## _pdp09

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### Additional ways of evaluating debt restructurings (Box 1)
- Profile of debt service and near-term cash savings
  - Restructurings often reprofile debt-service with lower near-term payments and higher later payments; may free up collateral (e.g., Brady exchanges).
  - Qualitative benefit: “breathing space” to implement reforms.
- Required fiscal position
  - Assessment must account for the primary surplus needed to meet future debt-service payments; debt sustainability is not restored if the required fiscal effort is unrealistic.
- Impact on default premium and market access
  - Movements in spreads are observable; harder to assess whether a debt exchange will reduce rollover risks via improved market access.
- Removal of a debt overhang and growth effects
  - Debt overhang theory suggests high debt stock reduces investment incentives and growth; removal via restructuring can improve growth prospects.
  - Critical to evaluate whether the debtor can use breathing space to implement policies and whether linkages between required policy adjustment and growth path allow the debtor to “grow out” of the debt problem.
- Methods beyond NPV
  - Because of difficulties in reaching consensus on the discount rate, other methods accompanied by stress tests may be useful.

### Framework and recommendations on discount-rate selection
- Use of the internal rate of return (IRR) as a benchmark
  - IRR defined as “the discount rate that equalizes the NPV of two streams of debt-service payments.”
- Use of a range of discount rates when evaluating restructurings
  - Lower bound guided by a measure of the debtor’s repayment capacity such as the GDP or export growth rate.
  - Upper bound guided by spreads likely to prevail after the debt restructuring, but outside the period of financial distress, to avoid distortions associated with abnormal risks of default.
- Suggested benefits
  - Using a range could improve transparency within the IMF on the use of discount rates in NPV calculations.

### Conceptual considerations on NPV and discounting (Section II and Box 2)
- NPV interpretation and purpose
  - NPV should represent the “commercial equivalent” of the stream of payments discounted; amount that, if invested at the commercial interest rate the country can earn, would cover obligations.
- Opportunity cost for sovereigns
  - Discount rate captures value of future payments versus today; opportunity cost is return country can obtain by investing funds rather than paying debt service.
- Alternate perspectives on NPV (Box 2)
  - Creditor/debtor perspective: NPV may differ depending on whether creditor or debtor viewpoint is used, because creditors include a default premium.
  - Repayment capacity: Discount rates reflecting GDP or export growth sometimes used to evaluate tolerance for debt burden.
  - Debt stock: NPV can derive a debt stock concept; if debt issued at market rates and discounted at same market rate, NPV equals face value (if not issued at a discount). An NPV lower than face value implies a grant element equal to one minus the ratio of NPV to face value.
- Caution on discount rates that incorporate default risk
  - Using a discount rate that includes a high risk of nonpayment reduces NPV relative to a lower-risk rate; when assessing debt sustainability, ensure NPV reduction comes from debt-service profile adjustments (interest rate reductions, lengthened duration) rather than adjustments in the discount rate.

### Market’s perspective on discount rates (Section III)
- Divergent objectives
  - Debtors and the IMF focus on restoring debt sustainability; creditors focus on maximizing risk-adjusted expected returns.
- Market participants’ approach
  - Market assesses streams of payments pre- and post-restructuring and selects a discount rate reflecting probability of non-payment, typically represented by the yield curve or the exit yield.
  - Exit yield: yield that would prevail immediately after a restructuring (post-restructuring yield) and at which newly issued debt would be priced.
  - Yields around the time of restructuring often higher than those expected after a successful restructuring.
- Practical implication
  - Creditors who mark-to-market use prevailing market rates (including exit yields) to calculate the haircut they accept; exit yield projections need continuous monitoring to gauge market attitudes toward exchange offers.

