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Present Value – Power of Discounting

Present Value - Power of Discounting
Welcome back. Now let me show you power of discounting, which is kind of power of compounding in reverse, right? So let's stare at what I'm asking you to do. Remember, I asked you figure out changing n, n is very important. But the combination of n and interest rate is what it's all about. So the lower the n, and the lower the interest rate, the less you'll see the power of compounding and discounting, right. So let's do power of discounting. What are the present values of receiving $1 billion. Remember $1 billion that's a lot of money, nine zeros. I always forget how many zeros in million, billion but you can always Google.
So at 5% versus 15 remember where I'm pulling these 5 and 15. I'm pulling them from historical data. Admittedly peculiar to the US. But I'm choosing 50 years from today instead of 90, just to see what happens. So, formulaically, it's very tough, and I'm gonna talk, and right as I talk, okay? So what is the first one? Let's write down the formula. So you take the first at 5% will be You'll be taking a $1 billion
And dividing by 1.05 raised to power, how much? 50. This is the calculation they're doing. And the second one is, figure out a present value at which interest rate? At 15%. So you'll just replace this 0.05 our 1.05, this whole thing, by 1.15. Of course, raise to power what? 50. So these are the two different calculations I'm asking you to do. Now, if you stare at this and if you can do it in your head, as I said earlier, there's something very bizarre about you. But we'll assume that you're not going to do it in your head, and so we are going to use Excel.
So what I'm going to do is show you what Excel will do a little bit so that you can figure it out. So okay, going to Excel, we still have our old buddy over there. And we're going to delete it. We're going to now write the numbers, so let's write =, but now after pressing equals, what will you enter? You'll enter not FV but PV and then (. When you open the parenthesis you'll clearly identify what all you are looking at, right? So the first number is rate, so let's put 0.05. And let's put number of predetermined, how much did we have in our problem? I think we had 50 years.
Did we have any payments in between? Answer is no, so you got to put 0. When I do this many times, I'm just doing it quickly and I forget that PMT is in there. Just be careful, because you're taking advantage of Excel, but Excel has rules to follow too, right. So how much are you getting paid now? Here, enter a bunch of zeros, 1000000000. And then press Enter. You should get, and I'm just looking over to make sure we have the right numbers. Let me just make sure I'm getting all this. You should get, I think, at 5%, 50 years, $1 billion. You should get 87 million 203 726 or almost 727. $87,203,727. That's gone down, but not drastically.
Now what I'm going to do, I'm going to keep this excess widget open. I am going to press 0.15 and what do you think is going to happen?
You are left with how much? Only $922,000. So the number should be 922 800.84. What I'm going to do is I'm going to let you take a break. Do this on your own and when we come back, I'll pick up where we left. Given the two numbers and move on to more more exciting stuff. See you soon, bye.
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