CHAPTER FOURTEEN BOND PRICES AND YIELDS
CHAPTER OVERVIEW
This chapter presents a thorough discussion of the various types of bonds, bond characteristics, determinants of bond risk, bond ratings, and the pricing and yield calculations of various types of bonds.
LEARNING OBJECTIVES
After studying this chapter, the student should have a thorough understanding of the pricing, characteristics, and risk determinants of bonds. The student should be able to calculate yields and prices of various types of bonds and be able to identify factors used by the rating agencies in rating bonds.
Presentation of Chapter Material
1. Bond Characteristics Key characteristics of bonds are displayed in PPT 14-2. Prices that are quoted in the financial pages do not contain accrued interest. Most pricing examples that we use in finance also do not include discussion of accrued interest. Actual transaction prices will include any interest that has accrued since the last coupon payment. The key provisions for a bond are outlined in the indenture of the bond.
PPT 14-2 Bond Characteristics
The major issuers of bonds are listed in 14-3 along with a few examples of innovative bond structures. Samples of bond pricing are displayed in PPT 14-4 and 14-5.
PPT 14-3 Different Issuers of Bonds PPT 14-4 Figure 14.1 Listing of Treasury Issues PPT 14-5 Figure 14.2 Corporate Bond Listings
A list of major bond provisions is contained in PPT 14-6. Secured bonds are backed by assets of the corporation that serve as collateral for the bond. Unsecured bonds, referred to as debentures, have no specific assets that serve as collateral. A callable bond gives the issuing corporation the right to call the bond back from the bondholders. Call is typically delayed and there is a penalty or premium that the issuing corporation must pay to recall the bonds. Putable bonds contain an option that allows the bondholder to put the bond back on the issuer. Sinking funds require some systematic repayment of the principal. PPT 14-7 displays principal and interest payments on a treasury inflation protected security
PPT 14-6 Provisions of Bonds PPT 14-7 Table 14.1 Principal and Interest Payments for
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Treasury Inflation Protected Security
2. Bond Pricing The bond pricing equation and a sample calculation are presented in PPT 14-8 and PPT 14-9. The concept of yield to maturity can be related to prior work the students have done by equating it to the IRR. The yield to maturity is simply the discount rate that equates the present value of the cash flows from the bond to its current price.
PPT 14-8 Bond Pricing PPT 14-9 Price: 10 yr, 8% Coupon, Face=$1000
The relationship between bond prices and yields along with a graph of the relationship are presented in PPT 14-10 and 14-11. Table 14.2 shows bond price calculations for bonds of various maturities at different yields to maturity.
PPT 14-10 Bond Prices and Yields PPT 14-11 Figure 14.3 The Inverse Relationship Between Bond Prices and Yields PPT 14-12 Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually
3. Bond Yields Yield to maturity is described in PPT 14-13. The yield to maturity is the interest rate that makes the present value of the bond’s payments equal to its price. PPT 14-14 presents an example of calculation of semiannual yield to maturity.
PPT 14-13 Yield to Maturity PPT 14-14 Yield to Maturity Example
Alternative measures of yield are presented in 14-15. The bond equivalent yield is extensively used in industry. The difference between the bond equivalent yield and the effective annual yield is the assumption of compounding with the effective annual yield. The current yield is generally reported in financial press. It only considers the income and current market price. It does not consider capital gains or losses that are implicit in the yield to maturity. An example of a callable security is shown in PPT 1416 and 14-17
PPT 14-15 Yield Measures PPT 14-16 Figure 14.4 Bond Prices: Callable and Straight Debt PPT 14-17 Example 14.4 Yield to Call
Actual or realized yield on a bond depends on reinvestment return and on any changes in price if the bond is sold before maturity. Reinvestment return and price move in opposite directions. If rates increase, reinvestment return will be higher than what is implied in the bond’s yield to maturity. The
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market price of the bond will fall if rates increase. Figure 14.6 shows how the value of discount and premium bonds approaches the par value over maturity
PPT 14-18 Realized Yield versus YTM PPT 14-19 Figure 14.5 Growth of Invested Funds PPT 14-20 Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds
4. Bond Prices over Time The formula for calculation of a single period holding-period return and an example are presented in PPT 14-21 and PPT 14-22. The example assumes a six-month holding period, so the return that is calculated is a six-month return. Figure 14.7 traces the value of a zero-coupon bond as it approaches maturity.
PPT 14-21 Holding-Period Return: Single Period PPT 14-22 Holding-Period Return Example PPT 14-23 Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to Maturity of 10%
5. Default Risk and Bond Pricing The major companies that provide ratings on bond are listed in PPT 14-24. The rating systems contain major and sub-categories that allow for differentiation in the major categories. The highest four major categories are labeled as investment grade. Bonds that have ratings in lower major categories are referred to as speculative grade or junk bonds.
PPT 14-24 Default Risk and Ratings PPT 14-25 Figure 14.8 Definitions of Each Bond Rating Class
PPT 14-26 lists the major factors that determine a bond's rating. The highest rated firms have high levels of profitability, high levels of cash flow to debt, high levels of coverage and liquidity ratios and low levels of financial leverage.
PPT 14-26 Factors Used by Rating Companies
Table 14.3 displays median ratio values for bonds ratings categories from AAA to CCC. PPT 14-28 shows how coverage ratios can be used to predict safety or financial difficulty.
PPT 14-27 Table 14.3 Financial Ratios and Default Risk by Rating Class, Long-Term Debt PPT 14-28 Figure 14.9 Discriminant Analysis
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PPT 14-29 contains a list of factors that can be used in protection against default. Sinking funds can prevent a crisis at maturity since they require the firm to systematically repay the principal. The larger cash flow requirements of a sinking fund can substantially reduce coverage and cash flow ratios prior to maturity and may not serve their intended purpose for all issues. Subordination of future debt and dividend restrictions serves to protect existing creditors. Collateral provides the protection of asset value in case of default. Actual provisions on a callable bond are displayed in PPT 14-30.
PPT 14-29 Protection Against Default PPT 14-30 Figure 14.10 Callable Bond Issue by Mobil
The relationship between yield and default risk is referred to as the risk structure of interest rates. Default premiums on bonds generally follow rating categories. The spreads or differences between the yields on the various categories vary over the business cycle.
PPT 14-31 Default Risk and Yield PPT 14-32 Figure 14.11 Yields on Long-Term Bonds, 1954 – 2006
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