### Practical issues from the debtor’s perspective (Section IV)
- Difficulty in consensus within IMF and between parties
  - Creditors typically use exit yields, which may be inappropriate for debtors if market rates reflect large default premia.
  - IMF must ensure discount-rate choice does not produce NPV calculations that understate debtor’s burden.
- Challenges in selecting market interest rates
  - Market rates vary over time and across currencies; they reflect country-specific and global conditions.
  - Aim to select a time-invariant discount rate for IMF assessments of a restructuring’s contribution to restoring sustainability.
- Example rate considered: Risk-free world interest rate (Subsection A)
  - Risk-free world interest rate (e.g., U.S. Treasury rates) often used; represents opportunity cost of funds and allows a common rate across countries.
  - Use implies NPVs differ only by debt-service profile and would represent cost/benefit compared with truly risk-free asset.
  - Using risk-free rate corresponds to debtor commitment to fully service obligations or negligible default probability.
  - Caveat: if creditors perceive default risk while debtor does not, asymmetric information issues arise.

### Box 3. Use of Time-Varying Discount Rates — Overview and arguments
- Uniform, constant discount rates
  - In most cases a uniform, constant, discount rate is used to examine debt restructurings or other debt operations.
  - Use of a uniform rate adds simplicity and clarity to NPV calculations.
  - Variable rates are not discussed for most analyses because:
    - At times of extreme financial distress the yield curve may be subject to significant volatility with frequent shifts in position and slope.
    - The yield curve often becomes inverted, complicating NPV calculations.
    - In post-default cases the yield curve essentially collapses to one point as all claims become due and payable, making variable rates along a term structure arbitrary.
- Arguments for using time-varying discount rates
  - Market participants may use variable rates (e.g., a yield curve) in some evaluations.
  - Possible patterns:
    - Lower rates for payments falling due in the near term (e.g., the next 1-2 years) and higher rates further out, reflecting more certainty in the near term.
    - Higher discount rates in the near term and lower rates later on if debtors face tougher near-term financing constraints; consistent with inverted yield curves at times of crisis and observed declines in spreads over time after restructurings.
    - Use of discount rates reflecting repayment capacity could capture a post-crisis “rebound effect” on measures such as export or GDP growth, followed by a lower, “steady state”, growth.

### Box 3.B. GDP or Export Growth Rates (discounting by growth)
- Concept
  - NPV may be used to measure repayment capacity, with discount rates reflecting economic fundamentals—GDP or exports growth rates.
  - Analogy to debt-to-GDP or debt-to-exports indicators; repayment capacity depends on the relationship between GDP (or export) growth and the interest rate paid on debt.
- Advantages
  - Discounting debt-service payments by the GDP growth rate captures repayment capacity in a single measure.
- Cautions and limitations
  - Determining potential growth rates for emerging markets is not straightforward; NPV is very sensitive to growth assumptions.
  - Long-run average historical growth rates can be misleading if structural shifts occur.
  - Use of U.S. dollar growth rates implicitly assumes evolution of the real exchange rate and/or dollar inflation; NPV calculations depend on these assumptions.
  - If actual realizations differ significantly from assumptions, future debt-to-GDP ratios could diverge from NPV predictions.
- Footnote clarifications
  - Use of exports is only relevant for foreign currency-denominated debt; GDP growth must be adjusted for exchange rate movements when looking at foreign-currency denominated debt.
  - Simplified debt sustainability relation: required primary surplus for maintaining a constant debt-to-GDP ratio equals d*(i-g)/(1+g), where d = debt-to-GDP ratio, i = nominal interest rate, g = nominal GDP growth rate (abstracts from exchange rate considerations, seignorage, and contingent liabilities).

### Box 3.C. Country-Specific Interest Rate
- Definition
  - Country-specific rate corresponds to a borrowing rate in “normal” circumstances, unaffected by a large default premium.
- Pros
  - Avoids incorporating crisis-related risk factors irrelevant over a long horizon.
- Cons
  - Many countries have never borrowed at rates reflecting low default risk.
  - Use complicates comparability: for the same debt-service stream, higher default-premium countries yield lower NPVs and vice versa.
  - Post-crisis “normal” borrowing costs may be higher than pre-crisis, requiring judgments about potential future spreads and reliance on historical information.
- Footnote
  - Country-specific long-term average rate would represent the average cost at which the debtor refinanced itself in the past; averaging smooths fluctuations and approximates an equilibrium rate.

