File Names: Real Options – Contraction American and European Option; Real Options – Contraction Bermudan Option; Real Options – Contraction Customized Option
Location: Modeling Toolkit | Real Options Models
Brief Description: Computes the contraction option (American, Bermudan, and European) with customizable and changing input parameters using closed-form models and custom binomial lattices
Requirements: Modeling Toolkit, Real Options SLS
A Contraction Option evaluates the flexibility value of being able to reduce production output or to contract the scale and scope of a project when conditions are not as amenable, thereby reducing the value of the asset or project by a Contraction Factor, but at the same time creating some cost Savings. As an example, suppose you work for a large aeronautical manufacturing firm that is unsure of the technological efficacy and market demand for its new fleet of long-range supersonic jets. The firm decides to hedge itself through the use of strategic options, specifically an option to contract 10% of its manufacturing facilities at any time within the next five years (i.e., the Contraction Factor is 0.9).
Suppose that the firm has a current operating structure whose static valuation of future profitability using a DCF model (in other words, the present value of the expected future cash flows discounted at an appropriate market risk-adjusted discount rate) is found to be $1,000M (PV Asset). Using Monte Carlo simulation, you calculate the implied volatility of the logarithmic returns of the asset value of the projected future cash flows to be 30%. The risk-free rate on a riskless asset (five-year U.S. Treasury Note with zero coupons) is found to be yielding 5%.
Further, suppose the firm has the option to contract 10% of its current operations at any time over the next five years, thereby creating an additional $50 million in savings after this contraction. These terms are arranged through a legal contractual agreement with one of the firm’s vendors, which had agreed to take up the firm’s excess capacity and space. At the same time, the firm can scale back and lay off part of its existing workforce to obtain this level of savings (in present values).
The results indicate that the strategic value of the project is $1,001.71M (using a 10-step lattice as seen in Figure 181.1), which means that the NPV currently is $1,000M and the additional $1.71M comes from this contraction option. This result is obtained because contracting now yields 90% of $1,000M + $50M, or $950M, which is less than staying in business and not contracting and obtaining $1,000M. Therefore, the optimal decision is not to contract immediately but keep the ability to do so open for the future. Hence, in comparing this optimal decision of $1,000M to $1,001.71M of being able to contract, the option to contract is worth $1.71M. This should be the maximum amount the firm is willing to spend to obtain this option (contractual fees and payments to the vendor counterparty).
Figure 181.1: American and European options to contract with a 10-step lattice
In contrast, if Savings were $200M instead, then the strategic project value becomes $1,100M, which means that starting at $1,000M and contracting 10% to $900M and keeping the $200 in savings yields $1,100M in total value. Hence, the additional option value is $0M which means that it is optimal to execute the contraction option immediately as there is no option value and no value to wait to contract. The value of executing now is $1,100M as compared to the strategic project value of $1,100M; there is no additional option value, and the contraction should be executed immediately. That is, instead of asking the vendor to wait, the firm is better off executing the contraction option now and capturing the savings.
Other applications include shelving an R&D project by spending a little to keep it going but reserving the right to come back to it should conditions improve; the value of synergy in a merger and acquisition where some management personnel are let go to create the additional savings; reducing the scope and size of a production facility; reducing production rates; a joint venture or alliance, and so forth.
To illustrate, here are some additional examples of the contraction option:
Figure 181.1 illustrates a simple 10-step Contraction Option while Figure 181.2 shows the same option using 100 lattice steps (example file: Contraction American and European Option).
Figure 181.2: American and European options to contract with a 100-step lattice
Figure 181.3 illustrates a five-year Bermudan Contraction Option with a four-year vesting period (blackout steps of 0 to 80 out of a five-year, 100-step lattice) where for the first four years, the option holder can only keep the option open and not execute it (example file used is Contraction Bermudan Option).
Figure 181.3: A Bermudan option to contract with blackout vesting periods
Figure 181.4 shows a customized option where there is a blackout period and the savings from contracting change over time (example file used is Contraction Customized Option). These results are for the aeronautical manufacturing example presented at the beginning of the chapter.
Figure 181.4: A customized option to contract with changing savings levels
You work for a large automobile spare parts manufacturing firm that is unsure of the technological efficacy and market demand of its products. The firm decides to hedge itself through the use of strategic options, specifically an option to contract 50% of its manufacturing facilities at any time within the next five years.
Suppose the firm has a current operating structure whose static valuation of future profitability using a DCF model (in other words, the present value of the expected future cash flows discounted at an appropriate market risk-adjusted discount rate) is found to be $1 billion. Using Monte Carlo simulation, you calculate the implied volatility of the logarithmic returns on the projected future cash flows to be 50%. The risk-free rate on a riskless asset for the next five years is found to be yielding 5%. Suppose the firm has the option to contract 50% of its current operations at any time over the next five years, thereby creating an additional $400 million in savings after this contraction. This is done through a legal contractual agreement with one of its vendors, which had agreed to take up the firm’s excess capacity and space. Then, the firm can scale back its existing workforce to obtain this level of savings.
A Closed-Form American Approximation Model can be used, because the option to contract the firm’s operations can be exercised at any time up to the expiration date and can be confirmed with a binomial lattice calculation. Do the following exercises, answering the questions that are posed: