Open access peer-reviewed chapter

# A Real Options Approach to Valuing the Risk Transfer in a Multi-Year Procurement Contract

By Scot A. Arnold and Marius S. Vassiliou

Published: January 1st 2010

DOI: 10.5772/7170

## 1. Introduction

The purpose of this paper is to develop methods to estimate the option value inherent in a multi-year government procurement (MYP), in comparison to a series of single-year procurements (SYP). This value accrues to the contractor, primarily in the form of increased revenue stability. In order to estimate the value, we apply real options techniques

E.g., Amram & Howe (2003)

.

The United States government normally procures weapons systems in single annual lots, or single year procurements (SYP). These procurements are usually funded through a Congressional Act (the annual National Defense Authorization Act or NDAA) one fiscal year at a time. This gives Congress a great deal of flexibility towards balancing long and short term demands. For defense contractors, however, the Government’s flexibility results in unique difficulties forecasting future sales when demand is driven by both customer needs and global politics.

Defense contractors face risks and advantages that set them apart from commercial businesses. Within a contract, the contractor faces a range of execution cost risk: from none in a cost plus fixed fee contract to high risk in a firm fixed price contract. The government also provides interest-free financing that can greatly reduce the amount of capital a contractor a contractor must raise through the capital markets. Additionally the government provides direct investment and profit incentives to contractors to invest in fixed assets. The net effect is that defense contractors can turn profit margins that may appear low when compared to other commercial capital goods sectors, into relatively high return on invested capital.

However, contractors have always faced high inter-contract uncertainty related to the short term funding horizon of the government. While the United States Department of Defense (DoD) has a multiyear business plan, in any given year, generating a budget entails delaying acquisition plans to accommodate changing demands and new information. At the end of the cold war, defense firms were allowed unprecedented freedom to consolidate. The resulting industrial base is composed of five surviving government contractors: Boeing, General Dynamics, Lockheed, Northrop Grumman, and Raytheon. By diversifying across a large number of government customers, these giants with thousands of contracts each have taken a giant step towards reducing inter-contract risk—no one contract is large enough to seriously harm the companies if it were canceled for convenience. However, the uncertainty around the likelihood of getting the next contract or how large it will be is still there and it is particularly important for large acquisition programs. For example, while Lockheed is the sole source for the F-22A, they always faced uncertainty in the number of units they will sell in the future. For example both the F-22A and the B-2 were originally expected to sell many more airplanes to the government than the actual number the government eventually purchased.

Under Title 10 Subtitle A Part IV Chapter 137 § 2306b, the military services can enter into multi-year procurement (MYP) contracts upon Congressional approval. There are six criteria that must be satisfied, listed in Table 1. The chief benefit for the government has been the “price break”, criterion 1, afforded through the operating efficiencies of a long term contract. This benefit is readily passed to the government because it funds the necessary working capital investments needed to optimize production. It is still possible for the government to cancel the MYP contract; however, significant financial barriers such as a cancellation or termination liability that make it undesirable to do so.

 Criteria Descriptions 1 That the use of such a contract will result in substantial savings of the total anticipated costs of carrying out the program through annual contracts. 2 That the minimum need for the property to be purchased is expected to remain substantially unchanged during the contemplated contract period in terms of production rate, procurement rate, and total quantities. 3 That there is a reasonable expectation that throughout the contemplated contract period the head of the agency will request funding for the contract at the level required to avoid contract cancellation. 4 That there is a stable design for the property to be acquired and that the technical risks associated with such property are not excessive. 5 That the estimates of both the cost of the contract and the anticipated cost avoidance through the use of a multiyear contract are realistic. 6 In the case of a purchase by the Department of Defense, that the use of such a contract will promote the national security of the United States.

### Table 1.

The Six Criteria for a Multi-Year Procurement

United States Code, Title 10, Subtitle A, Part IV, Chapter 137, Section 2306b

The government reaps operational savings by negotiating a lower up-frontprocurement price. These savings are achieved through more efficient production lot sizes and other efficiencies afforded through better long-term planning not possible with SYP contracts. The government can explicitly encourage additional savings by using a cost sharing contract. It can implicitly encourage additional savings with a fixed price contract. In the latter case the longer contract encourages the contractor to seek further efficiencies since it does not share the savings with the government. In fact some might propose this last reason is the best reason for a contractor to seek an MYP.