### Box 3.D. Benchmarking
- Approach
  - Construct “normal” borrowing costs using spreads from countries with similar economic circumstances.
  - Estimate average spread expected when the country returns to “normal” conditions and derive a (dollar) discount rate.
- Practical notes
  - Academic literature identifying factors that change spreads can inform benchmarking.
  - Simplified “guestimate” approach: e.g., assume average spread such as 500 bps and relate to prevailing EMBI+ or EMBIG spreads.
- Risks
  - Benchmarking may be biased upward if contagion affects comparator spreads, or downward if international liquidity conditions are unusually favorable.

### Box 3.E. Market Yields at Times of Distress
- Issues with using prevailing yield curves or exit yields at times of distress
  - Such yields include the risk-free rate plus a default premium, often inflated by the crisis legacy.
  - Yield curves vary significantly between tranquility and financial pressure; at crisis times they can be unstable, inverted, or collapse to a single point.
  - Using crisis-period yields may strip out normal borrowing costs and over-discount future debt-service payments, making restructurings that push liabilities forward appear to generate NPV savings.
  - This can mislead assessments where restoring solvency/sustainability is the paramount objective.

### V. A Suggested Framework (from Box 3)
- First step: calculate the IRR of the difference between two payment streams
  - Definition: the IRR is the discount rate at which the NPV of the difference between two debt-service streams equals zero.
  - Conceptually, IRR is the implicit borrowing cost of shifting debt service into the future.
  - If discount rate > IRR → NPV savings for debtor; if discount rate < IRR → NPV cost for debtor.
  - Practical note: cash flow differentials with multiple sign changes can yield non-unique IRR solutions, but tests can ensure uniqueness within a reasonable discount rate range.
- Complement IRR with sensitivity analysis across a range of discount rates
  - Range enhances transparency and highlights sensitivity of NPV calculations to discount rate choice.
  - Range should reflect the objective (typically, whether restructuring restores debt sustainability).
- Suggested bounds for the range
  - Lower bound: rate capturing ability to service debt (e.g., nominal GDP growth rate in the relevant currency).
  - Upper bound: country-specific factors capturing debtor’s ability to refinance under “normal” circumstances (outside financial distress).
  - Consider risk-free world rate as a commonly cited discount rate for comparability; however, it may understate costs for most countries because it is lower than typical borrowing costs.
  - Care needed for countries whose spreads are unlikely to return to pre-crisis levels; comparator-country spreads could be informative.
  - Judgment required to keep the range operationally useful and sufficiently confined.
- Interpretation using IRR
  - IRR > sovereign’s “normal” borrowing cost → sovereign is paying a high cost to shift debt service; restructuring may yield NPV cost and require careful examination.
  - IRR ≤ sovereign’s “normal” borrowing cost → restructuring may have capitalized on lower perceived future default risk and could yield NPV savings.

