metadata: authors: 0: author: Diwan, Ishac
1: author: Kletzer, Ken
count: Mexico
docna: 0: docna: Voluntary choices in concerted deals :
            mechanics and attributes of the menu approach
docty: Policy Research Working Paper
subtopic: Debt Relief and HIPC,Legal Institutions of the Market Economy,Banks & Banking Reform,External Debt,International Trade and Trade Rules,Inequality,Debt Markets
teratopic: Environment,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: When sovereign debt trades at a discount
            on secondary markets, a market buyback increases the
            secondary market price. The wealth of private creditors
            increases because part of the funds used in the repurchase
            is a transfer payment to them. This transfer of resources
            can be mitigated by imposing a capital gains tax on the
            remaining debt. The authors show how this can be achieved by
            including exit and new money options in a menu of options
            from which creditors can freely choose. The menu approach
            imposes an implicit tax on the capital gains on the
            remaining debt by requiring lenders that do not exit to
            extend new loans in proportion to the debt they retain. The
            menu approach does not require that particular choices from
            the menu be assigned to each lender. Instead, it implements
            debt reduction through a price system, allowing different
            creditors to select different portfolios in equilibrium from
            a common set of options. The authors illustrate some of
            their results by analyzing the recent Mexican debt
            agreement. They show how to read through the complex
            financial acrobatics to estimate the net debt reduction.
            Funds provided by international financial institutions
            benefited both Mexico and its creditors. Mexico directly
            retained 62 percent of these resources and the banks 34 percent.
geo_reg_key: 517191,119228
repnme: repnme: Voluntary choices in concerted deals :
            mechanics and attributes of the menu approach
display_title: Voluntary choices in concerted deals
            : mechanics and attributes of the menu approach
listing_relative_url: /research/1990/10/700158/voluntary-choices-concerted-deals-mechanics-attributes-menu-approach
topicv3: Commercial Banking m1326069 1236,Debt Relief m1326505 452,Poverty m1326687 695,Trade m1326924 698,Financial Institutions m1505015 3797
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Environment,Macroeconomics and Economic Growth,Finance and Financial Sector Development
origu: Policy, Research & Ect Affairs
no_of_pages: 33
model_extractions: **Policy, Research, and External Affairs|**

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- This paper a product of the Debt and Intemational Finance Division,<sup>Intemational Economics</sup> Department- is part of a larger effort in PRE to understand the costs<sup>and beneflts of various mechanisms</sup> of debt settlement in the context of the intcmational debt crisis. Copies are<sup>available free from the World</sup> Bank, 1818 H Street NW, Washington, DC 20433. Please contact<sup>Sheila King-Watson, room S8-025,</sup> extension 31047 (33 pages).

When sovereign debt trades at a discount on secondary markets, a market buyback increases the secondary market price. The wealth of private creditors increases because part of the funds used in the repurchase is a transfer payment to them.

This transfer of resources can be mitigated by imposing a capital gains tax on the remaining debt. Diwan and Kletzer show how this can be achieved by including exit and new-money options in a menu of options from which creditors can frecly choose. The menu approach imposes an implicit tax on the capital gains on the remaining debt by requiring lenders that do not exit to extend ncw loans in proportion to the debt they retain.

It is enough to make the buyback price equal to the earlier predeal price. Any new-money call will do the job. In equilibrium, creditors will provide enough new money to stabilizc the postdeal price at a level that Ieaves them indifferent to the exit option. Increasing the new money call increascs the cost of the menu as wcll as the cxtent of the debt reduction achieved.

The menu approach Diwan and Kletzcr describe does not require that particular choices from the menu be assigned to each lender. Instead, it implemcnts debt reduction through a price system, allowing different creditors to select diffcrent portfolios in equilibrium from a common set of options.

With heterogeneous banks, some resources will be transferred when participation in the debt - reduction plan is voluntary and the buyback price will generally need to be higher than the prebuyback price.

Diwan and Kletzer illustrate some of their rcsults by analyzing the reccnt Mexican debt agreement. They show how to read through the complex financial acrobatics to estimate the net debt reduction. Funds provided by intemational financial institutions beneflted both Mexico and its creditors. Mexico directly retained about 62 percent of these resources and the banks 34 percent.

When creditors are heterogeneous and possess private information about the value of debt reductio.. .o them, a mechanism is needed to elicit that information. Researchers should analyze how a menu can be combined with an auction of new money or exit instruments to elicit that inforrnation.

The PRE **Working** Paper Series disseminates the findings of work<sup>under way in the Bank's Policy, Research, and Extcmal</sup> AffairsComplex. An objcctive of the scries is to get thesc findings out quickly,<sup>evcn if prcscntations arc less than fullypolished.</sup> The findings, interpretations, and conclusions in these papers do not necessarily<sup>represent official Bank policy.</sup> Produced by the l'RE Dissemination Ccnter
# Table of Contents

|1.|Introduction|1|
|---|---|---|
|2.|The Effect of Pure Market Buybacks|3|
|3.|Simple Menus:<br>Relend or Exit|6|
|4.|Cost of Debt Reduction|9|
|5.|Underfunded Menus|13|
|6.|Heterogeneous Banks|15|
|7.|Evaluation of the Mexico 1990 Deal|17|
||The Deal<br>Evaluation<br>Analysis|18<br>19<br>20|
|8.|Concluding Remarks|23|
|Appe|ndix 1: The Case with Multilateral<sup>Loans</sup>|25|
|Appe|ndix 2: The Debt Value Curve<sup>and the Debt Reduction/</sup><br>New Money Frontier|27|
|Refe|rences|28|
# 1. **Introduction**

