Dec 05
Bond Valuation Basics: Coupon Rates and Yields
in Bonds

This post was originally made on July 27, 2006 on a former blog of mine.

Some people get confused between the coupon rate and yield of a bond so I wanted to go over some bond basics to sort of clear things up. The value of a bond is made up of several parts:


  • Par Value - this is the original face value of the bond. Most bonds have a par value of $1000 but there are some that are different.

  • Coupon Rate - this is the percentage used to determine the yearly payment based on the par value of the bond. If the coupon rate is 8% on a $1000 bond then you will get paid $80 per year until the bond matures.

  • Time to Maturity - this is the amount of time remaining until the bond matures, basically, this is when you will receive the par value of the bond back in addition to the final coupon payment. If a 30 year bond has 25 years left, its time to maturity is 25.

  • Current Prevailing Interest Rates - this is key because people are not going to buy bonds paying 5% if the current market interest rates on similar products is 7%.

Since the Coupon Rate, Par Value, and Duration of the bond are all fixed, the only thing that can change in the market is the price someone is willing to pay for that stream of cash flows. Just because someone paid $1000 for a $1000 8% 10 year bond today does not mean that the same bond will fetch $1000 in today’s market. It may trade above or below that amount depending upon the prevailing interest rates in relation to the coupon payment.

The way one determines how much a bond is worth is by setting the needed interest rate to whatever the prevailing market rates of the day are (also called Yield to Maturity) and then recalculating the bond price (you can use a financial calculator or Excel if you want).

Here is an example. Suppose you have a 30 year bond, $1000 par value, and its coupon payment is 5% (or $50 annual payments). If the current market interest rates were 5% then this bond would trade at its par value of $1000. If, however, rates were to rise then this is what would happen:

Suppose one year later interest rates were at 7% instead of 5%. This means in order for someone to want this stream of cash flows the yield on the bond would have to be at least equivalent to the current interest rates. Therefore we must pay LESS than par value for the bond in order for the rates to make it worth while. This is called trading at a discount.

If you set your calculator to FV=1000 (you get paid the 1000 par no matter how much you pay for the bond if you hold it to maturity), N=29 (29 yrs left to maturity since we are one year later than the original 30 year issue date), PMT=50 (the payment does not change, it will always be $50 or the original coupon rate times the original par value), and I/YR=7 (this is the NEW INTEREST RATE you require - NOT the coupon rate!!!). Then hit the PV (present value) button and you will get $754.45. This is how much the bond should now be trading for with 7% market interest rates. Note: in an Excel spreadsheet you could use the following formula =PV(0.07,29,50,1000).

It is also possible for bonds to trade at a premium, or above their par value. This happens when the present market interest rates are BELOW the coupon rate on the bond. People are then willing to pay more for that stream of cash flows. There are also callable bonds, which means the issuer can call them away before the maturity date. Valuing callable bonds is something I do not want to get into today.

So, there is your little basic primer on bond valuation. It’s not that difficult but all the different uses of percentages can be confusing. Just remember the Coupon Rate is fixed when the bond is originally issued and always simply reflects the payment amount based on the original par value of the bond. The Yield to Maturity (aka interest rate, yield) is the present rate required in order for someone to actually want to purchase the bond in the open market at this time.

“The Great Inflation of the 1970s destroyed faith in paper assets, because if you held a bond, suddenly the bond was worth much less money than it was before.” -Ron Chernow

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9 Responses to “Bond Valuation Basics: Coupon Rates and Yields”
 

A 20 year $1000 bond has a coupon rate of 8 percent. What would be the price if the coupon is paid semiannually and comparable bonds tield 10 percent?

anni wrote on February 2nd, 2008 at 1:14 pm

 

Hi Anni,

I would solve this problem one of two ways. Using a financial calculator I would plug in -$1000 for FV, $40 for payment (8% x $1000 / 2 since it is semi-annual), 5% for interest rate (10% / 2 since it is semi-annual), and 40 for number of payments (20 x 2 since it is semi-annual) assuming you still have 20 years remaining on the bond. Then hit PV to solve for present value. This gives you $828.41 as the price the bond would presently be valued at.

You could also do this in MS Excel using the formula =PV(0.05,40,40,-1000). This will give you the same answer.

You have to use negative in front of the FV because it is essentially an outgoing payment at the end.

Jeff wrote on February 4th, 2008 at 2:19 pm

 

A bond has the following characteristics
Coupon rate 15% p.a paid half yaerly. Settlement date 15 January 2007. Maturity date 28 February 2015. Yield to maturity is 16%.

Required
Find all in one price
the accrued interest
clean price

Patrick wrote on February 27th, 2008 at 1:43 am

 

With all due respect Patrick, I cannot simply continue to do bond valuations over and over. This looks like a homework problem and should be easy enough to figure out!

Sorry for the hassle, I just can’t get in the habit of doing math for everyone.

Thanks for visiting the site.

Jeff wrote on February 27th, 2008 at 8:40 am

 

I have a question here that is driving me crazy..
if i have the following bond information.. I/YR=? PMT=? PV=1000 FV=1000 N=17 and from the income statement i have that interest is $57.9 YTM=CR=I/YR since PV=FV how am I to find the payment value?

Ash wrote on March 24th, 2008 at 9:36 pm

 

Hi Ash,

The only thing I can think of here is that you would have to know the original length of the bond (how many pay periods had passed). If the original N=20 then 3 payments had been made and one could say the payment was $57.90/3 or $19.30. This would lend itself to a 3.86% YTM/CR if the payments were semi-annual and a 1.93% YTM/CR if they were annual.

That’s all I can come up with. Sorry but I am not a bond valuation expert. I know just enough to be dangerous.

Jeff

Jeff wrote on March 25th, 2008 at 6:02 am

 

Hi,
My problem is not to do the math or the concept of valuation but rather what independent rate to use to value the PV of these Bonds.

What is the most common? Sawp curves? LIBOR and Credit Yields?

Theuns wrote on August 19th, 2008 at 6:55 am

 

gosh,, i really don’t know how to do..

Large Industries bonds are selling at 112.23 (i.e., the price is $1,122.30 for the $1,000 bond). There are 8 years remaining until maturity on the bonds and the yield to maturity is 7.75%. If the bond pays interest quarterly, find the coupon rate. (Note: express your answer as an annual percentage).

kay wrote on September 30th, 2008 at 4:12 am

 

1.A Company issued bonds in 1998 with a 10% coupon rate, $1,000 par value, and maturity of 2028. The Company’s debentures are rated “A” by Moody’s and S & P. A rated bonds in today’s market provide investors with an 8% yield to maturity. A) What would you pay for the bond today? B) What if the bond was a zero coupon bond?

Sean wrote on October 12th, 2008 at 8:54 pm

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