30/07/2011: Some uncomfortable US debt arithmetic

In the light of the Senate vote yesterday, it is worth examining the extent of changes in the US debt and interest costs within the context of the Republican's-agreed plan (debt ceiling increase of $2,500-3,000 billion in exchange for 10-year deficit reductions of €917 billion).

There are a number of assumptions that we must make about the proposals, since it appears at this time that no clear picture is emerging as to what the specific details of spending and cuts might be.

Let us assume the following scenarios:

Scenario 1: Debt ceiling is increased by $2,500 billion to $16,800 billion
Scenario 2: Debt ceiling is increased by $3,000 billion to $17,300 billion

Assume that over the next 10 years there are no further increases in the debt ceiling.

Now, let us make some assumptions about the post-deal yields:

• Scenario A: assume that the current yields on US Treasuries - ca 3% - prevail over the next 10 years (this is extremely optimistic, since (1) it is likely that debt ceiling increase can lead to AAA downgrade one-two notches, (2) it is highly likely that US Fed is going to raise interest rates at least in some point in time between now and 2020. In this case, 10-year compounded interest charges on just the increase in the debt ceiling will be 34.39%.
  
• Scenario B: assume that average US Treasury yield rises to 3.5% post-deal. In this case, 10-year compounded interest charges on just the increase in the debt ceiling will be 41.06%.
• Scenario C: assume that average US Treasury yield rises to 4.0% post-deal. In this case, 10-year compounded interest charges on just the increase in the debt ceiling will be 48.02%.

Next, it is crucial to identify just how the 'savings' will be delivered and to what amounts cumulative to 2020. Let us make some assumptions on that:

• Republican plan of achieving savings of $917 billion by 2020, distributed:

1. Uniformly over 10 years in $91.7 billion increments
2. Front-loaded as follows: 175% of 91.7 billion in years 1 and 2, each, followed by 125% of that in years 3 and 4 each, followed by 100% in years 5 and 6 each and 50% in years 7-10 each, implying that through year 2 annual savings will be $91.7 billion plus $183.4 billion. By year 4 the savings will be running at $366.8 billion, by year 6 - at $550.5 billion and so on.
   

• Alternative plan (more like Democrats' plan) of achieving 1/2 of the Republican plan savings of ca $460 billion over 10 years, distributed:

1. Uniformly over 10 years in $46.0 billion increments
2. Front-loaded as follows: 175% of $46 billion in years 1 and 2, each, followed by 125% of that in years 3 and 4 each, followed by 100% in years 5 and 6 each and 50% in years 7-10 each, implying that through year 2 annual savings will be $161 billion. By year 4 the savings will be running at $276 billion, by year 6 - at $322 billion and so on.

Table below summarizes net savings (reductions - where positive) on the debt levels as the result of the proposed deal. These do not account for interest charges on the existent pre-debt deal debt level of $14,300 billion, nor for the costs of old debt financing that might rise in the wake of the debt ceiling hike.
In bold in the table above, I outline the more likely scenarios. Now, to arrive at the total debt ceiling hike impact we need to subtract from the above values the expected increase in the cost of Federal debt financing on the current $14,300 billion worth of debt. These are approximately $715 billion in the case of Scenario B and $1,430 billion in the case of Scenario C.

Thus, overall, in the most likely scenarios,

• The Republicans-proposed plan will achieve a reduction in the overall 2020 debt levels of just $802-1,994 billion in the most benign scenario or a reduction of $365 billion to an increase in debt of $827 billion in the more adverse case
• The Alternative plan will achieve increases in total debt burden for the US of between $573 and $1,171 billion in the more benign case and increases in total debt of $2,273 billion to $3,341 billion in the more adverse case.

In summary - neither potential outcome represents a significant departure for the US from the current massive debt levels. To achieve meaningful savings on the current debt, the US will require severe front loading of Republicans-proposed cuts and convincing the markets that its AAA rating must remain intact. However, even in this case, more likely effect will be to reduce debt levels by some €1,990 billion, or just 14%...