### Illustrative country cases and sensitivity
- General
  - Two country cases (Uruguay and Ukraine) illustrate sensitivity of NPVs to discount rates.
  - In both cases IRR ≈ 7 percent.
  - For discount rates below 7 percent → restructuring yields NPV cost; above 7 percent → NPV savings.
- Uruguay (summary)
  - May 2003 restructuring restructured nearly all external bonded debt.
  - Principal reduction: US$50 million (small).
  - Total debt service increased by around US$2.5 billion over the period 2003–33, mostly in later years.
  - The restructuring shifted debt service into the future, generating near-term cash flow relief.
  - Uruguay’s GDP growth rate (lower bound) based on medium term framework: nominal GDP growth in U.S. dollar terms likely to be around 5–6 percent.
  - Figure details and numeric highlights:
    - IRR = 6.95%
    - Suggested discount rate range shown in figure: 5.5–9.5 percent (implied by narrative summary).
    - The yield prevailing immediately before the exchange was 16 percent, and shortly thereafter it fell by 200 bps.
    - The discount rate used by the Fund to evaluate Uruguay's debt exchange was 16 percent.
    - Footnotes in figure:
      - 1/ 10 year average of interest rate on 5-year U.S. Treasury bonds.
      - 2/ Defined 1 - (NPV(after restructuring)/NPV(before restructuring)). NPVs are evaluated at the same, constant, discount rate.
      - 3/ The yield prevailing immediately before the exchange was 16 percent, and shortly thereafter it fell by 200 bps (see Uruguay staff report, EBS/03/93, Appendix II). The discount rate used by the Fund to evaluate Uruguay's debt exchange was 16 percent.
- Ukraine (summary)
  - Proposed range of discount rates spans from 8.5 to 10.5 percent.
  - IRR is equal to roughly 7 percent.
  - Since IRR < lower bound (8.5 percent), the restructuring would yield NPV savings at any discount rate in the proposed range.
- Key conclusion from cases
  - NPV calculations are highly sensitive to discount rate choice.
  - Using spreads prevailing at times of financial distress would overstate NPV gains and implied debt relief to the debtor.
  - Using more conservative discount rates can avoid overstating debtor gains.

### Box 4. Country Example: Uruguay (continued) — sensitivity and implications
- Sensitivity of NPV calculations to the discount rate
  - NPV calculations are highly sensitive to the choice of the discount rate.
  - Using a discount rate closer to the current 9–10 percent implied yield on Uruguayan bonds would produce savings closer to 7 percent than to 20 percent (the market haircut quoted at the time of the exchange).
  - If the discount rate were closer to Uruguay’s nominal GDP growth rate, the savings would be negative, indicating an NPV cost to the country.
  - The example illustrates that using more conservative discount rates in evaluating debt restructurings will lead to conclusions of lower NPV savings from the perspective of the debtor.
- Segmentation of the discount-rate range
  - The upper bound is estimated as the average borrowing cost for Uruguay during “normal” times, with the understanding that Uruguay will likely face spreads in the 400 bps range over the medium term, rather than in the 200-300 bps range (as they were before the crisis when Uruguay had an investment grade rating).
  - For illustrative purposes, the range is segmented into two sub-ranges:
    - “Historical” sub-range: represents the range between potential GDP growth and the historical yield on government debt (at spreads of 200–300 bps).
    - “Judgmental” sub-range: reflects staff judgment regarding future spreads; for Uruguay it is assumed spreads will remain around 400 bps.
- Uruguay-specific observations and key statistics
  - Current implied yield on Uruguayan bonds at the time of the analysis: 9–10 percent.
  - Market haircut quoted at the time of the exchange: 20 percent.
  - Alternative implied savings using market yields: closer to 7 percent.
  - Historical spreads before the crisis: 200–300 bps.
  - Judged medium-term spreads for Uruguay: around 400 bps.
  - Average U.S. Treasury rate used in spread calculations: 5.5 percent (10 year average of the 5-year bond rate).
  - Currently, Uruguay’s spreads are around 300 bps, likely influenced by a benign international liquidity environment.
- Implications for evaluation of debt restructurings
  - The choice of discount rate determines whether a restructuring appears as an NPV saving or cost to the debtor.
  - Conservative (higher) discount rates reduce estimated NPV savings from the debtor’s perspective.
  - Evaluations should avoid selecting discount rates prevailing at times of financial distress, as these may significantly overstate financial relief and understate costs to the sovereign debtor.

