 Personal finance practice problem using one note coupon rate and current yield calculation prepare to get financially fit by practicing personal finance. You're not required to but if you have access to one note would like to follow along when the icon on the left hand side practice problems tab and the one one one two zero coupon rate and current yield tab also take a look at the immersive reader tool practice problems typically in the text area to 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 bond one bond two bond one says we have the face value of $1,000 the semi annual interest or a coupon payment of $50 it was issued at the face value. Now note when we think about the bonds we can basically think of it as though we are loaning money to the issuer of the bond the issuer typically being a corporation or a government entity. If the corporation or government entity issues the bonds right after they were created then they may be able to do so where the market rate matches the rate that is on the bond and therefore they may be able to issue it not at a premium or discount but for the actual face value of the bond it's more likely as time passes from the creation of the bond and possibly the bond being sold for example on the secondary market. Not buying the bond in that case from the issuer but from other investors that there's going to be a difference from the rate on the bond and the and the market rate which will result in us having to purchase the bond at a discount or a premium. So if we think about this first situation where they just created the bond they're going to issue the bond right away there's no difference between the market rate and the rate on the bond then they're going to issue it at the face value. Remember also that this coupon payment if we think about a bond as in essence us loaning money kind of to an organization government or corporation then they're going to be paying us interest on it. It's a little bit different than when we take out a loan such as a mortgage because when we take out a loan we typically pay it back in equal installments having both an interest and principal component of each of those payments. On the bond we're going to be paying in essence we're going to we're going to get paid basically the principal kind of back at the end although the discount and the premium kind of mess that up a little bit and then we're going to get a stream of kind of like the interest payments. Which is going to be the coupon payments that we're going to be receiving. So you might be given for example the coupon rate in which case you would then need to determine the coupon payments for example or you might know what the coupon payment is and then the want to determine the coupon rate which is the case here. Also keep in mind that you got to be familiar or understand what's going to happen with the semi annual payments that interest is not paid monthly it's paid on a semi annual basis. Okay so let's first think about the coupon rate and and this will be the same as the yield the current yield in this case and here's our two calculations down below because they were issued not at a premium or discount but at the face amount. So we've got the annual interest payment so note that we were paid semi annually for the $50 so for an annual payment because we usually think about in annual terms when we when we calculate the coupon rate and that's something you got to kind of keep in mind. If they're going to be paying us $50 each half period each six months times two then that's plus two 50 times two we get the $100 and then we're going to compare that to the face value and that's going to be the value of the bond the amount that we're going to get at maturity and the amount. And this case that we paid for it because we didn't buy it at a premium or discount but paid the face amount of it. So we're going to take the 100 divided by 1000 and we would get then the 10% or 0.1 10% now if we were given the 10% and didn't we're not given the 50. Then you can figure out the 50 semi annual interest or coupon payment by taking the 10% coupon rate times the 1000 that would give you 100 divided by two because it is semi annual you're getting $50 every six months. Now this all also happens to be the same as the current yield in this case because because of the situation of not having a premium or discount so the annual annual coupon payment divided by the bond price which in this case is equivalent to the face value. So let's take a look at bond number two where those two things will be different. So we've got the coupon rate is still going to be the $100 because we got bond number two face value of 1000 the semi annual still 50 but this time we did not buy it for 1000 we bought it at a discount we bought it for something less than the face value of the bond. That kind of messes things up with our loan with seeing it as a loan a little bit because at the end of the period we're going to get $1000 back but we only paid up front we're loaning basically 950 so the interest gets a little wonky there which means we have to do our present value calculations and so on to figure the price of the bonds which becomes you know a little bit confusion more confusion when when we have a discount or premium but in any case this first calculation will be the same be the hundred hundred dollars divided by the face amount the 50 times $200 divided by the face amount 10% no change to the coupon rate but if we're trying to figure out a rate which will be an easy rate that we can calculate that will be comparable to other types of investments for example we might be more likely to use the current yield and remember if you're looking at other investments you're trying to say where am I going to invest my money and you're looking at different kinds of investments it's useful oftentimes to think about the return you're getting on an annual basis so so you basically want that's kind of the calculation we're looking at but we're not going to compare it to the face value because we didn't pay fate the face value of 1000 we paid 950 for it so we would take the $100 divided by the 950 and that would give us then the 10.53 so 100 divided by the 950 would be the 10.953 about moving the decimal two places over now this estimate is a is a little bit more useful for us to figure the the current yield you know what we're earning which we can compare to other investments however it's not a perfect kind of investment as well because we can we can see that the bond is a little bit more complicated in that we put down you know this is what we're earning or this is the interest we're earning based on compared to the price we also got to realize that we're going to we're going to get you know the earnings for for however long the bond term is and we're going to get $1000 back at the end of the term so this is kind of a pretty quick you know back of the envelope as they would say calculation and then we can get into more more in depth calculations calculating something like the yield to maturity for example which will take a look at in future presentations