CONGRESS OF THE UNITED STATES

CONGRESSIONAL BUDGET OFFICE

A

CBO

STUDY

AUGUST 2004

Estimating the

Value of

Subsidies for

Federal Loans

and Loan

Guarantees

© Royalty-free/Corbis

The Congress of the United States O Congressional Budget Office

CBO

Estimating the Value of Subsidies

for Federal Loans

and Loan Guarantees

August 2004

A

STUDY

Preface

The Federal Credit Reform Act of 1990 (FCRA) changed the budgetary accounting for 

federal direct and guaranteed loans from a cash basis to an accrual basis. That shift requires 

that the government’s expected losses from such loans—because of defaults and interest rate 

subsidies—be recognized in the budget when the credit is extended. The FCRA specifies that 

uncertain future cash flows associated with such loans be converted (discounted) to their 

present values using the interest rates on Treasury securities.

With credit-reform rules having been in effect for more than a decade, the Chairman of the 

House Budget Committee has asked the Congressional Budget Office (CBO) to reexamine 

the provisions of the FCRA with an eye toward identifying possible improvements in, and 

extensions of, that accrual basis of budgetary accounting. This study—which is one part of 

CBO’s response to that request—focuses on using commercial interest rates, which incorporate risk, instead of risk-free Treasury rates to measure the cost of federal credit programs.

Deborah Lucas, Marvin Phaup, and Ravi Prasad prepared this report under the direction of 

Roger Hitchner of CBO’s Microeconomic and Financial Studies Division. (Ravi Prasad, now 

with Bank of America Securities, contributed to this study while serving as a consultant to 

CBO.) Kim Cawley, Paul Cullinan, Robert Dennis, Peter Fontaine, Kathy Gramp, Arlene 

Holen, Albert Metz, Elizabeth Robinson, Robert Sunshine, David Torregrosa, Eric Wang, 

and Thomas Woodward of CBO contributed helpful comments on earlier drafts, and Wendy 

Kiska provided technical assistance. Susan Woodward of Sand Hill Econometrics and Michael 

Falkenheim, Robert Kilpatrick, and Sangkyun Park of the Office of Management and Budget 

reviewed earlier versions of this report; Robert McDonald of Northwestern University offered 

technical advice. (The assistance of such external participants implies no responsibility for the 

final product, which rests solely with CBO.)

Christian Spoor edited the study, and John Skeen proofread it. Maureen Costantino produced 

the cover and prepared the report for publication. Lenny Skutnik printed the initial copies, 

and Annette Kalicki prepared the electronic versions for CBO’s Web site (www.cbo.gov).

Douglas Holtz-Eakin

Director

August 2004

Introduction and Summary 1

Costs Under the FCRA and with Market Prices 3

The Relevance of Market Prices and Market Risk to

Government Budgeting for Credit Programs 4

Is Market Risk Relevant? 4

Differences Between the Government 

and Private Financial Institutions 5

Methods for Valuing Federal Loans and Guarantees 6

The Treasury-Rate Approach 6

Risk-Adjusted Discount Rates 

and Options-Pricing Methods 7

Estimating the Subsidies to Chrysler and

America West Airlines 9

Chrysler’s Financial Condition and Guarantee Terms 9

AWA’s Financial Condition and Guarantee Terms 10

Treasury-Rate Subsidy Estimates 12

Market-Value Subsidy Estimates 14

The Effect of Market Risk on Subsidy Rates 15

Uncertainty and Reestimates 15

Appendix A: Volume and Cost of Federal

Credit Programs 21

Appendix B: An Example of Using the Binomial Model

to Price a Loan Guarantee 23

Appendix C: Parameter Estimates and Modeling

Assumptions Used in This Analysis 25

CONTENTS
vi ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

Tables

1. Estimated Federal Costs of Loan Guarantees to Chrysler and 

America West Airlines 13

2. Estimated Subsidy Rates for Federal Loan Guarantees to Chrysler

and America West Airlines 15

3. Initial and Reestimated Federal Costs from the Loan Guarantee

to America West Airlines 17

A-1. Federal Direct and Guaranteed Loans Outstanding, 1994 to 2003 21

A-2. Budget Authority for Subsidies for Federal Direct and Guaranteed 

Loans, 2003 22

Figures

S-1. Federal Credit Outstanding, 1993 to 2003 2

1. AWA Stock Prices, January 2000 to July 2004 16

2. Probability Distribution of Market Values of the AWA 

Loan Guarantee 18

3. Probability Distribution of Market Values of the AWA 

Warrants 19

B-1. Illustrative Possible Values of Assets, Cash Flows, and Bonds 

in One Year 24

Box

1. Loan Guarantees as Put Options 10
Estimating the Value of Subsidies

for Federal Loans

and Loan Guarantees

Introduction and Summary

To achieve some of its policy goals, the federal government reduces the price and increases the availability of 

credit for particular uses by guaranteeing private loans or 

making loans directly. In fiscal year 2003, the government guaranteed $365 billion in new loans. More than 

two-thirds of them were for home mortgages, although 

the government also provides loan guarantees to companies in specific sectors, such as the airline, steel, oil, gas, 

and rural television industries. In addition, the government extended $36 billion in direct loans in 2003, many 

of them through its student loan programs. In all, the 

federal direct and guaranteed loans that were outstanding 

last year had a total value of $1.4 trillion—nearly twothirds more than the value 10 years earlier (see Summary 

Figure 1).1

Those credit activities convey subsidies to borrowers—in 

the form of more-attractive loan terms than borrowers 

might otherwise obtain—at a cost to the government. 

The way that cost is treated in the federal budget has 

changed over time, most significantly in 1990 with the 

enactment of the Federal Credit Reform Act (FCRA). 

That legislation redefined the budgetary cost of federal 

credit activity: instead of the annual cash flow on all outstanding federal loans and loan guarantees, the budget 

now records the present value of future cash flows on 

credit extended in the current budget year. In making 

that change, the FCRA effectively put the accounting of 

federal credit on an accrual basis (as is the case for interest 

on federal debt held by the public and some pension costs 

for federal employees).2

The government’s estimates of its subsidy costs for loans 

and loan guarantees are modest, especially in relation to 

the volume of those loans. For example, the $36 billion in 

new direct loans obligated in 2003 are estimated to cost 

the government $657 million over the life of the loans—

or $1.83 for each $100 lent (a subsidy rate of 1.83 percent).3

 Similarly, the $365 billion in new guarantee commitments made in 2003 are estimated to cost $4.2 billion—or $1.15 per $100 guaranteed (a subsidy rate of 

1.15 percent). Some federal credit programs, such as direct student loans and the Federal Housing Administration’s mortgage insurance, appear to make money for the 

government. 

Although the government and private lenders estimate 

the value of loans and loan guarantees in essentially the 

same way, two exceptions make government credit programs seem less costly than comparable credit extended 

by private financial institutions. First, federal agencies’ 

administrative expenses are not included in estimates of 

subsidy costs (though they appear elsewhere in the federal 

budget). Second, those estimates exclude the cost of market risk—the compensation that investors require for the

1. For more details about the volume and cost of federal credit programs, see Appendix A.

2. See the Federal Credit Reform Act of 1990, included as title XIII, 

section 13201 of the Omnibus Budget Reconciliation Act of 

1990; 2 U.S.C. 661, 104 Stat. 1388-610. See also Congressional 

Budget Office, Estimating the Costs of One-Sided Bets: How CBO 

Analyzes Proposals with Asymmetric Uncertainties (October 1999); 

Office of Management and Budget, “Federal Credit,” part 5 of 

Preparation, Submission, and Execution of the Budget, Circular 

No. A-11 (July 2004), available at www.whitehouse.gov/omb/

circulars/a11/current_year/s185.pdf; and Marvin Phaup, “Credit 

Reform, Negative Subsidies, and FHA,” Public Budgeting & Finance, vol. 16, no. 1 (1996), pp. 23-36.

3. Budget of the United States Government, Fiscal Year 2005: Analytical Perspectives, Tables 7-3 and 7-4.
2 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

Summary Figure 1.

Federal Credit Outstanding, 1993 

to 2003

(Billions of dollars)

Source: Congressional Budget Office based on data from the 

Office of Management and Budget.

uncertainty of expected but risky cash flows. The reason 

is that the FCRA requires analysts to calculate present 

values by discounting expected cash flows at the interest 

rate on risk-free Treasury securities (the rate at which the 

government borrows money).4

 In contrast, private financial institutions use risk-adjusted discount rates to calculate present values.

Despite those limitations, credit-reform accounting provides more-useful cost estimates than did the cash-basis 

accounting it replaced. The current approach is forwardlooking for the life of a loan; it accounts for the time 

value of money; and it generally assigns the same budgetary cost to equivalent loans and loan guarantees. 

The FCRA adopted the private market’s definition of 

value (the present value of expected cash flows, with the 

two exceptions noted above) in an attempt to “place the 

cost of credit programs on a budgetary basis equivalent to 

other federal spending . . . and improve the allocation of 

resources among credit programs and between credit and 

other spending programs.”5 The costs of other programs 

in the federal budget are based on market prices—such as 

the estimated price of buying a weapon, repairing a road, 

or furnishing a service. In the case of credit programs, 

however, omitting some of the costs of providing credit 

results in an overstatement of the value of the government’s loans and guarantees. One indication of that overstatement is that proposed sales of federal loans to private 

investors usually appear to result in losses to the government because the market value of a loan is almost always 

less than the credit-reform value. The primary reason is 

the difference in discount rates used by the market and 

under credit reform.

Following more than a decade of experience with credit 

reform and rapid advances in financial theory and practice, this Congressional Budget Office (CBO) study reexamines the use of risk-free Treasury rates to value federal loans and guarantees and to estimate their subsidy 

costs.6

 It discusses two approximately equivalent modifications to the current approach, both of which would use 

market prices: risk-adjusted discounting and options 

pricing. The analysis then employs options pricing to 

show how that method’s estimates of federal subsidy costs 

differ from Treasury-rate estimates for two major government loan guarantees—those made to Chrysler in 1980 

and America West Airlines (AWA) in 2002.

Those two loan guarantees were riskier than the ones typically made under government credit programs. Thus, the 

difference between market-value estimates of their costs 

and Treasury-rate estimates would be expected to be 

greater than for many other programs. Nevertheless, for 

all programs, ignoring the cost of risk understates the federal cost of credit assistance, potentially biasing the allocation of budgetary resources. For example, excluding the 

4. Calculations of present value (a single number that expresses a 

flow of current and future payments in terms of an equivalent 

lump sum paid today) depend on the particular interest rate used. 

