## _wp0758 - Box 1: Risks Encountered in Sovereign Debt Management

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### Introduction and scope
- Liability management operations (debt buybacks and debt swaps) are used to:
  - Lower and smooth government debt service payments.
  - Reduce vulnerability of public debt to unexpected shocks.
  - Help attain debt management goals such as development and maintenance of an efficient market for government securities.
- Recent activity and scope:
  - In January through November 2006, buyback and swap operations in a group of thirteen emerging market countries rose to 5.3 percent of total external debt and 1.6 percent of GDP.
  - Outstanding Brady bond holdings declined from US$154 billion in 1994 to US$10.7 billion at mid-December 2006.
- Focus: voluntary buybacks undertaken as part of routine liability management by the government (not negotiated buybacks/swaps in a debt restructuring).

### Macroeconomic context and coordination requirements
- Constraints affecting implementation:
  - Condition of domestic and international capital markets; exchange rate regime; quality of macroeconomic policies; domestic and international regulatory environment; credit rating; objectives of debt policy; human and technological capacity.
- Coordination and transmission:
  - Debt management must be coordinated with fiscal and monetary policies to avoid inconsistencies.
  - Domestic-market buybacks increase liquidity, potentially expanding aggregate demand and inflating domestic asset prices—risk higher in illiquid markets.
  - Buybacks of foreign currency debt or swaps involving foreign/domestic debt directly affect foreign exchange reserves and may necessitate sterilization by the central bank; sterilization can be costly and push up interest rates.
  - Costs of sterilization, whether borne by the central bank or government, can partially cancel out benefits of debt buybacks.
- Asset-Liability Management (ALM):
  - Integrating debt management into public sector risk management (including government balance sheet analysis and ALM) strengthens coordination and allows better assessment of risks and matching of currency composition of debt and reserves.
  - ALM may be limited by central bank independence or the exchange rate regime.

### Objectives of buybacks and swaps
- Core objectives (not always mutually compatible):
  - To reduce debt service payments.
  - To minimize sovereign risk.
  - To develop domestic capital markets.
- Subsidiary objectives: releasing collateral, eliminating restrictive bond covenants (typically complementary to core objectives).
- Potential macroeconomic contributions if objectives achieved:
  - Strengthened fiscal and monetary policies.
  - Reduced debt overhang and external vulnerability.
  - Improved macroeconomic performance, higher domestic investment and growth, prevention of financial crises.
  - Potentially lower future tax rates and higher future generations’ incomes if debt stock and service are reduced.

### A. Reducing debt service payments — mechanisms and considerations
- Cash buybacks:
  - Financed through drawdown of cash reserves or other liquid assets.
  - Lower the debt stock by the face value of the buyback, saving interest on the bought debt and possibly principal if bought at a discount.
  - Secondary market purchases of discounted debt can help resolve a debt overhang.
- Debt refunding/swaps:
  - High-coupon refunding: replace high-coupon debt with lower-coupon debt to lower debt service.
  - Low-coupon refunding: replacement of low-coupon with high-coupon debt (opposite effect).
  - Swaps alter interest rate structure but net impact depends on interest-rate effect versus debt-stock (scale) effect; face value often assumed unchanged in net-benefit calculations.
- Opportunity costs and broader effects:
  - Assess opportunity cost of funds used for cash buybacks (forgone interest on government deposits, differences in central bank earnings on reserves).
  - General equilibrium effects (upward pressure on domestic bond prices; sterilization-induced higher domestic interest rates) can affect borrowing costs elsewhere and are difficult to quantify; qualitative assessments required when quantitative analysis shows marginal net benefits.
  - Buybacks and swaps may reduce future borrowing interest rates by improving creditworthiness and triggering credit rating upgrades and lower risk premia.

### B. Reducing sovereign risk — targets and caveats
- Principal sovereign risks targeted:
  - Rollover risk, interest rate risk, exchange rate risk, liquidity risk.
- Instruments and strategies:
  - Use buybacks and swaps to change maturity, interest rate, and currency structure; improve access to international capital markets.
- Risks created by operations:
  - Reputational risk if an operation is unsuccessful.
  - Risk that both refunding bond and refunded bond become illiquid if investor interest is insufficient.
  - Normal credit and operational risks.
- Implication: careful selection, timing, and due diligence regarding investor interest and demand are essential.

### Defined risk categories (definitions)
- Market Risk: sensitivity to interest rates, exchange rates; short-duration debt and foreign-currency denominated or indexed debt add volatility; bonds with embedded put options exacerbate market and rollover risks.
- Rollover Risk: risk that debt must be rolled over at unusually high cost or cannot be rolled over; particularly important for emerging market countries.
- Liquidity Risk: investor exit costs / lack of market depth; borrower-side risk from rapid diminution of liquid assets.
- Credit Risk: nonperformance by borrowers or counterparties; relevant for management of liquid assets and derivatives.
- Settlement Risk: loss from failure to settle by counterparty for reasons other than default.
- Operational Risk: failures in internal controls, systems, reputation, legal, security breaches, natural disasters.

_Source attribution: IMF and World Bank (2003) noted for definitions in this section._

### Changing portfolio structures to meet objectives
- Maturity structure:
  - Objectives (emerging markets): lengthen average maturity/duration; smooth debt service profile.
  - Instruments: buybacks and swaps to replace bullets with amortizing or differently-timed instruments; lengthening maturity reduces rollover risk but may increase long-term cost.
  - Use of swaps for spacing of bullet amortizations, sinking funds, and spreading principal repayments.
- Interest rate and currency structures:
  - Policy objective: reduce floating rate and foreign-currency exposure by swapping for fixed-rate and domestic-currency debt.
  - Constraints: size and liquidity of domestic capital markets (the “original sin” problem); underdeveloped derivative markets limit scope.
  - Examples: Colombia (2004), Brazil (2005), Bulgaria (dollar/euro swap November 2003).
- Maintaining/expanding international market access:
  - Uses: enhance creditworthiness and sovereign credit ratings (examples: Mexico, Brazil); lower credit spreads; increase financing options.
  - Caveat: repurchase of domestic debt held by public sector agencies does not improve net fiscal balance of the public sector and likely does not affect creditworthiness.
- Developing domestic capital markets:
  - Roles of buybacks and swaps:
    - Increase liquidity in domestic markets.
    - Develop benchmark bond issues.
    - Smooth and rationalize the bond yield curve.
  - Market infrastructure benefits: development of reverse auctions, clearing and settlement systems.
  - Practices: retire small illiquid non-benchmark bonds; re-open or create benchmark issues; maintain coupons “current” via swaps; eliminate illiquid bonds that carry higher risk premia.