*Source: IMF PDF chapter/section content provided in the input*

### conclusions) in analyzing the impact of debt restructurings. Thus, the evaluation of debt

### _pdp09 - conclusions) in analyzing the impact of debt restructurings. Thus, the evaluation of debt

### Additional ways of evaluating debt restructurings (Box 1)
- Profile of debt service and near-term cash savings
  - Restructurings often reprofile debt-service with lower near-term payments and higher later payments; may free up collateral (e.g., Brady exchanges).
  - Qualitative benefit: “breathing space” to implement reforms.
- Required fiscal position
  - Assessment must account for the primary surplus needed to meet future debt-service payments; debt sustainability is not restored if the required fiscal effort is unrealistic.
- Impact on default premium and market access
  - Movements in spreads are observable; harder to assess whether a debt exchange will reduce rollover risks via improved market access.
- Removal of a debt overhang and growth effects
  - Debt overhang theory suggests high debt stock reduces investment incentives and growth; removal via restructuring can improve growth prospects.
  - Critical to evaluate whether the debtor can use breathing space to implement policies and whether linkages between required policy adjustment and growth path allow the debtor to “grow out” of the debt problem.
- Methods beyond NPV
  - Because of difficulties in reaching consensus on the discount rate, other methods accompanied by stress tests may be useful.

### Framework and recommendations on discount-rate selection
- Paper proposes use of the internal rate of return (IRR) as a benchmark
  - IRR defined as “the discount rate that equalizes the NPV of two streams of debt-service payments.”
- Suggests use of a range of discount rates when evaluating restructurings
  - Lower bound guided by a measure of the debtor’s repayment capacity such as the GDP or export growth rate.
  - Upper bound guided by spreads likely to prevail after the debt restructuring, but outside the period of financial distress, to avoid distortions associated with abnormal risks of default.
- Suggested benefits
  - Using a range could improve transparency within the IMF on the use of discount rates in NPV calculations.

### Conceptual considerations on NPV and discounting (Section II and Box 2)
- NPV interpretation and purpose
  - NPV should represent the “commercial equivalent” of the stream of payments discounted; amount that, if invested at the commercial interest rate the country can earn, would cover obligations.
- Opportunity cost for sovereigns
  - Discount rate captures value of future payments versus today; opportunity cost is return country can obtain by investing funds rather than paying debt service.
- Alternate perspectives on NPV (Box 2)
  - Creditor/debtor perspective: NPV may differ depending on whether creditor or debtor viewpoint is used, because creditors include a default premium.
  - Repayment capacity: Discount rates reflecting GDP or export growth sometimes used to evaluate tolerance for debt burden.
  - Debt stock: NPV can derive a debt stock concept; if debt issued at market rates and discounted at same market rate, NPV equals face value (if not issued at a discount). An NPV lower than face value implies a grant element equal to one minus the ratio of NPV to face value.
- Caution on discount rates that incorporate default risk
  - Using a discount rate that includes a high risk of nonpayment reduces NPV relative to a lower-risk rate; when assessing debt sustainability, ensure NPV reduction comes from debt-service profile adjustments (interest rate reductions, lengthened duration) rather than adjustments in the discount rate.

### Market’s perspective on discount rates (Section III)
- Divergent objectives
  - Debtors and the IMF focus on restoring debt sustainability; creditors focus on maximizing risk-adjusted expected returns.
- Market participants’ approach
  - Market assesses streams of payments pre- and post-restructuring and selects a discount rate reflecting probability of non-payment, typically represented by the yield curve or the exit yield.
  - Exit yield: yield that would prevail immediately after a restructuring (post-restructuring yield) and at which newly issued debt would be priced.
  - Yields around the time of restructuring often higher than those expected after a successful restructuring.
- Practical implication
  - Creditors who mark-to-market use prevailing market rates (including exit yields) to calculate the haircut they accept; exit yield projections need continuous monitoring to gauge market attitudes toward exchange offers.

