Internal Rate of Return (IRR) and Net Present Value (NPV)

In this video I go over through some basics in economics and financing and discuss the Internal Rate of Return (IRR) as well as derive the formula for the Net Present Value (NPV). In financial budgeting and investment analysis, to compare different projects or investments the interest rate at which all current and future cash flows break even in terms of their present values is called the internal rate of return (IRR) and is simply an interest or discount rate. The Present Value (PV) is the value of any future cash flows but set to the date of valuation. The value of money increases with time so $1 today is worth more than $1 tomorrow due to the ability to gain value through interest. The NPV is simply the sum of all the PVs and when equal to 0, the corresponding interest rate is the IRR.

In this video I go over an example in which I derive the NPV formula and solve for the IRR using an Microsoft Excel spreadsheet to manipulate the IRR until the NPV = 0. This is a very useful introductory video to financing and investing so make sure to watch it!

Download the notes in my video:

PDF Notes: http://1drv.ms/1f25p5I
Excel Notes: http://1drv.ms/1f25zu4

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Closed Caption:

I had some from the math easy solution
to discuss the internal rate of return
as well as net present value and also go
over the derivation of it basically
internal rate of return or ir r this is
also called economic rate of return
grr discounted cash flow rate of return
DCF ro R or the effective interest rate
dir cetera busy it's a rate of return of
an investment and it's used in capital
budgeting or any project that you're
trying to a financer order to see
whether it's profitable or not and it's
basically used to measure and compare
the probability probability of
investments and rate of return is just
basic profit of an investment over a
period of time usually expressed as a
proportion of the original investment
this and it's called internal because
its calculation is not include
environmental factors such as inflation
or interest rate so this is purely on
the cash flows of yet that you are given
per year and it is calculated by it's
basically setting the net present value
over the bed to 0 and solving for the
discount rate or the interest rate on
the investment and put basically just
the interest rate on a loan or
investment where the cash flows
break-even so if you were to get alone
you're gonna have to obviously pay
interest on it so if you're doing an
investment and it's been getting castles
on that basis that you would get be
finding out the interest rate that you
would break even with all your cash
flows and basically higher the irr the
more desirable the investment is it
because basically this means that that
you are breaking even at a really high
interest rate so you could do you could
add 4 to afford to take a loan even it's
a really high interest rate so now the
net present value this is basically the
sum of the present values of all
incoming and outgoing cash flows over a
period of time and what this basically
means first we look at what present
value is the value of any future cash
flows that
permanent at the date evaluation 40
basically any this is usually less than
future value because money has interest
earning potential except during rare
times of negative interest rates which
is actually going on in Europe right now
basically in the the idea of this this
is all called the this is referred to as
time value of money because basically a
dollar today is worth more than a dollar
tomorrow so if you had a hundred dollars
10 years ago
that's worth more than it is now and one
reason is inflation and also the fact
that if you had a hundred dollars you
put in a bank you would have been
collecting interest on it so now the IR
calculation and not derive this in the
example for their own is especially the
some right here wear ne20 up to capital
n of CN over 1 plus r power of end and
then setting this equal to 0
we're basically ends a time . as a
positive integer for example it's your
one year 2 and n is the total number of
time raise example 30 years and r is the
well in the internal rate of return so
this is the interest rate right here and
CN is the cash flow at time . add for
example so you make twenty thousand
dollars in year 3 etc so what setting
this equal 0 UT basic to solve for R and
now a simple summary of all these
definitions that can seem overly
technical and complex or just just too
much wording so there's some applied
definition irr can simply be considered
as the average its interest rate on
investment that have all cash flows
breakeven not like explained earlier and
raise the higher the IR of the better
because it means that investment can be
profitable even at very high interest
rates and now over a pretty useful
example and also derive the formula for
the net present value and
the second equals 0 so basically if you
say you put 70 thousand dollar dollar
down for an investment and have the
following cash flows from the investment
you're one you get 12,000 your 215 and
your 318 and here for 21 in your 526 so
basically promise given info
what is the internal rate of return also
derive it arrived and explain the
formula for net present value
yes so now to get the to the solution
visit to understand the irr we first
look at what the present values are our
for each cat following each year so the
Year Zero this is the initial start and
this is basically Arlo our downpayment
writer so basically lost seven thousand
our investment that's because we're
playing in an investment so this is the
initial start of the year in which we
have to lower or discount all cash flows
to so this is the year where we have to
bring all these 15,000 20,000 all these
back to year zero right here to bring it
all the way back two years 0 and see
what their work then add them all up
there's also when we get our alone thus
we at this point will call this C 0 and
this see that's for a casual if you go
back to the formula C and so this would
be our c0 this would equal to well
negative 70 thousand dollars right here
so now that we have our COO let's look
at the year one so now at the end of the
first year we have a cash flow of well
twelve-thousand dollars since this is at
the end of the year we have to find out
how much twelve-thousand dollars worth
at the very start of events mentor the
Year Zero this is because that's the
tested earlier the time value of money
and its ability to increase in value to
interest you could have been gaining or
due to basically inflation
yeah so basically the value of that
