 # Bond Valuation | Finance | Chegg Tutors

##### Bond valuation is used to determine the fair price of a bond. A bond is a debt instrument used by corporations and governments to borrow capital. Normally, the bond issuer agrees to make periodic interest payments (coupons) on the funds received, as well as repay the principal on a specific date (maturity or par value). The value of a bond is calculated using discounted cash flow analysis. That is, a bond’s value is equal to the present value of its future coupons, plus the present value of the principal repayment. There are a number of other factors usually considered in evaluating a bond, including the issuer’s credit rating and the risk that interest rates will go up (decreasing the value of the bond).

Hey there students my name is nathan and i am a chegg tutor today we’re going to be talking about bond valuation how do you evaluate a bond well first off what is a bond a bond is a form of long-term debt companies issue them or they take on that debt so usually fund some sort of project in the future be it build a new work site or if you buy a new piece of equipment

Something along those lines so they take out a bond for a basically future debt to usually take on some sort of project that requires a lot of money up front now to evaluate a bond that’s a little tricky there’s a lot of steps that go into so bond valuation is used to determine the fair price of the bond and then to calculate the price of the bond what it’s selling

For you take the present value of the bond repayment and you add the present value of the interest payments so you gotta do these separately so you have a bond and there’s a principle involved with that meaning that whatever money you borrow up front that’s the principal and you’ll have to repay that at the maturity date but along with paying back the principal you

Must also pay back the interest involved so that’s why you price a bond you get to go and calculate both components to get the real fair price at the bond both the bond principal and the bond interest now sometimes these bonds they’re sold on the market for more than what they were stated for on what they call a bond indenture the bond indenture is kind of like a

Certificate that gives all the details of the original bond sometimes the bond is sold for more than what was on the bond indenture sometimes it’s sold for less so if it’s sold for more they call that selling the bond at a premium if it was sold for less they called in a discount and there’s two types of interest rates with a bond you have the effective rate and

The stated rate sometimes they call the effective rate the market rate there’s two names for that so if the effective rate is greater than the stated rate the bond is sold at a discount if the effective rate is less than stated the bond is sold at a premium so you need to know that because later on when we price the bond you’re gonna see both interest rates upfront

And later on when you get to the ending value of that bond you want to make sure it matches up with these interest rate comparisons now that’s more of the background of what a bond is and how it works now to actually evaluate it or price the bond there’s a lot of steps that go into it and it’s easy to get lost but what i’ve been telling my students over the years

Is i just give them my simple five-step method and if you follow these five steps you’re almost guaranteed to get the answer correct you just gotta follow these steps and make sure you know what you’re doing and focus on each step now here’s my five step method so first off what you’re gonna do on step one you’re gonna convert your interest rates and the repayment

Period so sometimes when interest is paid other than annually you have to go ahead and convert interest rates to what they would be paid if they are either semi-annually or quarterly and you also have to convert the periods so the periods is how often you pay that interest so for example if you pay interest semi-annually there’s gonna be two periods a year not

Just one and again you’re gonna see more how this works with a practice problem it’ll make a lot more sense trust me let’s keep going over these steps so that’s the first step you convert your interest rates and your repayment period second you’re gonna calculate the interest paid how much you’re paying and interest and that number actually stays the same from

Period to period it’s a constant number next you’re gonna calculate the present value of interest payments so you have to use a little table it’s actually figure out how much you need to discount these interest payments because once again when you pay this interest off in the future that’s gonna be a different number than it was today that’s called time value of

Money that’s a different video but pretty much over time through inflation money is worth more in the future than it is today so when you actually pay back those interests interest payments you have to discount that value back to one of me worth in the present day so we use a little annuity table for that a present value of annuity table and you’ll see that in a

Sec step 4 you’re gonna calculate the present value of the bond so the actual bond principal are going to calculate that separately in the interest payments and you’re gonna use a table called present value of 1 or present value of single sump for that then on step 5 you calculate the bonds price so that’s all it is is just adding step 4 and step 3 together and

That’s it now the reason why you use an annuity table for the interest payments because annuity means a series of payments or receipts in this situation since you’re paying the interest in a series that’s why it’s called an annuity it’s a series of payments and then the present value of the bond is just one lump sum number there’s no series of payments there so