### Trade-offs and complementarities among objectives
- Principal trade-offs:
  - Increasing average maturity or switching floating→fixed normally increases cost because long-term rates usually higher than short-term.
  - Switching foreign-currency to domestic-currency debt may increase cost due to higher domestic rates, larger risk premia, inflation risk, and lower confidence in domestic currency.
  - Trade-off between foreign exchange risk and rollover risk when domestic markets are underdeveloped.
- Factors affecting magnitude of trade-offs:
  - Slope of the yield curve, size of risk premia, average maturity of debt stock, share of foreign- or floating-rate debt.
- Complementarities:
  - Short run: potential complementarity between risk reduction and capital market development if rollover risk is low.
  - Long run: capital market development can reduce liquidity and rollover risk premia, complementing cost and risk reduction.
- Decision implication: each buyback/swap results in particular cost and risk attributes and affects market development; evaluation must determine whether resulting combination is superior to alternatives.

### Analytical framework and decision process — three necessary conditions
- Three necessary conditions to undertake a buyback or swap:
  - Operation must accomplish its intended/primary objective (requires clear objectives and decision rules).
  - Operation must not unfavorably impact other objectives, or any adverse impact must be of lesser priority.
  - Operation must contribute more to the intended objective than any other buyback or swap that could be undertaken for the same purpose (requires ranking alternatives).
- Practical assessment: debt managers must address five specific questions (detailed in Section IV.A).

### Five questions for the debt manager (decision checklist)
- What is the Objective of the Operation?
  - Preferably a single, clearly-defined objective; if multiple objectives are pursued, use multiple operations or designate a primary objective.
- Will the Operation Achieve its Intended Objective?
  - Treat as an investment decision: future benefits vs. investment costs; non-negative NPV necessary but not sufficient.
  - For cost-reduction objectives, NPV calculable. For risk or capital market objectives, use strategic benchmarks.
- What Are the Trade-Offs and Complementarities?
  - Evaluate impacts across cost, risk, and capital market development; unintended benefits/costs must be considered.
- Do the Trade-Offs and Complementarities Affect the Decision?
  - Assess priorities among objectives; acceptable trade-offs necessary to proceed.
- What is the Ranking of the Buyback or Swap?
  - Rank prospective operations achieving the intended objective; select highest-priority operation for execution.

### Illustrative sequential decision procedure
- Stage 1: Does the operation achieve intended objective? (Is NPV non-negative?)
- Stage 2: Are there adverse or favorable effects on risk and/or capital market development?
- Stage 3: Are adverse effects acceptable or do favorable effects outweigh cost?
- Stage 4: Is the operation ranked above alternatives that achieve the same objective?
- Example (cost-reduction): if NPV non-negative and no adverse effects (or acceptable adverse effects), tentatively accept pending ranking; if NPV negative and no favorable effects, reject; if favorable effects more important than cost, reclassify objective and compare alternatives accordingly.

### Measuring the Net Financial Advantage (NFA) of a buyback or swap
- General approach:
  - Apply corporate bond refunding logic to sovereign swaps/buybacks.
  - Assume replacement by a non-callable bond of identical maturity and par value; use r' (interest rate on new bond) as discount rate.
  - Assume 100 percent bondholder participation for decision calculations (actual participation affects realized outcome).
- Components:
  - Benefits: saving of principal and interest on old bond; net proceeds from sale of new bond.
  - Costs: re-purchase price of old bond E (call price if exercised or market price); principal/interest on new bond; transactions costs A (flotation, retirement, overlapping interest, accrued interest, discounts/premia).
- Discount rate practice:
  - Standard: use interest rate on the new bond r' as discount rate (opportunity cost).
  - Alternative: compute break-even discount rate (IRR) by setting NPV = 0.
- Key interpretations:
  - For swap to be profitable, market value of old bond (discounted at r') must exceed purchase price plus transactions costs.
  - There must be a minimum transfer of wealth from bondholders to government to cover transactions costs; secondary-market swaps may fail if bondholders find transfer unacceptable.
  - Exercising a call option (predetermined E) increases likelihood of success because bondholders are compelled to sell.

- Floating-rate and foreign-currency cases:
  - Floating rates introduce time-varying r and/or r'; discounting must adjust period-to-period.
  - General floating-to-floating and foreign-currency-inclusive expressions are provided (equations referenced).

- Cash buyback:
  - Conceptually equivalent to swap when using present-value identities; decision rule identical: proceed if AE V ≥ − (i.e., NPV non-negative accounting for transactions costs and opportunity cost of funds).
  - Discount-rate choice for cash buyback not unique (could use existing debt rate, rate of return on investments, deposit rate foregone, or economy-wide risk-adjusted return on government assets).

### Determining strategic benchmarks (when objectives are risk reduction or market development)
- Benchmarks define desired debt structure using quantitative indicators; guide buybacks/swaps and new issuance.
- Common benchmarks and indicators preserved from the source:
  - Interest rate risk:
    - Ratio of fixed-rate to floating-rate debt (or ratio to total debt).
    - Duration and modified/Macaulay duration formulas (equations provided in the source).
    - Convexity (formulas provided).
    - Cost-at-Risk (maximum rise in interest costs with high probability).
    - Portfolio duration: ∑_{i=1}^n w_i D_i.
  - Exchange rate risk:
    - Ratio of domestic currency debt to foreign currency debt; currency composition considerations (trade invoicing currency, peg currency, government revenue currency).
  - Liquidity and rollover risk:
    - Percent of debt maturing in given periods (common targets: next 6 or 12 months).
    - Average term to maturity (weighted average remaining term).
  - Capital market development:
    - Ratio of domestic bonds outstanding to GDP.
    - Ratio of domestic bonds to total bonds outstanding.

### Selection rules for operations
- Selection influenced by:
  - Ranking of operations by contribution to the pursued objective.
  - Funds available in the budget period.
  - Distance between actual structure and desired/optimal structure.
- Decision Rule 1 — Reducing level of debt service payments:
  - Undertake operations in order of highest NPV first; continue until all non-negative NPV operations are done or funds exhausted.
- Decision Rule 2 — Reducing sovereign risk or developing domestic capital markets:
  - Undertake operations in order of biggest impact on targeted strategic benchmark(s) until desired structure achieved or funds exhausted.
- When differing trade-offs exist, obtain policy guidance from policymakers.