For example, if $100 is invested on January 1 at an annual interest 

rate of 5 percent, it will grow to $105 by January 1 of the next 

year. Hence, under the assumption of a 5 percent annual interest 

rate (or discount rate), the present value of $105 payable a year 

from today would be $100.

1993 1995 1997 1999 2001 2003

0

200

400

600

800

1,000

1,200

1,400

1,600

Total

Guaranteed Loans

Direct Loans

5. 2 U.S.C. 661.

6. Although Treasury securities are free from the risk of default, they 

are subject to other risks, including price risk (the risk that 

changes in market interest rates or other factors will alter the value 

of the securities). That risk is reflected in the market prices and 

yields on Treasury debt. In this study, the term “risk- free Treasury 

rates” refers only to the default-free quality of those securities.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 3

cost of risk from budget and program decisions may mislead policymakers by suggesting that some federal credit 

programs provide financial resources to the government 

at no cost to taxpayers. It also encourages reliance on 

credit rather than other policies that might be more efficient in achieving particular goals.

The principal conclusions of this study are these:

B Market risk is a cost to the government.

B With the exception of administrative costs, projected 

cash flows on federal loans and loan guarantees are 

identical under credit-reform and market valuation. 

The key difference between the two methods is the use 

of different discount rates.

B Using Treasury rates to discount expected cash flows 

neglects the cost of market risk and results in the systematic understatement of costs for both direct and 

guaranteed loans. Using risk-adjusted discount rates, 

which include the cost of market risk, would correct 

that understatement and improve the comparability of 

budgetary costs for credit and other programs.

B For some federal loans and guarantees, risk adjustment 

can have a significant effect on cost estimates. For instance, when the market price of risk is taken into account, the subsidy rate on the Chrysler loan guarantee 

is 15.9 percent rather than 7.2 percent, CBO estimates, and the subsidy rate on the America West guarantee is 6.9 percent instead of -12.7 percent. For other 

programs with less exposure to market risk, the effect 

on subsidy estimates may be much smaller. (Producing 

estimates for other programs was beyond the scope of 

this analysis.)

B Which market-pricing method is appropriate to use 

for a federal credit program depends on the characteristics of the program and of borrowers. This study uses 

an options-pricing approach to estimate the value of 

the Chrysler and AWA loan guarantees. That method 

is well suited to valuing federal loans and guarantees to 

private companies. For other programs, such as those 

providing student loans and home mortgage guarantees, alternative approaches to adjusting discount rates 

for risk are likely to be easier to apply. 

Costs Under the FCRA 

and with Market Prices 

To calculate lifetime costs for new direct and guaranteed 

loans in a budget year, analysts project the government’s 

expected cash flows for loan disbursements, defaults, interest payments, fees, and repayments for the expected 

lives of the loans. Those future dollars are converted to 

present values through discounting to take account of the 

time value of money (the fact that a dollar tomorrow is 

worth less than a dollar today because of the interest that 

could have been earned on that dollar in the meantime). 

The credit-reform subsidy is the estimated difference between the present value of expected cash outflows and expected cash inflows at the time the credit is extended. As 

the financial condition of borrowers changes over time, 

the value of a loan or guarantee also changes. Periodic 

budget reestimates allow those changes to be recognized 

in the budget over the life of the loan. 

The FCRA mandates that future cash flows be discounted using interest rates on marketable Treasury securities with similar maturities to the loans in question. In 

the case of risk-free loans (those whose cash flows are certain and do not change with the state of the economy), 

that method results in an estimate of the market value of 

the loans, just as it does for a promise of payment by the 

Treasury.7 In the case of risky loans (those whose expected cash flows are uncertain), that procedure systematically overestimates the market value of promised cash 

flows by discounting at too low a rate. Equivalently, it 

underestimates the cost of loan guarantees—that is, the 

value of cash shortfalls that the government has to make 

up when an underlying loan defaults.

Market prices, by contrast, reflect the fact that risky 

future cash flows are discounted by investors at riskadjusted rates. For loans, higher market risk implies a 

higher discount rate and a lower present value of expected 

cash flows. Since the value of a loan guarantee is the difference between the value of the loan’s principal and the 

present value of expected repayments, higher market risk 

implies a higher value for the guarantee. Private financial 

institutions use a variety of methods to estimate the mar7. In other words, if the Treasury promises with certainty to pay 

$106 one year from now (backed by the government’s sovereign 

power to tax and to print money), and the market rate on Treasury securities is 6 percent, then the present value of the promise is 

$100. That result can be confirmed by observing that such a 

promise will have a current market price of $100. 
4 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

ket value of loans and loan guarantees. Some of those approaches could be adapted to valuing federal credit. This 

study focuses primarily on one widely used method, options pricing, although it also discusses an alternative, 

risk-adjusted discount rates. 

The Relevance of Market Prices and 

Market Risk to Government Budgeting 

for Credit Programs

The main rationales for using market prices to estimate 

the cost of federal credit assistance are that such prices 

provide a comprehensive measure of cost, are consistent 

with the measurement of other programs’ costs, and offer 

the best available way to gauge the opportunity costs to 

society from such credit assistance.8

 If the government 

provides goods or services at a below-market price, it incurs an opportunity cost on behalf of its stakeholders 

(taxpayers and beneficiaries of government programs) in 

the amount of the underpricing. When the government 

assumes credit risk, that risk is passed on to government 

stakeholders, and its value represents a cost. With the exception of a few differences described below, the government is like any financial institution that assumes costly 

risks on behalf of others. Thus, assumed risks are as relevant to the government as to other financial intermediaries and constitute a cost to its stakeholders. Relying on 

market prices offers a straightforward way to measure that 

cost and one that is consistent with other budgetary practices.9

Market risk arises from the volatility of the economy and 

from associated changes in the value of aggregate wealth. 

Because those changes create undesired uncertainty, they 

are costly to investors and are reflected in market prices. 

Market risk differs from diversifiable risk, which can 

effectively be eliminated by pooling it—in the case of 

financial assets, for example, by diversifying a portfolio so 

that unexpected gains on some investments offset unexpected losses on others. Market risk, by contrast, is associated with economywide increases or decreases in asset values, so it cannot be eliminated through portfolio 

diversification.10

Is Market Risk Relevant?

Some observers have argued that market risk is not a cost 

to the government and that Treasury rates are appropriate 

for valuing government cash flows, even if those flows are 

risky. Two main justifications are sometimes offered for 

that view: first, that the government can borrow at Treasury rates, so its costs are lower than those of other financial institutions; and second, that the government can 

spread financial risk more widely than other institutions 

can, effectively making the risk diversifiable and thus 

without cost to stakeholders. 

The first argument—that the government can borrow at 

a risk-free rate—ignores the role of stakeholders in enhancing the government’s credit quality. The Treasury 

can borrow at a relatively low rate (by creating nominally 

safe securities) in part because of its sovereign power to 

tax. However, the authority to draw on the resources of 

others to ensure repayment of debt obligations does not 

reduce the risk that the government assumes by extending 

risky loans and guarantees. Rather, it is the means by 

which such risk is shifted to taxpayers and beneficiaries of 

government programs, who are, in essence, equity holders 

in the government’s financial activities.

For example, suppose the government borrows $1,000 

through the sale of Treasury securities and makes a risky 

loan for $1,000. In balance-sheet terms, the government 

has acquired a risky asset that will pay $1,000 at most and 

a risk-free liability of $1,000. That transaction adversely 

affects stakeholders because they now bear more financial 

risk than before the loan was made: they are liable for repayment of the government securities, independent of 

the performance of the loan. If the loan returns only 

$900, stakeholders lose $100. In fact, financing a loan 

with a debt issue implies that stakeholders have the equivalent of a highly leveraged, and hence very risky, ownership position in the loan. The critical implication of that 

example is that the government’s ability to create a risk8. Opportunity cost is the highest value of resources in alternative 

uses. Putting resources into one activity prevents their use in other 

activities. The highest value of a forgone alternative is the opportunity cost of the chosen activity.

9. David F. Bradford, “On the Uses of Benefit-Cost Reasoning in 

Choosing Policy Toward Global Climate Change,” in Paul R. 

Portney and John P. Weyant, eds., Discounting and Intergenerational Equity (Washington, D.C.: Resources for the Future, 1999), 

pp. 37-43. See also the statement of Douglas Holtz-Eakin, Director, Congressional Budget Office, “The Economic Costs of LongTerm Federal Obligations,” before the House Committee on the 

Budget, July 24, 2003.

10. Thomas E. Copeland and J. Fred Weston, Financial Theory and 

Corporate Policy, 3rd ed. (New York: Addison-Wesley, 1992), 

Chapter 6.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 5

free liability results from its sovereign authority to draw 

on the people’s resources. That authority does not protect 

stakeholders from market risk, nor does it increase the 

value of a loan above its market value.

The second argument—that the cost of risk is lower to 

the government because it can spread the risk more 

widely—is relevant to diversifiable risk but not to market 

risk. It is sometimes argued that the government can 

spread losses more widely over the population than, say, 

insurance companies can by compelling participation in 

the risk pool. However, as noted above, market risk cannot be eliminated by diversification because it results 

from an aggregate change in asset values. Even if the government eliminated the diversifiable risk inherent in its 

lending activities, the associated market risk would remain. At best, a government guarantee could shift the 

market risk from one group (lenders) to another (taxpayers and other government stakeholders). 

A related argument is that the government’s ability to 

borrow and repay that borrowing with future taxes allows 

it to reduce market risk by spreading the risk among generations. However, borrowing does not increase total 

resources; rather, it redistributes existing resources from 

lenders to borrowers. Moreover, risk is not reduced by the 

government’s power to print money, because financing 

credit losses by creating money substitutes an inflation 

tax for a pecuniary tax. In the end, someone must bear 

the consequences of unpredictable financial returns, and 

markets determine a price for assuming that risk. 

Differences Between the Government 

and Private Financial Institutions

Although the government does not have a capacity to 

bear risk on its own, it may have some advantages over 

private institutions that reduce its relative borrowing 

costs. The Treasury benefits from economies of scale in 

issuing, placing, and servicing debt, which lowers its 

transaction costs. The high liquidity of Treasury debt also 

reduces federal borrowing costs. But liquidity does not 

represent true savings if it comes at a cost to stakeholders 

through the backstop they provide against losses. In addition, the fact that Treasury securities are exempt from 

state and local taxes reduces the yield that investors require on them relative to the yield on private borrowing. 

However, lower state and local tax collections do not represent an economic gain to citizens, who have to pay 

more of those taxes to support services because states and 

localities cannot tax Treasury securities.

More fundamentally, none of those advantages are relevant from the perspective that the appropriate measure of 

the government’s cost of providing credit is its opportunity cost. That cost is the least expensive alternative for 

accomplishing a goal—in other words, the cost of credit 

provided by private lenders.

