the time value of money is an important concept to understand investors can use
the time value of money to calculate the fair value of a company and people
trying to save money can use it to calculate how long it will take or how
much they would need to put aside each week month or year to achieve their
financial goal the best news is the concept is actually quite simple
so we're gonna walk through two examples the first will examine a family that
wants to save for a house the second will act as an investor who wants to
value a business so at the core of the time value of money concept is that a
dollar today is not worth the same amount as a dollar next year to
illustrate this point imagine I came to you and said I'm gonna give you a
thousand dollars and I pause during that pause you start asking yourself what
could I buy with that thousand dollars what would I use it for and then after
my unnecessarily long drama building pause I finish that sentence by saying
in ten years well that changes everything I have no idea what I would
do with it in ten years but I knew what I would do with it now I was going to
save for a house now the time value of money matters more than just knowing
what you're going to do with it or not in fact one thousand dollars today is
actually worth more than one thousand dollars in ten years much of the
difference in value revolves around what is known as opportunity cost opportunity
cost is the value of different opportunities that were forfeited by not
having that cash today so let's see how this works we're saving for a house for
now you have a thousand dollars to start saving we want to save for ten years how
much will we have in ten years let's look closer so here we are today we have
our thousand dollars what will it be worth next year well that depends on
what you do with it if you put it in a savings account that pays 2% per year
well that $1,000 is worth one thousand twenty dollars next year not bad but
what if we found two other investment opportunities one would pay us 5% and
the other would pay us 10% well the 5% is worth $1,050 next year and the 10% is
worth $1,100 I bring this out to illustrate how important the return you
get on your initial investment is and to illustrate opportunity cost
so let's stick with the 5% return from here and keep it simple and if we
stopped right here at this point well you could probably see that the $1,000
today is actually worth $50 more than $1,000 in one year in this example that
is the opportunity cost if I had offered you $1,000 today or $1,050 next year
which would you choose well if you knew you had a chance to invest the $1,000
today and get a 5% return well it wouldn't have mattered which one you
took now if I offered you one thousand sixty dollars next year well you should
take that your potential return is just five percent with today's money and I
just offered you the equivalent of six percent assuming you believe me waiting
a year makes the most sense so now let's do the math which is actually quite simple
so if we continue our example to get our $1,000 into the future we simply need to
increase that amount by our expected return
so it's $1,000 times 1 plus r, r is the return in our case we're expecting a 5%
return so $1000 times 1.05 equals $1,050 now just in case you're not super
confident with this type of math you add one to your expected return because one
represents 100% of your initial number you might have done this exact math in a
restaurant if you wanted to leave a tip you take the final bill of let's say a
hundred dollars and multiply it by the tip of let's say 20% which is 1.2 and
you end up with $120 now some people may think to themselves okay what is 20% of
$100 well that's 20 dollars then you add that $20 to the starting bill of 100 and
we get 120 dollars well this is that exact same thing just a bit shorter so
when we multiply our starting number by 1.05 or 105 percent of our starting
value this gives us next year's value they call this future value now we could
do this quite simply for each time period if you take the $1,050 times 1.05
we get 1102 dollars and 50 cents now it's important to recognize here that
during the first year our money grew by $50 and in the second year it grew by
$52.50 and that is what known as compound interest or the power
of compounding see that $50 he earned in the first year earned two dollars and
fifty cents in the second year and now it just keep happening every year the
money you earn will earn more money for you so we could do that math for each
year and keep going right down the line and that would be easy enough but there
is another shortcut so we know that this formula is the future value formula and
that is true as long as the future value is in one time period well in our case
if we wanted to skip ahead to see what the value would be in year 10 well the
only adjustment we'd have to make to the formula is to add the number of periods
right here so if we want to know the future value in year 10 we simply add 10
here and this future value will now be the value of our $1000 in year 10
assuming we earn 5% a year and in year 10 we will end up with 1628 dollars and
89 cents so if you had a calculator or Excel you can easily calculate what the
future value will be in five years or 20 years or whatever the math stays the
same so now let's see how a potential investor can use the time value of money
let's imagine that we're looking to buy a business and based on our research we
are expecting that business to generate free cash flow of ten thousand dollars
next year and thirteen thousand the year after then 17, 22, and
28 thousand in each of the following years then after that the
business is going to cease to exist so now the question is what are each of
these future cash flows worth today so the math is very similar to what we
already know instead of trying to calculate the future value like we did
before now we're going to calculate the present value here's what that formula
looks like so all we do is we take the future value let's use year five as an
example well we have $28,000 and we divide that by one plus the discount
rate and since it was year five we raised this to the power of five so
let's also imagine that our discount rate is five percent now the discount
rate we're using here is similar to the return rate we used before sometimes
when we calculate the future value like we did before well they call that rate
the interest rate but when we're calculating present value they called
the discount rate you might also hear it called a required rate of return so
basically if we require a return of five percent assuming that each of our
projected cash flow numbers are accurate then the
present value we calculate will be exactly what the business is worth if we
want a 5% return if we want a 10% return what we should use that as our discount
rate and this formula would give us what we should pay for the business to get a
10% return so if we finish our math here is each of the formulas
and here's what each year's cashflow is worth today so now all we have to do is
add each of these up and get the total value of the business today and that
turns out to be 76039 dollars at a 5% return or to say more accurately using a
5% discount rate now if we wanted a 10% return the value falls to 65,019 dollars
and this number being lower makes sense if you want to return more well you want
to pay less today well if you paid less than this 65,000 well your return would
be greater than the 10% discount rate we used to calculate the present value now
we did a lot of this mouth by hand and I did it using Excel which can be simple
enough because as you can see the math is not terribly complicated once you
understand the concept but there are calculators out there that have
functions that solved these exact problems as an example I use the Texas
Instruments business analyst plus calculator and I find it to be great for
this type of calculation but at the end of the day however you calculate it if
you understand the concept behind the time value of money it could be very
useful you can use it to see what your investments would be worth in five or
ten years if you invest at a certain amount of money every month now one
quick point if you adjust the frequency of deposits or investments don't forget
to adjust a number of periods in your formula so if you added money each month
and you were expecting a 5% return each year well you have to divide that 5% by
the 12 months that are in a year and that would give you a monthly return
rate of zero point four one six seven now this becomes the R in the 1 plus R
part of the formula and now you raise it to the number of months so a 5-year
investment would be 60 months so you'd raise this to the power of 60 on a
calculator they call this number of periods compounding periods and this
adjustment is true when you're calculating for either future value or
present value now if you flip this formula around a bit you can see what
our needs to be to achieve a certain goal so if you have $10,000 today and
you needed to grow to $20,000 in let's say 5 years while you plug that in and
then you can see that your calculation says that you need to return 14.87% a
year to get to your $20,000 goal within 5 years and those are just a few
examples of how people can utilize the time value of money