### Selected execution issues (strategy elements)
- Amortizing versus bullet bonds:
  - Amortizing bonds smooth redemption profile and may reduce risk premia; bullets concentrate payments.
- New issues versus re-opening existing issues:
  - New benchmark issues facilitate price discovery; re-openings increase liquidity of existing benchmarks and reduce fragmentation; timing matters.
- Call options versus secondary market purchases:
  - Call options force repurchase at indenture price but raise borrowing cost via call premium.
- Open market purchases versus open tenders:
  - Open market: buy at market price—cheaper if liquid but limited by size and price impact.
  - Tender: uniform pricing, larger operations, clearer rules—preferable in illiquid markets; tender design choices (scope, amount, bid price ranges, allocation rules).
- Opportunistic versus rules-based approach:
  - Opportunistic: time market, potential larger savings but requires expertise and may increase volatility.
  - Rules-based: predefined parameters support stability and predictability.
  - Regular buyback programs may raise borrowing costs by increasing bond prices and reinvestment risk; credible funding source and transparent governance (trust fund or independent management) recommended.
- Transparency and investor relations:
  - Communicate objectives, responsibilities, rules/procedures, and instrument characteristics.
  - Disclose program details at start and results at conclusion; review/audit outcomes; explain rationale to public.
  - For swaps: inform investors about objectives, available funds, impact on debt risk profile; obtain investor feedback (roadshows, creditor meetings) to maximize participation.

### Appendix 1 — Hypothetical debt swap operation (numerical example)
- Setup and assumptions:
  - Existing (old) bond:
    - Face value: US$1 billion
    - Coupon: 10 percent (paid semi-annually)
    - Macaulay duration: 4.12 years
    - Trading price: 112 percent of face value (US$1.125 billion)
    - Yield: 7 percent
  - New bond (issued at par, non-callable):
    - Face value: US$1 billion
    - Coupon: 7 percent
    - Yield: 7 percent
    - Market value: US$1,000.00 million
    - Macaulay duration: 4.3 years
  - Transactions costs (A): half of one percent of the sum of the face values of the two bonds = US$10 million
  - Strike (re-purchase) price for callable bond scenario: 105 percent of face value = US$1.05 billion
  - Discount rate used to value old bond cash flows in swap analysis: yield on the new bond
- Callable bond case:
  - Discounted value of old bond (V_old): US$1.125 billion
  - Re-purchase price (E): US$1.05 billion
  - Transactions costs (A): US$10 million
  - NPV = V_old − E − A = US$1.125 billion − US$1.050 billion − US$10 million = US$65 million (presented as US$64.75 million in table summary and US$65 million in text)
  - Interpretation: positive NPV (US$65 million) is net benefit from refinancing via callable repurchase.
- Non-callable bond case:
  - V_old = US$1.125 billion; E = V_old = US$1.125 billion; A = US$10 million
  - NPV = US$1.125 billion − US$1.125 billion − US$10 million = −US$10 million
  - Conditions for positive NPV in non-callable case:
    - Yield on new bond must be lower than that on the old bond (breakeven just above 6.75 percent), or
    - Re-purchase price of the old bond must be less than market value by at least US$10 million (a required transfer of wealth from bondholders to government).
- Appendix table (selected figures):
  - Old bond market value (non-callable): 1,124.75 (US$ million)
  - New bond market value: 1,000.00 (US$ million)
  - Interest cash flows (old): 50.00 (ten semi-annual occurrences)
  - Interest cash flows (new): 35.00 (ten semi-annual occurrences)
  - Discount factors and present value cash flow entries provided; Macaulay durations: old 4.12, new 4.30
  - Re-purchase price of old bond:
    - Callable bond: 1,050.00 (US$ million)
    - Non-callable bond: 1,124.75 (US$ million)
  - Transactions costs: 10.00 (US$ million)
  - NPV of swap:
    - Callable bond: 64.75 (US$ million)
    - Non-callable bond: −10.00 (US$ million)
- Key analytical implications:
  - Positive NPV possible when callable bond repurchase price E < discounted market value V_old.
  - Non-callable case yields negative NPV equal to transactions costs unless new-yield is sufficiently lower or repurchase price below market value by at least transactions costs.

*Source: _wp0758 - Box 1: Risks Encountered in Sovereign Debt Management — supplied IMF working paper content.*

### Box 1: Risks Encountered in Sovereign Debt Management .....................................................9

### Box 1: Risks Encountered in Sovereign Debt Management

### Introduction and scope
- Liability management operations (debt buybacks and debt swaps) are used to:
  - Lower and smooth government debt service payments.
  - Reduce vulnerability of public debt to unexpected shocks.
  - Help attain debt management goals such as development and maintenance of an efficient market for government securities.
- External debt buyback and swap activity has risen in recent years:
  - In the period January through November 2006, buyback and swap operations in a group of thirteen emerging market countries rose to 5.3 percent of total external debt and 1.6 percent of GDP.
  - Outstanding Brady bond holdings declined from US$154 billion in 1994 to US$10.7 billion at mid-December 2006.
- The paper focuses on voluntary buybacks undertaken as part of routine liability management by the government (not negotiated buybacks/swaps in a debt restructuring).

### Macroeconomic context of buybacks and swaps
- Debt management operations must be implemented under multiple macroeconomic constraints, including:
  - Condition of domestic and international capital markets.
  - Exchange rate regime.
  - Quality of macroeconomic policies.
  - Regulatory environment (domestic and international).
  - Credit rating of the country.
  - Objectives of debt policy.
  - Human and technological capacity to conduct operations.
- Coordination requirements and potential effects:
  - Debt management should be coordinated with fiscal and monetary policies to avoid inconsistencies.
  - Domestic-market buybacks increase liquidity in the financial system, potentially expanding aggregate demand and inflating domestic asset prices—risk is higher in illiquid markets.
  - Buybacks of foreign currency debt or swaps involving foreign/domestic debt directly affect foreign exchange reserves and may necessitate sterilization by the central bank; sterilization can be costly and push up interest rates.
  - Costs of sterilization, whether borne by the central bank or government, can partially cancel out benefits of debt buybacks.
- Asset-Liability Management (ALM) and public sector risk management:
  - Integrating debt management into public sector risk management (including government balance sheet analysis and ALM) can strengthen coordination and allow better assessment of risks and matching of currency composition of debt and reserves.
  - The ALM approach may be limited by central bank independence or the exchange rate regime.