A reduction in the nominal debt burden of a sovereign<sup>whose debt</sup> trades at a discount on secondary markets<sup>leads to a rise in the secondary</sup> market price. Dooley (1987) argues that if debt<sup>is repurchase1 by the borrower</sup> on the secondary market, then the price that<sup>must be paid is the equilibrium</sup> price of debt claims after the borrower's indebtedness<sup>is reduced. If any</sup> lender can choose between selling debt claims back<sup>to the debtor and retaining</sup> those claims, then his opportunity cost for<sup>selling is the secondary market</sup> price after the debt reduction. Therefore, when<sup>lender participation in a</sup> buyback of debt claims is voluntary, both the price<sup>paid for repurchased</sup> claims and the secondary market price of remaining<sup>debt rise, so that all</sup> creditors realize a net benefit. The amount<sup>received from the sale of debt</sup> plus the ex post value of remaining debt exceeds<sup>the ex ante value of the</sup> original outstanding debt.<sup>1</sup> When a debt buyback is financed using the debtor<sup>country's reserves or</sup> a concessionary loan or official aid from abroad,<sup>there is a transfer of part</sup> of the funds used in the repurchase to the<sup>private creditors. The transfer</sup> from the party providing the resources for the<sup>buyback to the private</sup> creditors is an undesirable consequence of equilibrium<sup>under the simple</sup> repurchase program. But this transfer of resources<sup>can be mitigated by</sup> imposing a capital gains tax on remaining debt.<sup>If a tax is levied on the</sup> remaining debt, then the opportunity cost<sup>to lenders of selling their debt</sup> claims is reduced for any given net repurchase.<sup>The equilibrium buyback price</sup> will be less than the ex post equilibrium secondary<sup>market price by the</sup> capital gains (specific) tax rate on debt claims<sup>remaining after debt</sup> reduction. There is a tax rate such that the<sup>equilibrium price of repurchased</sup> debt is the ex ante secondary market price of<sup>the debt. The tax revenue</sup> 1 Equivalently, Bulow and Rogoff (1989) show that in a market repurchase that marginal buybacks occur at the average cost<sup>ofdebt service while they only</sup> reduce the debt burden by the marginal cost<sup>ofdebt service, which is smaller.</sup>
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.ollected will be positive if the debt reduction raises the secondary market price. While explicit taxation of creditors' gains may be politically or legally infeasible, there may be alternative schemes to impose such taxes on the capital gains realized by debt-holders during a buyback.

Recently, attempts have been made to reduce the external debt overhang of some highly indebted countries by negotiating a menu of options from which the creditor will select latez. An agreed upon menu is a contract, that may be partly implicit, establishing a future opportunity set for the lenders. An improvement upon the status quo is possible only if some degree of contract enforcement is available. The menu approach requires that lenders can commit to choose from amongst a restricted set of actions ex post. The possible means for enforcing a menu include creditor country legal and political institutions and agreements between creditor nations. By agreeing to the contract, lenders face the possibility that they will be penalized for reneging ex post by refusing to allocate their existing debt claims across a por.folio using the menu options. Agreement to a menu of options ex ante can be voluntary and may be necessary for political or, even, legal reasons. While private creditors restrict their options ex post, they may be able to raise their net worth in negotiations. That is, lenders can increase the value of their loan portfolios ex ante by agreeing to choose from a menu of restricted options ex post.

A menu approach can be used to impose an implicit tax on the capital gains on the remaining debt. Such a tax can be set by requiring lenders to extend new loans in proportion to the debt they retain. In some of the recent menu negotiations, the options have included selling back debt claims and retaining them with a pledge of new money. Because debt trades at a discount, a portion of any new money spent to purchase a new debt of equal face value represents a tax. That is, if a dollar is lent and the secondary price is
-3-

sixty cents, then the new debt claim is worth sixty cents and the rest is a tax with the revenue accruing to the debtor. A commitment to provide new loans in proportion to retained debt creates a wedge between the price paid to buyback debt and the secondary price of debt after debt is reduced.

Below, we discuss how concerted arrangements for debt reduction can be devised which eliminate the transfer of debtor or donor resources to private debt holders. The menu approach we describe does not require assignment of particular choices from the menu to each lender. The menu offers a set of prices for different options which implement a decentralized equilibrium ex post. Commitments to accept a menu of options including new loans and debt forgiveness along with repurchases may be enforceable. We assume below that private creditors do not need to accept a menu over the status quo, but that once they do, reneging is costly.

The interaction between debt buybacks and the provision of new funds has lead to confusing statements in the debt literature. For example, SaT-hs (1989) states that money center banks "gain by having the small banks cash in and accept losses by exit bonds, secondary sales and so on. Since any cred; is made better off if another creditor voluntarily makes a concession to the debtor, the large banks have an added incentive to let the small bank get out at a loss, while the big bank postpones any significant concession.' Cline (1989) argues that new money is needed in the Brady type deals "to help finance the interest coming due on the unconverted debt." Both authors ignore the important link between the size of the new money call and the equilibrium price of repurchased debt.

