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Option value = .5MAX
= .5 MAX
Now the value of flexibility has increased to $673, because the amount of uncertainty has increased. The value of an option increases as the variability in the value of the underlying risky asset (the cash flow per unit) increases. As with financial options, the value of a real option depends on five parameters: the market value of the underlying asset on which the option is contingent; the exercise price of the option; the time remaining until the maturity of the option; the volatility of the underlying asset, and the risk-free rate of interest. These are all clearly defined for financial options, but require better understanding for real options. A sixth parameter is the amount of dividends paid by the underlying risky asset. We shall come back to it a little later.
The parameters that affect the value of a real option are summarized in Exhibit 20.2. Note that an important difference between financial and real options is that management can affect the value of the underlying risky asset (a physical project under its control) while financial options are side bets owned by third parties that cannot affect the outcome of the underlying asset (e.g., a share of IBM).
Without training, executives often fail to recognize real options and how valuable they can be. One example is a story about the life insurance industry. In the early 1970s, it was common to be able to buy a whole life policy with a clause that allowed you to borrow against the cash value of the policy at, let's say, a 9 percent interest rate, for the life of the policy. At the time, interest rates were about 4 percent on long-term government bonds. No one expected that they would go as high as 9 percent. But the
Exhibit 20.2 Option Value Is Determined by Six Variables
life of a policy can be long—as long as the life expectancy of the policyholder. What kind of option was imbedded in the contract, and what were the parameters? The policyholder had a long-term call option on the right to borrow (i.e., on the value of a bond issued by the insurance company) against the cash value (which determines the amount of the loan) of the policy at a fixed rate, for the life of the policy. The underlying uncertainty is the variance of interest rates. In 1981-1982 when interest rates went to double-digit levels, policyholders began to borrow at 9 percent, invest the money in government bonds at double-digit rates, and keep the difference. The losers were the life companies that had to borrow at double-digit rates and receive 9 percent. Several life companies went bankrupt as a result. The executives who originally sold life policies with these valuable options imbedded in them had not clearly understood the value of the options in the life contracts they were writing.
T axonomy of Options
To identify potential operating flexibility and strategic factors, we can classify asset options into five mutually exclusive (but not exhaustive) categories.
Abandonment option. The option to abandon (or sell) a project—the right to abandon an open pit coal mine—is formally equivalent to an American put
option on a stock.3 If the bad outcome occurs at the end of the first period, the decision maker may abandon the project and realize the expected liquidation value. Then, the expected liquidation (or resale) value of the project may be thought of as the exercise price of the put. When the present value of the asset falls below the liquidation value, the act of abandoning (or selling) the project is equivalent to exercising the put. Because the liquidation value of the project sets a lower bound on the value of the project, the option to liquidate is valuable. A project that can be liquidated is worth more than the same project without the possibility of abandonment.
Option to defer development. The option to defer an investment to develop a property is formally equivalent to an American call option on the stock. The owner of a lease on an undeveloped oil reserve has the right to acquire a developed reserve by paying a lease-on-development cost. The owner can defer the development process until oil prices rise. In other words, the managerial option implicit in holding an undeveloped reserve is a deferral option. The expected development cost may be thought of as the exercise price of the call. The net production revenue less depletion of the developed reserve is the opportunity cost incurred by deferring the investment. If this opportunity cost is too high, the decision maker may want to exercise the option (that is, develop the reserve) before its relinquishment date.
Option to expand or contract. The option to expand the scale of a project is formally equivalent to an American call option on the stock. Management may choose to build capacity in excess of the expected level of output so that it can manufacture at a higher rate if the product is more successful than was anticipated. The expansion option gives management the right, but not the obligation, to make additional follow-on investment (for example, to increase the production rate) if project conditions turn out to be favorable. The option to contract the scale of a project's operation is formally equivalent to an American put option on stock. Many projects can be engineered so that output can be contracted. Foregoing future spending on the project is equivalent to the exercise price of the put.