Chapter 7: Interest Rates and Bond Valuation, Part II

Transcription

1 Chapter 7: Interest Rates and Bond Valuation, Part II Faculty of Business Administration Lakehead University Spring 2003 May 15, 2003 Outline 7A-C Review Questions 7.2 More on Bond Features 7.3 Bond Ratings 7.4 Some Different Types of Bonds 7.5 Bond Markets 7.6 Inflation and Interest Rates 7.6 Determinants of Bond Yields 1

2 Review Questions on Duration 1. Explain the concept of duration. 2. You are managing a bond portfolio following a policy of interest rate anticipation. You think that rates have bottomed and are likely to rise. Which bonds are more attractive for new purchases, those with a 10-year duration or those with a 3-year duration? 3. Calculate the duration of a 7-year bond with a 9 percent coupon rate and a yield of 6 percent. 2 Review Questions on Callable Bonds 1. Must callable bonds always pay higher coupon rates than similar non-callable bonds? 2. True of False? The smaller the call premium, the larger must the coupon rate of a callable bond be if the bond is to be sold at par. Note: Call price = Face value + Call premium CP = F + cp. (In the textbook, CP call premium.) 3

3 Review Questions on Callable Bonds 3. Atfan, Inc., has an outstanding callable bond issue with 15 years left until maturity, F = $1,000 and a 10 percent coupon rate. This issue must be called now or never. If it is called, it will be replaced with a non-callable issue that has a coupon rate of 6 percent, equal to the current interest rate. The call premium is $180 per bond. Should Atfan refund its outstanding bond issue? What is the NPV of the refunding? For what interest rate would Aftan be indifferent to refunding or not? 4 Net Present Value of Refunding Suppose a callable bond with T years left until maturity has a coupon rate i c, a call premium cp and suppose that the current market interest rate is y. If the bond issue is not refunded, the firm will make T interest payments of i c F (per bond). The present value of these payments is i c F y ( ( ) ) 1 T. 1 + y 5

4 Net Present Value of Refunding If the bond issue is refunded and replaced with a non-callable issue (sold at par, with T years to maturity), the firm will make T interest payments of yf. The present value of these payments is ( ( ) ) yf 1 T. y 1 + y Interest savings from refunding the issue are then i c F y ( ( 1 ) ) T 1 + y yf y ( ( 1 ) ) T 1 + y = (i c y)f y ( ( ) ) 1 T. 1 + y 6 Net Present Value of Refunding When refunding, the firm pays F + cp to each callable-bond holder but also receives F from each buyer of the new issue. The net cost of refunding the issue is then F + cp F = cp. Therefore, the net present value of refunding the issue is ( ( ) ) (i c y)f 1 T cp. y 1 + y 7

5 Review Questions on Callable Bonds 4. SPS Corp. has decided to finance its expansion with a 20-year bond issue. The current interest rate is 7 percent. In one year, there is an equal chance that the interest rate will either be 6 percent or 8 percent. If this is a callable issue and the call premium to be paid is $80 per bond, what does the coupon rate have to be for the bond to sell at par? Bond Ratings Bond ratings only concern the possibility of default, they do not address interest rate risk issues. Highly rated bonds may be very sensitive to changes in interest rates. Bonds rated AAA are of the highest credit quality, bonds rated BBB are of adequate quality. Bonds rated below BBB are called junk, or high-yield, bonds. 9

6 7.6 Inflation and Interest Rates Real versus Nominal Rates Nominal rates are rates before inflation. Real rates are rates after adjusting for inflation. What is inflation? Inflation and Interest Rates Suppose an asset provides a nominal return of 10% annually and, at the same time, the annual inflation rate is 5%. $100 invested in this asset will grow to $110, but this amount of money won t purchase the same quantity of goods as it would have a year earlier. Inflation erodes purchasing power. 11

7 7.6 Inflation and Interest Rates With an inflation rate of 5%, the price of goods in a given year are 1.05 times what they were one year earlier, and thus what could have been purchased with $1 a year earlier now requires $1.05. Let p 0 denote the price of one green pea today. The quantity of green peas that can be purchased today with $100, denoted q 0, is then q 0 = 100 p Inflation and Interest Rates Due to inflation, the price of a pea will be 1.05p 0 next year, and thus $110 will then buy green peas. q 1 = p 0 Hence, in real terms, i.e. in terms of green peas, the return from investing $100 in the asset is q q 0 q 0 = 110/1.05p 0 100/p 0 100/p 0 =

8 7.6 Inflation and Interest Rates More generally, let R denote the nominal return on an investment, let h denote the inflation rate and let r denote the real return. Then r = 1 + R 1 + h 1. That is, (1 + r)(1 + h) = 1 + R 1 + r + h + rh = 1 + R, and thus r = R h rh Inflation and Interest Rates Since r and h are usually small fractions, the term rh is often neglibible and thus r can be approximated with r R h. 15

9 7.7 Determinants of Bond Yields Short-term and long-term interest rates are usually different. The term structure of interest rates tells us what nominal interest rates are on default-free, pure discount bonds of all maturities. When long-term rates are higher than short-term rates, the term structure is upward sloping. When long-term rates are lower than short-term rates, the term structure is downward sloping. The term structure can also be humped, i.e. increasing and then decreasing Determinants of Bond Yields The term structure of interest rates has three basic components: Real Rate of Interest: Does not really affect the shape of the term structure, mostly affects the overall level of interest rates. Inflation Premium: Future inflation stongly affects the shape of the term structure. Interest Rate Risk Premium: Interest rate risk increases with time to maturity. 17

10 7.7 Determinants of Bond Yields Whether the term structure is increasing or decreasing mostly depends on the expected increase in inflation. The term structure will be decreasing if inflation is expected to decrease strongly. Note, however, that the term structure can be increasing even if inflation is expected to decrease. If, on the other hand, inflation is expected to increase, then the term structure is necessarily increasing. 18 The Yield Curve The Canada Yield Curve plots the yield on Canada bonds in terms of their time to maturity. This curve is about coupon-paying bonds. The Canada yield curve is usually identical to the term structure of interest rates. 19