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Time value of money. IRR and net
present value our time value of money measures
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here in this movie, we're going to cover
the idea of time value of money.
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We're going to use the utilities cash
flow analysis to cover that. When we click
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into cash flow analysis will be in an area
that will let us look at the details
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and how the net present value and IRR are a time
value of money listener in a sample
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cash flow. Now, let's look at the definition
of present value, the present
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value at percent of future cash flow
to be received in and years, in this case,
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10 years from today in this case,
which is January 1st, 2010, as defined as
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the amount you would need to have
deposited today, January 1st, 2010,
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drawing an interest rate that we enter
compounded yearly to accumulate the cash
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flow dollars in the 10 years or 10
years. The interest rate used in the calculation
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is called the present value discount
rate. Now let's look at these cash flows with
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this definition we're solving for present
value because we're putting zero
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in the beginning. This is a common
appraiser's approach, looking at cash flow
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before debt, putting a zero in the beginning
and valuing the cash flows given
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a discount rate. To begin, we're
going to start with a discount rate of zero,
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basically meaning cash. What's the value
of these cash flows, 120000 given to us
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in five years and 100000 given us to 10
years, given a zero discount rate? Well,
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if we can't make any percentage
of our money, then we would need to put
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in the exact amount that it would be
added up in the end. Here we show the cash flow
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equaling 220, and that would be the amount,
the present value assuming a zero
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percent discount rate. Now, let's
think about the time value of that money
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by putting in a one percent discount
rate. So we have the money of 120000 in five
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years. But what is the value of that
money? Well, if we're going to receive
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it in five years and we have a one
percent discount rate, the value is 114, 172
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and 77 cents, because that's how much
we would have to deposit in the beginning
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five years earlier to equal to 120000.
Given the one percent discount rate
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and the value of one hundred thousand
dollars in ten years time, the time value
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of that is 90000, 523, 76, given
the one percent discount rate. Now,
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let's concentrate on the time aspect
at 120000 five years that says that we need
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to put in one hundred and fourteen
thousand 172. But what's the value
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of that? If it only took us four years
to get that 120000, let's change the date
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to one year earlier. And now you can
see that has changed to 115, 314, 50.
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And that's because we're getting it one
year earlier and we have deposit more
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money. Given that is going to grow
and grow at one percent to equal 120000
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and these cash flows are more
valuable, they're worth more. It's gone up to 2.5
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because we received that money
earlier. One of the truisms of the time value
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of money is the same amount of money
earlier is better than the same amount
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of money later. Now, if we change the discount
rate to, let's say, 10 percent,
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what would be the time value of money
there? So now we're saying we have 120000
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given to us in four years, that a 10
percent discount rate. How much would that
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be needed? We need to deposit eighty
one thousand 940 to equal the 120000 in four
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years. That doesn't always happen that
we can get things right at the year mark.
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So let's change the date to mid-year.
So now we're getting it in July of 2013.
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And you can see that has more value
and we need to deposit more money. To receive
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the 120000 at that time. Now let's
introduce the idea of net present value
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is simply the present value, but we're
going to net it from the beginning. No.
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So now we're going to say that we're
going to invest 100000 dollars. And given that
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we're going to put in 100000 dollars
and we want to receive a 10 percent return,
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compounded yearly return on our money,
how much more or less what we need to invest
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to receive the 10 percent return. And the net
present value here is showing twenty
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four thousand five 07, forty nine
dollars, which is positive, which means that
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we could spend twenty four thousand
five 07 and for nine cents more than 100000
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that we're already putting in and still
receive 10 percent. So let's do that. Now,
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the net present value says 49 cents
because we didn't put the 49 cents in,
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but if we invest 124 thousand five 07,
then we're getting basically exactly a 10
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percent return, assuming that we're
getting 127 thousand in July of. To 2013
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and 100000 in January 1st of 2020,
let's change this date. Again, in this market,
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though, earlier and see how that
affects the net present value. Now receiving
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the money, December 15th, 2011,
and the net present value has increased,
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meaning we could we could invest even
more and still be receiving the 10 percent
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because getting it earlier means is more
valuable. Let's try changing the date
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later and see what happens. Now,
the net present value shows as a negative.
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In fact, it shows his negative 26
zero nine zero 54 cents because we're not
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receiving 120000 all the way until April
16th, 2017. Let's change the initial
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investment back to one hundred and see
if we can find the exact amount that would
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receive, give us a 10 percent
return. So now it shows that we're still need
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to spend 1583 dollars less. So let's
do that. So 98000, 417, if we invested that
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amount of money and received these cash
flows at that time, then we would get a 10
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percent discount rate. But what if we wanted
to make sure that we put in 100000
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dollars and wanted to find out what
discount rate would make the net present
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value zero versus put in the hundred
thousand? And we can see that 10 percent
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discount rate, the net present
value is negative and it's negative by 1500.
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So negative means that we could need
we could spend less. And still make the 10
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percent or we could lower the discount
rate to make a net present value zero.
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Let's make it to nine. Now, the net
present value is positive, so that means
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we could spend more and still make
nine percent or we can increase the discount
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rate and get the net present value
closer to zero. Let's change it to nine point
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one. It's closer, but still positive.