The question of the appropriate discount rate for the government dates back at least to the classic 1970 paper of 

Kenneth Arrow and Robert Lind, which formalized the 

argument that when all risks are diversifiable, the government’s cost for bearing those risks is minimal.11 Although 

that paper is widely cited to justify the use of risk-free 

rates to discount federal cash flows, its conclusions do not 

apply to situations with market risk. Later authors, such 

as Robert Merton, distinguish between diversifiable and 

market risk and include the market price of the latter in 

their analyses of federal financial programs that have significant exposure to market risk (such as programs that 

provide deposit and pension insurance).12

The issue of discount rates also arises in accounting for 

federal investments in private securities. Without recognition of the cost of market risk, the budget will give the 

appearance that the government can finance itself by borrowing at the risk-free rate and investing in a portfolio of 

risky private securities with an expected return higher 

than that rate.13

11. Kenneth J. Arrow and Robert C. Lind, “Uncertainty and the Evaluation of Public Investment Decisions,” American Economic 

Review, vol. 60, no. 3 (1970), pp. 364-378.

12. Robert C. Merton, “An Analytic Derivation of the Cost of 

Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory,” Journal of Banking and Finance, vol. 

I, no. 1 (June 1977), pp. 3-11; and Merton, “Applications of 

Option-Pricing Theory: Twenty-Five Years Later,” American Economic Review, vol. 88, no. 1 (March 1988), pp. 323-349. For a 

more recent discussion, see Steven Boyce and Richard A. Ippolito, 

“The Cost of Pension Insurance,” Journal of Risk and Insurance,

vol. 69, no. 2 (2002), pp. 121-170.

13. For a parallel discussion of the budgetary treatment of federal 

investments in equity securities, see Budget of the United States 

Government, Fiscal Year 2004: Analytical Perspectives, “Railroad 

Retirement Board Investments,” p. 471; and Congressional Budget Office, Evaluating and Accounting for Federal Investment in 

Corporate Stocks and Other Private Securities (January 2003).
6 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

Methods for Valuing Federal Loans 

and Guarantees

For both Treasury-rate and market-value estimates, the 

subsidy cost is the difference between the value of what 

the government gives and what it receives in a transaction. In the case of a direct loan, the government gives 

cash now and receives a promise of repayments of principal, interest, and fees in the future. In the case of a loan 

guarantee, the government commits to pay off the lender 

if the borrower defaults. For that commitment, the government often receives fees paid by the borrower. When 

the borrower is a publicly traded corporation, the government sometimes also receives compensation in the form 

of warrants to purchase stock. (A warrant is a type of call 

option that gives the government the right to buy shares 

of the company’s stock in the future for a predetermined 

price.) To calculate the net cost of such a loan guarantee, 

it is necessary to value all of the components of the agreement: the guarantee itself, the fees, and the warrants. This 

section explains various methods for determining that 

value, and the next section applies some of those methods 

to the guarantees, fees, and warrants in two large federal 

credit deals.

The Treasury-Rate Approach

Under current practice, the first step in estimating subsidy costs for a direct or guaranteed loan is to project the 

government’s expected cash inflows and outflows from 

the transaction. Projected cash flows include the disbursement of principal, expected repayments, and fees. Expected values for the government’s cash receipts depend 

on the probability of default each year, the recovery rate 

on defaulted loans, the planned repayment (amortization) schedule of a loan, estimated voluntary prepayments, and the fee schedule. As required by the FCRA, 

projected future cash flows are discounted at Treasury 

rates to obtain the present value of the direct loan or 

guarantee.

A few simple examples illustrate the process. First, suppose a federal agency makes a direct loan of $100 for one 

year at the government’s borrowing rate of 5 percent. If 

the loan is free of credit risk, the agency is certain of being 

repaid $105 in principal and interest at the end of the 

year. Under credit reform, the value to the government of 

that loan at its origination is the discounted present value 

of $105 in one year. Using the government’s borrowing 

rate of 5 percent as the discount rate, the loan value (V) 

is:

1) V = $105/1.05

= $100

Because the loan is repaid in full with interest, the present 

value of the future repayment ($100) is equal to the 

amount advanced ($100), so the cost of the loan to the 

government is zero.

Second, suppose the agency makes a loan for the same 

amount on the same terms but with some credit risk involved. On the basis of experience, the agency projects 

that 25 percent of loans like this one will default at the 

end of a year. In such defaults, the government expects to 

recover only $30 from the borrower. Under the current 

approach, the value of this loan to the government is the 

present value of the weighted average expected return, 

with the weights being the probability of default and repayment in full, respectively.14 That is:

2) V = 0.25 ($30/1.05) + 0.75 ($105/1.05) 

= 0.25 ($28.57) + 0.75 ($100) 

= $82.14

In that case, the government has given greater value 

($100) than it expects to receive, on average, in return 

($82.14). The cost (C) of the direct loan is the difference 

between value given and received. That is:

3) C = -$100 + [0.25 ($28.57) + 0.75 ($100)] 

= -$17.86

Third, suppose that instead of making a direct loan, the 

agency simply guarantees that a private lender making the 

loan to the same borrower on the same terms will be paid 

in full if the borrower defaults. As guarantor, the government will have to pay off the lender 25 percent of the 

time, in each such case giving the lender $105 in principal and interest and collecting $30 from the borrower. 

The government’s cost will be the discounted present 

value of those net payments (given that 75 percent of the 

time the government will pay nothing). That is:

4) C = 0.25 [(-$105/1.05) + ($30/1.05)] + 0.75 ($0)

= 0.25 [-$100 + 28.57] + 0

= -$17.86

14. See Congressional Budget Office, Estimating the Costs of OneSided Bets.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 7

which is the same as the cost to the government of the direct loan in the previous example. That result illustrates 

the general principle that the cost of a direct loan is the 

same as the cost of a guarantee made on the same terms 

with the same risks. In both cases, the budgetary cost is 

the present value of expected losses.

Although those examples are illustrative, they oversimplify the analytical difficulty of accurately projecting future cash flows from federal credit activity. Most federal 

direct and guaranteed loans have a longer maturity than 

one year, so defaults and recoveries are spread over a 

longer period. Moreover, the probability of default and 

the amount expected to be recovered are likely to vary 

with many things, including the length of time since 

origination. 

More important, defaults do not occur randomly. They 

result from economic decisions and factors that can be 

used to project cash flows more accurately. For example, 

borrowers rarely default on loans when the value of the 

asset used as collateral exceeds the amount of the unpaid 

loan balance. Instead, they can sell the asset, pay off the 

loan, and keep the difference. To predict defaults and the 

associated cash flows on some loans, therefore, budget analysts could project the expected evolution of the price of 

the borrower’s assets along with the unpaid balance of the 

loan. As the price of a collateral asset falls, the probability 

of default increases. Thus, the probability of default at 

each point in time can be determined from the probability distribution of asset prices. And those distributions 

can be projected into the future on the basis of the starting price of the asset, its volatility, and its expected rate of 

return. 

Prepayments—which are permitted without penalty for 

most federal credit programs—also affect the expected 

cash flows to the government from direct loans and guarantees. Prepayments extinguish the risk of default and 

terminate the collection of fees. Like defaults, prepayments are usually economically motivated and can be predicted from rising asset values and other factors associated 

with attractive refinancing opportunities, such as declining interest rates. Successfully projecting those factors can 

significantly improve the accuracy of estimates of cash 

flows to the government.

In practice, time and resource limitations often preclude 

such detailed modeling of projected cash flows for subsidy estimates. Budget analysts have a variety of simpler 

methods available for assessing the government’s exposure 

to the risk of default or prepayment—including, for example, the use of historical default rates for loans with 

specific credit ratings. However, focusing on the future 

evolution of the value of the borrower’s assets is consistent 

with the rules of credit reform and is a straightforward 

means of getting at the economic motive for default. It is 

also the method that most closely parallels modern private-sector methods for estimating the value of credit 

guarantees. CBO is currently exploring the usefulness of 

those methods to budget analysts, both for improving the 

accuracy of cash flow projections and for providing additional information about the cost of risk. 

Risk-Adjusted Discount Rates 

and Options-Pricing Methods

As with Treasury-rate estimates, producing market-value 

estimates of subsidy costs also requires estimating the 

probability distribution of cash flows over the life of a 

loan or guarantee. The key difference is that the rates 

used to discount projected cash flows reflect the market 

price of risk. The financial sector commonly uses several 

methods to incorporate the price of market risk into estimates of value. For securities that are actively traded, the 

simplest and most reliable approach is to rely on observed 

market prices. For loans and guarantees for which market 

prices are unavailable or unreliable, one alternative is to 

use an adjusted-discount-rate (ADR) method. Another is 

to apply options-pricing methods. 

Adjusted Discount Rates. The ADR method adds a 

spread—the difference between the interest rate on a 

Treasury security and the rate on a risky security—to 

Treasury rates and uses the resulting adjusted rate to discount expected cash flows associated with a loan. That 

higher rate results in a smaller present value of expected 

future payments, reflecting the cost of market risk. As before, the subsidy cost of a loan or loan guarantee is the extent to which the present value of expected payments falls 

short of the loan principal. The procedure is the same for 

both loans and loan guarantees because, in either case, 

the loss to the government reflects the shortfall in expected repayment value.

To illustrate, consider the previous example of a $100 

one-year loan with a 25 percent chance of default and an 

expected recovery of $30 in the case of default. If the riskadjusted discount rate is 7 percent instead of the risk-free 

rate of 5 percent used in equation 2, the estimated market 

value of the loan will be:
8 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

5) V = 0.25 ($30/1.07) + 0.75 ($105/1.07) 

= 0.25 ($28.04) + 0.75 ($98.13) 

= $80.61

That value is $1.53 less than the estimated value with 

risk-free discounting; thus, the subsidy cost of the loan is 

higher by the same amount—$19.39 instead of $17.86. 

As is always the case, the value of a guarantee on that loan 

is identical to the subsidy on the loan, because the guarantor (the government) makes up for the difference between the principal of the loan and the value of what is 

repaid, which is the $19.39 subsidy cost. 

One difficulty in applying the ADR method to a loan or 

guarantee is that the implicit market risk—and hence the 

appropriate discount rate—can vary significantly over the 

life of the loan.15 Another issue is that spreads between 

Treasury rates and private lending rates are influenced by 

a variety of factors other than market risk, such as differential tax treatment, transaction costs, and liquidity.16

Some or all of those other factors could be considered 

legitimate elements of the opportunity cost to the government of making or guaranteeing loans since they affect 

people’s willingness to pay for those credit services. If 

such factors were considered significant, adjustments 

would be necessary to reflect only that part of the rate 

spread attributable to market risk. 