# 2. **The Effect of Pure Market Buybacks**

Sovereign borrowers choose to service external debt obligations because it is in their enlightened self-interest to do so. Under sovereign
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immunity, cr( itors do not have recourse to an international court to assure settlement of debts through a direct lien on the country's assets as they would in the case of an insolvent domestic client. The threat E the imposition of sanctions in the event of non-payment or insufficient payment provides sovereigns with the incentive to make debt payments. In addition to denials of future official aid flows, the penalties for default include restrictions on the future trading opportunities on international markets for the debtor. These include the disruption of commodity trade, suspension of trade preferences, and reduced access to international financial markets. Because the repayments made by a sovereign lebtor are linked to the expected present value of the social cost of sanctions, they need not be strictly proportional to the total outstanding contractual debt burden. Moreover, as the probability of sanctions being exercised (or being used by creditors as a threat to extract higher net repay.-ents) increases, debtor countries can take actions to reduce the effectiveness of sanctiorns, for example by underinvesting, or by shifting resources to the non-tradable and to the import competing sectors of the economy.2 In this paper, we summarize the various arguments made by the recent debt literature by assuming that the present value of expected debt service payments is an increasing and concave function of nominal debt burden, that is, we take the value of debt to be a smooth function f(D), where f(D) is the value of the total debt claim, D, and f"'D) < 0 for all D > 0. The marginal price of debt, f'(D), can be positive or negative, although we will assume it is positive: if the present value curve is first upward, then downward sloping, none of the arguments below is changed.3 To illustrate the costs of market-based buybacks, suppose that the 2See Diwan (forthcoming). 3Similarly, our main arguments hold if the debt value function is not smooth.
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initial debt is Do and that an amount of funds, a < Do is made<sup>available for a</sup> debt buyback. If the options available to creditors are to<sup>sell debt or simply</sup> hang onto debt, the secondary market price of debt will rise<sup>from p</sup> 0<sup>-</sup> f(Do)/DO to p1 - f(DO-(a/pj))/[Do-(a/p1<sup>)], where a/p</sup> 1<sup>is the face value of the</sup> debt reduced. Because f(x) is concave, p1 exceeds po for a ><sup>0. The ex post</sup> value of creditor assets is:

# pl(Do - a/p1) + a - p1DO > poDo - f(DO)

The capital gain realized by the creditors retaining claims<sup>is:</sup> The percentage gain received by those who sell claims<sup>and those who retain</sup> them is equal.

When contracts that bind the actions of private<sup>creditors are feasible</sup> and credible, the conversion of the sLacus quo debt<sup>claims to a package of</sup> assets that has expected present value at least as great can be<sup>negotiated.</sup> We assume that enforcement of an agreement by private creditors with their home governments and international financial institutions is possible but that creditors do not need to accept a contract which reduces the present<sup>value of</sup> their assets. Once an agreement is reached, lenders face penalties<sup>if they</sup> refuse to perform according to the contract (in the<sup>recent Mexico deal for</sup> example, creditors that did not participate were effectively made junior; see section 7). If enforcement of a contract is only possible for a subset of the creditors, then a debt reduction menu can still be negotiated<sup>involving these</sup> creditors alone. However, the non-participants free ride, realizing a net
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increase in the value of t.heir portfolios. The participating creditors can still increase the value of their assets despite providing pecuniary external benefits to the non-participants. For simplicity, we assume that the entire stock of outstanding claims is represented in the negotiations.

3. **Simple Menus: Relend or Exit** To illustrate the role of a menu of options for creditors to choose amongst, suppose that creditor banks are presented with a simple menu of options represented by the pair (p, n): for each dollar of claim they hold, banks can choose between exiting at a price of p, and relending n dollars.

Given a menu (p, n), can we tell how much debt reduction, B, and how much new money, N, will actually be achieved? Somehow surprisingly, :he answer is yes. More precisely, when "sufficient" funds are available for debt reduction, competition between banks insures a unique equilibrium. To see - that, let Di stand for debt stocks and Pi for debt prices, i (1,2), where period t-1 refers to the level of the variables before the debt deal, and t=2 after the deal is completed. We have: (1) D1 - Do - B + _N_

- (2) Pi - f(Di) / Di

- (3) n - _N /_ (Di - N)

Lenders choose between the two option in a manner that maximizes the value of their assets subject to the terms of the menu (p, n). After the deal is completed, debt prices are expected to be higher at p1 > p. This encourages relending as a bank that relends n dollars, will have its old claim revalued.
-7-

However, its new claim n will be only valued at p1, implying a capital lcss of - (1 p1). Thus, the opportunity cost for holding a unit of debt back from repurchase at price p is pl(l + n) - n. This implies that when p1 exceeds (p + n) / (1 + n), the new money option is preferred to the exit option. Thus, less debt will be sold and more new money offered, resulting ir less than expected debt reduction. This leads to an increase in D1 (using equation 1), and thus to a reduction in p1 (using equation 2). Since creditors are price takers when they optimize ex post, and because the expected present value of debt function, f(x) is strictly concave, the solution to portfolio value maximization by creditors is unique. In equilibrium, we must then have:

# - (4) p, (p + n) / (1 + n)

The system of equation (1) to (4) can be solved for B , N, D1 and p1 in terms of any menu (p , n).

