FIN 14 Time Value of Money

Let's jump into module three of our course. This is, I think, the most important module of the whole course. I don't think it's the hardest, but it's so fundamental to everything we do in finance that if you don't understand annuities and the time value of money well, you'll be in trouble in your course. So let's just sort of jump into it. I brought this slide up in lots of my videos so far. The value of anything is the present value of the future cash flows. Well, again, that word future, that makes me think, okay, there's time involved, right? This time value of money. A dollar a year from now is not worth the same thing as a dollar today, right? So you would rather have the dollar today than a dollar promised to you in a year. Money changes value over time. And that's where the math of finance comes in. So a simple example to kind of get us started and get us thinking about this, I buy $1,000 investment that offers 5% annual interest. Whenever you're quoted interest that doesn't say annual or when you assume annual question, how much is it worth in a year? Okay. So your intuition and my intuition here should be pretty much right, right? It's a thousand dollar investment. It offers 5% interest. That means it's $50 in interest. A thousand times 5% is 50. And so if I don't lose that original investment, I'll have a thousand plus 50, I'll have 1050 in a year. And we of course are right now. Yes, we can solve. I would call this a future value of a lump sum question, right? And it's only one year away. We can solve this just in our head, just with our own intuition. But what if I said, oh, we left it in and let it roll over for 10 years. Oh, it's a little bit more complicated. My intuition doesn't quite get there because year one, I have a thousand year two, I have 1050 for another year, year three, I roll that over. And if it keeps rolling, the math gets like, you know, it's, it's not so easy. And so because of that, we're going to use, I'll show you how to solve things by hand using formulas this chapter, but also show you how to use a financial calculator. So let's solve this very basic one just by hand and with our financial calculator, the more proper way. And as we jump into the chapter, you're going to do tons of examples. This chapter has more examples than any other chapter I've ever written, but let's solve this one using a formula. And this is a formula that's again, future value of a lump sum. So it says, well, let's keep the question on screen. Future value, that's what we're solving for. That's our like X, our unknown equals PV. Well, what's the value of the investment today on time zero, the value of the investment is a thousand bucks, right? This is what I'm putting in today. Times one plus R to the T R is the interest rate. In this case, it's, it's often called a discount rate or acquired rate of return. It's R is sort of a stand in. You might have I as your notation in your textbook and T is the number of years, or the number of compounding interest periods. In this case, it's one. So one plus R to the T one plus 5%, which of course we're going to put in as 0.05 to the power of T. So it's a thousand times. And then again, raise some of the power of one. It's just that number. So it's 1.05 to the first power. It's a thousand times 1.05. It's 10 50 big surprise. We kind of knew that already. Again, we wouldn't likely use a formula like this for a one year annuity, but if I want to do 10 years, real easy, right? You just put the exponent to 10. In fact, why don't we just for fun do go out to 10 years? All right. So X equals a thousand times 1.05 to the 10th power. You get my calculator out. I wasn't planning on doing this, but why not? It's fun. So it's 1.05. This little button is to the power of the Y to the X. You'll see it on even your non-financial calculator. Y to the X 10, 1.62. I multiply that by a thousand. So this, this number in brackets is where this right here is worth 1.62, 1.63. I should say 1.62889. I multiply this by a thousand and I get the value in 10 years, 1.62889. Okay. So there we have it. We've solved for 10 years, which I couldn't do just with my intuition and my cunning and my guile to solve that. I needed a formula. I needed some support, right? Doing it in one year. No problem doing it out 10 years. I need something a little bit more than just my intuition to help me solve that one. Now I think that formula is good and I think that's how I would solve it, but there are many things that even get more complicated that have bigger, more detailed formulas that we'll learn this chapter and I'll show you the formula way for pretty much everything. But it's also useful if you have the ability to use a financial calculator in your class, I highly recommend it. And if I had this problem in a financial calculator, it's actually a little slower to solve in financial calculators. As problems get more complicated, it's actually easier, but let's do the 10-year one. The one-year one is too easy. Let's do them both. Okay. So I'll do the one-year one first. So here's what I input in my calculator. N is the number of periods. So we called it T in our formula, but same thing. It's one. IY is 5%. Now here we don't put in 0.05 into our calculator, we just put in five. PV is how much it's worth today. I'm going to put this in as a negative. Generally, if I'm making an investment, I'm giving you a thousand a day and I'm going to get back positive money later. PMT is if there's recurring payments, that's useful for annuities, another concept we learned this chapter. But here there's no ongoing payments between either us or the person we're investing in. And FV is what we're solving for. So let's put those numbers into our calculator. So I put one in. I put five IY. I put a thousand negative PV. PMT I put in as zero. And then I forget how to do this. I think I go compute FV. Yeah. Compute FV and you can see it's 10.50. So CPT FV. It's been a while since I've used my financial calculator and you can see it's 10.50. Well, let's quickly do this for 10 and see if we match. So this is the number we're looking for. 1628.89. That's what we got with our formula. Let's see. Now, the good thing about a financial calculator is we've already got all the inputs in. All I have to do is put 10 in for N and all the other numbers are in. So now I'm going to compute FV and I get FV is 1628.89. And sure enough, it matches. So the purpose of this chapter is there's these types of calculations all over finance. And this was as easy as it gets, right? It gets harder and harder and harder. And so you really got to grasp what's going on. So find out from your professor, if you can use a financial calculator, if you can, you know, you should be zipping along with your financial calculator. If you can't, it's totally okay. It's totally appropriate. You're going to need to learn the formulas that we introduce through the chapter. But that's, you know, I can't speak to what your professor is doing. I think it's appropriate to allow a financial calculator. I think it's appropriate if they don't allow it. So you have to figure out what your professor's doing and work with them. In our videos, I'll do both. All right. Thanks so much for watching and practice, practice, practice. You're going to want to do lots of examples and I've got lots for you. Stay tuned for the next video. Bye-bye.