CHAPTER 6 – Valuing Bonds

Questions

1. What does a call provision allow the issuer to do, and why would they do it?

A call provision on a bond issue allows the issuer to pay off the bond debt early at a cost of the principal plus any call premium. Most of the time a bond issuer is called, it is because interest rates have substantially declined in the economy. The issuer calls the existing bonds and issues new bonds at the lower interest rate. This reduces the interest payments the issuer must pay each year.

2. List the differences between the new TIPS and traditional Treasury bonds.

Traditional Treasury bonds have a fixed principal and constant payments. Because the principal and coupon rate are fixed, interest rate changes in the economy cause the market price of the bonds to have large fluctuations. On the other hand, the principal of a TIPS increases with the rate of inflation. Similar to a T-bond, the TIPS has a constant coupon rate. However, since the principal of the TIPS increases over time, the interest payment increases over time. This inflation rate adjustment of a TIPS’ principal every six months reduces the amount of downward price change in the price of the bond when interest rates increase.

3. Explain how mortgage-backed securities work.

A large amount of home mortgages are purchased and pooled together. The home owners pay interest and principal monthly on their mortgages. Bonds are issued from the pool of mortgages, using the mortgages as collateral. The interest payments and bond principal payments for these mortgage-backed securities (MBS) originate from the mortgage borrowers and flow through the pool of mortgages. As the home owners pay off their mortgages over time, the MBS are also paid.

4. Provide the definitions of a discount bond and a premium bond. Give examples.

A discount bond is simply a bond that is selling below its par value. It would be quoted at a price that is less than 100 percent of par, like 99.05. A premium bond is a bond selling above its par value. Its price will be quoted as over 100 percent of par value, like 101.15. A bond becomes a discount bond when market interest rates rise above the bond’s coupon rate. A bond becomes a premium bond when market interest rates fall below the bond’s coupon rate.

5. Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zero coupon bond.

The 5 percent coupon bond pays annual interest of 5 percent of the bond’s par value. For $1,000 par value bond, this would be $50 per year. This interest might be paid in two payments of $25. The price of the coupon bond tends to stay near its par value. The zero coupon bond pays no interest payments. The bondholder earns a return from the increase of the bond’s market price over time. The bond’s price is initially much lower than its par value. When the zero coupon bond finally matures, the par value is paid.

6. All else equal, which bond’s price is more affected by a change in interest rates, a short-term bond or a longer-term bond? Why?

All else equal, a long-term bond experiences larger price changes when interest rates change than a short-term bond. A bond’s price is the present value of all its cash flows. Changes in the discount rate (the interest rate) impact present values more for cash flows that are further out in time.

7. All else equal, which bond’s price is more effected by a change in interest rates, a bond with a large coupon or a small coupon? Why?

The price of the bond with the small coupon will be impacted more by a change in interest rates than the price of the large coupon bond. For a small coupon bond, the cash flows are weighted much more toward the maturity date because of the small interest payments. The large coupon bond has high interest payments, many occur soon. These higher cash flows made earlier dampen the impact of interest rate changes because those changes in the discount rate impact the earlier cash flows to a lesser degree than the later cash flows.

Problems

6-1 Interest Payments Determine the interest payment for the following three bonds: 3 ½ percent coupon corporate bond (paid semi-annually), 4.25 percent coupon Treasury note, and a corporate zero coupon bond maturing in 10 years. (Assume a $1,000 par value.)

3 ½ percent coupon corporate bond (paid semi-annually): ½ × 3.5% × $1,000 = $17.50

4.25 percent coupon Treasury note: ½ × 4.25% × $1,000 = $21.25

corporate zero coupon bond maturing in 10 years: 0% × $1,000 = $0

6-2 Interest Payments Determine the interest payment for the following three bonds: 4 ½ percent coupon corporate bond (paid semi-annually), 5.15 percent coupon Treasury note, and a corporate zero coupon bond maturing in 15 years. (Assume a $1,000 par value.)

4 ½ percent coupon corporate bond (paid semi-annually): ½ × 4.5% × $1,000 = $22.50

5.15 percent coupon Treasury note: ½ × 5.15% × $1,000 = $25.75

corporate zero coupon bond maturing in 10 years: 0% × $1,000 = $0

6-3 Time to Maturity A bond issued by Ford on May 15, 1997 is scheduled to mature on May 15, 2097. If today is November 16, 2008, what is this bond’s time to maturity?

May 15, 2097 minus November 16, 2008 = 88 years and 6 months

6-4 Time to Maturity A bond issued by IBM on December 1, 1996 is scheduled to mature on December 1, 2096. If today is December 2, 2007, what is this bond’s time to maturity?

December 1, 2096 minus December 2, 2007 = 89 years

6-5 Call Premium A 7 percent corporate coupon bond is callable in five years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond?

principal + call premium = $1,000 + 7%×$1,000 = $1,070

6-6 Call Premium A 6.5 percent corporate coupon bond is callable in ten years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond?

principal + call premium = $1,000 + 6.5%×$1,000 = $1,065

6-7 TIPS Interest and Par Value A 2 ¾ percent TIPS has an original reference CPI of 185.4. If the current CPI is 210.7, what is the current interest payment and par value of the TIPS?

par value = 210.7/185.4 × $1,000 = $1,136.46

interest payment = ½ × 2.75% × $1,136.46 = $15.63

6-8 TIPS Interest and Par Value A 3 1/8 percent TIPS has an original reference CPI of 180.5. If the current CPI is 206.8, what is the current interest payment and par value of the TIPS?

par value = 206.8/180.5 × $1,000 = $1,145.71

interest payment = ½ × 3.125% × $1,145.71 = $17.90

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