Let us focus on the menus that leave the commercial banks indifferent with the status quo. Those menus are simply characterized by:

# (5) P Po-

Equation (5) insures that banks are indifferent between exiting at p and the initial status quo vaiued at p0. In equilibrium, equation (4) insures that they are also indifferent between the initial status quo and the relending option. We show below that as n increases, so does the ex post debt price p1. Thus, there is a maximum n above which p1 reaches 1. What is remarkable is that any menu (p0, n), with n positive and smaller than n, will produce an equilibrium in which all the banks, whether they exit or relend retain a
-8-

payoff exactly equal to po. Thus, the menu effectively eliini-ates any transfer of resources to the creditors that could arise from the debt reduction operation. Moreover, knowledge of the function f(D) is not needed to construct menus that allow for debt reduction -jith no transfer of resources to creditors.

Equations (4) and (5) insure that the post-deal price, p1, will be higher than the ex ante price, p0. The result that p1 exceeds p0 while the buyback price is po way create some confusion. Why is some debt sold at po when the temaining lebt clainis rise in value to p1? The choice between the options of selling debt or staying in is voluntary, but there is a tax to staying in. This tax is exactly the difference, (p1 - po), per unit of remaining debt. With a positive tax, the post-tax price must rise if the ex ante value of lenders' assets does not fall. Private creditors are indifferent in equilibrium between selling an additional unit of debt and retaining afn extra unit of debt since the net value of a unit of debt held back is equal to the price paid in repurchase.

How does the equilibrium amount of debt reduction vary as the new money call is increased? To answer this question, we must determine how D varies with n. Using equations (1) to (5), we get: (6) f(D1 ) /D1'D (po + n) / (1 + n) For any n, equation (6) car ,e solved for D1(n). Differentiating (6) with respect to n and rearranging, we get: (7) 8D1/On - - [D,/(l+n)] [(1 - p1) / (p1 - f'(D1 ))] < 0
-9-

Thus, as n increases, the equilibrium amount of remaining debt falls. Although a-priori counter-intuitive, this result illustrates well the effect of equilibrium considerations applied to free choice among a menu. As the new money call, n, is increased, the exit option becomes more desirable than the relending option. But in equilibrium, both options must be equally desirable. As a result, it becomes necessary to achieve larger debt reductions in order to boost the ex post debt price p1, and thus increase the attractiveness of the relending option.

# 4. Cost **of** Debt Reduction

If funds, a, are supplied by a third party seeking to benefit the debtor, then a package that effectively taxes in full the capital gains of lenders assures that a net t.ansfer is not made to the creditors. Lenders can agree to choose between selling debt back to the debtor and holding claims 4 with the obligation to provide new loans. A menu that costs exactly a resources can be designed to ensure that lenders are indifferent between the two options and their status quo payoff if the relationship between the present value of debt and the face value of debt, f(x), is known.

IrT general, the new loans forthcoming under the relending option can be used by the debtor country either for domestic absorption or for further debt repurchases. If they are used for buybacks, then the debt is reduced by more and the tax rate, n, should be higher since the secondary market price rises further. We extend the analysis here to exam'ine the effect of a and of the share of new loans retained by the country for domestic absorption on the types of mentus that can be negotiated.

Suppose now that N is the total of new loans made by the remaining 4With no loss of generality, we assume that new and old loans have equivalent terms and that interest payments occur just before the debt agreements. More generally, new money can be interpreted as part rescheduling.
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creditors and p is the part of the new financing, (N+a), that is kept by the deLLor country to finance domestic absorption. We assume that the net resource transfer to the country, p, is a monotone 'ncreasing function of (N+a). The amount of new funds used to repurchase debt is (N+a-p), so that after the debt reduction program, the remaining debt is given by: where p is the price paid in the buyback. To assure that creditors receive no net surplus, we let p equal p0 - f(DO)/DO. In equilibrium, we have: (9) N* + f(DO) - (a + N* - _p)_ + f(D 1*).

where D1* is given by (1) evaluated at N*. The left hand side of (9) is the value of the creditors assets before the buyback, while the right hand side expresses the value of their assets after the whole operation is completed. In addition to the value of remaining debt f(D1*), the creditors receive a net amount (a _+_ N* _-_ p). When a exceeds p(a), the private lenders gain, so that, if required, they are willing to pay a positive price for debt reduction. The amount of new money necessary for creditors to retain no net increase in the value of their portfolios is positive. There is a solution, N* > 0, to equation (9) given a whenever a part of a is spent on buybacks. Denote this solution by N*(a;p), and the associated ex post debt level by D1*(a;p). - The secondary price, p1, with p1(a,p) f(D,*)/D1<sup>*, is higher than po</sup> whenever N* exceeds zero. This follows from the concavity of the debt value function, f(x).<sup>5</sup>

> 5Proof: For Do larger than zero, Do > f(DO), so that, -Do(a-js) > Nf(DO) - D (N+a-p), for N > 0. Adding Dof(D ) to each side and rearranging terms, we obtain DO[f(DO) - _(a-p)]_ > (Do + _A)_ f(DO) - [(a-p+N) Do f(DO)] / f(DO)]
-11-

When debt reduction creates no change in the value of creditor's - - assets, the implicit tax rate imposed on remaining debt is t (p1 po). The capital gains realized by remaining debt ho'ders are taxed one hundred percent. The capital gain due to debt reduction is 7 - [Do - (a-p+N)/pO (p1 - po), and the total tax revenue, which accrues to the debtor, is A - _N(l_ - pl). - N* is the solution to y A, which is equivalent to (9). The amount of new money required per unit of old debt held back from repurchase is which is equivalent to equation (4). Since the buyback occurs at the ex ante price po, the exiting creditors also break even.