### Objectives of debt buybacks and swaps
- Debt managers must be clear about objectives; they are not necessarily mutually compatible.
- Three core objectives:
  - To reduce debt service payments.
  - To minimize sovereign risk.
  - To develop domestic capital markets.
- Subsidiary objectives may include releasing collateral and eliminating restrictive bond covenants; these typically complement core objectives rather than justify operations on their own.
- Achieving core objectives can contribute to:
  - Strengthened fiscal and monetary policies.
  - Reduced debt overhang and external vulnerability.
  - Improved macroeconomic performance, higher domestic investment and growth, and prevention of financial crises.
  - Potentially lower future tax rates and higher future generations’ incomes if debt stock and service are reduced.

### A. Reducing debt service payments — mechanisms and considerations
- Cash buybacks:
  - Financed through drawdown of cash reserves or other liquid assets.
  - Lower the debt stock by the face value of the buyback, saving interest on the bought debt and possibly principal if bought at a discount.
  - Secondary market purchases of discounted debt have been advocated as a way to resolve a debt overhang.
- Debt refunding/swaps:
  - Seek to lower debt service by replacing high-coupon debt with lower-coupon debt (high-coupon refunding).
  - Replacement of low-coupon with high-coupon debt is referred to as low-coupon refunding.
  - Swaps alter interest rate structure but do not necessarily leave debt stock unchanged; governments may issue a larger replacement bond to increase liquidity or cover transaction costs, so net impact depends on interest-rate effect versus debt-stock (scale) effect.
  - In net-benefit calculations of swaps it is normally assumed that the face value of the debt remains unchanged.
- Opportunity costs and broader effects:
  - Assessment of cash buybacks must account for opportunity cost of funds used (e.g., forgone interest earnings on government deposits or differences in central bank earnings on international reserves versus domestic assets).
  - General equilibrium effects—such as upward pressure on domestic bond prices or sterilization-induced higher domestic interest rates—can affect government borrowing costs elsewhere and are difficult to quantify; debt managers should at least undertake qualitative assessments, particularly when quantitative analysis shows only marginal net benefits.
  - Buybacks and swaps may reduce future borrowing interest rates by improving creditworthiness and triggering credit rating upgrades and lower risk premia.

### B. Reducing sovereign risk — targets and caveats
- Principal sovereign risks targeted by buybacks and swaps:
  - Rollover risk.
  - Interest rate risk.
  - Exchange rate risk.
  - Liquidity risk.
- Instruments and strategies:
  - Use buybacks and swaps to change debt maturity structure, interest rate structure, and currency structure, and to improve access to international capital markets.
- Risks created by buyback and swap operations themselves:
  - Reputational risk if an operation is unsuccessful, potentially harming creditworthiness.
  - Risk that both the refunding bond and the refunded bond become illiquid if investor interest is insufficient.
  - Normal credit and operational risks associated with any transaction.
- Implication:
  - Careful selection, timing, and due diligence regarding investor interest and demand are essential to mitigate transaction-specific sovereign risks.

*Source: _wp0758 - Box 1: Risks Encountered in Sovereign Debt Management — https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0758.pdf*

### Box 1: Risks Encountered in Sovereign Debt Management

### _wp0758 - Box 1: Risks Encountered in Sovereign Debt Management

### Risks Encountered (definitions)
- Market Risk
  - Refers to the risks associated with changes in market prices, such as interest rates, exchange rates, commodity prices, on the cost of the government’s debt servicing.
  - For both domestic and foreign currency debt, changes in interest rates affect debt servicing cost on new issues when fixed rate debt is refinanced, and on floating rate debt at the rate reset dates.
  - Short-duration debt (short-term or floating rate) is usually considered to be more risky than long-term, fixed rate debt. (Excessive concentration in very long-term, fixed rate debt also can be risky as future financing requirements are uncertain.)
  - Debt denominated in or indexed to foreign currencies adds volatility to debt servicing costs as measured in domestic currency owing to exchange rate movements.
  - Bonds with embedded put options can exacerbate market and rollover risks.

- Rollover Risk
  - The risk that debt will have to be rolled over at an unusually high cost or, in extreme cases, cannot be rolled over at all.
  - If limited to higher interest rates (including changes in credit spreads), may be considered a type of market risk.
  - Because inability to roll over debt and/or exceptionally large increases in government funding costs can lead to, or exacerbate, a debt crisis and cause real economic losses, it is often treated separately.
  - Managing this risk is particularly important for emerging market countries.

- Liquidity Risk
  - Two types:
    - Investor exit cost/penalty when number of transactors decreases or market depth is lacking (relevant when debt management includes management of liquidity assets or use of derivatives).
    - Borrower-side risk: rapid diminution of liquid assets in face of unanticipated cash flow obligations and/or difficulty raising cash quickly.

- Credit Risk
  - Risk of nonperformance by borrowers on loans or other financial assets or by a counterparty on financial contracts.
  - Relevant where debt management includes management of liquid assets, acceptance of bids in auctions of securities issued by the government, contingent liabilities, and derivative contracts entered into by the debt manager.

- Settlement Risk
  - Potential loss that the government, as a counterparty, could suffer as a result of failure to settle, for whatever reason other than default, by another counterparty.

- Operational Risk
  - Includes transactions; inadequacies or failures in internal controls, or in systems and services; reputation risk; legal risk; security breaches; or natural disasters that affect business activity.

_Source: IMF and World Bank (2003)_

### Changing the Maturity Structure (rationale and methods)
- Objectives for emerging market countries:
  - Lengthen average maturity or duration of debt.
  - Smooth (flatten) debt service (particularly redemption) profile to better match government’s steady flow of revenues.
- Rationale:
  - Longer average maturity and smoother debt service better match long-term nature of government assets and revenue flows, and reduce duration risk.
  - Duration risk may materialize as a liquidity or rollover crisis.
- Vulnerabilities:
  - Shorter-term debt is more susceptible to market and rollover risk; domestic short-term debt in shallow, illiquid domestic markets is particularly exposed.
  - Governments try to avoid bunching of short-term maturities, especially of domestic debt.
- Instruments and effects:
  - Buybacks and swaps: buy back bonds or replace them with bonds of different maturity (refundings usually longer maturity than refunded bonds to lengthen average maturity and duration).
  - Swaps used to create better spacing of bullet amortizations, replace with sinking fund debt, and spread principal repayments.
  - Lengthening maturity pushes debt service payments into the future, providing temporary relief from short-term budgetary pressures and reducing rollover risk.
  - When used for short-term budget relief, swaps function as cash management rather than pure debt management, blurring the distinction between debt management and financing operations of the government.
  - In the absence of short-term financing pressures, maturity alteration is routine liability management to satisfy financing needs at minimum cost and risk.

