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

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

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 $

NPV is $6.51k..

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.

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

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

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

Requesting vectors for landing

+6510.79 DOLLARS

very helpful thanks!

Nice

I have one problem l need to solve it plz

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

the first answer is 0.088229 and the answer for the second one is 2.8829