The Option to Delay a Project

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

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Under traditional investment analysis (such as that accomplished by the Investment Valuation model), it is reasonable to accept or reject an investment proposal based on its net present value based on the expected cash flows and discount rates at the time of the analysis. However, such cash flows and discount rates change over time, therefore a proposal that has a negative net present value today may have a positive net present value in the future. The option to Delay a project represents the value gained by waiting to take advantage of any upside volatility in the net present value.

Inputs

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

• Name of the proposed project. This is used for output display purposes.
• Present Value of cash flows from investing in the project today. This represents the present value of cash flows received by making the investment but does not include the actual investment cost. This input can be obtained directly from traditional discounted cash flow analysis, such as that supplied by the Investment Valuation model.
• Standard deviation of present value. This represents the uncertainty surrounding the cash flows and resulting present value of the investment. Such variations in cash flow estimations are likely to be due to uncertain market size and share, technology shifts, and/or supply costs.  Nevertheless, the standard deviation of present value can be estimated by one of the following methods, in order of preference:
1. 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.
2. 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.
3. 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 present value of investment needed to take the project today.  The option to delay the project is exercised when it is decided to invest in it. The investment required, therefore, represents the exercise price of the option. This can be obtained directly from the traditional discounted cash flow analysis, such as that supplied by the Investment Valuation model.
• Life of the project rights and corresponding risk-free rate. The option to delay the investment expires when net present value from doing so is zero.  This is based on the assumption that the market forces of competition will eventually drive the return down to the discount rate. As such, the expected life of the option should represent the period in which exclusive rights or competitive advantage is expected to prevail for. This may be estimated from previous investments made by the firm or in the industry, or from the capital budgeting assumptions used in the traditional discounted cash flow analysis.  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 Delay (dividend yield). For every year after the net present value of the project turns positive, there is a cost of delaying the project equal to the positive cash flows forgone by not undertaking it. If these cash flow are distributed evenly over the life of the option (n), then the annual cost of delay can be expressed as 1/n (e.g. a 5 year option translates into a 20% annual cost of delay). The default option here calculates the cost of delay along these lines; however, an alternative percentage annual cost of delay can be used here to evaluate other cash inflows or outflows forgone on delaying the investment.

Results

Upon clicking OK, the resulting valuation of the option to Delay 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 delay, and a textual summary of the results. The parameters N(d1) and N(d2) represent the range of probability that the project will become viable before the end of the options life. The detailed formula for actual valuation of the call 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 project, the textual summary concludes as to whether the project should or should not be undertaken immediately. 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 the project cash flows. 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 project cash flows. 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 cash flows from the project is at or just below the present value of costs needed to make the investment.
• 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 increase the value of call options, such as the option to Delay.

Screenshot: The Option to Delay a Project

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