Volatility Estimation of Forecasted Project Returns for Real Options Analysis

Real Options Analysis is a technique that offers advantages over the traditional Discounted Cash Flow (DCF) approach for determining project valuation. Although options analysis uses some of the same input variables used in the DCF approach, it requires one additional variable, the volatility of the project’s forecasted returns, which is notoriously difficult to estimate reliably. There are several techniques that are used to model volatility when relevant historical data from similar projects are not available. This paper reviews the nature and potential limitations of these approaches, and provides recommendations regarding the appropriate uses of the estimates resulting from these methods. Introduction Projects are periodically evaluated to determine if they are feasible and worthy of continued funding. Most organizations have more ideas than they have resources to fund them, so projects compete for available resources, including money and talent. The most widely used technique for evaluating projects is discounted cash flow. In this method, the net present value (NPV) is determined by discounting forecasted future cash flows by a required rate of return. Despite its wide use, DCF suffers from a problem of being too conservative. Good ideas are sometimes not pursued because the method provides an NPV that is too low. The difficulty lies in the fact that management has flexibility during the course of development projects, and this flexibility is not accounted for in the DCF technique. Projects with very high net present values are considered good investments from the DCF perspective. Projects with net present values that are negative are often abandoned because they do not appear to deliver the required return. Projects with net present values close to zero are dealt with in a variety of ways, and significant time is often spent trying to determine if such projects should be funded or abandoned. Real options analysis can be used to add insight to the funding decision, especially when DCF analysis finds a net present value that is close to zero. Real options analysis offers an alternative that determines a value for managerial flexibility and provides an expanded net present value (ENPV). In the case of funding under certainty, discounted cash flow analysis works very well. Under conditions of uncertainty, real options analysis may be preferred because project volatility is taken into consideration. There are five primary management options regarding R&D projects. First, a project can be abandoned if its salvage value exceeds the project’s future returns at some time in the future. Second, a project may be delayed if future information will decrease the decision risks. Projects may be expanded or contracted at a later date, depending on market conditions. Finally, many projects occur in several phases, each phase dependent on the success of a previous one. Each of these scenarios represents distinct options that can be simulated. All of these options are dependent on five variables: the future cash flows, the cost of implementation, the time horizon under consideration, the risk-free cost of money, and the volatility of the future cash flows. In discounted cash flow analysis, the required rate of return is adjusted to reflect the risk. Instead of using the weighted average cost of capital (WACC) as the interest rate, many firms increase the required rate to compensate for risk, creating what is known as the “hurdle rate”. High-risk projects carry higher required rates of return, which in turn decrease the NPV. The difficulty is that there is no direct relation between risk and the rate of return. Assignment of a hurdle rate must be arbitrary. In real options analysis, rather than directly adjusting the required rate of return for the level of risk, the risk-free rate of return is used in conjunction with a separate volatility parameter. It is this inclusion of volatility that mathematically differentiates real options analysis from discounted cash flow. Options analysis recognizes that different types of projects will have different levels of volatility, or risk. Under real options analysis, when the volatility approaches zero, the valuation approaches the NPV. The volatility is the most difficult of all of the variables to forecast and measure, and the option value is highly dependent on the volatility estimate. A variety of methods can be used for estimating a project’s volatility. Background A financial option is an asset that gives the owner the right, without an obligation, to buy or sell another asset (such as a quantity of corporate stock) for a specified price at or before some specified time in the future. An option that can be exercised only on its expiration date is known as a European option. An option that can be exercised at any time up to its expiration date is known as an American option. The option creates an expanded net present value (ENPV), which is defined as (Trigeorgis, 1996; Contractor, 2001): ENPV = NPV + Option Value (1) When NPV is quite large, the option value will not have a significant impact on the decision: the NPV signals that the project is worthy of investment. When NPV is very negative, even the best option values will not be large enough to create a positive ENPV, and the project should not be pursued. If the future cash flows are known with certainty, then the discounted cash flow technique should be used. Real options have their best use under conditions of uncertainty, and where management has the ability and the willingness to exercise its flexibility. The option value places a price on the worth of this flexibility, and the ENPV identifies how much the firm should be willing to pay to keep the project (or option) open. Call Options. A call option gives the owner the right to buy an asset for a specified price, called a strike price or exercise price, on or before a specified expiration date. For example, an American call option on Microsoft stock with an exercise price of $27.50 and an expiration date of April gives the option’s owner the right to purchase Microsoft stock for $27.50 at any time until its expiration date in April. This call option flexibility will have a cost. The owner of the option is not required to exercise the option; in other words, there is no obligation to purchase the stock. If the option is not exercised, it simply expires worthless. If the price of the stock is greater than the strike price, then it may be in the owner’s best interest to exercise the option. If the stock price exceeds the strike price, the value of the option will be positive, and the option itself can potentially be sold at a profit. If the stock price is below the strike price at the expiration date, there is also no obligation to purchase the stock, and the option is allowed to expire. At this point, the value of the option is zero. The value of the option never goes below zero because there is no obligation to purchase the stock at a loss. An option is considered to be in the money when exercising the option would create a profit for its owner. An option is considered to be out of the money when exercising the option will not create a profit. An option is at the money when the strike price is equal to the price of the underlying stock. Put Options. A put option gives the owner the right to sell an asset for a specified price on or before a specified expiration date. For example, an American put option on Microsoft stock with an exercise price of $27.50 and an expiration date of next April gives the option’s owner the right to sell Microsoft stock for $27.50 at any time until its expiration date in April. The owner of the option is not required to exercise the option; there is no obligation to sell the stock. If the price of the stock is less than the strike price, then it may be profitable to exercise the option. If the stock price is less than the strike price of a put option, the value of the put option will be positive and the option itself may be sold at a profit. If the stock price is above the strike price of the put option on the expiration date, there is no obligation to sell the stock and the option is allowed to expire. Because there is no obligation to sell the stock at a loss, the value of the put option never goes below zero. Valuation of Call and Put Options. Fisher Black and Myron Scholes (1973), along with Robert Merton (1973), were the first to publish an accepted pricing model for options. The Black-Scholes model continues to be one of the most widely used methods of calculating option prices, despite many modifications that others have proposed over the years. The equation approximates the value of a European call option, based on the current stock price (S0), strike price (X), volatility (σ), risk-free interest rate (r), and time to expiration (T). The equation is: 0 1 2 ( ) ( ) rT C S N d Xe N d − = − (2)