So far, we’ve been assuming that the discount rate is the same thing no matter how long of a period we’re talking about but we know if you go to the bank and you say, “Hey bank, I want to essentially invest in a one-year CD.” They will say, “Okay, one-year CD will give you 2%.” And they’re like, “Well, what if we give you the money for two years so if you can keep out money locked in for even longer. They’ll say “Oh, then we will give you a little bit more interest” because we have more flexibility for two years and we don’t have to worry about paying you so instead of giving you 2%, I don’t know we’ll give you 7% because we get to keep your money for two years and maybe if you say, “Well, you know I actually don’t even need my money for 10 years so let me give you the money for 10 years.” You’ll say, “Oh, 10 years if we get to keep your money will give you 12%.” So in general and this tends to be the case although it’s not always the case that the longer that you defer your money or the longer you lock up the money, the higher an interest rate you get. So, the same thing is true when you’re doing a discount rate. Oftentimes, you want to discount a payment two years out by a higher value than something that’s only one year out so how do you do that?
So, let’s say the risk for your rates, so if you were to go out and get a government bond, if you were to get a government bond, the one year rate that they are only giving you 1% but let’s say that the two year they will give you 5%, so what does that mean? Well, we just take the example. So, that means you could take that 100 dollars and essentially lend it to the federal government. And in a year, they’ll give you 1% on it. So that these are annual rates so 1%, 1.01 times a 100, that’s just a 101 dollars right? Fair enough. Now, your other option is you could lock it in. You could lend it to the federal government for two years, not see your money and they say, “Oh, then we are going to give you 5% a year.” So then you are going to go 5% a year so how much do you end up within two years? Well remember, this is an annual rate. These are always coded in annual rates. So, if you are getting 5% a year, that’s going to be equal to—let’s do it on the calculator. That’s going to be a hundred. After one year, you are going to get 1.05 and then after two years, you are going to get 1.05 or you can view that as a hundred times 1.052 so you would have a $110.25.
So, you already see not even doing any present value. This is actually you can almost use this as a future value calculation. If you take a future value, you already know that this option is better than this option when you have kind of these varying interest rates. But anyway, the whole topic of this is to talk about present value so let’s do that. So, in this circumstance, what is the present value of the $1100.00? Well actually, what is the present value of the $100.00? So, we always know that, that’s easy, that is a $100.00. Our present value of a $ 100.00 is a $100.00. What is the present value of the $110.00? So, we take a $110.00 and we are going to use the two year rate and discount twice and that makes sense because essentially you are deferring your money for two years. You are not going to get anything even a year from now so you are deferring your money for two years so you divide it by one, so it’s all 5% rate and then that is equal to—I think that was our first problem so I’ll just do it again.
$110.00 divided by 1.052 that is equal to $99.77. Write that as our first problem. And now, this one is interesting. The $20.00 you get today and this is a sign, it’s very important when you are doing this. When they talk about year one or year zero, just make sure is that today? Is that a year from now because if it’s a year from now, you would have to discount it by the one year interest rate. If it is today, you don’t discount it. So anyway, I clarify that I was a little ambiguous about that in the last few videos but I clarified it. The $20.00 is now so the present value of something given you today is the value of it so it’s $20.00 plus $50.00. Now $50, what do we use? Do we use a one year rate or the two year rate? Well, of course we use the one year rate because you are; you are not deferring the pleasure of that $50.00 for two years. You are actually getting it in one year so plus $50.00 divided by one point the one year rate divided by 1.01 plus $35.00 divided by the two year rate but this is an annual rate so you have to discount it twice divided by 1.052. And let’s get the t85 out and so you get 20 + 50 divided by 1.01 + 35 divided by 1.052 is equal to $101.25.
So notice the actual payment streams, I did not change in any of the three scenarios and let me just draw a line between them because they got a little bit messy. So that was scenario one. This is scenario two and this is scenario three. But in scenario one, because we use a 5% discount rate for all durations out, we use a 5% discount rate. We saw that choice number one was the best. But then, if the discount rate were to change, if we are to change our assumption and if we get a 2% rate, if for whatever reason, we could lend money to the federal government in the form of buying bonds from them. We can lend the federal government two years over any time period at 2% or any time period at 2% then all of a sudden, choice two became the best option.
And then finally, this is the most realistic scenario and eventhough the math is fairly simple, we are actually doing something fairly sophisticated here. When I had a different discount rate for my one year out Cash flows and my two year out Cash flows and there was this exact numbers, I had to play with the numbers to get the right result then all of a sudden, choice three was the best option. And so I'll leave it to you. I want you to think about why this was better for choice three that it was for choice two. And if you really understand that then you I think are just starting to have a lot of intuition about present values. And frankly, what we are learning here is a discounted cash flow. What is the discount of cash flow? I'm giving you, I am telling you, I am giving you a stream of Cash flows. $20.00 now, $50.00 a year from now, $35.00 on two years and you are essentially discounting them back to get today’s present value.
So, when someone says, “Oh you know I can use excel to do a discounting default” that’s all they are doing. They are making some assumption about the discount rates and they are just using this fairly straightforward Mathematics to get the present value of those future Cash flows but it’s a very powerful technique because if you were to take, if you are going to excel and you were to say, “Oh I have a business and based on my assumptions in year one and right now this business could be $20.00” and actually it’s going to get $50.00 and then year after that it’s $35.00 and this risk free is a big assumption but if it was risk free, you could discount it like that and you’ll say “Oh, this business is worth if these are the interest rates, this business is worth a $101.25.” That’s what I am willing to pay for. I'm neutral if I can get it for $90.00, that’s a good deal for me. That’s all a discounting Cash flow is but the big learning from this is how dependent the present value of a future payments are on your discount rate assumption. The discount rate assumption is everything in finance. And this is where finance really diverges from a lot of other field especially in the Sciences. There really is no correct answer. It’s all assumption driven. All of these, these kind of Cash flows and all these models, they are really just to help you understand the dynamics of things. And frankly, and this happens a lot in the real world of finance if you ever become an analyst at an investment bank you will probably do this yourself but you can almost justify any present value by picking the right discount rate and actually the whole topic of how do you decide on the right discount rate, because we assumed risk free right? Everything is risk free, you’re guaranteed this payment but we know in the real world if you are investing in pets.com, and they tell you that they are going to pay these Cash flows to you, that’s not risk free. There is some risky implicit in that. So, actually most to finance and most of—and modern finance is based on figuring out that discount rate and that is the cracks of everything because if we see that that completely changes which of these options would be best.
But anyway, I don’t want to confuse you too much. What you have already is a very powerful tool that if you can think of a discount rate, you can make a very rational comparison between three or 10 or whatever different types of payments and this is actually really useful. You don’t realize how many things in the world are like this. You know these college payment schemes where you pay some company $25.00 a year for 20 years and then in year 21 they are willing to pay for your college tuition or your kid’s college tuition. You can figure out what that really is worth, how much money are they making off of you by taking a discounted cash flow and of course, if you are paying out, this become negative numbers and when they pay you, it becomes a positive number.
Anyway, maybe I'll do that in a couple of videos because I think that’s a fairly useful thing to be analyzed. See you in the next video.
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