The effect a on N* and Di* can be calculated using (8) and (9): where f' f'(Dl*, 1 and ' p'(a,N*). When A' < 1, a rise in a increases both N* and D* until f'(D*) = po. Further debt reduction beyond this point through increases in a decrease the size of the net resource transfer. As long as the marginal value of debt, f'(D), is below the buyback price, po, remaining debtholders realize an increasing capital gain from further repurchases. Therefore, the compensating concession in new money that can be demanded respecting the constraint that creditors are at least as well off with the

> [Do + N - _(a_ - p + N) / po)] f(D ) - using the definition pn f(DO)/Do. Using equations (1) and Y2) the last inequality becomes DrjfPD) > Df(DO), implying that p1 > pO.
-12-

program as the status quo rises with debt reduction. However, when debt is reduced far enough so that f'(D) > p0, the implicit tax needed to assure that creditors are indifferent between selling and holding debt declines with further reductions in the debt.

Thus, until debt is reduced to the point that the marginal secondary value of debt, f'(D), equals the buyback price, p0, the debtor gains both net resource transfers and debt reduction from further buybacks. If the objectives of the donor place weight only on the debtor's benefits (excluding any other objectives, such as the cost of funds), then the optimal amount of remaining debt for the donor is less than or equal to the solution to f'(D) = po.

Figure 1 depicts the f(D) curve and initial value of debt po in the top panel. The relationship between N and the ex post debt level D* is portrayed in the lower panel for solutions to equations (8) and (9). The maximum amount of new money contributed by cred..tors is attained when f'(D) = p0. Figure 2 illustrates the relationship between N* and the amount of gift financing a. N* rises as a increases until the marginal value of debt f'(D) equals _p4,_ and then declines towards zero. D is zero when the gift is large enough to buyback the entire debt Do at price po, that is, (a-p)/p. = Do.

If the proportion of available funds used to repurchase debt can change, then an increase in p(a+N) for every value of (a+N) acts as a decrease in a. For simplicity, we analyze here the multiplicative case only. Suppose that p(a + _N) p.(a_ + N). It is then possible to show that: dN*/dp (f'- po) (a + N) / [po(p-f') + (1 _-A)]_ The denominator is always positive for all p e [0,1]. Thus, D* increases with
-13-

. Moreover, N* increases in u as long as f' > po.

These results partially extend to the case where the funds a are are a loan rather than a gift. When debt is repurchased with a loan from official sources, seniority considerations also matter. When all debt, regardless of the creditor, has equal priority in repayment, the results developed above go through. The only difference is that when part of the initial transfer is a loan, less new money is forthcoming than in the pure gift case because the new loans reduce the ex post debt price. Consequently, less debt reduction can be achieved for a given transfer. However, when the initial transfer takes the form of senior debt, it impairs the value of existing debt claims since junior debt is now serviced only after the senior loan is repaid. In that case, and in spite of the gains that are due to debt reduction, the value of private creditors' assets is reduced (see the appendix for a treatment of a as junior and senior debt).

In reality, it is probable that IFIs loans are senior to commercial loans, but that they also create efficiency gains due to conditionality (i.e, they lead to an upward shift in the f(D) curve). The net effect of those loans on the payoffs of commercial creditors can then be positive. The menu approach can help ensure that those net benefits are taxed so that the debtor country can retain a larger share of the efficiency gains due to conditionality. 5. **Underfunded Menus** When private creditors commit ex ante to choose between selling back debt and holding onto debt claims with an obligation to make new loans, an equilibrium debt reduction program that leaves commercial banks at their status quo payoff levels does not require that the ex post choice of each creditor from the menu be negotiated and specified or even that aggregate constraints be placed on the total amounts of debt reduction and new money. Prices, that is, the offer of po for debt bought back and any ratio of new
-14-

loans to remaining debt claims required, n (with n<n), are sufficient.

On the other hand, given available resources a, it is possible to pick an n that will lead in equilibrium to an allocation that costs exactly a: that is, for any amount of resources, a, and buyback price po in the simple model, there is a solution for n. With a competitive equilibrium in the debt market, the outcome that can be computed given the function f(D) and the prices p0 and n is attainable.

Selecting the appropriate value of n to assure that the defined amount of debt reduction is achieved in equilibrium requires knowledge of the debt value function, f(D). If there is uncertainty about f(D), then setting n leads to a random amount of debt reduction (and consequent demand for buybacks). Given p0 and n, there still need be no windfall gain to creditors, but the amount of resources required of the donor or lender is uncertain. If n turns out to be too low, only a portion of a will be used, but creditors will remain at their status quo payoff level. However, if n turns out to be too large, a will not be sufficient to buyback all the tendered debt. The possible responses in that case are to increase a, to lower n in a second round offer, or to ration buybacks using some reallocation mechanism.

In the latter case, creditors will suffer a loss compared to their status q-o payoffs. As a result, they will have to be compensated ex ante for this eventuality with a higher p and/or a lower n. To see that, suppose that a menu (p, n) is offered, but that it is known in advance by all the participants that the country is only prepared to spend a smaller amount 6 _<_ a. In that case, an equilibrium will not exist. Instead, all banks will prefer to exit rather than to relend. Remember that for an equilibrium to exist, sufficient funds are needed for buybacks so that the ex post debt price p1 is driven up to the point where relending is as desirable as exit. When the funds available to support the equilibrium are insufficient, p1 does not rise
-15-

sufficiently and relending at price n is not as desirable as exit; equation (4) will hold then as an inequality.

