 Personal finance practice problem using OneNote. Coupon rate, current yield, yield to maturity and market price for bond issued at a discount. 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 problem tab and the 112000 coupon rate, current yield, YTM and market price for discount bond tab. Also take a look at the immersive reader tool, practice problems typically in the text area too with the same name, same number, but with transcripts. Transcripts can be translated into multiple languages either listened to or read in them. Bond information on the left. We've got the par value at 1000. We've got the annual interest payment. So these are not semi-annual. We're saying the interest payments happen on an annual basis at $70. The market price is at the $840. That amount being less than the par value, which means it's issued at a discount, meaning if we were purchasing the bond, we'd be paying the 840 for it. We're gonna get a series of payments of $70 on a yearly basis until maturity, which is 10 years into the future. And then at the end, at the maturity, we'll also get the 1000 back, which is the face amount of the bond. Let's first calculate the coupon rate, which is basically the rate used to get to that $70. So if we got the $70, we can get to the coupon rate, which would be the 70 divided by the 1000. That given us then the 7%. 7% coupon rate, seven times the 1000 is the $70 that we're gonna be getting on an annual basis in this case. We can then calculate the current yield, the current yield now being the $70 that we're gonna get on a yearly basis, but we're not going to compare it to the par value because that's not what we paid for it, but instead we paid the $840 for it. So when we're trying to figure out basically what our return is, a quick and easy back of the envelope, as they say calculation would be 70 divided by the 840 or about 8.33. However, that's not completely precise because of course we've got two things happening. We've got a series of payments at $70 that are gonna be extending out for 10 years. And then we also have that $1000 that we're going to be receiving at the end or at maturity, which also throws off kind of this one yearly payment kind of calculation for one timeframe. So we could then get into some other calculations such as the market price calculation and the yield to maturity, for example. So when we're thinking about the yield to maturity, we could use a rate function such as this function in Excel to calculate it. Oftentimes you might kind of try to back into it because we've practiced a few times how to think about how to calculate the market price of the bond. And if you use Excel, you can use Excel to kind of back into what the yield to maturity would be. Let me show you how that might work. So for example, when we calculate the price of a bond, we're gonna take the present value of the stream of payments, in this case $70 that we're gonna be receiving every year for 10 years. And then we're gonna take the present value of the face amount that we're gonna get at maturity, that being the $1000 in this case that we're gonna receive at maturity in 10 years. And we discount that back using the market rate, which we don't know because that's the yield to maturity that would give us the market price. We could then assume in Excel making a number just picking a number like 5% or something, for example, to start with and calculate based on that rate in this cell doing our present value calculations and then use trial and error basically asking Excel, would you just use brute force to change this number until you get to a number that makes the result what we need it to be, which is 840, the market price. And that's a way that you kind of back into some calculations using kind of an algebraic method in that you're looking for the unknown, but instead of solving the algebra because we're using functions here, which makes it a little bit more complicated. We're just telling Excel, do it by trial and error, just keep on plugging in numbers to X, the unknown, until you figure the result out. So that's one way you can approach it here or any other kind of problem where you have a similar kind of thing where the unknown is somewhere within the function. If we were to calculate that, we'd say the present value then, present value of this stream of payments, if we did this at Excel, would be the rate, the rate would be the unknowns, would be picking this cell, which we could start off with a guess and then we got the number of periods, which would be 10, it's not semi-annual so we don't have to multiply it times two, it's an annual comma the number of payments or the payment would be $70 per year. But then we've got the present value of the face amount, which would be the rate, the cell, comma number of periods, which would be the 10, comma, comma to get to the future value, which would be the 1,000, that would give us adding them up, the market price. And then again, if I just guessed a number down here, we can ask Excel, change this number, the unknown, like the X and change it until it fits. Or we can use the rate function. So you can see in these two calculations here that the rate is what we're looking for. So that's the function. So we can look for a function that uses the rate, the rate function here and we could say equals the rate, the number of periods, the number of periods would then be the 10, comma, the payment. The payment would then be the $70, comma, the present value, you gotta have a negative, that's why it's a little bit confusing here. The present value would be the price, the 840, comma, the future value, the amount that we're gonna get in the future would be the $1,000. And that should get us to the rate here, which would be the yield to maturity in this case because these are not semi-annual bonds, these are simply annual bonds. So we don't have to multiply it by two. If they were semi-annual, we'd have to get that rate for the semi-annual or six month period and then multiply it basically by two. Now, once you get this number, if you would have used this rate function to calculate this number based on this data, I would double check it by doing what we did up top to make sure that you do your present value calculations here to calculate the price. And that's kind of like your check figure, right? So if I take my market price to figure out the yield to maturity, then I'm gonna plug that yield maturity back into my functions up top to make sure I get back to the market price, giving me a bit of security. You can also visualize this by mapping this out in terms of the periods into the future. And this gives you a much better understanding, I believe, of how these functions are working, these present value functions are working because these kind of seem kind of magical. The reason we can do these two are because the interest payments are an annuity formula and the face value is the present value of one formula. Now, that happens to be two things that are kind of uniform in nature, two streams of future payments that are uniform that we can break out into an annuity and present value of one. But you can't imagine situations like budgets, for example, where you're just gonna map out what you think the cash flows are happening in the future and then just one year at a time, discount them back to the current time frame. So you could do that with a bond as well. So we could say, here's our annuity, which from periods one to 10, we're gonna get $70, 70 times 10 is $700. We're gonna get throughout the 10 year timeframe in an annuity format on an annual basis. The face amount to 1,000, we're gonna get at the end of year 10. If I add those up, we've got an annuity up to year 10 where we get that lump sum plus the interest payment. Then we can present value this on one period at a time, meaning this $70, if I take the present value, rate is gonna be then the market rate yield to maturity, the 9.55 comma number of periods is now one, bringing it back one period at a time. It's not a payment calculation. That's why we got two commas. Future value would be the 70. That's 70 discounted back at 9.55% for one year, 64. 70 discounted back two years at the 9.55, 58. 70 discounted back three years at the 9.55, 53 and so on. And then we've got this lump sum payment at the end including the face amount that we are receiving that we're gonna bring back at the 9.55 for 10 years, 430. If we add them up then we should get once again to that 840 the market price once again. So these are great tools to kind of work through the time value of money calculations and work them backwards and forwards. Be able to calculate the rate over here, be able to kind of back into the rate if you so choose can give you a good understanding and use of that goal seat function which we do do in Excel. And then if you use the rate, use that to calculate the price, do it with the formulas and annuity formula and present value of one and then map out the actual stream of payments that happen in the future which is actually a tool that can be applied more universally even if we don't have something that fits right into like an annuity or present value of one, two nice neat streams of payments but rather have un-uniform payments over years into the future which we can then use this tool to discount back, useful tool to understand and the better you can visualize what is happening the better you can use this actual information for decision making.