So let's change it to nine point to. Closer,
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but still positive. So we're
getting closer. OK, nine point seven, the net
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present value is just positive. Let's
see what it is at nine point eight. Now it's
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negative, so somewhere between nine
point eight and nine point seven, the net
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present value would be zero. So let's
change it to nine point seventy five.
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And that's positive, so it's.
Somewhere between nine point seventy five and nine
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point eight, so let's change it to.
Nine point seventy six. Getting closer.
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Almost there. So at nine point seventy
nine percent, the net present value is 70
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cents, so that's very close and that
would be our return or compounded return
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annually if we put 100000 dollars down
and receive these cash flows. At these times
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now, wouldn't it be nice if there was a process
that would automatically tell us
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what our discount rate would be,
that would make the net present value zero?
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Well, there is, and that's called the internal
rate of return, the internal rate
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of return of an investment is defined
as the present value discount rate that makes
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the net present value of the investment
equal to zero. So if you click on the IRR
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here, you can see the IRR tells us
that the actual number should be nine point
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seventy nine oh one percent. That
makes a net positive value close to zero.
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You could see it actually makes it point
zero to. So it's almost there, Nessus,
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because of rounding to the to the four.
So let's go back to net present value
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and change that to zero one. And you could
see we get close to close to it. And even
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then because of the rounding, it's not
quite there. But that's what an IRR does,
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is actually goes through and finds the different.
Tries different present values
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and see is if it close to zero, and just
like the process that we saw there
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where we tried one wasn't there, tried
another wasn't there. It zeroes in on the.
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Present value that would make it zero
because this computer could do it very
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quickly. For instance, let's change
this date. To February 2nd, 2012, and we could
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see now the net present value is in zero
again, so I can go through this process
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of trying to get closer. But that's
going to take too long if we just click on IRR,
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the computer is going to go in and do
it for us and tells us that the discount rate
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that will make the net present value
zero is nineteen point three three four zero.
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So let's try that good net present
value. And that makes the net present value
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effectively zero. So we don't need
to find the discount rate, we can just use
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the IRR. Now that we could see how the IRR
and the net present value are related with
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the time value of money, let's
let's look at a file that's a little more
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complicated. I mean, import cash
flows from Atlantes file. And what this does
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is it brings in the cash flows and the cash
flows are brought in each month
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because that's how you collect them.
Those are the cash flows change each month.
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This is the same process as the X
IRR in Excel and Google and the Google
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spreadsheets. The Zahraa looks for the cash
flows at the end of each day.
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And here we're doing a mid-month
convention where we're putting the cash
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flows in the middle of each month and the cash
flows changing each month in real
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estate usually collect the money at the end
of each month, but we're putting
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it in the middle. And as you scroll
down, we can see how the cars are changing
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the present value. Let's go back to net
present value. We can see that for each
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month we're receiving money. Plannings
is looking at that cash flow and discounting
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it back and saying, well, at a 10
percent discount rate, how much will we have
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to have put in in the beginning to equal
that monthly cash flow? But the 10 percent
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discount rate is compounded annually
discount rate. So when we switch to IRR
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and we saw that the IRR goes through
and finds the discount rate, that makes a net
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present value zero. That's showing
us the compounded annual rate that this
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investment would equal, assuming we put
into one point eight to two million.
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And we scroll all the way down, this
is a 10 year investment, and so at the end
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of 10 years, we received that money
back. And this shows us that the net present
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value is within 56 cents. The IRR,
the discount rate, found the it found
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the discount rate that would make the net
present value almost zero. It's very close
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at 56 cents. So let's put that let's go
back to the net present value and put this
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IRR and the net present value. Which was.
And we put that in, it makes a net present
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value of six dollars and 61 cents, and that's
because of the rounding as it gets
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further out. We only round to four
decimal places. So if we go back to the internal
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rate of return, now that we have this
internal return and we have all these cash
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flows, we can modify any cash flow and see
how the internal rate of return would be.
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Affected, so let's take this cash flow
in May of 08, they make it a little bigger.
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And we can see that if we got that
kind of cash flow in the beginning, that would
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increase the compounded annual return
that we would expect to five point two nine
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six. And this is brings us to what the IRR
takes into account and why it's good.
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The IRR takes into account every
assumption that makes up the cash flows
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that it's receiving. So if it's a cash
flow before debt takes into every
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assumption, purchase sale, every cash
flow between before debt, cash before tax takes
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into account every cash flow that
made that cash flow before tax. So that would
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be the purchase. Any income, any
expenses, any capital spending, any debt service.
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Cash flow after tax would also
include all the taxes. That is the the beauty
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of the internal rate of return, the time
value of money process and the net present
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value is it takes everything into account.
The that is the limitation of also
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because it takes in every assumption
that you put in an over 10 years. There's lots
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of assumptions. And that's why you want
to use a program like plannings which allows
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you to vary those assumptions and sensitivity
and risk analysis and see
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which assumptions vary. The IRR or what is
the IRR sensitive to.