With insufficient funds, a distribution mechanism is needed to allocate the scarce buyback resources. For example, buybacks can be distributed on a pro-rata basis. If all banks are similar, they all end up with a similar mix of cash and new loans, per unit of old debt. Given n, what is the lowest exit price that the debtor can now offer in order to keep the banks at their initial status quo payoff level? The final allocation must produce a value equal to p0, per unit of old debt. Since relending is not as desirable as exiting, the exit price, p, must now be larger than po in order to produce a mix with a value of p0.

However, there are two major reasons why an underfunded deal is not in the interest of the debtor country. First, it is makes it more difficult for the debtor to capture all of the creditors surplus. In effect, it is necessary to estimate correctly the ex post price p1 in order to built relending/exit mixes that have value p0. On the other hand, a program that is adequately funded preserves the status quo as long as p is set equal to p0, even when f(D) is not known. The only disadvantage of not knowing exactly f(D) is to render the cost of the program is uncertain.

Second, adequately funded menus allow the debtor to discriminate better between different types of creditor banks. But as discussed in the next section, banks are in reality heterogeneous. Because equilibrium deals allow banks to choose themselves from the menu the options that they value most while ad-hoc distribution mechanisms do not, they allow the debtor to reap efficiency gains.

# 6. **Heterogeneous Banks**

In the analysis above, we assumed that each creditor bank valuation of country debt depends on aggregate debt outstanding only, but that it is
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independent of the quantity of debt held in its own portfolio. This implicitly assumes that the standard capital asset equilibrium mode'l applies: that is, the secondary debt market is competitive and efficient, banks are risk averse institutions, country debt is spanned by the universe of existing assets, and regulatory considerations do not influence debt valuation. In equilibrium, the demand for LDC debt is infinitely elastic as the marginal and average valuations of debt claims are equalized across all banks.

However, commercial banks' relative valuation of the exit and relending options may differ due to differences in expectations, in characteristics of their balance sheets, and in the regulatory, tax and accounting systems within which they operate. But with a competitive and efficient secondary debt market, and when country debt is spanned by the universe of existing securities, differences in expectations alone cannot explain the existence of a surplus over the secondary market price since those differences can be intermediated through the secondary market.<sup>6</sup> However, differences in regulatory treatment of debt results in valuations that are different despite the existence of a competitive market. Due to mispriced deposit insurance, banks gain by increasing leverage as much as possible (see Merton [1977], Sharpe [19781, Kane [1985]). While leverage is limited by capital adequacy requirements, book value application of those requirement create extra value for claims whose real value has fallen below book value. In effect, claims that are entered on the books at a premium over their real value allow banks to over-represent their own capital. As a result, banks holding such claims can increase their effective leverage above the allowed book leverage. Therefore, banks that sell inherited debt that is 6In contrast, with incomplete markets, the banks' demand function slopes down. Differences among banks imply that their own valuation of debt held is not the same in equilibrium. In such a case, choices over a menu of options can differ, despite the fact that the marginal valuations of all banks are equal.
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treated at par by regulators lose valuable rights to excess leverage. Since the FDIC insurance subsidy (and thus excess leverage) is more valuable to weak institutions, the loss incurred by selling debt at a discount is proportional to the selling bank's financial strength. Thus, choice over a menu will differ, with relatively stronger banks exiting, and relatively weaker banks relending (see Demirguc-Kunt and Diwan [1990] for such a model).

Note that the market does not intermediate these differences in valuation away. The market price is simply the price at which the strongest bank is willing to exit. The weaker banks however would lose if they exited at that price. In such a framework, it can be shown that a single buyback price has to be high enough to convince the marginal bank to exit. Stronger banks also exit and gain. Weaker banks relend and gain. As a result, a menu cannot extract all of the creditors' surplus (see Diwan and Spiegle for an analysis).

Heterogeneous creditors are likely to possess private information about their marginal valuation of debt. An auction can serve to reveal this information so that the single buyback price and single linear new money tax may not equivalent to other methods of implementation in the presence of asymmetric intormation. Different implementation mechanisms can achieve different results in taxing creditors' rents differentially, and supply constraints can result in efficiency losses. Also, more gains can be achieved by extending the menu. For example then banks may have different preferences over the timing of uncertain payments. In this case, more instruments are needed for the new money options. Similarly, when tax considerations and bank regulation impose different costs on banks that depend on the timing of the realization of losses, different exit options are needed. Those extensions are left for subsequent work.

# 7. **Evaluation of the Nexico** 1990 **deal**

We now apply the above analysis to the case of the recent Mexican debt
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agreement. First, we describe the deal. Second, we verify whether the actual bank choices resulted in an equilibrium as predicted by equation (4). We then discuss whether Mexico could have achieved a better deal. We note at the outset that our computations below are illustrative. They indicate orders of magnitude rather than exact values as second order effect are often ignored. **The Deal** Mexico and the steering committee of its creditor banks negotiated for approximately 4 months. On July 23, an agreement was reached on a package that covers about $48.9 billion in medium-term and long-term debt. It offers commercial banks a menu of three options:

1. a discount bond: a 30 year bond with a discounted principal of 65% of the face value of existing debt and an interest rate of LIBOR plus 13/16;

