceptability at that time
If the expected cash flows on the project were known with certainty and were not expected to change, there would be no need to adopt an option pricing framework, since there would be no value to the option
Calculating the exclusive rights to this Project using the Black-Scholes formula for different variance parameters we obtain the results shown in the figure below
Summary
Projects are typically analyzed based upon their expected cash flows and discount rates at the time of the analysis; the net present value calculated on that basis is a measure of its value and acceptability at that time. Expected cash flows and discount rates change over time and so does the net present value. C – Call Value, V – current value of the underlying asset (present value of expected cash inflows from Project), X – strike price of the option (an initial up-front investment) t – life to expiration of the option (period of exclusive rights to Project), V variance (volatility) in the value of the underlying asset (the variance/volatility in the present value of cash flows from Project), r – riskless interest rate corresponding to the life of the option, N(d1) – cumulative distribution of the standard normal distribution for the argument d1, N(d2) – cumulative distribution of the standard normal distribution for the argument d2; d1 ln§ V· ©X1. Assuming (for the analyzed case study) that: Project will generate 100 000 EUR in after tax cash flows for the 5 years, discount rate is 10% (r=10%), we obtain:
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