In addition to the cost savings achieved through more stable production planning horizon, we see that the MYP provides the contractor with intrinsic value through the stabilization of its medium term revenue outlook. Thus an MYP is also coveted by defense contractors because it provides lower revenue risk. What about the possibility that a longer term firm fixed price contract exposes the contractor to higher cost risk? This risk is often eliminated through economic pricing adjustment (EPA) clauses that provide a hedge against unanticipated labor and material inflation. Furthermore, from the criteria in Table 1, MYP contracts are only allowed for programs with stable designs that have low technical risk. As stated above, it is more likely that the MYP offers the contractor the opportunity to exploit the principle-agent information asymmetry and make further production innovations unanticipated at contract signing

United States Code, Title 10, Subtitle A, Part IV, Chapter 137, Section 2306b

.

We believe that the lower risk MYP contract will allow investors to discount contractors’ cash flow with a lower cost of capital creating higher equity valuations. From the contractors’ perspective, the MYP contract provides a hedge against revenue risk. We can estimate the incremental value of the MYP versus the equivalent SYP sequence using option pricing methods. Presently the government does not explicitly recognize this risk transfer in its contracting profit policy. The government profit policy is to steadily increase the contract margin as cost risk is transferred to the contractor. For example a cost plus fixed fee contract might have a profit margin of 7% while a fixed price contract, where the contractor is fully exposed to the cost-risk, of similar content could have a margin of 12%

Generally the project with a cost plus contract has higher technical uncertainty than the project with the fixed price contract. The government does not expect contractors to accept high technical risk projects using a fixed price contract.

. By limiting some of the contractor’s cost-risk exposure, an EPA clause might result in a lower profit margin; however, the profit policy makes no mention of an MYP contract, which reduces the contractor’s inter-contract risk. And while most of the profit policy is oriented towards compensating the contractor for exposing its capital to intra-contract risk and entrepreneurial effort, there are provisions designed to provide some compensation for exposing capital to inter-contract risk—e.g. the facilities capital markup. The implication is that as long as the government does not explicitly price the reduction in cost-risk going from a fixed price SYP contact to an MYP contract, the contractor is able to keep the “extra” profit.

In this paper we present a method to estimate the value an MYP creates for a defense contractor in its improved revenue stability. The contractor can use this information in two ways. First, the information provides guidance for how much pricing slack the contractor can afford as it negotiates an MYP with the government whether or not the latter recognizes that better revenue stability has discernable value. Second, if the government tries to reduce the contractor’s price based on this transfer of risk, the contractor has a quantitative tool to guide its negotiation with the government.

## 2. Financial structure and valuation of an MYP

### Table 3.

Contractor SYP Profit ($Mils). The present value total of$630 resents the projected total asset value (x2) of the last four lots of the SYP. We initially restrict x2 = x1, or that the option be “at the money”

This is a realistic assumption since the number of units in the MYP and SYP are assumed to be the same in the standard business case analysis.

.

## 11. Volatility

For most non-traded assets, such as the profits of Program G, even the historical volatility is difficult to measure

This is a realistic assumption since the number of units in the MYP and SYP are assumed to be the same in the standard business case analysis.

. To properly use the BS model to value Program G MYP option it is imperative to find a traded tracking asset whose volatility is highly correlated to the implied volatility of the asset underlying the embedded real option.

Fortunately, Company A’s equity is publicly traded. Company A is a moderately diversified government contractor with two divisions, Defense and Non-Defense, that serve different government sectors:. We find from their financial statements that Program G represents a substantial share of the Defense Division’s earnings before interest and tax (EBIT). The EBIT breakout by division is presented in Table 2. The Defense Division has contributed a significant portion of the total profits, particularly in recent years. Comparing Tables 1 and 2 we can see that Program G represents over half of the Defense Division’s historical EBIT.

 Year Non-Defense Defense Total Stock Price EBIT % Total 2001 $758$ 242 24% $1,000$ 13 2002 564 92 14% 656 7 2003 522 128 20% 650 13 2004 652 123 16% 775 20 2005 679 167 20% 846 19 2006 552 257 32% 809 19 2007 443 335 43% 778 21 2008 742 370 33% 1,113 26

### Table 4.

A’s EBIT Breakdown by Division ($Mils except for Stock Prices -$/Share).

Company A is a large enterprise, and while Program G contributes significant profits towards to total corporate profit, it is not necessarily enough to drive the overall equity performance. Before we can assign Company A’s equity volatility as a tracking asset for Program G, we need to establish a closer linkage. Table 3 shows Company A’s earnings growth and volatility by division as well as the market performance of its equity from 2000 to 2007. We see that the Defense Division tracks the overall stock performance better than the Non-Defense Division, and better than the company as a whole. This may be because Company A is often identified as a defense company and its stock price, which is forward looking, trades on the trends in the overall defense industry.