Since it’s a lump sum number you’ll use what they call a single sum table or present value of one table now i know it’s a lot of information and this is just more of a basic introduction to bond valuation but this will actually help you price these bonds if you are presented with an exam question or they’re asking you to do that so that’s more of the concept behind

Bond valuation and mice 5 step method on how to price it now let’s go and take a look at a practice problem this will make a lot more sense okay so now for the practice problem here it’s on the right side so on january 1st 2014 lifeworks incorporated issued one thousand two thousand dollar bonds at a stated rate of ten percent so let’s just stop there one thousand

Two thousand dollar months i know that sounds a little weird but what they’re saying is that each bond is worth two thousand dollars and you have one thousand of them so all you do is multiply those two together to eat the total value of that bond which would be stated on the bond indenture that’s just the stated value of it not the actual price and there’s a stated

Rate of ten percent now at this time the market is selling those bonds at twelve percent so right away we go into reference to our left our market rate or effective rate is gonna be greater than our stated rate right twelve percent is greater than ten percent so right away we know this bond is gonna be selling at a discount so when we go through all these five steps

Here and we get to the very end we know that the value that we get on our fifth step will be less than two thousand times a thousand that’s how it works so it’s sorted a discount so you receive less cash upfront that’s how you check your work in the end now this bond must be paid back by january 1st of 2024 so it’s about 10 years 10-year bond so it’s definitely alum

Form of long-term debt it’ll be paid back more than one year now interest is paid semi-annually starting june 30th 2014 so let’s go ahead and start with the five steps step one so first we’re gonna convert our interest rates in our repayment period so we know it’s paid semi-annually so it’s twice a year that’s when it’s paid so our interest rates stated interest

Rate is gonna go from 10% and divide it by 2 because it’s twice a year so becomes 5% and then your effective interest rate turns into 6% and then our periods well we know it’s 10 years but since it’s paid semi-annually twice a year our 10 years turns into 20 periods right because we pay it twice a year so it turns into 20 periods 10 years twice a year 10 times –

20 all right that’s step one now step two i’m gonna go and calculate the interest paid all you do there you just take your stated interest rate of 10% i’m sorry you know actually 5% we just converted that and you multiply that times the bonds face value which is that right there a thousand times 2,000 so what is a thousand times 2,000 here two million so it’s a

Two million dollar bond times the face value and that’s gonna equal a hundred thousand dollars so twice a year you pay a hundred thousand dollars in interest now step 3 calculate the present value of the interest payments well we take that hundred thousand dollars which is the interest payment and we’re gonna discount that value back to the sum of what it is now

So the sum of all those interest payments together for all those ten years we’re gonna discount it back to present day and see what it’s worth okay so when we discount these present value payments of interest when you go and take a look the present value of ordinary annuity table so if we go over here you can see that on the left side you have the periods so we’re

Looking for 20 periods that’s how many periods there are and we’re using 6% effective interest rate so we’re gonna be using this factor eleven point four six nine nine to go back to the question here and we just plug that in eleven point four six nine nine to go to multiply that out and you get 1 million one four six nine ninety-two then for step four calculate the

Present value of the bond so we go to our single sum table now which is very similar looking but it is different so notice present value of one it’s not an annuity we’re just looking at the principal and discounting the bonds principal back to present date the left side again look for 20 periods and then for 6% interests 0.3 one one eight zero so we have the two

Million dollar bond point three one one eight zero multiply that out six hundred and twenty three thousand six hundred then step five we just price the bond so add step three and four together one one four six nine ninety two plus six two three six hundred all right and so we get a price of 1 million seven seven oh five nine – and that is your price of the bond so

Using these five steps this will help you get to the answer first you convert your interest rates and your periods then you calculate your interest payment this is the only time you’ll use that stated interest rate step 3 go ahead and get the sum of those interest payments discounted to present value that’s where we use our effective interest rate for that table

Step 4 discount the bonds principal using the single sum table step 5 add step 3 and 4 together to price the bond and that’s it and remember we said it’s at a discount so you mean you receive less than what the bonds face value was bonds face value is 2 million you receive less cash 1 million 77059 – so you know that you got it right because it is at a discount

Okay hopefully that was helpful for y’all today here’s my link down here i am a tutor at check tutors i go by nathan g so if you need any kind of homework help or exam prep or one-on-one tutoring just go here send me a message and i can help you out once again thanks for listening today and i’ll see you in the next video

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Bond Valuation | Finance | Chegg Tutors By Chegg