10. Time Value of Money

Time Value of Money Equations

# Time Value of Money and Using Timelines

Brian Krogol

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All right. So we're going to discuss one of the more difficult topics for this course. It's the time value of money. Okay. So time value of money. This is how some amount of money today is going to be worth a different amount in the future. Okay. And we use this mostly when we deal with bonds payable. So the liability bonds payable. Well, we're gonna use time value of money when we're pricing these bonds. Alright, let's go ahead and dive right into the ideas of time value of money. So, I got a quick pretest for you to set your mind in the right direction. So it's my money and I want it blank now or some other time. It's my money and I want it now, right? It's my money and I want it now. So think about it if I offered you $1000 today or $1000.05 years from now, which one would you take? The $1000 today? Right. You want that money today and you can start spending it now or you could invest it and it will be worth more money in the future. So that's the main idea here. This is the big takeaway of time value of money. Is that a dollar today is worth more than a dollar tomorrow. Right? That same dollar could have earned some interest and have been worth more in the future. So when we talk about time value money, we're gonna talk about two main concepts and they're opposites of each other. The first one you might have heard of before, compounding. So you might have heard of compounding interest? Right? You might have talked about compounding interest at some point in a math class and your compounding interest into the future right? You're gonna have some current amount of money. So you're gonna take some current amount of money, say the $1000 that I offered you today and you're gonna earn interest, right? You're gonna take that money and you're gonna earn interest as time passes into the future. So you're compounding into the future, right? So you can imagine that there's gonna be an opposite to compounding and that's gonna be discounting. So we're gonna use this term discounting when we're taking some future sum of money. So now that $1000 that I offered you five years from now? Well if we were to take out the interest that would have occurred over the five years, it would have been worth some lower amount of money today. Right? So what we're taking is some future sum of money and removing the interest that occurs over time to find its value today. So think about back to that offer I made you write, I offered you either $1000 today or $1000.05 years from now. So that wasn't so enticing right? You want the $1000 today? But what if I offered you $1000 today or maybe $1500.05 years from now maybe? Now you'd weigh your options. What could I, how much could I earn on that $1000 or what is it worth to me to have that $1000 right now compared to the interest that I would earn or what would it be worth five years from now? Right? So now you have a little more options to weigh and that's because of the time value of money and it all comes down to that interest. So when we talk about time value of money, it becomes very useful to use timelines. I'm sure you've used timelines before in a math class. Um but it's very useful to see visualize these cash flows on a timeline. So you see them all in one place. Okay, so let's go ahead and do an example and build a timeline here. Today you invest $100 at Clutch Bank at a 10% interest rate for three years. So um what we're doing is we're gonna take that that $100 and we're investing it for three years and it'll be worth some amount of money in the future. We're compounding the $100 today into some future sum of money. So let's go ahead and draw a timeline so we can visualize what's happening here. So this is how we usually do a timeline. We're gonna draw something like this and then we're gonna draw the different years here. So we're dealing with three years. So we always start today. Today is gonna be zero and I like to put my years above the graph. So these are the years right here and we always talk about right now as zero. Okay, when we deal with this concept, we deal with it as zero. And before I go on here, I want to make a point that time value of money in this class, we usually keep it pretty basic. You're gonna go into a lot of detail with time value of money. When you take a finance class, finance you're gonna buy a financial calculator and you're gonna do all sorts of complicated time value of money uh equations and transactions. But at this point we keep it generally pretty simple and we mostly use it for valuing bonds payable that liability bonds payable. Alright, so let's go ahead and finish up our timeline. So we had year zero here, which is right now, year zero, then year 11 year from now, two years from now and three years from now. Pretty simple. Right? And then underneath the timeline you write your cash flows. So in this one is pretty simple. We only had one cash flow of $100. And the thing is, once you start doing bonds payable and once you get into higher level courses and doing more difficult transactions, you're gonna have multiple cash flows at different points in time. So the timeline helps you a lot to visualize and see where all these different cash flows are happening. Okay, so that $100 is what you invest today. And then we like to put our interest rate right here. So the interest rate was 10% in this case. So you can imagine you would earn 10% and we're not gonna do the calculations here and you would get in one year. Well, we could do this first one, right? You have $100 and you earn 10%. So it would be worth, say 100 and $10 a year from now, right? Because if you took it and in one year would be worth 100 and 10. And then you keep compounding, right? There's another 10% and keep going in the future 10%. And you keep earning interest, Right? And that's the whole thing when we're compounding we're earning interest on the interest because in the second year you're earning interest on the $110 not just the $100. So you're getting a little extra interest. So you can imagine it's gonna keep growing over time like that. All right. So that's what we're gonna do. We're gonna use timelines generally to visualize our cash flows. This one obviously was pretty simple. We just have one cash flow of $100 that we're investing for three years. Right? So let's pause real quick and then we're gonna discuss this time value of money equation. It's a very important equation. Let's do that in the next video

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