 Personal finance practice problem using OneNote. Zero coupon bond price calculation. Prepare to get financially fit by practicing personal finance. You're not required to, but if you have access to OneNote, would like to follow along. We're in the icon left-hand side, practice problems tab in the 1-1-2-8-0-0 coupon bond price calculation tab. Also, take a look at the immersive reader tool. The practice problems typically in the text area too with the same name, same number, but with transcripts. Transcripts that can be translated into multiple languages, either listened to or read in them. Remember that when we're thinking about investing in bonds, we can basically think of it as though we are loaning money to the issuer of the bond. That being either a government entity typically or a corporation in return for a series of payments like rent on the loaning of the money as well as the face amount that we will be receiving a lump sum at maturity. That lump sum we can typically think of as the return of the principal of the loan. Although the amount that we loaned, the amount that we purchase the bonds for in other words, may differ from the face amount if we purchase the bonds at a premium or a discount. When we look at the price of the bonds, calculating the price, we're going to think about those future cash flows that we will be receiving, the annuity component as well as that one lump sum we're going to get at maturity. We're going to use then the market rate to discount them back to the present value to help us to determine the price. Now, we could have a situation here where twisting things up a bit, a little bit of a curveball, should make things actually easier where we have a zero coupon rate bond, meaning they're not going to give you the interest payments. And you might be saying, well, that doesn't make sense. That would be like me renting an apartment to somebody and they're not going to pay me the rent on it, right? It's like, okay, you're going to live here. You're not going to pay me the rent and then you'll give me the apartment back at the end. But it's not quite the same thing because obviously the other component would be us purchasing the bond at a premium or a discount, in this case, the discount. So the interest is kind of imputed into the transaction by us paying for something less than the amount, the lump sum that we get at maturity. Now, this is often the format that you would get for very short-term bonds. So short-term bonds might be structured in this way because there's not going to be a lot of series of interest payments. If you're only going to have the bond for a short period of time, you just purchase it at, in essence, a discount and working the interest in, in essence, that way. But you could have longer-term bonds as well that are zero-coupon and structured in a similar way. So for example, if we've got a face amount of the bond, $1,000, the coupon rate of the bond, we don't have a coupon rate of the bond because there's zero-coupon bonds and then they're issued to yield 5%, which we can basically say is the market rate of the bond and the years to maturity are 15 years. How can we calculate the price of the bond? Well, normally we take the present value of the interest payments, the annuity component, but there aren't any because we're not getting any interest payments. So we don't have to do that part. Instead, we're just going to take the present value of the face amount. We're going to get $1,000 at the end of this bond. If we discount it back using the current market rate, we would take the present value of the rate 5%. The yearly rate, so we're just going to keep it as is, comma, number of periods is going to be 15 yearly periods. So we keep that as is, comma, comma, because there's no payment. There's no interest involved. We're just going to get that future value, that $1,000 at the end of the term. That being 15 years, we get $4801 and that is the price of the bonds because there's no interest component. If we do another one here, the face amount of $1,000, there's no coupon issued to yield 9% in 15 years. So similar process, we've got no interest payments. That's the point. So zero coupon bond, we don't get any interest payments, but why would we buy it? Because we're only going to buy this thing for $275 if they're going to give it to us because we're not going to get the $100,000 until 15 years into the future. Therefore, we're willing to pay, given our present value calculation, 8, 9%, comma, number of periods, 15 years at no payment. Future value, $1,000. If I bring that $1,000 back, discounting that at 9%, 15 years, we get the $275. So I'll give you $275 today. If you give me that $1,000 in the future, of course, the difference between the two $1,000 minus that, I've covered the number of minus the $275 is, in essence, interest, right? Imputed into the calculation. Okay, the last one. Lastly, face value, $1,000. What if the issue to yield was 12% in essence, the market rate? So now we're going to say we're not getting any coupon payments. We're going to say now the present value would be $183 because we're discounting that $1,000 back. Once again, this time at the higher rate, the 12% rate for that same 15 years. So I'm only willing to buy that bond, loan that money to the issuer of the bond for $183 if you're going to give me that $1,000 in the future in 15 years. And so that is the zero coupon bond. So once you get a hang of that, it should be an easier calculation, of course, to make because now we've only got that one kind of component instead of a normal bond, which is a little bit more confusing to think about over time because you've got those two different streams of cash flows happening in the future. One being an annuity, the interest components, which are not here on the zero coupon. The other being the present value of that one face amount, the amount, the lump sum at maturity.