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Discounted Cost of Future Care and Expenses
- Economists often discount the cost of future expenses. The reason
is that if money is invested now, its rate of growth is expected to exceed the depreciation in value
that results from inflation.
- The difference between the return on investment and the inflation rate
is generally termed the net discount rate, and is often taken to be in the vicinity of
2-3% per year. This means that a given bundle of goods and services to be delivered a year from
now is worth 2-3% less than the same bundle now. In general, let g(t) denote the present value
of a unit payment to be delivered at a time t years from now. In practice this discount rate is
often specified by law for the country, state, or province.
- The life table will specify p(t), the chance that the individual is alive t years from now.
- The life care plan will specify d(t), the dollar cost of care, services,
etc, t years from now under the assumption that the individual survives to that time.
- When the above are given, the expected present value of the cost of
future care is EPV = Sg(t)d(t)p(t), which is the sum over years
of the discounted cost times the chance that the individual will be alive to receive it. Economists
routinely compute such EPVs, using a spreadsheet format.
- In the special case when d(t), the annual dollar amount, is taken to be 1,
the expected value is often called a multiplier. For example, with a 3% net discount rate,
a newborn male in the general population has a multiplier of $28.96, representing the expected
present value of $1 per year for life. Thus if he were to receive, say $100,000 per year for life,
the expected present value would be $2.896 million.
- For further discussion see the full explanation on the discounting web
page
or one of the published articles on this topic.
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