...here goes anyway.
Consider a 30-year Treasury Bond with a coupon of 4 percent and a par value of $100. Treasuries pay every six months, so this produces 60 cash flows of $2 and then $100 at the end of the 30 years.
To make things easy, assume for a minute that that market is discounting 30-year bonds at 4 percent per year (or 2 percent per six months). Suppose the US government offers investors a swap of 4 percent coupon bonds for 8 percent coupon bonds. If we don't worry about duration issues for a moment, and use Excel notation (I don't know how to get Greek symbols in blogger), investors would be indifferent between:
PV(.02,60,2)+100/(1.02^60)
and
PV(.02,60,4X)+100X/(1.02^60).
X is the face value of the new bond, and comes out to about $58.99. So the face value of the debt is reduced by 41 percent, while the value to investors remains constant. Nothing of substance has changed (and actually duration risk is a little lower), but the balance sheet looks better.
I am sure I am missing some institutional thing here, or maybe my simple finance is off somehow, but still...
