Present Value Of An Annuity
Categories: Company Valuation
Ever hear your grandparents wax nostalgic about how much things cost when they were kids? Like, a movie only cost four dollars, and they could get a hot dog, fries, and a large Coke for three dollars. Or college came free with 10 cereal box tops, and you could trade three baseball cards and a bag of Red Vines for a 5-year-old Ford Focus.
The point of those stories (to the extent that there is one) is that inflation is a real thing. A dollar today is worth more than a dollar will be in the future. This fact makes it difficult to value contracts that take a long time to unfold.
For example, think of an annuity. These contracts involve you paying a large chunk of money now in order to receive periodic income at some point in the future, usually for retirement. Part of the challenge of figuring out whether you're getting a good deal when you buy an annuity comes from the fact that you don't get the pay off until well into the future. The present value of an annuity helps you make that calculation.
The equation can get complicated and, by necessity, it's based on a number of assumptions, often related to inflation or growth rates. But it puts the comparison on a more apples-to-apples framework.
The figure provides the current value for an annuity. It gives its worth as a present lump sum, even though the contract itself pays off in installments during some future period.
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Finance: What are Time-Weighted Rate Of ...1 Views
Finance allah shmoop what are time and risk waited rates
of return a dollar today is worth more than a
dollar tomorrow Like that's the central prayer of the financial
force Here's the gist You've double your money in an
investment Is that good Bad ugly mon We need a
whole lot more information here Tto answer Did you buy
thirty eight million and two dollars worth of lottery tickets
and that last two dollar ticket got you seventy six
million in winnings Was that like a good investment Or
how about this You took thirty six years to double
your money Was that good I answer to both No
not at all The lottery ticket example is a risk
waited return The lottery famously takes advantage of ignorant people
spending their hard earned money on tickets representing dreams but
which have horrible odds of any kind of decent pay
back But the lottery makes go into a vegas casino
look like actually a good deal so you may win
but it's a bad risk no matter how you look
at it And hey somebody has to pay those teacher
pension bill So why shouldn't it be people who didn't
graduate high school Right Well the time waiting is a
big deal to in a world where the stock market
broadly speaking doubles on its own About every eight nine
ten twelve years Something like that This calculation is done
over very long periods of time and it's held true
for about a century and change in america So if
he took thirty six years to double your money well
it implies you only made two percent a year as
your rate of return Remember that rule of seventy two
thing Yeah that right there Seventy two divided by thirty
six and you get a whopping two percent return Well
in that same period of time the market might have
doubled in four times So the ten grand that double
to be twenty grand in thirty six freakin years under
your watch we'll have you just put it into an
index fund of the s and p five hundred over
that same time period Well it would have doubled once
along the timeline here to be twenty grand then doubled
again here to be forty grand and then doubled again
here to be a tigre rine and then ah forthe
doubling right here after thirty six years maybe one hundred
sixty grand And that's just an index fund Nothing fancy
Not warren buffett Just a basic vanilla index fund that
anyone with two hundred fifty bucks in their pocket can
buy And it's worth noting dividends which often get ignored
in the financial press actually matter a ton when it
comes to the calculation of long term investment results Generally
speaking that continued payment of dividends is a low risk
adventure Very few companies ever cut or fully do away
with their dividends And if they do well it means
a pretty much everything is rotten in denmark so you
can count on dividends The bolster overall returns that historically
dividends have had a wide range of somewhere between two
and seven or eight percent for the mid range of
the s and p five hundred But if you pegged
them around and three ish percent today and changed to
reflect the modern era well then the overall market need
only compounded about five percent To deliver that five plus
three percent and change eight ish percent total returns That
will allow the stock market to double about every nine
years or so right so we're ignoring taxes here but
we're ignoring the use of dividends proceeds to buy more
shares every quarter as well when those dividends air paid
So when you think about time and risk think about
them like they're a kind of financial stone soup which
when mixed together with the right spices of tax hedges
leverage and a bull market well make a really nice
retirement meal and you don't even need your teeth on 00:03:22.773 --> [endTime] a bonus