Video Transcript: Future Value of an Uneven Cashflow

Hello, welcome. We're going to be discussing future value of an uneven cash  flow. So uneven cash flows are exactly what it says. The cash flows aren't even.  So you'll see in year one, in this example, that we receive a $2,000 cash flow.  Year 2 1500 our cash flow. Year three, $0 in cash flow. Year 4 3,500 and year 5  4, 800 we'll assume that it has an interest rate of 8% we want to know what is  the value of these cash flows at the end of year five? Okay, we want to estimate  out and project out, what will all these cash flows value be at the end of the five  year term? So let's write these down right. Year One, 2000 we receive a $2,000  cash flow. Year 2 1500. Year three, $0 year 4 3500 year 5 4,800 now we're  going to project out the future cash flows, or the future values of these cash  flows. So how figure out how to solve the question? This is a future value  question. In most cash flow equations that have future value, there are five  variables, present value, future value, number of payments, interest rate, or the  discount rate, as it's called sometimes, number of compounding periods. Is there a present value? No, no present value. Let's see zero. So we do have a present  value. Our present value are these cash flows, year one, 2000 1500 3500, 4800, those are the present values of those cash flows. What are the payments.  Payments are given, okay? These are our cash flow payments. The interest rate is also given 8% and for the time period we're going to we are going out to the  end of five years, we want to find out what is the future value of these cash  flows. So we need to go through and we need to calculate the future value  equation. Okay, future value equals present value times one plus the interest  rate raised to the number of periods. Okay? So here for year one, let's solve  let's say year one equals present value 2000 times one plus i. Interest rate is 8% right? So for our n, we have to subtract we're so we're going out to five years.  This is year one. So for this, we'll have to go five minus one. This will be raised  to four then. So the future value of the Year One cash flows. 2007, 2098, so we'll look at now let's look at year two, future value on this cash flow. So we've got  future value 1500 times one plus . 085, minus two. So we're going to raise the  N to three. So we'll do 1.08 raised to the third, we're going to multiply that by  1500 so the future value of cash flow, two equals 188 9.57 now let's look at  three. Three is zero, so obviously the future value of zero is zero. So we'll say  future value three equals zero. Now let's look at future value number four. Future value, year four equals 3500 times one plus .08. So we're going to do five minus four is one. So we'll go 3500 times, 1.08 3780 so we raise it to one. One by itself is just one or itself. So 37 future value, 437, 80. Now future value 5 4800 plus  one plus .08k raised to one because it's your five. So 4800 plus times 1.0 840,  80108, that's wrong. The correct answer should be 51 51 84 so now we're going to take the future values of these cash flows, and then we're going to add them  up, and now we're going to know the total of the future value of these cash flows after the five year period. So the future value of cash flow. 1 27, 2098 year 2 18,  8957 zero for year three, because there's no cash flow. 3500 is 3780 I 80 and 

for year five cash flow, 5184 so let's add these up, 2720 98 plus 18 89.57 plus  zero plus 3780 plus 5184 So the future value of these cash flows is 13,574.55