Bond Price Calculator tool

Bond Price Calculator tool

Financial tool
Bond Price Calculator
Inch Calculator LogoInch CalculatorThe cell os is calculate a bonds price given a market discount rate, so a quick little introduction, before, we jump into the calculations globally. The fixed income market is a key source of financing for businesses and governments. In fact, the total market value at standing of corporate and government bonds is significantly larger than that of equity securities.

standing of corporate and government
Similarly, the fixed income market, which is also called the debt market or bond market, represents a significant investing opportunity for institutions as well as individuals, pension funds, mutual funds, insurance companies and sovereign wealth funds, among others, are major, fixed income investors, retirees who desire a relatively stable income stream often hold fixed income securities, so clearly understanding how to value fixed income. Securities is important to investors, issuers and financial analysts, so this reading focuses on the valuation of traditional option: free, fixed rate bonds. Although other debt securities, such as floating rate, notes and money, market instruments is also covered later on, in other l, o s, bond prices and the time value of money on a traditional option, free, fixed rate bond, the promised future cash flows are a series of coupon interest payments and repayment of the full principal at maturity, the coupon payments, are on regularly scheduled dates. For an example, an annual payment bond may pay interest on 15th of june each of each year for five years. The final coupon typically is paid together with the full principal on the maturity date. The price of the bonded issuance is the present value of the promised cash flows. That's it. The price of the bond is the present value of the promised cash flows. The market discount rate is used in the time value of money calculation to obtain the present value. The market discount rate is also the rate of return required by investors, given the risk of the investment of the bond. It is also called the required yield or the required rate of return, bond prices and the time value of money. So just going to look at the calculator here for a second to see which keys we use to calculate a price of a bond and then we'll do an example. Okay, again we did this back in the accounting section when we looked at the l os.

did this back in the accounting section
With regards to the recognition, nevertheless, we'll do it again here so, first of all, you know the present value and the future value when we're calculating the price. One of these has to be negative. Okay, when we're using the time value of money calculations the the present value. That's the price, okay and the future value. That's the par value. Okay and the payment is going to be the coupon payment and that never changes. Unless it's a special like floating rate note, the iowa is the market. Discount rate and n equals the number of periods for semiannual and would equal the number of years times. Two. Okay and, as I said, my preference for doing these. Some people there's different strokes for different folks. Some people won't set the parameters and they'll adjust their answer. I don't agree with that method of using the calculator. So for me, if it's a semi-annual payment, I'm going to do 2nd p/y and make sure that I've set. My calculator to two okay and the other thing is to make sure that you're in the ending mode, remember sometimes they're going to give you a new ax t question annuity do or the payments are at the beginning and then the very next question you know you'll make sure that you have to make sure that you're not in the beginning mode and so always double check.

beginning and then the very next
Your calculator again. Second begin second enter. Oh wait! A minute! I'm in my beginning mode, so I need to change out of that. Second begin. Second enter; okay, it's gone so with regards to the bonds. If it's sammy annual sent your periods per year to two and the mode to the end mode again, here's the keys that we're using in iy present values our price payment is our coupon. Never changes be careful if it's semiannual you got to put in the semi-annual payment and, of course, our future value is our power value, ok, bond prices and the time value money.

value money so we're just going to do
So we're just going to do two examples here: how to calculate the price and in this case we're looking at a bond where the coupon payments are annual. Okay, it's not semiannual. So let's look at this first one, for example, suppose the coupon rate on a bond is 4% that never changes payment is made once of year. If the time to maturity is 5 years and the market discount rate is 6%, then the price of the bond is ninety one point: five, seven, five per hundred dollars of par value, the par value, is the amount of principal on the bond okay. So if we want to start with the algebra first down here, as we said, the price of the bond is simply the present value of the cash flows. So we can see our coupon is four percent on a hundred. So that's four, so we have one two. Three four five coupon payments remember the last coupon. This payment is paid with the par hundred dollars, so we have our five coupon payments and we're simply doing a present value calculation using 6%. So that's for one year, two year, three year, four year, five year and you add back, there's the present value of the first coupon second third, fourth and the president value of the fifth coupon, combined with the par value and using the algebra.

president value of the fifth coupon
We get. Ninety one point: five, seven: five: if I bring up the calculator again second pui wait a minute I had a semi-annual bond in there first I'm gonna change that to periods per year equals one and as we said we can scroll through this is a five-year bond the market rate is 6% the payment is four because it's annual and our future value is a hundred on the on the par value so we're going to compute our present value and we get ninety one point five seven five two ninety one point five seven five two okay very easy now again so we could see in this case that the coupon rate is four percent but the market discount rate has gone up to six percent so as we know as interest rates go up the price goes down that's why it's