 Non-Defense Defense Total Stock Growth 0% 6% 2% 10% Volatility (��) 29% 36% 22% 37%

### Table 5.

A’s EBIT Growth and Volatility by Division 2001 to 2008.

One more indication that Company A’s stock is a good tracking asset for Program G is the correlation between the division’s EBIT and the stock price, as shown in Table 4. Defense Division EBIT has a 72% correlation to the stock price—even higher than the company’s total EBIT. Note that this is not to imply that the stock price drives Program G profit volatility; but rather that the stock price mirrors the EBIT volatility of the Defense division which is strongly driven by the program G business. Since we cannot measure Program G EBIT volatility directly, we will use the stock price volatility as a proxy. We could use the Defense division’s historical EBIT volatility (Table 3) to track Defense division volatility, instead we prefer to use the forward-looking implied volatility estimated in Table 5.

 �� Division,Stock Price Non-Defense 18% Defense 72% Total 59%

### Table 6.

Correlation between Stock Price and Division EBIT from 2001 to 2008.

## 12. Time horizon

We have already hinted at the time horizon for the MYP option. It starts when congress gives the services authority to enter into an MYP with A. It expires at the beginning of the last year or lot of production (assuming one lot per fiscal year) since that would be the last point at which the government could have reduced the number of units in an SYP contract. Assume that the MYP authority is granted six months prior to negotiation. The total life of the MYP is then five years and six months.

## 13. Interest rate

The risk free interest rate used in the analysis is the rate on a Treasury bill whose maturity ties roughly to the expiry of the MYP option.

## 14. Option valuation

First we estimate the implied volatility of a Company A call option that expires close to the MYP expiry. Unfortunately options beyond two years are rare, even for established companies like A. Thus we use the Jan ’10 call option to estimate the implied volatility. The parameters to estimate the implied volatility are listed in Table 6. S*, X*, T*, and c* are the stock price, strike price, expiry, and option price for the A Jan ’10 $25 call. Using these values in the BS call option formula we can calculate the implied asset volatility We use an algorithm based on the Newton-Raphson method to solve for the implied volatility of a European option. . The asset volatilities are then used in (2) to estimate the exchange option price for the MYP. Table 6 summarizes the valuation of the MYP structured as an at-the-money exchange option. Setting the strike value equal to the spot value gives an option value of$127 million which the contractor would need to pay the government upon executing the MYP contract. Much of this value is in the time to expiration or “time premium”. Just to illustrate, if the option were for one month it would be worth $20 million and worth$4 million if it was for one day—all else equal.

 ($Millions) Present Value SYP (x 2 )$ 630 Strike Value (x 1 ) 630 Real Option Price $127 Expiry (yr) 5.0 ### Table 8. MYP Evaluated as an Exchange Option – Risk on SYP Cash Flow Only. The analogy between MYP and insurance is a good one because, as anyone who has made a claim might have discovered, the insurance pay-off is not certain. The MYP can have a variation-in-quantity clause that allows the government to reduce the number of units by a pre-determined number. For example, if the EPA clause is activated by unanticipated labor and materials inflation, the government might reduce the quantity purchased to maintain its bottom line budget. Thus there is some uncertainty around the MYP that must be considered in our risk transfer pricing. This is where the exchange option framework has an advantage over the plain put option structure. It can be used to value cash flow trades that have different levels of uncertainty. For the valuation in Table 6 we set σ’ = σ1 and σ2 = 0. Assume now the government and the contractor agree that the former could reduce the number of Program G units by 2 each year or 10% of the number of units in each lot. We use the exchange option structure to value the right to swap the SYP cash flow with volatility σ1 for the MYP volatility of volatility σ2 –see Table 7 for the valuation. $ Millions Present Value SYP (x 2 ) $630 Strike Value (x 1 )$ 630 Real Option Price $112 Combined Volatility (��) 26% SYP Volatility (�� 2 ) 29% MYP Volatility (�� 1 ) 10% SYP / MYP Volatility Correlation (��) 50% ### Table 9. MYP Evaluated as an Exchange Option with Risk on Both Cash Flows. The price of the option falls from$127 million to $112 million. It would drop to$84 million with 100% correlation; however, if there were no correlation between the two cash flows, the price would have increased to $134 million. This is due to the upside potential of the MYP and SYP. The exchange option is essentially a put option with a stochastic strike price which allows the protection buyer to capture more payoff if the MYP turns out to yield more units. This assumes that the risk of the MYP is symmetric. There is no reason to believe otherwise, since the government can always buy more units than planned, if they are needed. ## 15. Other real options embedded in an MYP Within this chapter, we only have the scope to focus on a single real option example within the MYP contract. However, there is at least one other real option available to the contractor with a sole source production franchise such as a major aircraft, missile, ship, etc. This is because defense contracts are incomplete leaving the contractor with residual control of cost reduction innovations. While we will not estimate the value of this real option here, we mention it because in some cases it is potentially worth far more than the revenue stabilization discussed here. Regulatory lag is an incentive concept that emerged from explicitly regulated industries such as utilities. These industries’ profits are regulated directly through rate setting, e.g.$/kWhr, or through rate of return settings by a regulatory authority. Between rate settings, the utility is free to innovate and achieve higher profits. Upon the next regulatory oversight review, the regulator discovers the new cost structure and adjusts the new rate accordingly to a lower profit level-presumably slightly above the weighted average cost of capital for the utility. Longer periods between regulatory oversight periods (i.e. higher regulatory lag), mean greater opportunities for higher profits.