### Changing the Interest Rate and Currency Structures
- Vulnerabilities identified:
  - Floating interest rate debt, foreign currency debt, and foreign-currency-linked debt are major sources of vulnerability in many emerging market countries.
  - Floating rate and foreign currency debt may create balance sheet mismatches if government revenues are not linked to interest rates and the exchange rate, creating liquidity and rollover risk.
- Policy objective:
  - Reduce interest rate and exchange rate risk by swapping floating rate debt for fixed-rate debt, and foreign-currency or foreign-currency-linked debt for domestic-currency debt.
  - Increase ratio of fixed-rate to floating-rate debt and of domestic-currency to foreign-currency debt to reduce sensitivity of debt service to shocks.
- Constraints and examples:
  - Extent of switching limited by size and liquidity of domestic capital markets (the problem of “original sin”).
  - Examples: Colombia in 2004 and Brazil in 2005 issued domestic currency debt in international capital markets.
  - Some countries issue domestic currency debt abroad as sovereign credit ratings and debt management policies strengthen.
  - Bulgaria undertook a dollar/euro swap with the World Bank in November 2003.
  - Scope for swaps limited by underdeveloped derivative markets; currency and interest rate mismatches are long-term structural problems requiring concerted liability management strategy.

### Maintaining and Expanding Access to International Capital Markets
- Uses of buybacks and swaps:
  - Enhance international creditworthiness and improve sovereign credit ratings (examples: Mexico and Brazil).
  - Maintain or expand access to international capital markets and lower credit spreads.
- Benefits of market access:
  - Ensures financing gaps can be closed at acceptable costs.
  - Increases financing options (e.g., ability to issue local-currency bonds in international capital markets).
  - Serves as insurance against liquidity and rollover risks.
  - Benefits corporate borrowers by expanding market access, lowering credit spreads, and providing benchmarks for corporate issuance.
- Operational considerations:
  - Frequent and successful buybacks and swaps raise a country’s profile and may improve debt and fiscal sustainability.
  - Unsuccessful operations may harm reputation and lower creditworthiness.
  - Re-purchase of domestic government debt held by public sector agencies (e.g., social security institutes) does not improve net fiscal balance of the public sector; such intra-sector transactions would be netted out and probably not affect creditworthiness.
  - To enhance creditworthiness by improving public finances, buybacks should target domestic debt held by the private sector or external debt.

### Developing Domestic Capital Markets (roles of buybacks and swaps)
- Objectives for emerging market countries:
  - Expand domestic borrowing opportunities to reduce dependence on foreign borrowing and exposure to exchange rate risk.
- Three ways buybacks and swaps help:
  - Increase liquidity in domestic markets.
  - Develop benchmark bond issues.
  - Smooth and rationalize the bond yield curve.
- Market infrastructure:
  - Use of buybacks and swaps helps develop reverse auction mechanisms and clearing and settlement systems.
- Liquidity and benchmark development:
  - Swaps of domestic for foreign bonds increase domestic supply of bonds and attract capital to the domestic market.
  - Swaps can expand investor base by eliminating restrictive bond covenants or changing maturity structure to accommodate investor preferences.
  - Development of liquid benchmark bonds facilitates pricing and price discovery for sovereign and corporate issuers.
  - When a benchmark bond nears maturity, it may be bought back and replaced to maintain volume outstanding.
  - Retire small and illiquid non-benchmark bonds; increase size of on-the-run benchmark issues by re-opening issues or creating new benchmarks to reduce market fragmentation.
  - These practices are often used when countries have limited scope to issue new debt (e.g., times of budget surplus or falling debt/GDP ratio).
- Coupon and yield curve management:
  - When market rates change since issue, bond coupon may be out of line with market rates; swaps used to maintain coupon rates “current”.
  - Illiquid bonds carry higher risk premia which distort pricing; buybacks or swaps target such bonds to eliminate distortions and smoothen the yield curve.9

### Trade-Offs and Complementarities Among Objectives
- Principal trade-offs:
  - Increasing average maturity or switching from floating-rate to fixed-rate debt will normally increase the cost of the debt because long-term interest rates are usually higher than short-term rates.
  - Switching from foreign currency or foreign currency-linked debt to domestic currency debt may increase cost because of higher interest rates and higher risk premia from less liquid domestic capital markets, inflation risk if macroeconomic policies are not appropriate, and lower confidence in the domestic currency.
  - Switching from foreign to domestic debt may involve a trade-off between foreign exchange risk and rollover risk, given that short-term and floating rate debt may be the only type of debt the government can issue in less developed domestic capital markets.10
- Factors influencing magnitude of trade-offs:
  - The slope of the yield curve: the steeper the curve (assuming a normal, positive slope), the larger the impact on debt service of lengthening maturity or switching from floating to fixed-rate debt.
  - The size of risk premia: the larger the risk premium paid in accomplishing the swap (for example, when switching from foreign currency to domestic currency debt or when lengthening maturity in a situation of possible default), the larger the impact on debt service.
  - The average maturity of the debt stock: the shorter the maturity, the larger the rollover and liquidity risk and the larger the impact on sovereign risk, at the margin, of any given debt swap.
  - The share of foreign-currency or foreign-currency-linked debt and floating-rate debt in total debt stock: the larger this share, the larger the impact on sovereign risk, at the margin, of a switch to domestic-currency or fixed-rate debt.
- Complementarities:
  - Short run: possible complementarity between risk reduction and capital market development if the trade-off between exchange rate and domestic rollover risk is favorable, or if little/no rollover risk is associated with domestic capital markets.
  - Long run: complementarity between cost and risk reduction and capital market development, since development should reduce liquidity and rollover risk premia.
- Decision implication:
  - Every buyback or swap leaves the debt portfolio with particular cost and risk attributes and places the capital market in a particular state of development; evaluation must determine whether the resulting combination is superior to alternatives.
  - Procedures for such evaluation are discussed in Section IV.

