Editing Variable-period BOND (section)

=== Constraint on BOND issuance ===
In order for a BOND contract to be fully paid, the DAO must remain solvent, meaning the fees it earns must be great enough for the present value to be eventually realized. In the case of riskless BONDs the fees must satisfy the constraint''<math display="block">\int_{0}^{\infty} \frac{e^{-rt}f'(t)}{q(t)+R(t)}dt\geq \frac{b}{q_0}  \qquad  \quad  {\scriptstyle\text{(Equation 8)}}</math>''

This gives a limit for how many bounties can be proposed, lest the BONDs cannot be paid if ''<math>f'</math>'' is too small.  

For example let us assume that the lifetime of REP tokens is ''<math>L<\infty</math>'' and all the parameters are constant, such as the rate fees ''<math>f'_0</math>''.  Assuming the group has reached REP equilibrium, we have '' <math>R_{\infty}=mf'_0L</math>.'' Further simplify by assuming the only outstanding BONDs ''<math>q(t)</math>'' are the ''<math>q_0</math>'' that are currently under consideration. Then the integral in Equation 8 may be solved to get''<math display="block">\frac{q_0f'_0}{r(q_0+mf'_0L)}\geq b</math>''

A DAO cannot repay a bounty ''<math>$b</math>'' that doesn’t satisfy this constraint. The limit is''<math display="block">b\leq\frac{f'_0}{r}</math>''

which is seen by letting ''<math>q_0\rightarrow \infty</math>'', because, in that case, the DAO will use all its fees to pay back the ''<math>q_0</math>'' BONDs for eternity.

'''Proposition 8.''' ''A DAO cannot mint bonds of value in excess of'' ''<math display="inline">f'_0/r</math>''.

Conversely, solving the above constraint for ''<math display="inline">f'_0</math>'' shows the rate of fees must be large enough to satisfy''<math display="block">f'_0>\frac{brq_0}{q_0-brmL}>br</math>''

or else the DAO cannot ever repay the bounty, no matter how large the stopping time. Therefore, a good rule of thumb is not to seek a bounty ''<math display="inline">$b</math>'' from a DAO unless you can expect their fee rate to eventually far exceed ''<math display="inline">br</math>''.