Calculating yield to maturity under the "rule of thumb" method is not difficult. The concept with it is the YTM is based on the Nominal Yield, Price and the years to maturity. So, the formula or calculation is based on that.
Premium bonds have a lower yield to maturity vs. the nominal rate. That is because the nominal yield only pays to par value. Thus if the bond was bought above par, the premium amount does not earn interest and the premium is not paid at maturity. The investor is losing the above par amount at the end of the term. If the investment was sold beforehand at a profit - the cost would be a profit.
Example
A 5% bond was purchased at $1150 and the maturity is 15 years. Calculating YTM would be based on all of this information. The total premium amount is $150 - divided over 15 years would give you $10 per year. That is the amount that is basically lost each year on the price - if held to maturity.
The way the formula is calculated is you take the yearly real interest - which is $50 and then subtract the lost above par yearly price of $10. This leaves you with a real yearly return of $40. Then divide $40 by the average price of the bond during it's life. Since par ($1000) is the redemption price and $1150 was the price that was paid - the median price would be $1075.
So $40 divided by $1075 would be the YTM = 3.72%
Discount bonds are calculated the same way - except the yearly discount is added on to the nominal interest payments. This would result in a higher YTM calculation.
http://www.aitraining.com/ytm.htm
Tuesday, July 31, 2007
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12 comments:
How did you get the $50 yearly real interest? Also how do you know that par is $1000?
Bonds generally have a par value of 1000. 5% of 1000 = 50
Does the formula change if coupon payments are semi-annual?
How would you calculate the Price of a bond bought 5 years ago at a premium of 103, if you know the YTM?
So to recap, if the interest rates today are 5% a new issue 10 year bond will sell at par - that is coupon rate will be %5 and you pay $1000 for the bond
If 5 yers from now interest rates are still 5% would you pay $1000 for the same bond on the secondary market?
Boyan, all bonds mature at par as well. So as long as interest rates on similar bonds with a 5 year maturity left on them were at or near 5% (hard to be exact here), then yes - a 5% coupon bond in the secondary market given that interest rate invironment would sell at or near par.
Nick
American Investment Training
Does the yield to maturity of a bond assume that the interest I recive during the life of the bond, untilk maturity, is invested at the same rate of return of the bond, the coupon rate, or is independent of that? Assume that I bought the bond at par and its life was 10 years and I held it to maturity.
Thanks' Irv
Does the yield to maturity of a bond assume that the interest I recive during the life of the bond, untilk maturity, is invested at the same rate of return of the bond, the coupon rate, or is independent of that? Assume that I bought the bond at par and its life was 10 years and I held it to maturity.
Thanks' Irv
Hello Irv. The yield to maturity is not based on any re-investment of interest payments. That would be impossible to price out at the time of purchase. A 10 year 6% bond bought at par would have a yield to maturity of 6%. That's it. In fact the maturity has nothing to do with that example I just did. A 20 year bond at par - same thing.
Reinvestmtn risk (the investing of your interest payments) is a huge factor with bonds and fixed income securities, but that is not reflected in the yield to maturity. It's really just a future risk that while very real, is not used in the initial pricing of the bond. Another reason is that bonds are priced on their merit to each other. Since all bonds have reinvestment risk (except 0 coupons), that risk is not priced in.
Nick Hunter
American Investment Training
More on Bond Yields
plz tell me can we get $1075. i got each and everything except $1075. how can we calculate it?
how we got $1075? i got each and everything except $1075 how can i calculate it? plz how we gor $1075. plz tell me it in an easy way.
It is the median price between par $1000 and the premium paid $1150. You add those 2 together and divide by 2. The yearly interest of $50 is the 5% coupon rate paid to par.
Nick
American Investment Training
Finance Glossary
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