2. a par bond: a bond with no discount but a low interest rate of 6.25% fixed for the lifetime of the bond; and 3. a new money package: 25 percent of exposure (7% of principal balance at the conclusion of the agreement and 6% in 1990, 1991 and 1992), at an interest rate of LIBOR plus 13/16.7 The principal of both bonds is guaranteed through collateralization of a 30-year zero-coupon bond (US-Treasury or its equivalent in case of other currencies) and 18 months of inteiest payment are guaranteed on a rolling basis through an escrow account. In addition, both bonds include a recapture clause which stipulates that, in case the oil-price increased by a certain percentage in the years 1997 and beyond, that the creditors would share in the increased revenue stream. The agreement also contained a financing facility contingent on oil prices.8 7Note that the present value of the new money call is approximatively given by _4.07_ + (.06/1.1) + (.06/1.1) + (.06/1.1) - .21. The agreement further specified a certain number of relending options, in which banks would be allowed to relend, up to a certain maximum fraction, their claims to Mexican public companies. In addition, banl.s participating in
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In total an amount of $7 billion have been used for debt and debt service reduction, of which $5.757 billion were available from new loans from the World Bank, IMF, and Japan, and $1.243 billion from Mexico's own reserves. The choices made by banks in early March were the following: 46.7 percent of the debt was swapped into the par bond; 40.2 was -wapped into the discount bond; and 13.1 percent contributed new money. Total new money amounted to $1.602 billion. Since Mexico provided $1.243 billion to finance the debt exchange, it was able to secure on a net basis $360 million of new liquidity.9 In terms of our model, we have: a - 5.757 billion; a - .36.

# **Evaluation**

The agreement effectively dealt with free riding incentives in the sense that non-exiting banks have to contribute with new money. An important part of the agreement was the explicit rewriting of the existing debt contracts so that the previous agreements, both between the debtor and the creditors and among creditors, are not longer binding. The major implication of this so called "novation" is that debt which is exchanged into the new instr ients (including some of the new money provided) would no longer be subject to the sharing clauses. This drastically reduced the problem of freeriders since they are not able to share equally in payments made by Mexico on its restructured debt. For instance, in case Mexico would pay in full on the new instruments, but would not pay in full on debt which was not exchanged, the holders of the non-exchanged debt would not be able to share in the payments the holders of the new instruments receive. The "novation" clause gave claim holders a greater incentive to accept one of the three options.

the debt relief are eligible to participate in a debt-for-equity swap program of at most $1 billion per year. The program would involve public sector companies being privatized and qualified infrastructure projects. 9For additional details on the agreement, see Lamdany (1989) and especially, van Wijnbergen (1990).
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However. one problem with the way in which the deal was structured is that the relative prices of the three options were predetermined and no single price was allowed to be determined in a competitive fashion.10 In our model, n is unique (in equilibrium) given po and a. Fixing n in the agreement is acceptable if correctly chosen. However, if an incorrect n is chosen, a needs to be adjusted ex post. It seems that due to the difficulty of estimating the f(D) curve, n was fixed too high given the available resources. As a result, additional financing had to be sought in order to complete the deal.

Analysis Instead of being bough back as assumed in the model, old debt was exchanged for newJ bonds, a mix of pure Mexican debt claims and riskless collateral. In order to analyze the deal, we need first undo the complex financial arrangement. As the deal eliminated one class of debt claims and created several new ones, we must carefully define our unit of pure Mexican risk. In the sequel, we define debt prices as the price of an unsecured 30 years bond with a coupon rate of LIBOR+13/16."1 As in our model, we denote by p the buyback price, and by pl, the ex post debt price.

To compute the implicit price of pure Mexican debt, we use market information on the discount bond. 12 Each discount bond is a mixture of pure Mexican risk valued at pl, and collateral, c. **13** For a $100 loan, it can be calculated that the value of the collateral is about c = $24.278 (7.785 for the principal, 12.29 for the 18 month interest, and $2 for the recapture value 4). Stripping the 18 month interest payments and the principal, we are 10The main reason being that US regulators may have obliged banks to set reserves according to their bid price rather than to their accepted price. 1 This can be compared with the pre-deal secondary market debt prices which were computed in a very similar fashion.

**12** Using the price of the par bond to extract the needed informastion is more problematic due to the fact that it offers a fix interest rate.

For a discussion of equivalences between buybacks and debt exchanges, see Lamdany and Underwood (1989) and Claessens and Diwan (1990). 14See The value of the recapture clause is calculated by Claessens and van
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left with less than our yardstick of Mexican risk, more precisely, with about .788 of a standard pure Mexican loan.

The post-deal price of pure Mexican risk, p1, can now be calculated using the technique outlined above. After the completion of the deal, the discount bond price stabilized at 65 cents, implying that p- 52 [(65 - 24.28)/.788].

The implicit buyback price p can also be approximated from the trading price of the discount bond. Since a unit of old debt was exchanged for .65 units of the exit bond, old debtholders were given a value of 42 cents (.65*.65).'5 What was the status quo price before the deal was achieved? Using an estimate of the debt value curve f(D), and given that at the time of the agreement, Mexico had $107 billion of mtedium and long term debt outstanding and its export were estimated at $28 billion, we can predict that the equilibrium secondary market value for Mexican debt of 38 cents (see appendix 2). This is in line with the observed market prices before the announcement of the deal. Prices in the secondary market were in fact quite volatile in the period leading to the Brady speech and the beginning of the Mexican debt negotiation, fluctuating between 35 cents and 40 cents. Thus, the price jump to p1 .52, in the order of 37 percent was remarkably large.