### Analytical Framework for Selecting Buybacks and Swaps (three necessary conditions)
- Three necessary conditions for undertaking a buyback or swap at a given time:
  - First: The operation must accomplish its intended or primary objective.
    - Requires clear objectives and decision rules; determining satisfaction can be difficult in practice.
  - Second: The operation either must not impact unfavorably on any other objective, or, if it does, that other objective must be of secondary importance or lesser priority.
    - Requires explicit consideration of trade-offs and priorities among objectives.
  - Third: The buyback or swap must contribute more to the attainment of the intended objective than any other buyback or swap that could be undertaken for the same purpose.
    - Requires ranking different buybacks and swaps that could achieve the given objective.
- Practical assessment:
  - Debt managers must answer five questions about the buyback or swap operation (questions are introduced but not listed in this excerpt).

*Source: IMF and World Bank (2003)*

### Section IV.A, roughly in the order in which they should be answered. This results in a

### _wp0758 - Section IV.A, roughly in the order in which they should be answered. This results in a 

### A. Five Questions for the Debt Manager
- What is the Objective of the Operation?
  - Any individual buyback or swap should preferably have a single, clearly-defined, objective (the intended objective).
  - If multiple objectives are sought, use more than one operation (e.g., one to reduce debt service payments, another to reduce risk).
  - When multiple but complementary objectives are pursued in one operation, designate a primary (intended) objective; treat others as external (unintended) benefits.
  - External benefits and costs should enter decision-making but not confuse assessment based on the intended objective.

- Will the Operation Achieve its Intended Objective?
  - View buyback or swap as an investment decision: future benefits (net savings in interest payments, reduction of sovereign risk, capital market development) vs. investment costs (transactions costs, cost of buyback, interest foregone).
  - A non-negative net present value (NPV) (or internal rate of return) of benefits minus costs is a necessary, but not sufficient, condition.
  - If objective is to reduce debt service payments, direct benefits and costs can be quantified; NPV calculable (see Section C).
  - If objective is to reduce sovereign risk or develop domestic capital market, quantification may be impractical; instead determine a desired debt structure and evaluate operations by whether they help attain strategic benchmarks (e.g., average term to maturity, ratio of fixed-to-floating debt, ratio of foreign-currency to domestic-currency debt, ratio of domestic debt to GDP).

- What Are the Trade-Offs and Complementarities?
  - Evaluate unintended impacts on debt structure against established strategic benchmarks.
  - For cost-driven operations, assess effects on sovereign risk and capital market development; for structure-driven operations, assess budgetary impact via NPV.
  - Evaluate operation from perspective of all three objectives (cost, risk, capital market development) to determine net effect on portfolio cost, risk attributes, and capital market state.

- Do the Trade-Offs and Complementarities Affect the Decision?
  - Assess trade-offs in light of government/society priorities among objectives; acceptable trade-offs are necessary to proceed.
  - Complementarities (unintended benefits) strengthen the case for proceeding.
  - Intended objective may not be highest-priority objective; even if operation achieves intended objective, it may be rejected if it adversely affects a higher-priority objective.
  - Priorities among cost, risk, and capital market development vary over time with fiscal stance, risk characteristics, capital market development, and absolute size of debt.

- What is the Ranking of the Buyback or Swap?
  - Rank prospective operations that achieve the intended objective against each other, considering combinations of portfolio cost, risk, and capital market development.
  - The operation with highest priority (ranking) is selected for execution.
  - Ranking may be objective in crises (cost/risk dictated by circumstances) or subjective under normal conditions; debt managers need general guidance from policymakers.

### B. Illustration of the Decision-Making Process
- Sequential decision procedure (illustrated in Figure 2):
  - Stage 1: Will the operation achieve its intended/primary objective? (Is the NPV non-negative?)
  - Stage 2: Are there adverse or favorable effects on risk and/or capital market development?
  - Stage 3: Are adverse effects acceptable? Are favorable effects more important than cost?
  - Stage 4: Is the operation ranked above alternatives that can achieve the same objective?
  - Example (cost-reduction objective): If NPV non-negative and no adverse effects (or acceptable adverse effects) then tentatively accept at Stage 3; final acceptance depends on ranking at Stage 4. If NPV negative and no favorable effects, reject at Stage 3; if favorable effects are more important than cost, reclassify intended objective accordingly and compare with alternatives for that objective.

### C. Measuring the Net Financial Advantage of a Buyback or Swap
- General approach:
  - Apply corporate bond refunding literature to sovereign swaps and buybacks (noting tax differences).
  - Assume hypothetical replacement by a non-callable bond of identical maturity and par value for swaps, so only coupon differs. Use r' (interest rate on new bond) as discount rate.
  - Assume 100 percent bond-holder participation for decision calculations (actual participation affects realized outcome).

- Benefits (cash inflows) and Costs (cash outflows) for swaps:
  - Benefits: Saving of principal payment on old bond (face value F due at period T); saving of interest payments on old bond (rF per period t); net proceeds from sale of new bond (assumed at par F unless discount/premium treated as transaction cost/inflow).
  - Costs: Re-purchase price of old bond E (call price if exercised); principal repayment of new bond F due at T; interest payments on new bond r'F each period; transactions costs A (including flotation costs, retirement costs, overlapping interest, accrued interest, discount/premium treatment).

- Discount rate:
  - Standard practice: use the interest rate on the new bond, r', as discount rate (opportunity cost of financing).
  - Alternative: compute break-even discount rate (IRR) by setting NPV = 0.

- Net advantage expressions (fixed interest and exchange rates):
  - Full expression (as presented):  
    AF
    r
    F
    r
    Fr
    E
    r
    F
    r
    rF
    Q
    T
    T
    t
    tT
    T
    t
    t
    −
    ⎥
    ⎦
    ⎤
    ⎢
    ⎣
    ⎡
    −
    ′
    +
    +
    ′
    +
    ′
    −
    ⎥
    ⎦
    ⎤
    ⎢
    ⎣
    ⎡
    −
    ′
    +
    +
    ′
    +
    =
    ∑∑
    ==
    )1()1()1()1(
    11       (1)

  - Price of new bond (non-callable):  
    T
    T
    t
    t
    r
    F
    r
    Fr
    F
    )1()1(
    1
    ′
    +
    +
    ′
    +
    ′
    =
    ∑
    =        (2)

  - Simplified net advantage (since second term = 0):  
    AE
    r
    F
    r
    rF
    Q
    T
    T
    t
    t
    −−
    ′
    +
    +
    ′
    +
    =
    ∑
    =
    )1()1(
    1
           (3)

  - Compact form: AEVQ
    old
    −−=         (4)

  - Necessary condition to proceed with swap:  
    AEV
    old
    +≥                                                                                                                (5)

  - Rearranged showing required transfer from bondholders:  
    AEV
    old
    ≥−          (6)

  - Interpretations:
    - For swap to be profitable, market value of old bond (discounted at r') must exceed purchase price plus transactions costs.
    - There must be a minimum transfer of wealth from bondholders to government to cover transactions costs; secondary-market swaps may fail if bondholders find transfer unacceptable.
    - Exercising a call option increases likelihood of success because E is predetermined and bondholders are compelled to sell; timing the call to ensure transfer and using break-even bond interest rate analysis helps.