Options Pricing. The general idea behind options-pricing 

methods is that assets with the same payoffs must have 

the same price; otherwise, investors would have the opportunity to earn a risk-free profit by buying low and selling high. The options-pricing method that CBO used for 

this analysis—the binomial pricing model—exploits that 

“no arbitrage” assumption by inferring the value of an 

option (in this case, a loan guarantee) from the price of a 

portfolio of assets that has the same payoff to the government as the guarantee.17 (For an explanation of why a 

loan guarantee can be considered an option, see Box 1 on 

page 11.) A highly useful feature of that approach is that 

the payoff from a loan guarantee can be approximately 

replicated using a portfolio made up of risk-free bonds 

and assets of the borrowing firm, all of whose prices can 

be estimated.

In principle, both options pricing and risk-adjusted discount rates should yield identical subsidy estimates. As a 

practical matter, they entail different types of approximations. Because options-pricing methods account for the 

changing risk of loan guarantees over time, they are likely 

to be more accurate at estimating the market value of 

subsidies—but only when the necessary data and models 

are available. Otherwise, they may be difficult or cumbersome to apply. 

The practices of private financial institutions offer some 

guidance about which method is likely to prove the most 

accurate and feasible in particular cases. Options-pricing 

methods are often used for estimating the value of credit 

guarantees to businesses, which suggests that they are 

most suitable for credit to commercial enterprises. In 

those cases, the fact that things other than market risk can 

affect interest rate spreads is less relevant, because the 

value of the reference assets used for pricing (generally, 

publicly traded stocks) are less sensitive to those nonrisk 

factors. Private financial institutions also rely on optionspricing methods to value the option to prepay residential 

mortgages. Hence, those methods may be applicable to 

the many government mortgage programs that include a 

prepayment option. In addition, analysts have used 

options-pricing methods to value deposit insurance.18

Options-based methods are rarely used, however, to value 

loans or loan guarantees extended to individuals because 

of the difficulty of estimating the required variables, such 

as expected rates of return on borrowers’ assets. For federal loans or guarantees made to individuals (such as student loans), a more standard approach would be to use 

15. For example, many firms use the capital asset pricing model 

(CAPM) to adjust discount rates for risk when valuing capital 

investments. For a loan guarantee, the correct CAPM rate and 

thus the value of the guarantee change with time and with the 

assets and liabilities of the borrower and so are difficult to estimate.

16. See, for example, R. Glenn Hubbard, Money, the Financial System, 

and the Economy (New York: Addison-Wesley, 1994), pp. 143-

155.

17. Appendix B provides an example of how the binomial pricing 

model might be used to estimate the value of a loan guarantee. For 

more information about such models, see Robert L. McDonald, 

Derivatives Markets (New York: Addison-Wesley, 2003), Chapter 

10.

18. Alan Marcus and Israel Shaked, “The Valuation of FDIC Deposit 

Insurance Using Option-Pricing Estimates,” Journal of Money, 

Credit, and Banking (November 1984), pp. 446-460; and Ehud 

Ronn and Avinash Verma, “Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model,” Journal of Finance (September 

1986), pp. 871-895.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 9

private-sector rates of return on consumer credit of similar quality to identify a risk-adjusted discount rate.19

That rate would be used to discount expected net cash 

flows and thus to calculate the difference between those 

flows and the loan principal. 

Other federal credit programs—such as loan assistance to 

sovereign states, municipalities, and special-purpose enterprises—do not fit directly into either the commercial 

or consumer categories. Estimating the cost of such programs is difficult even under current budgetary rules because there often is little or no experience with a similar 

transaction on which to draw. In some of those cases, an 

options-pricing approach is likely to be feasible; in others, 

using the ADR method will be preferable. 

Estimating the Subsidies to Chrysler 

and America West Airlines

As noted in Box 1, options pricing is an especially useful 

type of risk adjustment for valuing complex loan guarantees extended to firms. Accordingly, this analysis illustrates the effect of risk adjustment on federal creditsubsidy estimates by applying options pricing to the federal guarantees extended to Chrysler and America West 

Airlines in 1980 and 2002, respectively—two instances of 

complicated guarantee transactions between the government and severely distressed companies. For comparison, 

this analysis also estimates the value of those guarantees 

using the Treasury-rate approach.

The government’s cost of extending a loan guarantee—

whether estimated using Treasury-rate or market-based 

methods—depends on the present and future financial 

condition of the borrower and the terms of the guarantee. 

With both the Chrysler and AWA guarantees, the financial outlook for the firms was highly uncertain and the 

guarantee terms were complex. That uncertainty and 

complexity must be addressed regardless of the estimating 

method used.

Chrysler’s Financial Condition and Guarantee Terms

In the 1970s, rising energy prices and the associated 

growth in demand for fuel-efficient cars hurt the U.S. 

auto industry.20 Chrysler was especially hard hit because 

of its high costs, weak financial condition, and unfavorable mix of vehicles. By 1979, the company faced a 

declining market share, a reduced credit rating, and operating losses of more than $1 billion. With its financial 

survival in doubt, Chrysler asked the federal government 

for assistance to avoid bankruptcy and possible liquidation. 

The Congress held hearings on Chrysler’s financial condition in October and November of 1979. Arguments in 

favor of federal assistance included the temporary nature 

of Chrysler’s difficulties and their external causes: “a series 

of energy-related external shocks not of the company’s 

making, which are unique to the automobile industry.”21

Advocates of assistance also argued that the direct cost of 

inaction—more than 500,000 job losses and a $3 billion 

to $10 billion increase in the federal deficit, they 

claimed—was greater than the maximum cost to the government. Opponents of federal assistance argued that the 

projected 

social costs of Chrysler’s failure were exaggerated, that 

federal aid would expose the government to large losses, 

and that the discipline of the private market would be 

diminished if the government encouraged expectations 

that it would intervene to save large failing companies. 

In the end, lawmakers enacted the Chrysler Corporation 

Loan Guarantee Act in December 1979.

The following spring, in negotiations between Chrysler 

and the Secretary of Treasury, the government agreed to a 

loan guarantee of up to $1.5 billion of principal plus accrued interest—contingent on the company’s obtaining 

$1.5 billion in financial assistance and commitments 

from nongovernmental sources. The government became 

Chrysler’s senior creditor, meaning that it would be first 

in line to take the company’s assets in the event of default. 

Chrysler also agreed to pay the government an annual 

guarantee fee of 1.0 percent of the guaranteed amount 

and to furnish it with warrants for 14.4 million common

19. That rate, which reflects the cost of the capital backing the loans, 

is generally lower than the quoted borrowing rate, which includes 

additional compensation for default losses. For an extensive discussion of the cost of capital, see, for example, Richard Brealey 

and Stewart Myers, Corporate Finance, 7th ed. (New York: 

McGraw Hill, 2003).

20. This Chrysler analysis is based in part on Robert F. Bruner, 

Chrysler’s Warrants: September 1983, Case No. UVA-F-0682 

(Charlottesville, Va.: University of Virginia, Darden Graduate 

School of Business Administration, 1991).

21. House Report No. 96-690 to accompany H.R. 5860 and House 

Conference Report No. 95-730, December 20, 1979.
10 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

shares of Chrysler stock. Those warrants gave the government the right to buy Chrysler stock at $13 per share 

through 1990. (Participating banks were also given warrants on the same terms for nearly 13.3 million shares.)22

With the guarantees, Chrysler was able to borrow at an 

average interest rate of 12.12 percent, much lower than 

the 20 percent rate it had paid before receiving the guarantee. 

AWA’s Financial Condition and Guarantee Terms 

America West Airlines was the eighth largest U.S. passenger airline in 2002, with a fleet of 146 planes serving 59 

destinations.23 Its operations were concentrated around 

principal hubs in Phoenix and Las Vegas and a minor hub 

in Columbus, Ohio. In 2001, AWA flew 20 million 

passengers and generated $2 billion in revenues.

Box 1.

Loan Guarantees as Put Options

In general, options-pricing methods are applicable to 

loans and loan guarantees because a loan guarantee is 

a type of “put option”—a contract that gives the 

holder the right (though not the obligation) to sell 

specified assets for a predetermined price, no matter 

how little they turn out to be worth.1

Suppose a factory owner obtains a put option to sell 

the factory for a “strike price” of $1 million during 

the next three months. If the market value of the factory is greater than $1 million, the owner will not exercise the option because other buyers would be 

likely to pay more than that strike price. However, if 

the value of the factory falls below $1 million during 

the life of the option, the owner will exercise the option and gain the difference between the market 

value of the asset and the strike price. For instance, as 

illustrated in the figure to the right, if the price of the 

factory declines to $750,000, the owner will exercise 

the option to sell at $1 million and make $250,000. 

In the extreme, if the value of the factory drops to 

Payoff to the Holder of an Option

to Sell an Asset for $1 Million

zero, the owner will collect $1 million from the seller 

(the writer of the option). The put option thereby 

insures the factory owner against a decline in asset 

price.

Now consider a buyer who purchases the factory at 

its current market value of $1 million with money 

obtained from a federally guaranteed loan secured by 

the factory. Suppose that with a 100 percent federal 

guarantee, a bank is willing to lend the buyer $1 million to purchase the plant. In that case, the potential 

1. This discussion draws on “Options Are Insurance,” Chapter 

2, Section 5 in Robert L. McDonald, Derivatives Markets 

(New York: Addison-Wesley, 2003).

0.25

0.75

1.00

1.00

0

0

Gain (Millions of dollars)

Price of Asset (Millions of dollars)

22. Ultimately, Chrysler borrowed just $1.2 billion and issued less 

than the full number of warrants. It issued $500 million in notes 

at 10.35 percent in June 1980, another $300 million in July at 

11.40 percent, and $400 million in February 1981 at 14.90 percent. The valuations in this analysis are based on the full amount 

of the initial agreements, since it was not known at the time that 

less than the full amount would be utilized.

23. America West Holdings Corporation—which trades on the New 

York Stock Exchange under the symbol AWA—is the parent company of America West Airlines. In 2002, the airline was the only 

operating subsidiary of America West Holdings, although there is 

now a second subsidiary (the Leisure Company). This report uses 

AWA, America West Holdings, and America West Airlines interchangeably.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 11

That year was a difficult one for U.S. airlines, however. 

Earnings were in decline even before the terrorist attacks 

of September 11 because of a fall in high-yield business 

traffic, rising fuel costs, and reduced operating margins. 

The terrorist attacks dramatically worsened the economic 

condition of the airline industry, including AWA, whose 

credit rating was downgraded in a series of steps. Moody’s 

reduced its rating of AWA’s senior unsecured debt from 

B1 in April 2001 to Ca on November 21, 2001. Standard 

& Poor’s similarly lowered AWA’s credit rating from B+ 

on September 18, 2001, to CCC- on November 1, 2001.