Did the creditors anticipate this price jump? Evidence can be gathered using the equilibrium condition in (4). Given that banks were free to choose between the options that were offered, if the banks correctly anticipated the amount of debt reduction, the ex post price p, should have obeyed the equation p, - (p + n) / (1 + n) - (.42 + .21)/ (1.21) = .52 (see footnote 6). Somewhat surprisingly, the answer thus seems to be that the market ieacted in an Wijnbergen (1<sup>989</sup> j 15Using a different technique, Lamdany (1990) finds a similar value.
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# extremely rational fashion.

We can now compute the implied amotnts of debt reduction and new money achieved in the deal. This is not an easy matter because the exit and discount bonds are a mixture of buybacks and relending (since the collateral has been spent, the collateralized portion corresponds to an implicit buyback). But we can use shortcuts. The remaining nominal debt claims (in terms of old debt) are given by equation (12': D1 - 48.9 - (5.397 + Ll)/.42 + N. From equation (14), n - N/(D1 - N) - .21. We can solve those two equations to get: D1 - $29.066 billion and N - $5.057 billion.

Let us check the consistency of our estimates. The menu must have - ensured that all creditors retained a value of p .42 per unit of old debt, irrespective of whether they exited or relent. The capital gain of the - - creditors that stayed in that was due to to debt reduction is y (D1 N)(p, - p) - (29 - 5)(.52-.42) = $2.4 billion. On the other hand, the tax revenue to Mexico from the new loans those creditors had make to is given by: A - N (1 - - - - p1) 5(1 .52) $2.4 billion. So indeed, they just broke even and got as much as those that exited, i.e 42 cents on the dollar.

We can compute now the characteristics of the deal: $24.89 billion of old nominal debt claims were bought back (5.397 + 5.057)/.42), leading to a net debt reduction of (old nominal) commercial debt claim of $19.8 billion (24.89-5.057).

Before the deal, the market value of Mexico treatable debt was about $18.6 billion [48.9 * .38]. After the deal was completed, the value of its remaining commercial debt evaluated at the new (and higher) debt price was about $15.114 billion [29.006 * .52]. The value of its debt was thus reduced by $3.468 billion. Mexico also retained $.36 billion in liquidity, for a total value of $3.83. Compare that with the IFIs contribution of $ 5.8 billion.
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$1.95 billion have disappearedl This is in fact the banks gain over their status quo payoffs.

A deal that would have left the banks at their status quo payoff level should have set p0 at about 38 cents. Therefore, the implicit buyback price of - 42 cents increesed the payoff of the banks by about 4 cents (.42 .38] per unit of old debt, for a total of about $1.95 billion [48.9 * .04]. Thus, of the 5.78 billion contributed by the IFIs, Mexico retained 3.5 billion (or 66 percent), and the banks $1.9 billion (34 percent).

Finally, we check that our technique that reduce the deal into its basic components is relevant. Under our interpretation, each new bond offered is part exit and part new money. Consider the discount bond for example. One dollar of old debt was swapped for .65 discount bond. Since there is $.243 of collateral in each discount bond, a dollar of old debt received $.157 in quasi-cash (.65*.243). It also received a claim worth $.512 in old debt units (.65*.788). Is this mix consistent with the menu (p-.42, n-.21) ?

From the $.512 of debt received by each old claim, .089 must have been the required new loan, and $.423 the old debt (check that .423*1.21=.512). Since the old debt retained is $.423, $.576 of old debt must have been bough back for an amount of $.242 (.577*.42). Therefore, an holder of an old unit of debt received $.242 for the buyback portion of the deal, and he contributed $.089 for the new money portion. Thus on net, he received $.153. This is indeed very close to the quasi-cash received of $.157 computed above.

# **8. Concluding Reuarks**

When sovereign debt trades at a discount on secondary markets, a market buyback leads to an increase in the secondary market price. The wealth of private creditors increases because part of the funds used in the buyback is a transfer payment to them. When banks are homogeneous banks, we show how
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the inclusion of an exit option and a new money option in a menu of options fram which the private creditors freely choose can eliminate the wealth transfers due to the debt reduction. It is sufficient to set the buyback price equal to the ex ante status quo price. Any new money call will do the job. In equilibrium, creditors will provide enough new money to stabilize the ex post debt price at a level that leave then indifferent to the exit option. The important effect of increasing the new money call is to reduce the cost of the menu and the extent of debt reduction achieved.

The menu approach we describe does not require assignments of particular choice form the menu to each lenders. Rather, it implements debt reduction through a price system, allowing different creditors to select different portfolio in equilibrium from a common set of options. However, with heterogeneous banks, some transfer of resources will occur when participation in the debt reduction plan is voluntary and the buyback price will generally need to be above the pre-buyback price.

To illustrate some of our results, we analyze the recent Mexican debt agreement. We show how to read through the complex financial acrobatics to estimate the extent of net debt reduction achieved. We show that the funds provided by IFIs benefited both Mexico and its creditors. Mexico retained about 62 percent of that transfer, and the banks 34 percent.

When creditors are heterogeneous and possess private information about the value of debt reduction to them, a mechanism is needed to elicit that information. Important topics for future research include analyses of how a menu can be combined with an auction over new money or exit instruments to induce revelation, and of the efficiency of various possible implementation mechanisms in the presence of market distortions and with heterogeneous creditors.