- Floating-rate and foreign-currency swaps:
  - Floating rates introduce time-varying r and/or r'; discounting must adjust period-to-period; two-step discounting procedure used when fixing periods differ.
  - General floating-to-floating expression (simplified form given as equation 8), and foreign-currency-inclusive general expression: equation (9) (exchange-rate conversions using jt e and TK e and e at purchase).

- Net Financial Advantage of a Cash Buyback:
  - Conceptual equivalence to swap: compare present value of foregone revenues from using government’s own funds (opportunity cost) with present value of savings from buyback net of transactions costs.
  - Discount rate choice not unique: could use risk-adjusted interest rate on existing debt, rate of return on investments, deposit rate foregone, or economy-wide risk-adjusted return on government assets; must be assessed case-by-case.
  - Cash buyback net advantage expression (domestic, fixed-rate bond):  
    A
    r
    E
    r
    Er
    r
    F
    r
    rF
    Q
    T
    t
    Tt
    T
    t
    Tt
    −
    ⎥
    ⎦
    ⎤
    ⎢
    ⎣
    ⎡
    ′
    +
    +
    ′
    +
    ′
    −
    ⎥
    ⎦
    ⎤
    ⎢
    ⎣
    ⎡
    ′
    +
    +
    ′
    +
    =
    ∑∑
    ==11
    )1()1()1()1(
                                       (10)

  - Using present value identity E (equation 11), cash buyback net advantage reduces to equation (12), identical to swap result:  
    AE
    r
    F
    r
    rF
    Q
    T
    T
    t
    t
    −−
    ′
    +
    +
    ′
    +
    =
    ∑
    =
    )1()1(
    1
    .                                                                             (12)

  - Decision rule identical to swap: AE V ≥ − .                                                                                                                    (13)

  - Floating and foreign-currency buybacks map to floating and FX swap expressions (equations 14 and 15), identical in form to equations 8 and 9.

### D. Determining the Strategic Benchmarks
- Purpose:
  - Use strategic benchmarks when objectives are risk reduction or domestic capital market development (benefits hard to quantify).
  - Strategic benchmarks define the government’s desired/optimal debt structure in quantitative indicators; guide both buybacks/swaps and new issuance (backward- and forward-looking).

- Benchmarks vary with capital market depth and policy environment; some constraints (e.g., “original sin”) may limit feasible targets.

- Common benchmarks (examples and definitions preserved):
  - Interest Rate Risk:
    - Ratio of fixed-rate to floating-rate debt (or alternatively ratio of fixed-rate or floating-rate debt to total debt).
    - Duration: measure of sensitivity of bond price to interest rate changes; formulas provided:
      - D = (r/P) (ΔP/Δr) − 1  (textual presentation as equation (16): r P P D Δ Δ − = 1)
      - First-order approximation: rD P P Δ − ≅ Δ (17)
      - Explicit bond pricing formula for semi-annual fixed cash flows: equation (19) and derivative equation (20).
      - Modified duration: equation (21).
      - Macaulay duration relation: mod 2 1 D r D Mac ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ +=  (23), and explicit Macaulay duration formula (24).
      - Portfolio duration: ∑_{i=1}^n w_i D_i  (25).
    - Convexity: second derivative measure; formulas (26) through (33) and portfolio convexity (34).
    - Cost-at-Risk: maximum rise in interest costs with high probability; akin to value-at-risk but focused on interest costs.

  - Exchange Rate Risk:
    - Ratio of domestic currency debt to foreign currency debt (domestic currency debt includes debt issued abroad in domestic currency; foreign currency debt includes debt issued domestically in foreign currency and domestic currency debt linked to exchange rate).
    - Currency composition of foreign debt: consider trade invoicing currency, peg currency, currency composition of government revenue; use underlying balance-sheet restructurings or derivatives (currency swaps) where markets permit.

  - Liquidity and Rollover Risk:
    - Percent of debt maturing in any given period (targets often set for next 6 or 12 months, sometimes longer).
    - Average term to maturity (weighted average remaining term).

  - Capital Market Development:
    - Ratio of domestic bonds outstanding to GDP (domestic bonds include all bonds issued in domestic market regardless of currency).
    - Ratio of domestic bonds to total bonds outstanding (less precise but useful).

### E. Selection of Buybacks and Swaps
- Final selection influenced by:
  - Ranking of operations (extent they contribute to the pursued objective).
  - Amount of funds available in budget period for operations.
  - Distance of actual structure from desired/optimal structure.

- Decision Rule 1: Reducing the Level of Debt Service Payments
  - The operation with the highest NPV should be undertaken first, then next-highest, and so on until all operations with non-negative NPVs have been undertaken or funds exhausted.
  - Illustration: NPV-ranking curve (Figure 3); undertake operations up to point A if funds suffice, else up to point B within budget.

- Decision Rule 2: Reducing Sovereign Risk or Developing Domestic Capital Markets
  - Undertake operations in order of biggest impact on targeted strategic benchmark(s), proceeding until actual debt structure equals desired structure or funds exhausted.

- When operations present differing trade-offs among objectives, debt manager should seek input and guidance from policymakers.

### V. Elements of Buyback and Swap Strategy (selected execution issues)
- Amortizing Versus Bullet Bonds
  - Amortizing bonds spread face value payments over time -> smoother redemption profile; useful for less mature issuers, may reduce risk premium.
  - Bullet bonds concentrate payment at single date -> lumpiness and increased repayment risk; mature issuers may prefer bullet bonds but often buy back part of bullet issues ahead of maturity.

