# Valuation Bonds

After bonds are issued, they are rarely negotiated at their par value ($1000) in the secondary market because interest rates are always changing. Some bonds are sold at premium prices and others at discounted prices. The market price of a bond is determined using the bond’s coupon payment, the principal repayment, and the investor’s required rate of return.

Using the time value of money this stream of future interest payments and repay of the principal is discounted from the return rate required by the investor or the market’s current interest rate at the current value of money.

The majority of corporate bonds pay their interest every six months, which means that the coupon rate is halved and the length of time to maturity is multiplied by 2 to convert it to six-month periods. Using this modification the bonds price is easily determined using Microsoft Excel.

Which is the price of a bond that has a 10% coupon rate, that pays interests every six months, and that has a 3 year maturity period? The required rate of return by the investor for this bond is 6%.

A coupon at 10%, payable every semester has as result a coupon payment of $50 for every six-month period, and the annual 6% of the discount rate is divided into a 3% for six-month periods until maturity.

Use Excel to find the bond price, click on “PV” in the right hand box, and enter data as illustrated:

- RNTE 0.03

NPER 6

PMT 50

FV 1,000

TYPE 0

Formula Result = 1,108.34

The bond price is subject to its coupon payment, market rates of interest or investors required rate of return, risk of the bond, and the length of time to maturity. If you compare the price of a US Treasury Note with the same coupon rate and maturity as that of a corporate bond, notice the difference in price.

Treasury notes are negotiated at higher prices than those of corporate bonds because there is a greater risk of default with bonds. That is why prices are estimated charging them with the highest discount rate (or yield-to-maturity). Then you require of a greater coupon yield (and required rate of return), in the corporate bond so as to assume a greater risk of default.

This description confirms why an AAA-rated corporate bond is negotiated at higher prices than the BBB-rated corporate bond if the coupon and its maturity are similar. The difference in yield between an AAA-Y, a BBB-rated bond is referred to as an excess yield to which issuers must pay for the extra grade of credit risk.

Bond prices fluctuate depending on the investors assessments of the bonds risk. This relation can synthesized in the following ways: while greater risks the bond has, higher the yield, and lower the market price.