**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, *B*_{0} = *B*_{1} = *B*_{2},

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 *B*_{0}/*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}].