In the wake of the September 11 attacks, lawmakers enacted the Air Transportation Safety and System Stabilization Act, which allowed airlines to apply for credit guarantees from the federal government. The credit downgrades described above meant that AWA would have 

found it expensive—if not impossible—to raise funds in 

private markets. Accordingly, in November 2001, the airline applied for a federal loan guarantee. In January 2002, 

it received final approval from the Air Transportation Stabilization Board for a $380 million guarantee.

Supported by that guarantee, AWA was able to borrow 

$429 million from private lenders and obtain additional 

concessions and financing (mainly reductions in rent on 

aircraft it leased and commitments for future financing). 

That funding allowed AWA to restructure its debt and 

lease commitments.24 The AWA loan that the governBox 1.

Continued

payoffs to the borrower from the guarantee would be 

the same as those shown in the figure for the original 

owner who held an option to sell the factory. In 

other words, the guaranteed loan secured by the factory gives the borrower the right to “put” the collateral asset to the government at a price equal to the 

balance on the loan. Of course, the borrower will exercise that option only if the price of the factory falls 

below the amount of the loan, or $1 million. Thus, 

the loan guarantee is insurance against a drop in the 

value of the factory, which was the source of the 

loan’s credit risk. The loan guarantee shifts the risk of 

a decline in the price of the collateral asset from the 

lender to the government.

Thus, the position of a borrower is similar to that of 

the holder of a put option, whereas the position of 

the lender or guarantor is akin to that of the writer of 

the option. That is, the borrower can “sell” (put) the 

collateral assets to the lender or guarantor at a price 

equal to the unpaid balance on the loan. In fact, the 

relationship between the value of collateral assets and 

of debt is a key factor affecting the likelihood and expected cost of default—just as the value of the underlying assets relative to the strike price is key to the 

value of a put option. When the value of the assets is 

substantially above the amount owed, the borrower 

will refinance or sell the assets and pay off the debt 

rather than default on the loan obligation. But when 

the value of the assets is less than the unpaid balance, 

the borrower no longer has the opportunity to refinance or to liquidate the assets and repay the loan 

obligation. In that case, default is more likely. If default occurs, the guarantor pays the amount due to 

the lender, seizes the collateral assets, and takes a loss 

equal to the difference between the promised loan 

payments and the residual value of the assets. In the 

case of a loan to a commercial enterprise, the potential range of losses to the guarantor is equivalent to 

that for a written put option on the assets of the firm 

with a strike price equal to the face value of the loan.

The correspondence between put options and loan 

guarantees—along with the availability of computer 

programs for calculating option values—makes options pricing a natural choice for estimating riskadjusted subsidy costs for some federal direct and 

guaranteed loans. Options-pricing methods are especially useful in valuing complex loan guarantees extended to companies, such as the federal guarantees 

to Chrysler and America West Airlines that are analyzed in this study.

24. As compensation for rent reductions on aircraft and other concessions, America West issued some of its lessors approximately 

$104.5 million in convertible senior notes, with an interest rate of 

7.5 percent, which were due in 2009 and guaranteed by the company. AWA also converted its existing revolving credit facility into 

an $89.9 million term loan maturing in 2007.
12 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

ment guaranteed had a seven-year term with equal repayments of principal scheduled for years three to seven. It 

could also be prepaid at any time without penalty. Because of the guarantee, the loan carried a relatively low interest rate—the three-month London interbank offer rate 

(LIBOR) plus 0.4 percentage points, paid quarterly to 

the lender.

AWA was also obligated to pay guarantee fees to the government and other loan participants equaling 5.5 percent 

of the loan balance in the first year and 8.0 percent thereafter. Those fees left the company with a high effective interest rate—LIBOR plus 8.4 percentage points—and 

thus a strong incentive to prepay the loan if its financial 

condition improved. As further compensation to the government, America West issued it warrants to purchase up 

to 18.8 million shares of Class B common stock at $3 per 

share for 10 years.25

Treasury-Rate Subsidy Estimates

The net cost to the government of the AWA and Chrysler 

guarantees is the cost of the guarantees minus the value of 

the warrants and guarantee fees. The value of each of 

those components is affected by uncertainty about default, prepayment, and future asset and stock values. For 

this analysis, CBO used the same statistical models to 

estimate the distribution of future cash flows for both the 

Treasury-rate and market-value estimates so that only the 

discount rates would differ between the two sets of estimates. To determine the effect of risk adjustment on each 

component of cost, CBO estimated the value of the guarantees, warrants, and fees separately.26

Guarantee Value. Under credit reform, the cost of default 

is the discounted present value of expected federal outlays 

to lenders resulting from borrowers’ failure to make 

scheduled payments, net of any recoveries. Currently, 

those outlays are discounted to the present using the rate 

on Treasury securities with the same maturities as the 

cash flows. The first step in estimating that cost, therefore, is to specify the annual distribution of the probability and severity of default.

Various analytical methods are available to model the 

government’s exposure to the risk that a guaranteed borrower will default. A method that takes into account the 

economic causes of default should be based on the projected path of the value of the borrower’s assets. Such an 

approach, which CBO used to develop market-value estimates as well as Treasury-rate estimates, yields estimates 

of the probability of default over time and the amounts 

expected to be recovered in default. In the case of the 

AWA guarantee, CBO projected the value of the company’s assets on the basis of their value at the time of the 

guarantee and the historical returns on and volatilities of 

airline-industry assets as a whole. The distribution of 

Chrysler’s future asset values was similarly based on historical returns and volatilities for the auto industry. (For 

information about the parameter values used in those calculations, see Appendix C.)

Another critical variable in the event of default—the unpaid loan balance—depends in part on the amortization 

schedule for the guaranteed loan. It is also affected by the 

probability of voluntary prepayment. The high annual 

fees paid by AWA suggest that the airline will prepay its 

loan when it can find more favorable terms from private 

lenders. In CBO’s analysis, prepayment is assumed to 

occur when AWA’s asset value rises above the book value 

of its liabilities. The loan terms that Chrysler received 

were more favorable, but the automaker was also projected to prepay its loan if the market value of its assets 

exceeded the value of its liabilities. In those cases, the 

quality of both AWA’s and Chrysler’s credit would probably rise to the point that they could find private financing 

at a lower rate than that on their guaranteed loan.

The priority of the government’s claim in the event of default affects the expected recovery from the borrower. In 

the case of AWA, the government-guaranteed loan has 

lowest priority in liquidation proceedings—all other debt 

holders would be paid before the government. In the case 

of Chrysler, by contrast, the government-guaranteed loan 

had highest priority after current liabilities.

25. In addition, other loan participants received warrants to purchase 

as many as 3.8 million shares of AWA’s Class B common stock.

26. The Treasury-rate estimates presented here are not the budget estimates that were made at the time of the guarantees. In 2001, 

CBO estimated the total cost of the Air Transportation Safety and 

System Stabilization Act (H.R. 2926), which provided authority 

for the government to guarantee loans to qualified airlines under 

terms to be agreed to by the Air Transportation Stabilization 

Board. CBO estimated that under that act, $8 billion in guarantees would be issued at an average subsidy rate of 25 percent, for a 

total cost of $2 billion. (At that point, neither the terms of the 

guarantees nor the specific recipients were known.) The Chrysler 

guarantee was issued prior to the Federal Credit Reform Act, so it 

was accounted for in the budget on a cash basis.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 13

Table 1.

Estimated Federal Costs of Loan 

Guarantees to Chrysler

and America West Airlines

(Millions of dollars)

Source: Congressional Budget Office.

Note: These estimates reflect conditions when the guarantees 

were made, not the final results.

CBO discounted expected cash flows from the AWA 

guarantee at a rate of 4 percent (the rate on seven-year 

Treasury bonds). That procedure yielded a present-value 

cost of $84.8 million for the AWA guarantee (see Table 

1). For Chrysler, expected cash flows were discounted at 

the then-prevailing 10-year Treasury rate of 10.52 percent, producing an estimated cost of $255.5 million. In 

the Treasury-rate calculations, the value of the Chrysler 

guarantee is three times that of the AWA guarantee 

mostly because the guaranteed loan to the automaker was 

much larger (up to $1.5 billion versus $380 million for 

AWA).

Warrant Values. As noted above, AWA partially compensated the government for the loan guarantee by giving it 

warrants to buy as many as 18.8 million shares of the 

company’s Class B common stock at an exercise price of 

$3 per share (the strike price) for a term of 10 years. 

Those warrants increase in value with the market price of 

AWA stock and thus provide the government with additional compensation if its guarantee allows the company 

to return to profitability. Similarly, Chrysler issued warrants to the government to purchase up to 14.4 million 

shares of Chrysler’s common stock, also with a term of 10 

years.

CBO calculated the Treasury-rate value of those warrants 

with the same type of probabilistic analysis that it used to 

estimate the cost of the guarantees—in other words, it 

calculated a probability distribution of future stock 

prices. The sum of the differences between those probability-weighted prices and the strike price is the expected 

future value of the warrants. Discounting that future 

value at a risk-free rate (the same 4 percent and 10.52 

percent used above) produces Treasury-rate estimates of 

the warrants’ value at the time they were issued: $79.7 

million in the case of AWA and $119.0 million in the 

case of Chrysler.

Fees. The present value of the guarantee fees to be paid to 

the government depends on the same variables that determine the value of the guarantee itself. The probabilities of 

default and prepayment every year are especially important because fee income to the government terminates 

with either event. For each company, CBO used the same 

assumptions about those variables to value guarantee fees 

that it used to estimate loan guarantee and warrant values. Besides those probabilities, fee income also depends 

on the fee rate (a percentage of the outstanding balance) 

and the amortization schedule of the loan.

AWA agreed to pay guarantee fees of 5.5 percent of the 

unpaid balance in year one and 8.0 percent in later years 

as long as the loan was outstanding. Chrysler agreed to 

pay guarantee fees of 1.0 percent of the unpaid balance 

each year for the duration of the loan. (In Chrysler’s case, 

the government-guaranteed loan did not have a planned 

amortization schedule.) Under the current approach, the 

present value of expected guarantee fees is $52.5 million 

for AWA and $28.9 million for Chrysler, CBO estimates.

