Bond Pricing

this video is going to walk us through some of the bond calculations that we do in class depending on the time it takes me to work through this it might be one video or it might be split into a couple videos YouTube has a ten minute time limit at the time I'm recording and posting these up on YouTube so if we exceed 10 minutes it'll be broken down into multiple parts but there are four basic bond pricing problems that we're going to encounter the first is a pricing of an ordinary bond next we have yield to maturity and yield to call situations for an ordinary bond and then we'll also introduce the idea of a zero coupon bond in this class and so I want to walk through the calculation of bond pricing with a zero coupon bond let's start with the first case the bond pricing problem for an ordinary bond in this problem you are considering the purchase of a 10-year 5.5% coupon bond with a 7.1% required return we want to know what the value of this bond is right now whenever we do bond pricing what we want to think of is we're purchasing a set of cash flows so we need to a forecast what those cash flows are be choose an appropriate discount rate and then sea salt for the present value of those cash flows now in real-world situations with bond pricing probably the biggest challenge of those steps is be choosing the appropriate discount rate in order to determine the appropriate discount rate you need to consider how risky the bond is you need to consider expected inflation what other interest rates are at the current point in time lots of different factors go into determining exactly what the appropriate required return is we're going to talk about some of those things in chapter 3 when we look at the financial system and interest rates but really in order to get good at determining an appropriate required return you need to develop a lot more knowledge of finance beyond this business finance course hopefully by the time if you're a finance major by the time you're done with the major you'd have a little bit better idea but it goes beyond just the academic training and into some real-world practice in order to get good at determining that required return it requires a little bit of seasoning practice going through doing it in real-world scenarios and I would argue that this is the key to becoming a successful bond investor the better you can do at determining what that appropriate discount rate or required return is the more successful you're going to be as a professional bond investor that's where they get their edge that being said let's focus now in solving the problem in class the required return for our bond pricing problems always be given so you don't have to worry about determining what it should be that's going to be provided for us so we said the first thing we need to do is forecast the cash flows now bonds are easy because bonds have a fixed time horizon this bond is going to mature in ten years so we know we're going to be receiving cash flows for ten years they also have a fixed coupon payment our cash flow each year cash flow each year is based on this coupon rate the five point five percent coupon tells us that each year we're going to receive five and a half percent of the par value in coupon payments now a lot of times bonds will split that coupon payment into two semiannual payments and that's what we're gonna do in this class we're gonna assume bonds pay interest semi-annually so that fifty five dollars per year is gonna break down to $27.50 every six months so now we know what the cash flows are each period we know how long we're gonna receive them there's one more cash flow and that's at maturity bonds when they mature return the par value to their investors par value is $1,000 so that's going to be returned to investors at the end of the tenth year once the bond matures so if we want to look at a timeline for this bond we have a ten year time horizon our required return is seven point one percent each year we're going to receive fifty five dollars so we said that's going to be split semi-annually so we're going to get two payments each year fifty five divided by two it's twenty seven fifty so each year we're gonna get twenty seven dollars are each six months we're going to get $27.50 all the way through to the end of year 10 then at the end of year 10 we're gonna get our last $27.50 and we're going to get one thousand dollars that's the par value or maturity value which gets returned to us at the end of the bonds life now what we want to do is move from this time line and set it up into a five key approach so we've got our time line here we want to convert that to our financial calculator first thing is because the bond pays semiannual we have two periods per year so you want to set your calculator to two periods per year and then you can just start with your five key approach so once your calculator sets two periods per year you have your five keys your n your I / y pv p mt + FV now I'm gonna walk through this problem on my HP 10 B but regardless of which calculator you're using you should be comfortable with your 5 key approach at this point so you need to start by setting your periods per year to two and then use the 5 key approach on your calculator because we have two periods per year ten years is actually 20 semiannual time periods the interest rate is that required return count rate that we talked about earlier so that's seven point one percent for our interest rate the present value is what we're solving for we want to know what the bond is worth today so we're solving for that PV the payment is the annuity that annuity is the $27.50 each six months that we're going to receive so that's twenty seven fifty for our payment and the future value is the one thousand dollar par value so now we plug these into our financial calculator and note that the payment and the future value are both positive here that's because as a bond investor you're going to pay money today to buy this bond and in exchange for that money you give up today you're going to receive that coupon payment every six months so your payment is positive it's coming to you and you're going to receive the one thousand dollars at mature that maturity it's positive so it's coming to you so now we get out our financial calculator I want to start by setting my periods per year to two so I do to set that in to my periods per year again that procedure might be a little different depending if what calculator are you using but the key is we start with two periods per year once our calculator is set to two periods per year we're gonna use our five key approach my n was 20 so just plug that into my hand my interest rate is seven point one percent just pull that into my interest per year present value is what I'm solving for so skip over for that at for now twenty seven fifty is my payment and 1000 is my future value once those are all into my calculator just solve for my present value or get an answer of eight hundred and eighty six dollars and 81 cents now that answer came out as negative on our financial calculator because we're paying that today it's a cash outflow we don't need to write the negative down in our hand sir because we're saying what's the value of the bond it's worth eight hundred and eighty six dollars if we were to sell it it's going to cost this eight hundred eighty six dollars in one sense if we're going to buy it so we don't need that negative sign but the calculator uses that negative in order to show you whether it's a cash inflow a cash outflow since our payment and future value were inflows the present value was an outflow

Channel: Kevin Bracker

Views: 87,452

Rating: 4.7068062 out of 5

Keywords: Bond, Pricing

Id: yUrrz5cByk0

Length: 9min 49sec (589 seconds)

Published: Thu Aug 06 2009