Chap 6 Compound and Switching Options
Compound and Switching Options • Compound options are options whose value is contingent on other options. • Switching options allow the owner to start up and shut down operations, to switch from one mode of operation to another, or to enter and exit an industry.
Valuing compound options • Compound options are options whose value is contingent on the value of other options. • This type of compounding is called a simultaneous compound option because the equity and the call option on equity are alive simultaneously. • Compound options can also be sequential. • Any type of phased investment fits this category.
Methodology for simultaneous compound options • The key feature of “simultaneous” compound options is the underlying option and the option on it are simultaneous available. • They are not sequential in time. • The solution proceeds in two steps.
First, we value the equity as an American call on the value of the firm with its exercise price equal to the face value of debt.
Note that since the entity value of the firm was assumed to be $1,000, the market value of its risky debt must be $1,000 - $365.56 = $634.44.
Since it matures in 3 years with a face value of $800, its yield to maturity is 8.03 percent.
Since both options are alive during the same interval of time, the call contingent on the equity is a simultaneous compound option.
Review of compound options • With sequential compound options the order of economic priority is the opposite of the time sequence. • In our example, the compound option was worth $30.93.
Valuing switching options • Switching options give their owner the right to switch between two modes of operation at a fixed cost. • Assume that a company already has a manufacturing facility operating that uses technology X. • Due to increased demand, we are considering a new factory with the following options : to use technology X again, to use alternative technology Y, or to invest in a flexible technology Z that allows us to switch from X to Y for $15 and from Y to X for $10.
These switching costs are designed Cxy and Cyx respectively. The flexible technology Z requires a higher investment of $110.
We ask the same question twice : Assuming we have been in mode X at the previous state, would we stay in X or would we switch to Y and pay the switching cost? Assuming we have been in mode Y at the previous state, would we stay in Y or would we switch to X and pay the switching cost?