Similarly, a defense contractor with a sole source series of production contracts for a weapon system has the incentive to achieve greater than expected efficiency innovations even if the savings are passed on to the government in subsequent contracts. It turns out that there is a substantial regulatory lag in defense contracts due to the length of time it takes for cost reports to be submitted to the government. The regulatory lag increases substantially in a MYP contract.

These innovations are real options since the contractor is not obligated to make the necessary investment to achieve the cost savings. They can use real options valuation tool to estimate the worth of these options before a program is executed by looking at prior history of achieving cost reduction innovations as well as a forward looking assessment of the opportunities in a specific weapon system. Unlike the revenue stabilization option, there is considerable information asymmetry between the government and contractor with the regulatory lag options. However, the government could look at prior programs and assess the degree of regulatory lag driven innovation that occurred in past programs and roughly estimate the value of this type of incentive on a new program. This valuation can provide important insight into how aggressively contractors will compete to win a large sole source program.

## 16. Conclusion: the cost implications of the MYP option

Options pricing analysis offers a way to systematically estimate value from the MYP contract earned by the Government for which they have not previously been explicitly compensated. This incremental value is the revenue risk transferred to the Government from the contractor upon signing an MYP. The MYP does not eliminate the revenue risk for the contractor associated with SYP contracts; rather it transfers it to the government and it becomes budget risk. The Congress clearly values its budget flexibility, as evidenced by the statutory criteria to judge the worth of an MYP proposal.

MYP cost savings are usually through operational efficiencies earned through process and purchasing improvements funded by the Government’s “economic order quantity” advance funding. The transfer of revenue risk to the Government is a cash flow hedge that provides real value to the contractor just as any financial hedge does for currency, commodity, or interest rate risks--or property and casualty insurance does for operational risks. Lockheed and Raytheon, for example, carry interest rate swaps that hedge interest rate risk for notional $1 billion and$600 million respectively

Lockheed Martin Corporation, Securities and Exchange Commission Form 10-K, Commission file number 1-11437, Fiscal Year December 31, 2006, p.71.

,

Raytheon Company, Securities and Exchange Commission Form 10-K, Commission file number 1-13699, Fiscal Year December 31, 2006, p. 74.

,. General Dynamics reported a currency swap to hedge a Canadian denominated loan with a fair value of \$42 million

General Dynamics Corporation, Securities and Exchange Commission Form 10-K, Commission file number 1-13671, Fiscal Year December 31, 2006, p. 49.

. It also reported embedded options in the terms of its long term labor and commodity contracts. One can argue that just as public companies are expected to incur expenses as they pay for insurance and financial hedges, they should pay the government when it reduces the contractor’s risk.

The option methodology helps the government objectively quantify some of the cost in relinquishing its budget flexibility with a relatively simple tool that has widespread use in the financial community. We do not try to value the cost of transferring the risk from the Government’s side because there is not a readily available tracking asset to estimate the volatility of the revenue risk. It is possible to estimate the actuarial loss history of certain procurements by looking at the Selected Acquisition Report over the span of past programs. If such data were available, it might be desirable to use it in lieu of the equity volatility of the contractor. One benefit of using the contractor’s volatility, however, is that it is more closely coupled to the risk the contractor might be willing to hedge.

The option value of the MYP has not been explicitly paid to the government in the past. Thus any method that helps rationalize the cost of this risk transfer is a benefit to the government. Furthermore, the contractor will likely see the value of the MYP option if it is evaluated in its own financial terms.

