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It is not unusual for firms to make 'seed' investments into projects, which may even have negative net present values by themselves, but allow the possibility to enter other projects and markets in the future. In such cases the firm is willing to pay a price for the possibility of expanding into these new markets. The option to Expand a project represents the value gained by entering a project today that can offer the ability to participate in future projects with potential upside value.

Inputs

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

- Name of the proposed project. This is used for output display purposes.
- Present Value of expected cash flows that will accrue from expansion. This represents the present value of cash flows received in the future by expanding into new markets, not including the cost of making the expansion.
- Standard deviation of present value. This represents the uncertainty surrounding the cash flows and resulting present value of the cash flows from expansion. Such variations in cash flow estimations are likely to be due to unknown market dynamics that can change the profitability of expansion. 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 present value of investment costs needed to make the expansion. The future investment required to make the expansion represents the exercise price of the option. This can be obtained directly from traditional discounted cash flow analysis, such as that supplied by the Investment Valuation model. The present value of this cost is likely to be higher than the present value of expected cash flows from making the expansion; otherwise the expansion would be undertaken immediately.
- Life of the expansion rights and corresponding risk-free rate. The option to expand the project expires when the opportunity to expand is no longer possible. This is based on the assumption that expansion of the project after this date would yield a net present value of zero as competition would have already entered and dominated the market. As such, the expected life of the option should represent the period in which exclusive rights to expand is expected to prevail for. This may be estimated from previous investments made by the firm or in the industry, market dynamics and competitive environment, 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.
- Annual cost of waiting to expand when expansion is viable. As soon as the present value of cash flows from expansion outweighs the present value of cost to expand, there is a cost of delaying the expansion. This input represents the annual cost of delaying expansion, represented by a percentage of the present value of cash flows expected to be accrued from expansion (the first input). In determining this percentage, consideration should be given to the responsive ability of competitors to make the expansion instead.

Results

Upon clicking OK, the resulting valuation of the option to Expand 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 option to expand 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 calculates the total value of the project including the embedded option value to expand. 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 cash flows from expansion is at or just below the present value of costs to make the expansion.
- 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 Expand.

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