CH 10: Bond Prices and Yields

Bond Basics

Issued by a government or corporation to raise capital over a certain period of time.

A straight bond is an IOU that obligates the issuer of the bond to pay the holder of the bond:

• A fixed sum of money (Principal, par value or face value) at the maturity of the bond and sometimes

• Constant, periodic interest payment (coupons) during the life of the bond.

The lower the bond rating, the higher the coupon rate the issuer would have to pay.

Straight Bond Prices and Yield to Maturity

Price of a bond = PV of bonds coupon payments + PV of bonds face value

The yield to maturity (YTM) of a bond is the discount rate that equates today’s bond price with the present value of the FCF of the bond.

**Note that YTM in most cases is not equal to coupon rate.

YTM is the actual overall rate of return, whereas the coupon rate is used to calculate the annual interest amount.

Special Feature Bonds

Convertible bonds

Holders can convert the bond into a specified number of common shares in the issuing company.

Protects the principle on the downside but provides an opportunity to participate in the upside if the company’s stock is rising.

Like a bond with a call option.

Since it is an added benefit to investors, convertible bonds are generally issued at lower coupon rates compared to standard bond issues.

Benefits the issuer as they can pay lower coupon payments and can raise capital without immediately diluting shares

Mostly issued by companies experiencing high growth but with poor credit rating to entice investors.

Retractable bonds

Allow bondholders to redeem their bonds with the issuer at par before the maturity date.

Bondholders are protected from interest rate risk.

Pay lower coupon rates than standard bonds without the retractable feature.

Like a bond with a put option (Forces issuer to buy back the bond early when the holder no longer wants to hold the bond).

Callable bonds

Allows issuers to call or buy back the bond issue prior to the maturity date at a specified call price.

A call will generally occur when the market interest rates drop below the issued coupon rate so the issuer can reissue the bond at a lower coupon rate.

The issuer cannot call back the bond within the call protection period.

Due to the call risk, issuers have to compensate bondholders by paying a higher coupon rate.

Bonds are generally called back at the par value, and sometimes, issuers may pay a premium above the par value.

The earlier the call protection period ends compared to the maturity date, the higher the call price.

Some callable bonds have a make-whole provision. Under the provision, the issuer must call back the bond at the net present value (NPV) of the remaining scheduled coupon payments and the principle.

• NPV is calculated based on the market discount rate, not on the original coupon rate. Better for investors as the NPV is higher when the rate is lower.

• Can be called back at any time, whereas the traditional call can only be called after call protection period.

Yield to Call (YTC)

For callable bonds, YTM might not be useful since bondholders are not able to hold until maturity.

YTC:

• A yield measure that assumes a bond will be called at its earliest possible call date

• FV will be the call price, not the par value.

• Coupon payments are still calculated using par value.

Interest Rate Risk

Bondholders face interest rate risk, the possibility that changes in interest rates will result in losses in the bonds' value.

Bond prices move in the opposite direction to interest rate movements.

The yield earned or “realized” on a bond is called the realized yield over the holding period.

Realized yield is rarely exactly equal to the yield to maturity or coupon rate due to interest rate fluctuations.

Premium, Par, and Discount Bonds

Bonds are given names according to the relationship between the bonds selling price and its par value.

*Remember: CY PF (Can You Pass Finance?)

Premium bonds: If Coupon rate > YTM then Price > Face (par value)

Discount bonds: If Coupon rate < YTM then Price < Face (par value)

Par bonds: If Coupon rate = YTM then Price = Face (par value)

In general, when the coupon rate and YTM are held constant:

For premium bonds: The longer the term to maturity, the greater the premium over par value.

For discount bonds: The longer the term to maturity, the greater the discount from par value.

Quick Note on Bond Quotations

If you buy a bond between coupon payment dates, the price you pay will usually be more than the price you are quoted. You must compensate the seller for any accrued interest.

The convention is bond price quotes is to ignore accrued interest. Results in what is commonly called a clean price (i.e., a quoted price net of accrued interest).

The price the buyer actually pays is called the dirty price. (Accrued interest is added to the clean price.) (Dirty price is also known as the full price, or invoice price)

Malkiel’s Theorems