Strategically, the MYP option value represents a significant reduction in the contractor’s profits. Given the skill and sophistication that contractors employ to manage their government customers, they will likely argue that the MYP real option has limited value as an earnings hedge. They could contend that financial hedges are only appropriate for risks that are outside of managers’ control, such as interest and exchange rates, and cannot be offset within the business. They might also contend that not only is their portfolio of business well diversified among a broad scope of government elements but that they have enough support on Capitol Hill to ensure that they will sell all the units in the SYP plan. They would be arguing that the program is less risky than their business in total (i.e. their equity volatility). This would be a difficult argument for most businesses. However, initially it is unlikely the contractors will proactively volunteer to pay for it.

However, the fact is that the lower earnings risk from an MYP has tangible value whether or not the contractors wish to pay for it. The option has the same value no matter what the contractors’ risk preference. If there is no risk hedge in an MYP, why do the contractors routinely enter into this type of contract? In fact Lockheed readily acknowledged that the value of the MYP is its long term stability

LMT-Q3 2006 Lockheed Martin Earnings Conference Call, Preliminary Transcript, Thompson StreetEvents, Thompson Financial, October 24, 2006, 11:00AM ET

.

The options methodology allows the Government to build a logical business case for reducing the profit on cost paid to contractors when switching from an SYP series to an MYP contract. The exchange option model in particular allows the Government to quickly estimate changes in the value of the contract as the details, e.g. the EPA and VIQ clauses, become more complete.

## Notes

• E.g., Amram & Howe (2003)
• United States Code, Title 10, Subtitle A, Part IV, Chapter 137, Section 2306b
• Generally the project with a cost plus contract has higher technical uncertainty than the project with the fixed price contract. The government does not expect contractors to accept high technical risk projects using a fixed price contract.
• Margrabe, W., Journal of Finance, 33, 177-86 (1978)
• Black & Scholes (1973)
• E.g., Copeland & Tufano (2004)
• Richard L. Shockley, J. of Applied Corporate Finance, 19(2), Spring 2007
• Scott Matthews, Vinay Datar, and Blake Johnson, J. of Applied Corporate Finance, 19 (2), Spring 2007
• Charnes et al. (2004)
• Cornelius et al. (2005)
• Colwell et al. (2003)
• Duan et al. (2003)
• Ekelund (2005), Remer et al. (2001)
• Ford et al (2004) ; Rothwell (2006)
• Fourt (2004) ; Oppenheimer (2002)
• Nembhard et al. (2003)
• Laxman & Aggarwal (20030
• Paxson (2002), MacMillan et al. (2006)
• Cornelius et al. (2005), IOMA (2001)
• IOMA (2001)
• Maumo (2005)
• Amram & Howe (2003), Copeland & Tufano (2004)
• Although with mixed results in structured finance and credit default swap applications.
• The bank may also hedge its foreign exchange exposure.
• Canceling the contract usually would come with considerable cost to the government.
• European options can only be exercised on the expiration data while American options can be exercised on or before expiry.
• Technically it is the instantaneous volatility – something that is hard to measure.
• p(S,t) is found by solving the following partial differential equation: pt = ½ σ2S2pSS + rSpS – rp. The equation is subject to the terminal condition: p=max[0,X-S], and to upper and lower boundary conditions: p=Xe-rT for S=0 and p=0 for S→∞. S follows the Wiener process through the following stochastic differential equation: dS = μSdt+σSdz. Here μ is the average growth rate; σ is the standard deviation of this growth process; and r is the risk free interest rate.
• We assume a dollar for dollar profit cash flow conversion.
• This is a realistic assumption since the number of units in the MYP and SYP are assumed to be the same in the standard business case analysis.
• This is a realistic assumption since the number of units in the MYP and SYP are assumed to be the same in the standard business case analysis.
• We use an algorithm based on the Newton-Raphson method to solve for the implied volatility of a European option.
• Lockheed Martin Corporation, Securities and Exchange Commission Form 10-K, Commission file number 1-11437, Fiscal Year December 31, 2006, p.71.
• Raytheon Company, Securities and Exchange Commission Form 10-K, Commission file number 1-13699, Fiscal Year December 31, 2006, p. 74.
• General Dynamics Corporation, Securities and Exchange Commission Form 10-K, Commission file number 1-13671, Fiscal Year December 31, 2006, p. 49.
• LMT-Q3 2006 Lockheed Martin Earnings Conference Call, Preliminary Transcript, Thompson StreetEvents, Thompson Financial, October 24, 2006, 11:00AM ET

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Scot A. Arnold and Marius S. Vassiliou (January 1st 2010). A Real Options Approach to Valuing the Risk Transfer in a Multi-Year Procurement Contract, Aerospace Technologies Advancements, Thawar T. Arif, IntechOpen, DOI: 10.5772/7170. Available from:

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