### Practical issues from the debtor’s perspective (Section IV)
- Difficulty in consensus within IMF and between parties
  - Creditors typically use exit yields, which may be inappropriate for debtors if market rates reflect large default premia.
  - IMF must ensure discount-rate choice does not produce NPV calculations that understate debtor’s burden.
- Challenges in selecting market interest rates
  - Market rates vary over time and across currencies; they reflect country-specific and global conditions.
  - Aim to select a time-invariant discount rate for IMF assessments of a restructuring’s contribution to restoring sustainability.
- Example rate considered: Risk-free world interest rate (Subsection A)
  - Risk-free world interest rate (e.g., U.S. Treasury rates) often used; represents opportunity cost of funds and allows a common rate across countries.
  - Use implies NPVs differ only by debt-service profile and would represent cost/benefit compared with truly risk-free asset.
  - Using risk-free rate corresponds to debtor commitment to fully service obligations or negligible default probability.
  - Caveat: if creditors perceive default risk while debtor does not, asymmetric information issues arise.

*Source: IMF PDF chapter/section content provided in the input.*

### Box 3. Use of Time-Varying Discount Rates

### Box 3. Use of Time-Varying Discount Rates

### Overview
- In most cases a uniform, constant, discount rate is used to examine debt restructurings or other debt operations.
- Use of a uniform rate adds simplicity and clarity to NPV calculations.
- The paper does not discuss the use of variable rates for most analyses because:
  - At times of extreme financial distress the yield curve may be subject to significant volatility with frequent shifts in position and slope.
  - The yield curve often becomes inverted, complicating NPV calculations.
  - In post-default cases the yield curve essentially collapses to one point as all claims become due and payable, making variable rates along a term structure arbitrary.

### Arguments for using time-varying discount rates
- Market participants may use variable rates (e.g., a yield curve) in some evaluations.
- Possible rationale and patterns:
  - Lower rates for payments falling due in the near term (e.g., the next 1-2 years) and higher rates further out, reflecting more certainty in the near term (e.g., reduced policy uncertainty associated with a Fund-supported program).
  - Higher discount rates in the near term and lower rates later on if debtors face tougher near-term financing constraints; consistent with inverted yield curves at times of crisis and observed declines in spreads over time after restructurings.
  - Use of discount rates reflecting repayment capacity could capture a post-crisis “rebound effect” on measures such as export or GDP growth, followed by a lower, “steady state”, growth.

### B. GDP or Export Growth Rates (discounting by growth)
- Concept:
  - NPV may be used to measure repayment capacity, with discount rates reflecting economic fundamentals—GDP or exports growth rates.
  - Analogy to debt-to-GDP or debt-to-exports indicators; repayment capacity depends on the relationship between GDP (or export) growth and the interest rate paid on debt.
- Advantages:
  - Discounting debt-service payments by the GDP growth rate captures repayment capacity in a single measure.
- Cautions and limitations:
  - Determining potential growth rates for emerging markets is not straightforward; NPV is very sensitive to growth assumptions.
  - Long-run average historical growth rates can be misleading if structural shifts occur.
  - Use of U.S. dollar growth rates implicitly assumes evolution of the real exchange rate and/or dollar inflation; NPV calculations depend on these assumptions.
  - If actual realizations differ significantly from assumptions, future debt-to-GDP ratios could diverge from NPV predictions.
- Footnote clarifications:
  - Use of exports is only relevant for foreign currency-denominated debt; GDP growth must be adjusted for exchange rate movements when looking at foreign-currency denominated debt.
  - Simplified debt sustainability relation: required primary surplus for maintaining a constant debt-to-GDP ratio equals d*(i-g)/(1+g), where d = debt-to-GDP ratio, i = nominal interest rate, g = nominal GDP growth rate (abstracts from exchange rate considerations, seignorage, and contingent liabilities).

### C. Country-Specific Interest Rate
- Definition:
  - Country-specific rate corresponds to a borrowing rate in “normal” circumstances, unaffected by a large default premium.
- Pros:
  - Avoids incorporating crisis-related risk factors irrelevant over a long horizon.
- Cons:
  - Many countries have never borrowed at rates reflecting low default risk.
  - Use complicates comparability: for the same debt-service stream, higher default-premium countries yield lower NPVs and vice versa.
  - Post-crisis “normal” borrowing costs may be higher than pre-crisis, requiring judgments about potential future spreads and reliance on historical information.
- Footnote:
  - Country-specific long-term average rate would represent the average cost at which the debtor refinanced itself in the past; averaging smooths fluctuations and approximates an equilibrium rate.

