 Personal finance practice problem using OneNote. Coupon rate, current yield, yield to maturity and market price for bond issued at a premium. 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 and the 11200 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 that can be translated into multiple languages either listened to or read in them. Information on the left-hand side related to a bond outstanding, remembering that when we're investing in bonds we can basically think of them as us loaning money to the issuer of the bond. That being typically a government or a corporation in exchange for basically rent on that money, that being a series of interest payments typically as well as a face amount that we're gonna receive at the end which you can think of as in essence a return on the principal, a return on the original loan amount if it was issued at par at the face amount. However, we could have situations where the bond is issued either at a premium or a discount in this case at a premium. So we got the par value on the left-hand side. This is the amount that we're gonna receive at maturity, the $1,000, the annual interest payments. So we're not getting them semi-annual, we're getting interest payments in essence rent on the money that we are loaning in essence at $120 on an annual basis until maturity which is gonna be in eight years. The market price, what we're actually paying for the bond, $1,400. That being higher than the par value of the bond which means that we're buying this at a premium. So we can calculate the rates then on the left-hand side, the coupon rate could be calculated as the 120, that's the annual payments that we're gonna get from for the bond. And then we're gonna be dividing that by the 1,000 that will then give us the 12% coupon rate. So if they were given the coupon rate, we could take then the 1,000 times the 0.12 to calculate the coupon payment which in this case is a yearly payment of 120 as opposed to semi-annual. The current yield then we're gonna take that 120 that we're gonna be receiving, the annual payments that we're gonna get and compare that not to the par value but to the market price, which this time is higher than the par value or the face value of the bond to get kind of a somewhat crude back of the envelope quick calculation for our annual yield or current yield that we can then use and compare possibly to other investments although it's not perfect because we're really only comparing the price that we're paying to the return we're getting in one year but that's a little bit more complex given the fact that we have those payments happening for eight years and we also paid more than the amount that we're gonna receive at the maturity of the bond after eight years of the 1,000. So this calculation was the 120 divided by 1,400 the amount that we pay for the bonds giving us the 8.57. So we might wanna calculate then the yield to maturity which is kind of like the market rate of the bond. We're gonna do this a couple different ways. Remember that you might understand how to calculate the bond price if you had the market rate, the yield to maturity which would be the present value of the stream of payments, interest payments and the present value of the face amount the amount that you would receive at the end or maturity of the bond which is the $1,000. So adding those up if we knew the market price if we can discount those back if the market price would get us to the 1,400. One way you can do that in Excel and kind of back into this the other way you can do it is use the rate function which we will do but if you don't know that you can use kind of a goal seek function to basically do these two calculations based on a yield to maturity that you would guess and then use Excel to kind of use an algebraic type of approach solving for the unknown, solving for X here but instead of doing it with algebra you tell Excel do a trial and error method use goal seek to figure whatever this needs to be to get the end result here to be what we know it should be 1,400 market price. So if you were to think about it that way you can calculate the present value of the interest payments which would be the rate. The rate would be this one that we don't know but we would be using that cell at first which will eventually be that 5.65. Comma number of periods would be the eight years until maturity comma the payment would be the 120 coupon payment discounting that annuity back would give us the 756. If we took the present value of the face amount the rate once again this amount comma number of periods would be eight years comma comma because it's not an annuity present value I mean the future value the amount we're gonna get at maturity 1,000 that would give us the 644 adding those up would give us the bond price. If it didn't add up to 1,400 both those calculations being dependent upon this percent we can ask Excel to then change this percent to whatever it needs to be to make that bond price 1,400 that's a useful tool to just understand know about we can also of course noting that these two calculations we used the rate so the rate is the function that we might be able to apply here so we can use the rate function to get to that number as well so we could say the rate function would be the number of periods number of periods would be eight comma the payment would be the 120 the present value would be then the current market price it would have to be negative 1,400 because that's the amount we're paying out at this point and then the future value would be the amount we get at maturity the 1,000 that should also give us that one point with a 5.65 now note that if you knew this information over here the market price, the par value the annual interest payments, the maturity and you used this calculation the rate calculation to figure the market rate to yield to maturity then I would double check that right I would use that number to figure this 5.65 and then use that to get back to my bond price so then I would solve for the bond price using this rate present valuing using that 5.65 which we just talked about here and then double check that you get back to the bond price just to get a better understanding making sure that I'm understanding going back and forth on that calculation you can also break this out which is again a great tool to do by breaking these series of payments out on an annual basis remember that the bond is a nice tool to use for present value calculations because you have these two streams of payments one is an annuity, a nice neat annuity then the next is that one payment we're gonna get at the end which we can then basically calculate using these two functions and add them together but if they weren't quite so neat in a situation like a budget or something like that you might have cash flows that are happening out into the future which are not consistent or not uniform in a nice neat annuity for example and in that case you can always just basically break out your future cash flows on a year by year basis or period by period basis and then present value them and it's really good conceptually to do that because then you hopefully get a better conceptual idea of what is happening and that always helps you to kind of understand and possibly be able to make better connections and make better decisions so if we were to say that the interest payments that we have in the future if we mapped them out we would get $120 each year for eight years which would total up to 960 through the eight year time period that we would get we'd get the face amount back at the end of the maturity at the end of eight years in this case if I look at the cash flow on a period by period in this case year by year basis we'd get 120, 120 each year until year eight where we would get 1,000 plus 120 or 1,120 if we discount each year back each period we would take that 120 discounted back at the rate of the 5.65% and then we would bring it back one year so the rate 5.65 number of periods one and then we're not doing a payment because it's not an annuity the future value would be the 120 if I discounted this 120 back two years at the rate of the 5.65 we would get the 108 if I discount this 120 back three years at the rate of 5.65 we're gonna get the 102 and on and on until year eight where we got that lump sum payment because we're receiving the face amount at the maturity at that point so if I discount that back then I get the 722 discounting eight years at the rate of 5.65 and that once again if I add that up should give us that 1,400 adding these numbers up that series up we get the bond price adding the 144, the 108, the 102 and so on up to the 277 so it's useful to be able to imagine this calculation here as well also just realize that when we look at the rates, the coupon rate we're getting paid the 12% on the coupon rate and the market rate is at the 5.65 so meaning people on the market basically what that means is that other investments of a similar nature are paying something less getting a lesser yield which means that these bond payments at 12% are better we can't change the coupon rate on the bond if it had already been issued for example if it's already on the market and therefore the thing that we can change is how much we're gonna sell the bond for and that's why we're adjusting the price in this case increasing the price to account for the fact that the bond is paying out a coupon of 12% and the market rate for similar bonds or similar investments is at the 5.65 and therefore the market is willing to pay a premium for the bonds in this case 1,400 as opposed to the price of the 1,000 if the company was issuing the bonds and they're turning it around quickly and issuing them quickly they would try to issue the bonds you would think for the market rate which would be in this case the market rate of the 5.65 and then you can issue the bonds not at a premium or a discount but as time passes once the bonds are created the thing that you can change is not the coupon rate at that point in time but the price at that point in time now note that if you do these in Excel you can put this data on the left hand side and you can then adjust this data and make it a premium make it a discount and see what the impacts will be on your rates and your present value calculations and just get a better understanding of how bonds work how present value calculations work and so on