The Option to Abandon a Project

Help for the option to abandon a project in the real options valuation template for Excel

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Real Options Valuation Help Topics: Option Pricing Fundamentals The Option to Delay a Project The Option to Expand a Project The Option to Abandon a Project Binomial Option Pricing Game Theory Analysis

Not all projects or investments are successful and when the cash flows do not measure up to the original expectations, it is useful to value the option to Abandon the project. The option to Abandon a project represents the difference between the present value of continuing the project to the end of its useful life and the present liquidation value of the project.

Inputs

On clicking the 'Start' button in the 'Menu' sheet, a form is displayed for the inputs for the option to Abandon a project. These are:

Name of the existing project. This is used for output display purposes.
Present Value of expected cash flows from continuing with the project as planned. This represents the present value of re-evaluated cash flows received by continuing with the project or investment until the end of its useful life.
Standard deviation of present value. This represents the uncertainty surrounding the cash flows for the remaining expected life of the project which is why the option to abandon it is being considered. Nevertheless, the standard deviation of present value can be estimated by one of the following methods, in order of preference:

If similar projects or investments have been undertaken or made in the past the standard deviation of cash flows resulting from these projects can be used as a proxy for the standard deviation in cash flows for the proposed investment.

Probability analysis can be run on simulations of key inputs, such as revenue and cost drivers, market size and market share, to estimate the standard deviation of the resulting present value. While this type of analysis can be accomplished by using sampling analysis in the Analysis ToolPak add-in shipped with Excel, third-party add-ins can facilitate more sophisticated applications.

The standard deviation of publicly traded firms in the same business or industry can be used a proxy for the proposed investment. This is the least preferred method due to the likely diversity of activities undertaken in other firms and resulting differences in variance characteristics. Such industry specific volatility data can be obtained from third party market data providers (such as those recommended at the Business-Spreadsheets.com web site) and entered into the Pre-Defined sheet for future use across models and proposals. It should be noted that the Pre-Defined sheet can also be utilized to store standard deviation data from similar projects undertaken in the past as described in the first method.

The expected proceeds from abandonment (net of abandonment costs). The expected proceeds from abandonment represent the exercise price on the put option. However, this assumes that the liquidation proceeds do not change over the remaining life of the project. In absence of any contractual agreements on liquidation value, this makes such a value difficult to estimate. In such a case, sensitivity of the valuation to this can be a worthwhile exercise. If the overall proceeds are negative (due to the costs of abandonment outweighing the liquidation value), it would only be worth considering the option to abandon if the remaining present value of cash flows were even more negative.
Time for which the option to abandon holds and corresponding risk-free rate. The option to abandon the project expires when it is no longer possible to liquidate. This is determined on the overall ability to abandon the project and/or contractual arrangements. This may be estimated from market analysis and evaluation of potential synergies that would make the project marketable to interested parties. The risk-free rate corresponding to this period should also be entered here and can be obtained from the equivalent government bond rate prevailing for the same period.
Cost of Abandonment (Dividend Yield). There is a cost to abandoning the project as any value creating cash flows that would have been received after abandonment are forgone. If these cash flow are distributed evenly over the life of the option (n), then the annual cost of abandonment can be expressed as 1/n (e.g. a 5 year option translates into a 20% annual cost). The default option here calculates the cost of abandonment along these lines; however, an alternative percentage annual cost of abandonment can be used here to evaluate other cash inflows or outflows forgone after abandoning the project.

Results

Upon clicking OK, the resulting valuation of the option to abandon is displayed on the 'ModBS' sheet. The first section shows the inputs from the form that can be altered directly here for sensitivity testing.

The next section displays the Outputs, including the key calculation parameters, overall valuation of the option to abandon, and a textual summary of the results. The parameters N(d1) and N(d2) represent the range of probability that the project will be abandoned before the date when it is no longer possible to abandon. The detailed formula for actual valuation of the put option can be viewed by Clicking on the Overview button in the top right corner of this section. Based on this valuation and the traditional net present value of the projects remaining cash flows, the textual summary calculates the total value of the project including the embedded option value to abandon. This summary can be useful for direct insertion into business case proposals and reports.

The final section displays the Partials of the valuation, which are essentially calculations to test the sensitivity of the options value to changes in input values. These are:

Delta. Delta represents the amount that the option price will move given a small change in value of cash flows from expansion. An increase in volatility will tend to move the delta of the option towards 50.
Gamma. Gamma represents the amount that the options delta will move given a small change in value of the underlying asset. Gamma increases as expiration approaches.
Theta. Theta represents the rate that the value of the option decreases, as the time remaining to expiration decreases. Theta is also referred to as time decay or amortization. Theta is highest when the present value of the project's remaining cash flows is at or just below the expected net proceeds from abandonment.
Vega. Vega represents the options sensitivity to changes in volatility. Longer term options are more sensitive to changes in volatility and therefore have higher Vega.
Rho. Rho represents the options change in value given a change in interest rates (risk-free rate). Increased interest rates will decrease the value of put options, such as the option to Abandon.

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