### D. Benchmarking
- Approach:
  - Construct “normal” borrowing costs using spreads from countries with similar economic circumstances.
  - Estimate average spread expected when the country returns to “normal” conditions and derive a (dollar) discount rate.
- Practical notes:
  - Academic literature identifying factors that change spreads can inform benchmarking.
  - Simplified “guestimate” approach: e.g., assume average spread such as 500 bps and relate to prevailing EMBI+ or EMBIG spreads.
- Risks:
  - Benchmarking may be biased upward if contagion affects comparator spreads, or downward if international liquidity conditions are unusually favorable.

### E. Market Yields at Times of Distress
- Issues with using prevailing yield curves or exit yields at times of distress:
  - Such yields include the risk-free rate plus a default premium, often inflated by the crisis legacy.
  - Yield curves vary significantly between tranquility and financial pressure; at crisis times they can be unstable, inverted, or collapse to a single point.
  - Using crisis-period yields may strip out normal borrowing costs and over-discount future debt-service payments, making restructurings that push liabilities forward appear to generate NPV savings.
  - This can mislead assessments where restoring solvency/sustainability is the paramount objective.

### V. A Suggested Framework
- First step: calculate the IRR of the difference between two payment streams.
  - Definition: the IRR is the discount rate at which the NPV of the difference between two debt-service streams equals zero.
  - Conceptually, IRR is the implicit borrowing cost of shifting debt service into the future.
  - If discount rate > IRR → NPV savings for debtor; if discount rate < IRR → NPV cost for debtor.
  - Practical note: cash flow differentials with multiple sign changes can yield non-unique IRR solutions, but tests can ensure uniqueness within a reasonable discount rate range.
- Complement IRR with sensitivity analysis across a range of discount rates:
  - Range enhances transparency and highlights sensitivity of NPV calculations to discount rate choice.
  - Range should reflect the objective (typically, whether restructuring restores debt sustainability).
- Suggested bounds for the range:
  - Lower bound: rate capturing ability to service debt (e.g., nominal GDP growth rate in the relevant currency).
  - Upper bound: country-specific factors capturing debtor’s ability to refinance under “normal” circumstances (outside financial distress).
  - Consider risk-free world rate as a commonly cited discount rate for comparability; however, it may understate costs for most countries because it is lower than typical borrowing costs.
  - Care needed for countries whose spreads are unlikely to return to pre-crisis levels; comparator-country spreads could be informative.
  - Judgment required to keep the range operationally useful and sufficiently confined.
- Interpretation using IRR:
  - IRR > sovereign’s “normal” borrowing cost → sovereign is paying a high cost to shift debt service; restructuring may yield NPV cost and require careful examination.
  - IRR ≤ sovereign’s “normal” borrowing cost → restructuring may have capitalized on lower perceived future default risk and could yield NPV savings.