Net Cost. In Treasury-rate terms, when all of the components of the loan guarantee are taken into account, the 

AWA deal is expected to produce a net gain to the government, in that the value of the warrants and fees that it received exceeds the value of the loan guarantee by $47.4 

million (see Table 1). That gain can be attributed to the 

assumption under the current approach that the price of 

market risk is zero. Such an assumption creates the appearance that AWA paid the government more than the 

value of its guarantee. If that were true, then AWA should 

have rejected the offered terms because it should have 

America 

West Chrysler

Treasury-Rate Estimates

Loan Guarantee -84.8 -255.5

Warrants 79.7 119.0

Guarantee Fees 52.5 28.9

Net Gain or Loss (-) 

to the Government 47.4 -107.6

Market-Value Estimates

Loan Guarantee -133.2 -347.5

Warrants 50.4 80.6

Guarantee Fees 56.6 27.9

Net Gain or Loss (-) 

to the Government -26.3 -239.0
14 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

been able to obtain credit support on more-favorable 

terms privately.

The Treasury-rate estimates for the Chrysler guarantee, 

by contrast, suggest that the company received a guarantee worth $107.6 million more than the fees and warrants 

it paid in return.

As those calculations show, accurately estimating the subsidy cost of a loan guarantee under current credit-reform 

rules requires complex analysis, even in the absence of 

warrants. From an analyst’s perspective, if an appropriate 

options-pricing model is available, along with the requisite data, the difficulty of estimating that cost should be 

similar using either approach.

Market-Value Subsidy Estimates

Using an options-pricing method, CBO also estimated 

the market value of the AWA and Chrysler guarantees 

from separate estimates of the value of the guarantees, 

warrants, and fees. Both the market-value and Treasuryrate estimates were based on the same expected cash 

flows, ensuring that differences between them were attributable to risk adjustment.

Guarantee Value. CBO estimated the market value of 

each loan guarantee by treating it as a put option held by 

the borrower to sell the assets of the company to the government at a price equal to the unpaid loan balance for 

the life of the loan (see Box 1). To calculate the price of 

the option, CBO used a binomial options-pricing 

model.27 The information needed to value the loan guarantee using that method is identical to that required for 

the Treasury-rate estimates. Further, defaults and prepayments are assumed to be triggered by the same conditions 

as those used for the Treasury-rate estimates.28 On the 

basis of that options-pricing approach, CBO estimates 

that the AWA guarantee had a fair-market value of 

$133.2 million; and the Chrysler guarantee, $347.5 million (see Table 1).

Warrant Values. Determining the market value of the 

warrants granted to the government is a relatively simple 

calculation.29 Again, the underlying cash flows are the 

same as for the Treasury-rate estimates; only the discount 

rate is different.

The market-based estimates of the value of the warrants 

differ substantially from the Treasury-rate estimates because warrants have significant exposure to market risk. 

CBO’s options-pricing analysis estimates a warrant price 

of $2.67 per AWA share, or a total market value of $50.4 

million for 18.8 million common shares, compared with 

$79.7 million under the current approach. For Chrysler, 

the market-value estimate of the warrant price is $5.60 

per share, or $80.6 million for 14.4 million shares, versus 

$119.0 million using Treasury rates. Those differences 

result from recognizing the cost of market risk.

Fees. CBO estimated the value of the guarantee fees, like 

the value of the guarantee itself, using a binomial options-pricing model. The inputs are the same as those 

used to value the cost of the guarantee, with the addition 

of the schedule for guarantee fees.

For AWA, the expected value of guarantee-fee payments 

to the government is $56.6 million, about $4 million 

more than the estimate using the current approach. Conversely, Chrysler’s guarantee-fee payments to the government have an expected value of $27.9 million, about $1 

million less than the Treasury-rate estimate. The marketvalue estimates of guarantee fees can be either higher or 

lower than the Treasury-rate estimates because of the different effects that prepayment and default have on the 

market risk of such fees.30 In contrast, the estimated cost 

of guarantees is consistently higher under market valua27. See McDonald, Derivatives Markets, Chapters 10 and 11. That 

model is also sometimes referred to as the Cox-Ross-Rubinstein 

pricing model after its developers. CBO used a binomial model 

rather than the more familiar Black-Scholes model because it 

yields more-accurate values by accounting for specific features of 

loan guarantees.

28. For more details, see Appendix C and the companion technical 

paper by the authors of this report, “Valuing Federal Loans and 

Loan Guarantees Using Options-Pricing Models,” available at 

www.cbo.gov/Tech.cfm.

29. CBO used a version of the Black-Scholes model to calculate warrant values.

30. The flow of guarantee fees to the government stops when the borrower prepays or defaults. If the borrower is more likely to default 

than to prepay, the market value of fees tends to be lower than 

under the current approach because the guarantee fees are positively correlated with the economy. Conversely, if prepayment is 

more likely than default, the market value of the fees tends to be 

higher because the fees are more likely to continue in bad economic conditions and end in good conditions.
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 15

Table 2.

Estimated Subsidy Rates for Federal Loan Guarantees to Chrysler

and America West Airlines

(Percentage of amount guaranteed)

Source: Congressional Budget Office.

tion than under the current approach, and the estimated 

value of warrants is consistently lower.31

Net Cost. The market-value estimates of the AWA and 

Chrysler guarantees (including all parts of the transactions) are higher than the estimates produced under current credit-reform rules. Moreover, both transactions are 

estimated to cost the government money—$239.0 billion 

in the case of Chrysler and $26.3 billion in the case of 

AWA—which indicates that the government gave greater 

value than it received in those deals. That result is consistent with the proposition that if the government had 

charged more than the market price for credit assistance, 

the borrowers would have been able to obtain such assistance at a lower cost from the private sector.

The Effect of Market Risk 

on Subsidy Rates

Converting those Treasury-rate and market-value estimates to a percentage of the amount guaranteed produces 

estimated subsidy rates for the various components of the 

loan guarantees (see Table 2). The government received 

much higher rates of compensation in fees and warrants 

from AWA than from Chrysler. For the warrants, 

Chrysler’s strike price was so far above its market price 

that the probability that the warrants would be exercised 

was small, resulting in a low estimated warrant value under both methods. The AWA warrants were “in the 

money” when they were issued (in other words, valuable 

even if exercised immediately) and thus were much more 

likely to be of value to the government. AWA also agreed 

to considerably higher guarantee fees. Nevertheless, the 

AWA deal still involved a net government subsidy of 6.9 

percent on a market-value basis. The Chrysler guarantee, 

by comparison, involved a federal subsidy of 15.9 percent.

Those overall subsidy rates differ substantially from the 

ones in the Treasury-rate estimates. The market-value 

subsidy rates for both Chrysler and AWA are more than 

double the rates estimated under current credit-reform 

rules. Those differences result solely from including the 

market price of risk.

Uncertainty and Reestimates

Federal budget analysts initially estimate subsidy costs 

when a loan guarantee is extended; hence, those estimates 

are subject to uncertainty about the ultimate costs. Information available when the guaranteed loans were made 

indicated that the AWA and Chrysler guarantees would 

be expensive to the government. In fact, both deals may 

end up being favorable for the government. Chrysler repaid its guaranteed loan in full by September 1983. Instead of holding on to the warrants, the Treasury sold 

them in a sealed-bid auction. Chrysler bought back its 

warrants for $21.60 a share, yielding the government 

$311 million. AWA’s guaranteed loan is still outstanding. 

The year after the guarantee was made, the company’s

America West Chrysler

Treasury-Rate 

Estimate

Market-Value 

Estimate

Treasury-Rate

Estimate

Market-Value

Estimate

Loan Guarantee -22.3 -35.1 -17.0 -23.2

Warrants 21.0 13.3 7.9 5.4

Guarantee Fees 13.8 14.9 1.9 1.9

Net Government Subsidy 12.5 -6.9 -7.2 -15.9

31. The reason is that the payoff to the government from warrants is 

highest in good economic conditions, when resources are more 

plentiful and thus less highly valued, and is lowest in bad economic conditions. The opposite is true with guarantees: they 

require the most government resources during bad times, when 

resources are scarcer and thus more highly valued.
16 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

Figure 1.

AWA Stock Prices, January 2000 to July 2004

(Dollars)

Source: Standard & Poor’s COMPUSTAT database.

stock price declined, but it rebounded thereafter (see Figure 1). In March 2004, the price stood at more than $9 

per share, implying that if the government exercised its 

$3 per-share warrants at that price, it would gain more 

than $100 million. (Since then, AWA’s stock price has declined further, but at $6 per share, it remains above the 

warrant price.)

Those cases might suggest that Treasury-rate subsidy estimates are too high rather than too low. However, a more 

valid conclusion is that such estimates are uncertain. In 

fact, many examples exist of loan guarantees whose value 

has deteriorated over time. For instance, the $100 billion 

in loan guarantees that the Federal Housing Administration’s Mutual Mortgage Insurance Fund made in 2000 

were initially estimated to net the government approximately $2 billion. Since then, that estimate has been 

revised three times to indicate progressively smaller expected gains. Currently, those loan guarantees are projected to net only about $680 million—one-third of the 

amount originally estimated.32

The Federal Credit Reform Act recognizes that subsidy 

costs are uncertain and that realized gains and losses will 

deviate from initial estimates. It deals with that uncertainty in a logical way: by allowing analysts to make the 

best estimate possible when a loan or guarantee is originated and then revise that estimate as new information 

becomes available. Under the FCRA, initial subsidy estimates are reestimated over the life of a loan or guarantee 

to reflect actual cash flows and other factors.33 The original estimate plus the sum of lifetime reestimates equals 

the realized subsidy. Consistent with the principles of accrual accounting, those reestimates are included in annual 

budget outlays and in the budget deficit or surplus.34

Market-value reestimates can be calculated analogously to 

Treasury-rate reestimates, using the same models initially

Jan-00 Jul-00 Jan-01 Jul-01 Jan-02 Jul-02 Jan-03 Jul-03 Jan-04 Jul-04

0

2

4

6

8

10

12

14

16

18

20

AWA Receives

Federal Loan

Guarantee

32. See the Office of Management and Budget’s annual Federal Credit 

Supplement for fiscal years 2003, 2004, and 2005, Table 8.

33. The Office of Management and Budget currently requires two 

types of reestimates. The first type is a one-time adjustment for 

interest rates, which corrects for any discrepancy between interest 

rates at the time of the original estimate and interest rates at the 

time the loans are disbursed. The second type is an annual technical reestimate, which adjusts for factors such as changes in prepayments, defaults, and recoveries (but not interest rates).

34. See Congressional Budget Office, Credit Subsidy Reestimates, 

1993-1999 (September 2000).
Table 3.

Initial and Reestimated Federal Costs from the Loan Guarantee

to America West Airlines

(Millions of dollars)

Source: Congressional Budget Office.