dollar was more back then with inflation
so thus we assume that the present value
of the cash flow increases year by year
by the internal rate of return
there are so this is the interest rate
that we're just gonna is like an average
one we're saying that someone just it's
going to be increasing but so what this
means is that our cash flow of 12 so if
we were to right let's say present value
so let's say we had pv pv will cause pv1
and also going back to this this is co
this is also the same as our present
value zero of the present value of
70,000 70,000 because that's just that's
what we're valuing everything at so RPV
one if we had this present value then
let's say we added by the interest rate
so we add pv 1 times it by well are our
this is now equal to twelve thousand
dollars so that's basically whole idea
were increasing this value by our
because did interest inflation etc to
twelve thousand dollars so then this is
divided this out is 1 plus R and assess
equals twelve thousand respected dpv one
out so basically pv 1 equals $OPERAND to
12,000 / 1 + R and this is our present
value for this cash flow this one will
call it c1 now when we look at year to
as with your one we need to go backwards
and time and figure out what the present
value or the worth of our visit the
starter investment is for this new
$15,000 cash flow doesn't but this time
we need to go back well two years
because we're end-of-year too so we got
to go back to your one in the back to
year zero at the very start and after
year to you know the castle as 15,000
does the present values derived as shown
below
let's call this PV of our cash flow to
and then this is at year zero so we'll
call this year zero or the start but
then we also have a year one here I'll
put our oldest x and then we have a year
to that is our $15,000
and this one will call this well value
at the other bases value at year one of
the 15,000 so we know from this one here
we went back one year and we made it
like that so basically calling for
actually don't x times y 1 plus r or x
plus x times are like this this equals 2
well $15,000 so our X is we're just
going back one year is equal to 15,000 /
1 + R but now we're going back another
year so this is going to that is this
and now we gotta go back one more year
so we have our pv2 is one of 1 plus r
equals to this let's move this down here
so basically this equals to now well
this is now our X right here so this
equals 2x which equals $OPERAND to
15,000 / 1 + R so there's a second 1
plus R so our present value of our
second cash flow is 15,000 / 1 + R
squared and now there's a pattern to
this so basically that as you can see it
for three or four years three and four
every time we get another year we add
this this value right here which is the
year so for year three we are present
value 3 is equal to what we it was
eighteen thousand and then we have to
divide by 1 plus r cube then for the TV
for this equals tues was twenty-one
thousand divided by 1 plus r4 and
similar the last 1 p-5 this was
twenty-six thousand dollars divided by 1
plus r4 and r5 writing so these are the
present values and as you can see these
are dividing by number assuming this is
positive it's going to be well / number
greater than 1 so this would be less
then our actual cash flows there which
should be yeah and thus putting this all
together we get our net present value
which is just the summation of all of
them so NP equals to negative 70,000
that's our loan plus now the first year
which was scroll back up that's 12,000
so plus twelve thousand divided by 1
plus R and then plus now this is our
18001 soon 18,000 forgot the 15 as
15,000 that's right here that's a second
value 1 plus R squared and then plus
this one right here one now it's 18
eighteen thousand what about 1 plus r
cubed and then plus 21 and then this is
going to be 1 plus R for the last 1.5
thousand 1 plus r power 5 and I was
going to part of the pages copied it
moved it over to here so as you can see
from these games you can see the pattern
these are exactly that formula is I put
a 1 here and if i do this and put a well
1 plus R put a 0 there is basically our
formula and then and then this is if you
look at it in generally then this equals
to $OPERAND and p is equal to this is
going to be well summation of of n equal
to 0 which is this is our end to start
off at zero and then CN this is RC 0
this is our see one at center and then
this is going to be 1 plus our finances
and all the way up to and in this case
we have and equals 25 and this is well
and you
I was 20 and as N equals 1 equals 2 at
cetera so this is visit derivation and
proof for our net present value formula
and now all we have to do is basically
set this equal to 0 if we set this equal
to 0 we get now RR is equal to our
internal rate of vert turn so if we said
all these two are and I mean episodes to
this whole thing 20 equals 20 and then
we solve this and that will be our
internal rate of work
fern and to do that although you could
do it this is hard to solve it forward
like this is pretty complex equation so
there's a calculation that you can do to
do with a lot of numerical ones i like
using Excel is the right here here's an
excel sheet and bed into this document
basically out with the best way that i
like using the calculator is basically I
feel this table out and put this this
bracket that's just a negative right
here night get the calculation for net
present value here and I would just
change the irr manually until this net
present value is 0 and this one so i
would change this manually put that here
and then these are just format we all
need to ride so if i go edit yeah so
this is editing it right now
yes so here if you're doing it changes
outs eight points aid etc then there can
be a negative number right there said is
so this one is saying the net present
value is negative we don't want that to
this interest rate is too high i go to
six basically now our president we this
is this is making more money so that's
why it's positive so basically the
higher than $PERCENT interest rate it's
usually better for investment this means
you get low not even if their banks are
charging you a lot you can still make
breakeven so this is a good way of
basically seeing if your proper
investment is worth that are not working
very different project and I close this
just say that anyways yeah this is
pretty much it
hopefully learn about ir foreign & P B
and like always you can download these
exact notes in the link below and also i
put that link to excel sheet also in the
link below so you can play around with
that anyways that's all for today
hopefully learned and thanks for
watching and stay tuned for another math
easy solution