# Using a Cash Flow Diagram for Calculation of Net Present Value

Hello my name is Tom Seager. Welcome to
engineering business practices. In previous videos we’ve been looking at
the discount rate and interest rates and trying to understand the time equivalence
of money. In this video I’m gonna walk you through a problem that involves reducing a cash flow
diagram to a net present value We use present value because it reduces all the cash flows to a single point in time so we can compare
different alternatives. That is, if we have different business strategies or
different alternative investments that have different cash flow diagrams were unable to pick which should be
since best for us i must be reduced everything to a single
point in time so let’s take an example in this case we
might be trying to start a business uh… perhaps it’s a landscaping business we
need to buy some equipment right away and then we’re going to use the
equipment it’s truckers samal works uh… we’re gonna bill our client’s
organization arrayed revenues from the use of that equipment at the end of the like for the equipment
will tell what left for some amount of money that uh… helpless recover or initial
investment so the cash flow diagram might look
something like this at first we have a big initial
helplessly this would be the cost this equipment costs ten thousand dollars over the course of time that we’re gonna run this
business the bill our clients and look at it we
do the work every month and we bill our clients pay pay at the
end of the month each uh… month sit at home or business
so we have each month uh… we’re gonna collect three thousand dollars so we draw the amount of money that we
pay going down we draw the amount of money
that we collect going up of course it at the end of the summer we have to go back to college that means that we can no longer run our landscaping business but rather than keeping the equipment
idle over the course of the academic year we’re going to tell the quick and off to
other people it’s not can be worked as much as we paid for but it’s going to
be worked almost as much as we paid for it will call that a okay you might notice that that figure is not but that uh… units here or the first month second month and the third month here’s the fourth month to take us some
time to find a buyer for the equipment so we have a cash flow diagram and what
we want to know is whether these they’ve seen the future payment
justifies the initial investment of ten thousand dollars when we might be able to do something
else for about ten thousand dollars reveal take summer classes for example and graduate early at the graduate early will get a job so that’s a different cash flow diagram
will catch to compare that alternative and another video let’s break this one down the first step
is we’ve already drawn the cash flow diagram now we need to understand how to move
each one of these future values to a present value the aggregate of these positive flows is
greater than the costs that we have at the present
value then we could take definitively scan advantageous
investment is going to make us some amount of money one way to do just that we should
understand uh… right away to reviews each one of the to present value using what week study
previously called the discount rate libya formula for that the present value obese future values is going to be over one plots the discount rate amis idea is the
discount rate and this case we have to express i on a monthly basis multiplied by in our previous video we sybil where to
discount rates come from and we export lots of different options
one of those might be what does it cost us to borough ten thousand dollars if we don’t have
the cast but another might be um… what’s the rate of inflation uh… orchestra subjective expression of or
trying preference young people like college students
typically are ordinarily have pretty high discount
rates relative to the general population so we’re going to choose discount rate
here one which is one percent two months or when you compound that monthly about
twelve point two seven percent the to do this for the first month we today alright three thousand dollars divided by one point four one race into the first power the number of months in the future is
one him out of money three and this will
uh… resulted in presently were of the uh… month of billable but back in monthly we do it as a couple
of days for the third month we would do the containment calculation uh… we wait cclc repeat this three times for each month
with a different number of months in the future noted that that interchange it one
percent a month were compound here and then we get a present value of all
of our billable that you understand intuitively fifties billable cyp three plus three
plus three is only nine thousand dollars and that wouldn’t by itself justify a
ten thousand dollar expenditure we’re going to be in debt or having depleted or savings account until we get to tell the equipment at
the and of the year it’s not proper to say in present value
terms that our profit here at least three plus
three plus three plus eight minus it would look like our profit is seven
thousand dollars and that’s what we have to declare our schedule c_ tax return but that tiny bit value is different we know that delaying these revenues
into the future make them work left this is why we have to discount instead of doing this same calculation three times that would
be convenient if we could wrap all three of these
calculations single calculations and in fact there’s a way to do just that let me give you a different formulas
when we have any cash flow diagram that includes a series of pavement patrick are on a regular basis then we can use the formula that looks
like this we’re still working in terms of present
value but now we use a different variable eddie in any
represents this recurring and regular uh… series of payment and um… comes from annual typically people think in terms of
annuals cash flow diagrams we had a very short time horizon we’re looking at monthly and so we could do the variable m first take of convention brittany’s a
because most textbooks look at it as any now there’s a slightly more complicated
formula when you have a number of these periodic
payments the complications tapes other the labor
of the calculation plus hai to the number of compound interest in in
this case all of these compound in period all
three of them not just one of the time aka showed previously so it’s one plus uh… race to be a
minus one all over the interest rate again one-plus alright race to be had you might ask yourself why did this one
plus i_t_t_ and show up twice in the calculations it seems repetitive you can imagine that there is the
derivation that is behind this or formal we can we work out everything in this
factor you’re gonna see that it’s not three it would only be three if heidiwear zero
because we have three payments uh… but it alrighty kolkata zero we don’t really need to discount we were put in zero in here the whole
factor blows up so we’re expecting something in here that is left but close to less than three but close to three so let’s do or substitution we’re talking about three months our monthly discount rate points below one points below one and then of course here another point old one when we get this baxter we’ve been multiply that factor by the three thousand collected each
month this case and so are those of us three
thousand and three months because i don’t mean for you to confuse history outside the brackets with this history
in the exponents this is the total number of payments is for the amount of each payment
coincidentally they’re the same i’m gonna leave this has been exercise
for you to perform at home kim this uh… value multiplied by three and look at the present value of the
three for this black teacher payment we can
use formula i’d just to race raised to that but now it’s four months
in the future so we have to raise that to the fore perform these calculations at home post your answer on blog in response or as a comment in
reply uh… to this posting let me know what you think the present value of this summer
business yes thank you very much

### Paul Whisler

1. Robert Podgorski

For a person trying to learn a new subject less talking and get to the point. After that we can have story time

2. Soni Bros Investing

nice video. my channel has a video that talks about cash flow and it would be great if you could check it out. keep up the great work!

16510.79 \$

4. anto franklin joseph

NPV is \$6.51k..

5. Thomas Seager

Yes! A does stand for "annuity", but we use the same variable even if the payments come weekly, monthly or quarterly. In that case "A" is a bit of a misnomer.

Still, the mathematical formula is exactly the same. You just use an interest (or dicount) rate that corresponds to the period of the payments. For example, a rate of 12%/annum would break down to 1%/mo if you had a stream of monthly, rather than annual payments.

6. Kedah

This is Great stuff!!! Understood it in 10mins compared to a 2hr long lecture.

7. Ahmed G

Total Present Worth (P) = \$ 6,511   Is it right?

8. Ahmed G

…because we have to subtract the initial cost which is \$10k from \$16,511 to get the total present worth.

9. MrMeat42

Requesting vectors for landing

+6510.79 DOLLARS

11. Anthony Zaino

Nice

13. Ahmed Alajib

I have one problem l need to solve it plz

14. Sebastian Cardenas

Hey! nice videos, it would be cool to see you remake this one