selling below par
selling below par but let's look at this case it's got a coupon rate of 8% and the market just going to rate is 6% we can see it's going to sell at a premium and again I won't go through all the algebra here but down here we've got just got the algebra old-school the price of the bond is simply the present value of the all the cash flows so again let's just do it on the calculator though it's 5n and now it's 8 interest rate well sorry market discount rate has gone to 6 s'alright backwards 6iy and our payment though is the 8 8 is our payment and 100 is our future value so we're going to compute our present value and we've got 108 point 4 2 okay so by now at this stage calculating the price of a bond should be fairly easy calculating the yield to maturity of a bond is when we know the price and we're solving for I/o I should also be fairly easy okay bond prices and the time value of money so now we're looking at the yield to maturity if the market price of a bond is known we can calculate its yield to maturity sometimes called the redemption yield or yield to redemption okay the yield to maturity is the internal rate of return on the cash flows the uniform interest rate such that when the future cash flows are discounted at that rate the sum of the present values equals the price of the bond it is the implied market discount rate the yield to maturity is the rate of return on the bond to an investor given three critical assumptions this is important one the investor holds the bond to maturity to the issuer makes all of the coupon and principal payments in the full amount on

the scheduled dates
the scheduled dates therefore the yield to maturity is the promised yield field assuming the issuer does not default on any of the payments and finally three and this is a key one that we've seen the investor is able to reinvest coupon payments at that same yield this is a characteristic of internal rate of return okay on this slide were calculating the yield to maturity so for example suppose that a four-year 5% annual coupon payment bond is priced at 105 per hundred dollars of par value the yield to maturity we're solving for the iowa okay so I'll just bring up the calculator here and I'm just going to hit clear I just move it out of the way so we're gonna check 2nd p/y well we need to be in 1 hit enter because we're doing an annual pay so we can see over here it's 4 n for a year for n and 5 percent coupon so we know the payment is 5 is the payment 100 is the future value okay and the present value they're giving us the price so we're going to do 105 hit the plus or

minus key remember because one of them
minus key remember because one of them has to be negative so I'm doing that on the price and we're hitting that as the price present value and then we're computing for the ioi we get three point six three four three nine nine or a little bit of rounding here okay so I won't do that for the three other calculations here well that's just the table from the text where they gave the coupon payment per period they gave the number of periods to maturity and they gave the price and all these it's assuming that the future value is 100 based on hundred and here we calculated the iowa yield so I'll let you practice that okay so we're just going to finish this ls with a couple of practice questions with regards to calculating the price in calculating the yield on a bond so the first practice question a bond with two years remaining until maturity offers a three percent coupon rate with interest paid annually at a market discount rate of 4% the price of this bond per hundred dollars of par value is closest to a ninety five point three four be 98 or c 98 point 1 1 okay so we'll read the question carefully it's a two years remaining

until mature
until mature 33 percent coupon interest paid annually so the first thing we need to do is check 2nd p/y that we're set to 1 ok so that's good we've set to annual payment periods per year then we're just going to solve it on the calculator so we're going to do 2 n2 years remaining and the market discount rate is 4% so we're gonna hit 4iy and the coupon payment three percent coupon rate that never changes so that's three payment a hundred on the future value and we're going to compute the present value which is the price 98 point one one three nine zero five so the correct answer is c so do another quick practice question here an investor who owns a bond with a nine percent coupon rate that pays interest semi-annually and matures in three years is considering its sale if the required rate of return on the bond it's 11 percent the price of the bond per hundred of par value is closest to a 95 b ninety five point one one or c 105 point one five okay let's bring up the calculator to solve this one and you can see a hot semi-annual so I need to go to my 2nd p/y wait a minute the last question we did was annual need to change my parameter so I'm going to hit to enter appearance per years to okay and clear that up so now I can solve the question three years remaining so n equals six three years times semi-annual equals six so I could do three second and n is going to give me my six or I could just do six n okay interest rate 11 I why we don't adjust it because we

set our parameter
set our parameter however the its semiannual so nine percent coupon on a hundred that's nine but it's divided by two four point five on the payment four point five on the payment and it's $100 future value face value par value and we're going to compute the present value ninety five point zero zero so the correct answer is a one last practice question to finish this l os we're going to calculate the annual yield to maturity so a bond with

a twenty
a twenty remaining until maturity is currently trading at 111 per hundred dollars of par value the bond offers a 5% coupon rate with interest paid semi-annually the bonds annual yield to maturity is closest to a two point zero nine percent b four point one eight percent or c four point five percent okay so let's bring up the calculator again so it says that it's semiannual so when as soon as we see semiannual we got to check our parameter second pui yes because the last question we did was semiannual in this case we're calculating for the yield they're giving us the price okay so there's 20 years remaining so 20 times 2 is 40 n so I can just click in for t n okay and or as I've shown before you could do 22nd and n it's gonna give you the 40 all right now it's giving us the price a hundred eleven so we're gonna do 1 1 1 but we're going to hit the plus minus key because one has to be negative and we're gonna make the price

negative so that's the present value
negative so that's the present value okay it's a 5% coupon but it's semiannual 5% on 100 is five divided by two is two point five on the payment so two point five on the payment and of course it's $100 face value future value of par value and in this case we're computing the iowa and we're getting four point one eight two eight so the correct answer is b and that's the last slide for this ls thank you

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