### Illustrative country cases and sensitivity
- General:
  - Two country cases (Uruguay and Ukraine) illustrate sensitivity of NPVs to discount rates.
  - In both cases IRR ≈ 7 percent.
  - For discount rates below 7 percent → restructuring yields NPV cost; above 7 percent → NPV savings.
- Uruguay (summary of Box 4 and figure notes):
  - May 2003 restructuring restructured nearly all external bonded debt.
  - Principal reduction: US$50 million (small).
  - Total debt service increased by around US$2.5 billion over the period 2003–33, mostly in later years.
  - The restructuring shifted debt service into the future, generating near-term cash flow relief.
  - Uruguay’s GDP growth rate (lower bound) based on medium term framework: nominal GDP growth in U.S. dollar terms likely to be around 5–6 percent.
  - Figure details and numeric highlights:
    - IRR = 6.95%
    - Suggested discount rate range shown in figure: 5.5–9.5 percent (implied by narrative summary).
    - Exit yield and other annotations in figure:
      - The yield prevailing immediately before the exchange was 16 percent, and shortly thereafter it fell by 200 bps.
      - The discount rate used by the Fund to evaluate Uruguay's debt exchange was 16 percent.
    - Footnotes in figure:
      - 1/ 10 year average of interest rate on 5-year U.S. Treasury bonds.
      - 2/ Defined 1 - (NPV(after restructuring)/NPV(before restructuring)). NPVs are evaluated at the same, constant, discount rate.
      - 3/ The yield prevailing immediately before the exchange was 16 percent, and shortly thereafter it fell by 200 bps (see Uruguay staff report, EBS/03/93, Appendix II). The discount rate used by the Fund to evaluate Uruguay's debt exchange was 16 percent.
- Ukraine (summary):
  - Proposed range of discount rates spans from 8.5 to 10.5 percent.
  - IRR is equal to roughly 7 percent.
  - Since IRR < lower bound (8.5 percent), the restructuring would yield NPV savings at any discount rate in the proposed range.
- Key conclusion from cases:
  - NPV calculations are highly sensitive to discount rate choice.
  - Using spreads prevailing at times of financial distress would overstate NPV gains and implied debt relief to the debtor.
  - Using more conservative discount rates can avoid overstating debtor gains.

*Source: Box 3, “Use of Time-Varying Discount Rates,” _pdp09 - Box 3. Use of Time-Varying Discount Rates_*

### Box 4. Country Example: Uruguay (continued)

### Box 4. Country Example: Uruguay (continued)

### Sensitivity of NPV calculations to the discount rate
- NPV calculations are highly sensitive to the choice of the discount rate.
- Using a discount rate closer to the current 9–10 percent implied yield on Uruguayan bonds would produce savings closer to 7 percent than to 20 percent (the market haircut quoted at the time of the exchange).
- If the discount rate were closer to Uruguay’s nominal GDP growth rate, the savings would be negative, indicating an NPV cost to the country.
- The example illustrates that using more conservative discount rates in evaluating debt restructurings will lead to conclusions of lower NPV savings from the perspective of the debtor.

### Segmentation of the discount-rate range
- The upper bound is estimated as the average borrowing cost for Uruguay during “normal” times, with the understanding that Uruguay will likely face spreads in the 400 bps range over the medium term, rather than in the 200-300 bps range (as they were before the crisis when Uruguay had an investment grade rating).
- For illustrative purposes, the range is segmented into two sub-ranges:
  - “Historical” sub-range: represents the range between potential GDP growth and the historical yield on government debt (at spreads of 200–300 bps).
  - “Judgmental” sub-range: reflects staff judgment regarding future spreads; for Uruguay it is assumed spreads will remain around 400 bps.

### Uruguay-specific observations and key statistics
- Current implied yield on Uruguayan bonds at the time of the analysis: 9–10 percent.
- Market haircut quoted at the time of the exchange: 20 percent.
- Alternative implied savings using market yields: closer to 7 percent.
- Historical spreads before the crisis: 200–300 bps.
- Judged medium-term spreads for Uruguay: around 400 bps.
- Average U.S. Treasury rate used in spread calculations: 5.5 percent (10 year average of the 5-year bond rate).
- Currently, Uruguay’s spreads are around 300 bps, likely influenced by a benign international liquidity environment.

### Implications for evaluation of debt restructurings
- The choice of discount rate determines whether a restructuring appears as an NPV saving or cost to the debtor.
- Conservative (higher) discount rates reduce estimated NPV savings from the debtor’s perspective.
- Evaluations should avoid selecting discount rates prevailing at times of financial distress, as these may significantly overstate financial relief and understate costs to the sovereign debtor.

*Source: Box 4. Country Example: Uruguay (continued), _pdp09 - Box 4. Country Example: Uruguay (continued)_*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/pdp/2005/_pdp09.pdf_