Note: Reestimates are recorded in the federal budget as the change in subsidy value since the previous estimate or reestimate. For clarity, 

this table shows the subsidy value, not its change.

used to calculate subsidy values.35 Reestimation involves 

updating the parameters of a model to reflect differences 

between initial assumptions and current information. For 

comparative purposes, CBO calculated both types of reestimates for the AWA loan guarantee.36 In that case, the 

key variable driving the reestimates is stock price. The 

drop in the company’s stock price during the first year 

that the loan was outstanding implies a significant increase in the probability and severity of future default and 

thus a sharp decline in the value of the warrants. Both of 

those factors increase the estimated subsidy cost of the 

guarantee after one year—from a government gain of 

$47.4 million to a loss of $115.5 million under current 

credit-reform rules or from a loss of $26.3 million to a 

loss of $180.9 million with market risk taken into account (see Table 3). By January 2004, however, AWA’s 

greatly improved financial condition changed the net 

subsidy cost into an expected gain: of $250.0 million in 

the Treasury-rate estimates or $229.6 million in the market-value estimates.

The probabilistic models that underlie both the Treasuryrate and market-value estimates are useful for depicting 

the probability distribution of future guarantee costs and 

thus the uncertainty associated with the initial cost estimates. The probability distribution of the future market 

value of the AWA guarantee, projected forward two years 

from January 2002 (when the guarantee was approved), 

is shown in Figure 2. That guarantee value has a lower 

bound of zero, which reflects the possibility of a large increase in asset value that enables AWA to prepay the loan, 

extinguishing the value of the guarantee. It has an upper 

bound of $380 million, the figure that results when 

AWA’s asset value falls to the point where default occurs 

and the government recovers nothing from the company. 

The distribution in Figure 2 suggests that the most probable event, looking ahead two years, is a market value 

between $50 million and $100 million for the AWA 

guarantee. In that case, the company would still be operating, but the guarantee would remain costly to the govOriginal

Estimate

January 2003

Reestimate

January 2004

Reestimate

Loan Guarantee

Market-Value Estimate -133.2 -241.8 -8.2

Treasury-Rate Estimate -84.8 -189.9 -3.9

Warrants

Market-Value Estimate 50.4 13.7 231.6

Treasury-Rate Estimate 79.7 24.2 249.1

Guarantee Fees

Market-Value Estimate 56.6 47.2 6.1

Treasury-Rate Estimate 52.5 50.2 4.8

Net Gain or Loss (-) to the Government

Market-Value Estimate -26.3 -180.9 229.6

Treasury-Rate Estimate 47.4 -115.5 250.0

35. To account for the price of risk more accurately, the reestimate 

could be adjusted with a charge for market risk.

36. CBO did not produce reestimates for the Chrysler guarantee 

because the requisite historical data were not readily available. 
18 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

Figure 2.

Probability Distribution of Market Values of the AWA Loan Guarantee

Probability (Percent)

Source: Congressional Budget Office.

Note: These numbers are two-year projections looking forward from January 2002, when the America West Airlines (AWA) loan guarantee 

was approved.

ernment because of the significant possibility of a default 

during the five years left on the loan. 

The projected market-value distributions of fee income 

and warrant values can be obtained similarly by projecting the distributions of future cash flows from fees and 

warrants. (The distribution for warrant values is shown in 

Figure 3.) Indeed, much of the variation in CBO’s reestimates for AWA can be attributed to the high volatility of 

future warrant values, which is a consequence of the company’s highly volatile stock price. 

The distributions of future guarantee and warrant values 

shown in Figures 2 and 3 reveal that the January 2004 reestimates for AWA were extremely unlikely from the perspective of January 2002. The vertical line in Figure 2 indicates the guarantee value corresponding to AWA’s asset 

value at the end of 2003. As the figure illustrates, the 

probability of such a large reduction in guarantee value 

was small. Similarly, the vertical line in Figure 3 indicates 

that it was extremely unlikely that the value of the warrants would rise to the level that occurred.

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F F F F

F

F

F

F

F

F

F

F

F

F

F

FF

FF 0 F

1

2

3

4

5

6

7

0 50 100 150 200 250 300 350 400

January 2004

Reestimate:

$8.2 million

Market Value of Guarantee

(Millions of dollars)
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 19

Figure 3.

Probability Distribution of Market Values of the AWA Warrants

Probability (Percent)

Source: Congressional Budget Office.

Note: These numbers are two-year projections looking forward from January 2002, when the America West Airlines (AWA) loan guarantee 

was approved.

F

F

F

F

F

F

F

F

F

F

F

F

F

F F F F

F

F

F

F

F

F

F

F

F

F

F

FF

FF0 F

1

2

3

4

5

6

7

0 50 100 150 200 250 300 350 400 450 500

January 2004

Reestimate:

$231.6 million

Market Value of Warrants

(Millions of dollars)

A

Volume and Cost of Federal

Credit Programs

The tables in this appendix offer a sense of the scale 

of the federal government’s credit programs by detailing 

the total amounts of direct loans and loan guarantees that 

were outstanding at the end of each of the past 10 fiscal 

years (see Table A-1). They also show the budget authority provided for the subsidy costs of those loans and guarantees in 2003 (see Table A-2). In both cases, the numbers are broken down by major credit programs.

Table A-1.

Federal Direct and Guaranteed Loans Outstanding, 1994 to 2003

(Billions of dollars)

Source: Congressional Budget Office based on data from the Office of Management and Budget.

Notes: * = less than $50 million; FHA = Federal Housing Administration; VA = Department of Veterans Affairs; FFEL = Federal Family Education Loan program.

Excludes defaults on guarantees that result in recoveries. Excludes secondary loan guarantees issued by the Government National

Mortgage Association.

APPENDIX

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Direct Loans

Ford Student Loans * 2.8 11.6 21.2 31.7 45.8 57.7 70.5 80.1 84.5

Rural Housing and Community 

Development 35.3 36.2 36.3 36.4 36.3 35.2 33.3 33.5 33.4 32.9

Rural Electrification, Telephone, 

and Telecommunications 37.6 37.4 35.5 34.0 33.6 33.1 32.1 31.2 31.7 32.1

Export-Import Bank 7.5 7.6 7.9 10.1 10.8 12.2 11.1 11.7 11.4 11.1

Other 78.8 79.3 75.2 79.7 73.4 74.1 73.9 66.4 63.4 58.7

Total 159.2 163.3 166.5 181.4 185.8 200.4 208.1 213.3 220.0 219.3

Loan Guarantees

FHA Housing 381.9 401.4 455.2 448.6 469.6 504.1 548.5 557.9 563.4 496.4

VA Housing 155.0 154.5 154.8 170.5 200.2 221.3 224.3 236.9 264.5 323.1

FFEL Student Loans 75.0 86.1 101.9 101.0 100.5 126.7 144.2 159.3 181.9 213.3

Small Business Administration 23.6 28.6 30.9 35.2 37.5 39.4 33.8 36.6 41.1 53.4

Export-Import Bank 16.8 17.8 17.8 22.1 21.8 25.4 29.8 30.5 31.0 33.5

Other 46.5 38.4 45.5 44.5 52.1 58.9 62.3 62.9 63.7 64.8

Total 698.8 726.8 806.1 821.9 881.7 975.8 1,042.9 1,084.1 1,145.6 1,184.4
22 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

Table A-2.

Budget Authority for Subsidies for Federal Direct and Guaranteed Loans, 2003

Source: Congressional Budget Office based on data from the Office of Management and Budget.

Budget Authority

(Millions of dollars)

Direct Loans

Rural Housing and Community Development 288

Agricultural Credit and Community Advancement 259

International Debt Restructuring 211

Small Business Disaster Loans 117

Rural Electrification, Telephone, and Telecommunications -36

Ford Student Loans -318

Other 136

Total 657

Loan Guarantees

Federal Family Education Loan Program Student Loans 6,411

Department of Veterans Affairs Housing 547

Export-Import Bank 320

Air Transportation Stabilization 180

Commodity Credit Export Loans 170

Small Business Administration 118

Federal Housing Administration -3,584

Other 5

Total 4,167
B

An Example of Using the Binomial Model

to Price a Loan Guarantee

Assume that the federal government guarantees 

the repayment of principal and interest on $90 million in 

debt coming due in one year issued by a company with 

assets of $100 million. The guarantor has effectively 

given the owner of the company the equivalent of a “put 

option” on the company’s assets with a “strike price” of 

$90. That is, the guarantee gives the borrower (the company) the right to sell its assets to the guarantor for $90, 

whatever their current market value. Suppose that in one 

year, those assets will be worth either $140 million or $70 

million (as shown in the top tree diagram in Figure B-1). 

If the asset value rises to $140 million, the firm will be 

able to repay its $90 million debt without any contribution from the federal government. If the asset value falls 

to $70 million, however, the company will be unable to 

meet its debt obligation. In that case, it will “put” its assets to the government, which will pay $90 million to the 

lender and sell the assets for $70 million. 

Thus, the tree of the borrower’s asset values in Figure B-1 

implies the tree of cash flows for the government guarantor shown in the middle diagram of the figure. If the 

company’s asset value increases, the guarantee requires no 

payment by the government (the put option will expire 

unexercised); but if the asset value falls, the government 

will face net costs of $20 million ($90 million minus $70 

million) to honor its guarantee. 

The cost to the government of that guarantee when it is 

issued is the present value (P) of the distribution of possible cash flows in one year. That value can be inferred 

from the price of a portfolio composed of assets of the 

borrowing firm and risk-free bonds that has the same 

payoff to the government as the guarantee. If the payoffs 

are the same, the cost must be the same, and the cost of 

the guarantee can be inferred from the known prices of 

the borrower’s assets and risk-free bonds.

Suppose a risk-free zero-coupon bond with a face value of 

$100 and a maturity of one year has a current price of 

$95. Because the bond is risk-free, its value will be $100 

in one year regardless of what happens to the value of the 

firm’s assets (see the bottom tree diagram in Figure B-1). 

The problem of the value of the loan guarantee is thus reduced to the following question: how many risk-free 

bonds (X) and units of the borrower’s assets (Y) are required to generate the same payoff as the guarantee? The 

payoffs for both the guarantee and the portfolio need to 

match in both good and bad states of the economy. Thus:

X100 + Y140 = 0 (good states)

X100 + Y70 = -20 (bad states)

Those two equations can be solved for X and Y: X = -0.4 

and Y = 0.2857. The price of the portfolio—based on the 

$95 price of the bond and the $100 current asset value—

is -0.4($95) + 0.2857($100) = -$9.43. Thus, the guarantee is equivalent to selling -0.4 of the risk-free bonds 

(borrowing 0.4 x $95) at the risk-free rate and buying 

0.2857 of the assets. And the cost of the guarantee is the 

value of the portfolio, or -$9.43.

The value of that guarantee, or option, was inferred without an explicit assumption or information about the 

probabilities of the two possible outcomes. In valuing the 

federal loan guarantees to Chrysler and America West 

Airlines, however, the probabilities of up and down 

moves and the asset value of an up move were estimated 

using a required rate of return on company assets and the 

volatility of that return.

