A feature of a healthcare policy (such as screening) with interventions at
specific ages is that when it is introduced, part of the population is too
old to participate in the full programme. This fact changes the formulae to
be used for cost and benefit discounting in a non-intuitive way. General f
ormulae are derived for the expected discounted costs and benefits of such
health promotion policies, for a stationary population. Correct ways to cal
culate discounted costs and benefits via simulation are also described. The
formulae have some surprising properties, for example the relative cost of
two health policies does not depend on the discounting rate. They are also
relevant to the ongoing debate over the correct discounting rate for benef
its. It is shown that when health benefits follow quickly on treatments, va
rying the discounting rate for health benefits is merely equivalent to resc
aling the cash value of a benefit. It is only when benefit follows long aft
er treatment that the problem of choosing an appropriate discount rate for
benefits cannot be simplified.