[throwaway183839]

Not necessarily. The standard way of valuing a bond is future value discounting. If the annualized interest rate between times 0 and T is r, then a payment of 1 unit at time T is worth

  exp(-r * T)

and a stream of payments C1, C2, ... CN at times T1, T2, ... TN is worth

  C1 * exp(-r * T1) + C2 * exp(-r * T2) + ... + CN * exp(-r * TN)

In particular, N can be infinite, so that the value of a never-ending stream of payments is

  C1 * exp(-r * T1) + C2 * exp(-r * T2) + ...

which can sum to a finite value. For example, if all the C's are constant, and T1 = 1 year, T2 = 2 years etc, then the present value is

    C * exp(-r) + C * exp(-2r) + C * exp(-3r) + ...
  = C * (exp(-r) + exp(-2r) + exp(-3r) + ...)
  = C * exp(-r) / (1 - exp(-r))

so, for example, if C = $1,000 and r = 4%, then the value of this infinite stream of payments is about $24,500 - so if you had to lend more than $24,500 for a 4% consol paying $1,000 you would be getting a bad deal.

This is before taking account of the possibility of default, which means that what you thought was an infinite payment stream turns out to be quite finite.

Right now, when interest rates are low, a 4% consol looks like a great deal. But you obviously can't buy a 4% consol at the moment. Maybe you could buy a 1.5% consol, if you're lucky.

[bboreham]

Just to correct your last point, UK 30-year gilts are currently trading around 2.6% yield, so perpetual bonds should pay at least that.

And indeed, according to this page, they pay around 3.7%. They don't seeem to trade very often. https://www.fixedincomeinvestor.co.uk/x/bondtable.html?group...