- New Issues Versus Re-Opening Existing Issues
  - New issues (especially benchmarks) facilitate price discovery.
  - Re-openings increase liquidity of existing benchmark issues and avoid segmentation but can cause lumping of payments and timing risks; early re-openings encouraged.
  - Late re-openings can be problematic due to interest-rate or tax-law changes.

- Call Options Versus Secondary Market Purchases
  - Call options give government advantages (forced repurchase at indenture-defined price) but raise borrowing cost via call premium; value depends on interest rate movements.

- Open Market Purchases Versus Open Tenders
  - Open market: buy at market price; may be cheaper if market liquid but limited by size and potential price impact.
  - Tender: uniform pricing, larger operations, clearer rules; preferable when secondary markets are illiquid.
  - Tender design options listed (scope, total amount, bid price ranges, allocation rules).

- Opportunistic Versus Rules-Based Approach
  - Opportunistic: time market to buy when prices low -> potentially larger savings but requires market expertise and can increase volatility.
  - Rules-based: predefined parameters (e.g., total funds per period) -> supports market stability and predictability.
  - Regular buyback programs may raise borrowing costs (increased bond prices, higher risk premiums for reinvestment risk); credible funding source and transparent governance (trust fund or independent management) recommended.

- Transparency and Investor Relations
  - Transparency enhances credibility, lowers transaction costs, increases participation.
  - Authorities should communicate objectives, responsibilities, rules/procedures, and instrument characteristics.
  - For buybacks and swaps: disclose program details at start, results at conclusion, review/audit outcomes; explain rationale to public.
  - For swaps: inform investors about objectives, available funds, impact on debt risk profile; obtain investor feedback (roadshows, creditor meetings) to maximize participation.

*Italic: Source — Section IV.A–V (selected) of the supplied IMF working paper content.*

### Appendix 1.  A Hypothetical Debt Swap Operation

### Appendix 1.  A Hypothetical Debt Swap Operation

### Example setup and assumptions
- Existing (old) bond:
  - Face value: US$1 billion
  - Coupon: 10 percent (paid semi-annually)
  - Macaulay duration: 4.12 years
  - Trading price: 112 percent of face value (US$1.125 billion)
  - Yield: 7 percent
- New bond (issued at par, non-callable):
  - Face value: US$1 billion
  - Coupon: 7 percent
  - Yield: 7 percent
  - Market value: US$1,000.00 million
  - Macaulay duration: 4.3 years
- Transactions costs (A): half of one percent of the sum of the face values of the two bonds = US$10 million
- Strike (re-purchase) price for callable bond scenario: 105 percent of face value = US$1.05 billion
- Discount rate used to value old bond cash flows in swap analysis: yield on the new bond

### Callable bond case — valuation and net benefit
- Discounted value of cash flows of the old bond (V_old), using the yield on the new bond as discount rate: US$1.125 billion
- Re-purchase price (E): US$1.05 billion
- Transactions costs (A): US$10 million
- Net present value (NPV) of the swap calculation:
  - NPV = V_old − E − A
  - NPV = US$1.125 billion − US$1.050 billion − US$10 million
  - NPV = US$65 million
- Interpretation:
  - The NPV of US$65 million is described as the net benefit to the government from refinancing to take advantage of the decline in the interest rate.

### Non-callable bond case — valuation and required conditions for positive NPV
- Discounted value of cash flows of the old bond (V_old) remains: US$1.125 billion
- Market re-purchase price (E) for non-callable bond is assumed to equal the market value (bondholders will only sell at market price):
  - E = V_old = US$1.125 billion
- Transactions costs (A): US$10 million
- Net present value (NPV) of the swap calculation:
  - NPV = V_old − E − A
  - NPV = US$1.125 billion − US$1.125 billion − US$10 million
  - NPV = −US$10 million
- Conditions for NPV to be positive (as stated):
  - The yield on the new bond would have to be lower than that on the old bond (the breakeven rate is just above 6.75 percent), or
  - The re-purchase price of the old bond would have to be less than the market value by at least US$10 million (a required transfer of wealth from bondholders to the government to cover the transactions costs of the swap).

### Appendix Table 1 — illustrative cash flow and valuation figures (selected entries)
- Term of cash flows (years): 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5
- Old bond (US$ million):
  - Maturity (years): 5
  - Face value: 1,000.00
  - Market value (for a non-callable bond): 1,124.75
  - Coupon (percent): 0.10
  - Yield (percent): 0.07
  - Interest cash flows (each semi-annual): 50.00 (ten occurrences)
  - Principal at maturity: 1,000.00
  - Discount factors (using yield on new bond): 1.0350, 1.0712, 1.1087, 1.1475, 1.1877, 1.2293, 1.2723, 1.3168, 1.3629, 1.4106
  - Present value of cash flows (US$ million) (selected): 48.31, 46.68, 45.10, 43.57, 42.10, 40.68, 39.30, 37.97, 36.69, 744.36
  - Macaulay duration (years): 4.12
- New bond (non-callable) (US$ million):
  - Maturity (years): 5
  - Face value: 1,000.00
  - Market value: 1,000.00
  - Coupon (percent): 0.070
  - Yield (percent): 0.070
  - Interest cash flows (each semi-annual): 35.00 (ten occurrences)
  - Principal at maturity: 1,000.00
  - Discount factors: same as for old bond
  - Present value of cash flows (US$ million) (selected): 33.82, 32.67, 31.57, 30.50, 29.47, 28.47, 27.51, 26.58, 25.68, 733.73
  - Macaulay duration (years): 4.30
- Re-purchase price of old bond (US$ million):
  - Callable bond: 1,050.00
  - Non-callable bond: 1,124.75
- Transactions costs (US$ million): 10.00
- NPV of swap (US$ million):
  - Callable bond: 64.75
  - Non-callable bond: −10.00

### Key analytical implications
- A debt swap that exchanges a higher-coupon callable bond for a lower-coupon new bond can produce a positive NPV for the issuer when the callable bond can be repurchased at a strike price below the discounted market value of its cash flows (example NPV: US$65 million).
- When an existing bond is non-callable and its market price equals the discounted value of its cash flows at the new bond’s yield, a swap that requires paying market price yields a negative NPV equal to the transactions costs (example NPV: −US$10 million).
- To achieve a positive NPV in the non-callable case, either the new bond must be issued at a yield below the old bond’s yield (breakeven just above 6.75 percent), or the repurchase price must be below market value by at least the transactions costs (US$10 million).

*Source: Appendix 1. A Hypothetical Debt Swap Operation*

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