APPENDIX
24 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

To illustrate the relationship among those variables, assume that the probability of an up move is 0.6 and that of 

a down move is 0.4. Those probabilities are consistent

Figure B-1.

Illustrative Possible Values of Assets,

Cash Flows, and Bonds in One Year

Source: Congressional Budget Office.

with an expected rate of return on assets of 12 percent 

(because [0.4(70) + 0.6(140)]/1.12 = 100). The risk-free 

interest rate can also be inferred from the equation 

100/(1 + r) = 95, which implies a rate of 5.26 percent.

The government as guarantor has a portfolio position 

equivalent to a highly leveraged position in the firm’s assets—that is, issuing debt of $38 (0.4 x $95) and buying 

$28.57 of the firm’s assets. The market value of that portfolio is -$9.43, which is the fee the guarantor must be 

paid to accept the chance of losing $20. Using the probabilities inferred from market returns, the expected loss is 

0.4($20) = $8. 

Viewed from the lender’s perspective, the lender values 

an expected payment of $8 in one year at $9.43 today. 

The discount rate implied by 8/(1 + r) = 9.43 is -15.16 

percent, or about 20 percentage points lower than the 

risk-free rate of 5.26 percent. The expected loss of $8 discounted at 5.26 percent has a present value of $7.60, 

which understates the value of the guarantee by about 

19 percent.

That example illustrates that although future cash outflows on loan guarantees are risky, their risk-adjusted discount rate (unlike that of future cash inflows on loans) is 

not higher than the risk-free rate. The market implicitly 

discounts expected guarantee payments at an interest rate 

below the risk-free rate. The reason is that a loan guarantee transfers market risk from the lender to the guarantor. 

For the guarantor to get a commensurate return for assuming the market risk, the expected payments must be 

discounted at a rate lower than the risk-free rate. The 

borrower is paying the risk-free rate to the lender plus 

compensation to the guarantor for taking on the market 

risk, which has the effect of making the market value of 

the guarantee higher than the value obtained from discounting at the risk-free rate or an upwardly adjusted 

rate. Indeed, the guarantee has more market risk than the 

underlying assets because the guarantee is equivalent to a 

leveraged position in the assets, which always has more 

risk than the assets themselves do.

Possible Values of Borrower's Assets in One Year

Possible Values of Government's Cash Flows

from Guarantee in One Year

Possible Values of Government

Zero-Coupon Bond in One Year
C

Parameter Estimates and Modeling Assumptions

Used in This Analysis

This appendix provides additional information 

about some of the key parameters and behavioral rules 

that the Congressional Budget Office (CBO) used to estimate the value—under both current credit-reform rules 

and market valuation—of federal loan guarantees to 

Chrysler and America West Airlines (AWA). A companion technical paper by the authors of this report, titled 

“Valuing Federal Loans and Loan Guarantees Using Options-Pricing Methods,” contains details about the underlying options-pricing models.1

Asset Volatility

A critical input into both Treasury-rate and options-based 

estimates is the volatility of a firm’s asset value. Although 

that volatility is not directly observable, it can be estimated in a variety of ways. For AWA, this study uses a 

formula implied by the Black-Scholes options-pricing 

model:

C1) Volatility of Assets = Volatility of Equity (beta of Assets/beta of Equity)

The “beta” of a stock or asset is a measure of the correlation of its returns with those of the overall market. For 

publicly traded companies, estimates of equity betas are 

available from various public sources. Estimates of asset 

betas are also available for many industries.

The equity beta of AWA’s stock is 1.55.2 The beta of 

AWA’s assets was set to equal the unlevered beta of the airline industry (to remove the effect of debt), which is estimated at 0.67.3 The equity-volatility range that AWA 

uses to value its employee stock options is 44.9 percent to 

60 percent. On the basis of those parameters, CBO estimated the asset volatility at 19.4 percent to 25.9 percent. 

The estimates reported in this study use the high end of 

that range since it accords with independent estimates of 

asset volatility for the airline industry.

CBO used a different method to estimate asset volatility 

for Chrysler because not all of the necessary inputs for 

equation C1 were readily available. That company’s asset 

volatility was set to equal an average asset volatility for 

several firms in the automotive industry.4

 The current 

average volatility for automotive firms is 22.5 percent. 

Although the equity volatility of a particular company 

can change substantially in a short time, the asset volatility of an industry is likely to be more stable. Nonetheless, 

the 22 years between 1980 and 2002 are long enough for 

asset volatility to have altered greatly, and a more careful 

measure of that variable is recommended for any actual 

cost estimate. 

Market Value of Assets

For healthy publicly traded firms, adding the market 

value of equity to the book value of debt liabilities approximates the market value of assets. For financially distressed companies, the book value of debt is likely to be 

much higher than its market value, but obtaining accurate estimates of that market value is difficult. As explained in the companion technical paper, an optionspricing formula can be used interactively to estimate the 

APPENDIX

1. That paper is available at www.cbo.gov/Tech.cfm.

2. Market data for AWA from Bloomberg (www.bloomberg.com).

3. “Damodaran Online,” Web site of Prof. Aswath Damodaran, 

Stern School of Business, New York University (www.stern.nyu. 

edu/~adamodar).

4. Ibid.
26 ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES

market value of assets without requiring an estimate of 

the market value of debt. That is the approach that CBO 

took for this analysis.

Using options-pricing formulas to estimate the market 

price of assets requires the following six measures:

B Market value of equity, 

B Volatility of returns on assets, 

B Volatility of returns on equity, 

B Risk-free interest rate, 

B Strike price of the option, and 

B Maturity of the debt. 

For AWA, the initial market value of equity is $138 million (based on a share price of $4 and 34.6 million outstanding shares). The volatility of assets is 25.9 percent 

(as described above), and the volatility of equity is 50 percent. The risk-free rate is 3.5 percent (as described below). The strike price of this option is the book value of 

all of AWA’s liabilities as reported in the company’s 10-Q 

report for the first quarter of 2002 filed with the Securities and Exchange Commission, or $1,575 million (including pay-in-kind interest payments on AWA’s convertible senior notes during the first three years). The time to 

maturity of the call option is the weighted average time to 

maturity of all of AWA’s liabilities, or 3.82 years. The resulting estimate of the market value of the company’s assets is $1,113 million.

The calculation for Chrysler is similar. The market value 

of equity is $319 million (based on a share price of $7.5 

and 42.5 million shares outstanding). The volatility of assets is 22.5 percent, and the volatility of equity is based 

on the implied volatility of long-term warrants and set at 

70.5 percent. The risk-free rate is 10.02 percent (see below). The strike price for this option is the book value of 

all liabilities that Chrysler reported in its annual report 

for 1980, or $6,957 million (including preferred stock). 

The time to maturity of the call option is the weighted 

average time to maturity of all of Chrysler’s liabilities, or 

3.68 years. The market value of Chrysler’s long-term assets is thus estimated to be $3,750 million.

Default Triggers

If a firm’s asset value falls below the “default trigger,” the 

options-pricing models assume that a default occurs—in 

other words, that the put option is exercised—and any residual asset value is used to pay claimants (including the 

government) in order of their legal priority. In practice, 

the point at which firms declare bankruptcy varies considerably. Some companies hang on with very low asset 

values, whereas others seek the protection of bankruptcy 

court before they are forced to do so by creditors. As a result, some judgment is required in choosing a default 

trigger.

The default trigger for AWA was set as a function of time 

based on the company’s debt repayment schedule. For instance, for the first year after the loan guarantee was issued (year one), the default trigger was set equal to the 

book value of current liabilities, as described in AWA’s 10-

Q report for the first quarter of 2002. For year two, the 

default trigger is the sum of the current liabilities and the 

debt obligations coming due in the second year. That 

procedure is continued for the life of the governmentguaranteed loan. 

The assumption implicit in that procedure is that AWA 

can pay back principal due every year by refinancing it 

with short-term debt. One could argue that AWA can 

refinance maturing debt using long-term debt and, therefore, that its default trigger should not increase with time. 

Although that is a plausible argument, lenders will subject AWA to more-stringent requirements on its market 

value if the company chooses to issue long-term debt 

than they will if it issues short-term debt. In other words, 

the market value of AWA’s assets must be higher if it 

wants to refinance with long-term debt. In light of those 

two competing effects on the possibility of bankruptcy

—that issuing short-term debt raises the default trigger 

whereas issuing long-term debt sets more-stringent requirements on a firm’s value at the time of refinancing—

CBO believes that the procedure it used to set the default 

limit is a reasonable approximation.

The assumptions for Chrysler are similar. The default 

trigger is a function of time based on the company’s 

schedule of debt repayments. For the first year, the default trigger is the book value of Chrysler’s current liabilities. For year two, it is the sum of the current liabilities 

and half of the “other liabilities and deferred credits” reported on Chrysler’s balance sheet, or $646 million. Since 
ESTIMATING THE VALUE OF SUBSIDIES FOR FEDERAL LOANS AND LOAN GUARANTEES 27

the company’s long-term liabilities are nonamortizing, 

they do not change the default limit.

Prepayment Triggers

AWA has a strong incentive to prepay its high-cost government debt if it regains financial health. This analysis 

assumes that AWA prepays the government-guaranteed 

loan immediately if the market value of its assets exceeds 

the book value of its liabilities ($1,575 million). Clearly, 

that assumption is an oversimplified view of the firm’s behavior, but it reflects the fact that AWA will want to pay 

off high-cost government-guaranteed debt as soon as feasible.

Although the financial incentives for prepayment were 

weaker with the Chrysler guarantee, CBO assumed that 

Chrysler would prepay its government-guaranteed loan if 

the market value of its assets exceeded the book value of 

its liabilities ($6,957 million).

Risk-Free Rate

The risk-free interest rate required in the binomial options-pricing model is the average short-term rate expected to prevail over the life of the loan guarantee. For 

the AWA guarantee, that rate was estimated from the 

yield on seven-year Treasury notes, which consists of expected short-term rates over the seven years and a liquidity premium. The seven-year Treasury yield in January 

2002 was about 4.0 percent. Assuming a liquidity premium of 0.5 percentage points (consistent with historical 

averages) results in a risk-free rate of 3.5 percent. The rate 

for the warrant calculations was set at 4.0 percent because 

of the warrants’ 10-year maturity. 

The risk-free rate for Chrysler was estimated from the 

yield on 10-year Treasury notes, which also consists of expected short-term rates and a liquidity premium. The 10-

year Treasury yield at the time of Chrysler’s loan guarantee was 10.52 percent. Assuming a liquidity premium of 

0.5 percentage points produces a risk-free rate of 10.02 

percent.