# Discounting Future Values

Discounting Future Values

Another factor that affects
health-promotion behavior is the individual’s valuation of benefits in
different time periods. Health promotion activities, such as the use of
condoms, smoking cessation, vaccinations, and clean needles (for drug users)
and unhealthy activities, such as smoking, engaging in unsafe sex, and
excessive drug use, generally do not have good or bad impacts on health
immediately. It takes a long time, sometimes years, for individuals to
experience adverse health effects. The timing of health benefits will have an
influence on the demand for health-related activities that promote these
benefits.

It is generally assumed that \$1,000
in current benefits will be worth more to an individual than \$1,000 in benefits
one year from now. The value of the preference for earlier rather than later
periods can be expressed in terms of a discount rate, called r. If an
individual is asked how much money he or she would accept at the end of 2001
rather than have \$1,000 at the beginning of 2001, the person might take \$1,100
at the end of the period. In other words, \$1,000 on January 1, 2001, would be
worth as much as \$1,100 one year later. The discount rate is .1, and the
discounting equation is be expressed as \$1,000 × (1 + .1) = \$1,100, or
symbolically as \$1,000 × (1 + r) = \$1,100. This may be rewritten as
\$1,000 = \$1,100/(1 + r). This equation says that, in the individual’s
eyes, \$1,100 one year hence will be equivalent to \$1,100/(1 + r), or
\$1,000, now. The discount rate for an individual is derived largely from
introspection—from an acceptance that a given future amount and a lesser
current amount provide the same satisfaction at the present moment.

The same principle holds for
comparisons between December 31, 2001, and December 31, 2002. That is, \$1,000
at the end of 2001 is equivalent to \$1,100 at the end of 2002 if the
individual’s discount rate is .1. By inference, then, \$1,000 at the end of 2002
would be worth \$1,000/[(l + r) × (l + r)] on January 1, 2001
(also expressible as \$1,000/(l + r)2). Similarly, \$1,000 on
December 31, 2003, would be worth \$1,000/(l + r)3 at the
start of 2001, and so on. Generally, improved health or added life yields a
stream of benefits. That is, a saved life on January 1, 2001 will yield
benefits in 2001 (valued as of December 31, 2001), 2002 (valued as of December
31, 2002), 2003 (valued as of December 31, 2003), and so on. If the benefits
are \$2,000 each year, the present value of future benefits can be
expressed as \$2,000 + 2,000/(1 + r) + 2,000/(1 + r)2,
and so on, for as long as benefits last. The letter usually used to symbolize
the annual benefits is B, with subscripts 0, 1, 2, . . . for right now
(0), one year hence (1), two years hence (2), and so on. In our current
example, B0 = B1 = B2,
and the present value of benefits can be expressed symbolically as

If the number of years that benefits
will last is quite large and the value of the benefits for every year is the
same, the present value of the benefits can be expressed as B0/r.
If benefits of \$10,000 a year will last forever and if the discount rate is .1,
the present value of these benefits will be 10,000/.1, or \$100,000. Benefits
lasting for long periods can be approximated using this formula.

The discount factor can be quite
substantial for benefits that will not be experienced for many years. For example,
hepatitis C may not be recognized for 20 years. If hepatitis C imposes
health-related costs of \$1,000 in 20 years, and the discount rate is 10
percent, then the present value of these imposed costs is \$148.64
[\$1,000/(1+.1)20].

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