McGraw-Hill/Irwin

CHAPTER 10

Bond Prices and Yields

© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.

10.1 BOND CHARACTERISTICS

10-2

Bond Characteristics Face or par value Coupon rate – Zero coupon bond Compounding and payments – Accrued Interest 

Annual coupon pmnt

 2

Days from last pmnt Days between pmnts

Indenture: contract between bond issuer and bond holder 10-3

Treasury Notes and Bonds T-Note maturities range up to 10 years T-bond maturities range from 10 – 30 years Bid and ask price – Quoted in points and as a percent of par Accrued interest – Quoted price does not include interest accrued 10-4

Figure 10.1 Listing of Treasury Issues 10-5

Corporate Bonds Most bonds are traded over the counter (bond dealers linked by computer system; thin market) Registered (info on bond owner kept by issuer) Bearer bonds (more common in Europe, not US) Call provisions (issuing firm can pay off bond early) Convertible provision (bondholder can convert to common stock) Put provision (putable bonds – bondholder can extend maturity) Floating rate bonds Preferred Stock (promises a dividend stream, but failure to pay is not bankruptcy merely accumulates to be paid when funds available in future) 10-6

Figure 10.2 Investment Grade Bonds 10-7

Other Domestic Issuers Federal Home Loan Bank Board Farm Credit Agencies Ginnie Mae Fannie Mae Freddie Mac 10-8

Innovations in the Bond Market Reverse floaters (coupon rate falls when interest rates are rising!) Asset-backed bonds (income from a specific group of assets pays interest on bond. Walt Disney films, e.g.) Pay-in-kind bonds (Bond issuer can pay interest in cash or in additional bonds) Catastrophe bonds (payments contingent on whether an event occurs e.g. earthquake near Tokyo Disneyland) Indexed bonds – TIPS (Treasury Inflation Protected Securities) 10-9

10.2 BOND PRICING

10-10

Bond Pricing

P

B



t T

  1 ( 1

C

+

r

t

)

T

+

Par Value

( 1 +

r

)

T T

r P B = C t = Price of the bond interest or coupon payments T = number of periods to maturity = semi-annual discount rate or the semi-annual yield to maturity 10-11

Price: 10-yr, 8% Coupon, Face = $1,000

P

 40

t

20   1 1  1 .

03 

t P

 $ 1 , 148 .

77 + 1000 ( 1 .

03 ) 20 C t P r T = $40 (Semi-Annual payment, $80/1) = $1000 = 20 periods (10 years or 20 half years) = 3% (Semi-Annual; rate per ½ year) 10-12

10.3 BOND YIELDS

10-13

Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship When yields get very high the value of the bond will be very low When yields approach zero, the value of the bond approaches the sum of the cash flows 10-14

Yield to Maturity (YTM) YTM is the discount rate (r) that makes the present value of a bond’s payments equal to its price 8% coupon, 30-year bond selling at $1,276.76: 10-15

Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually) 10-16

Figure 10.3 The Inverse Relationship Between Bond Prices and Yields 10-17

Alternative Measures of Yield Current Yield (Coupon Payment/Price) Yield to Call – Call price replaces par – Call date replaces maturity Holding Period Yield – Considers actual reinvestment of coupons – Considers any change in price if the bond is held less than its maturity 10-18

Holding-Period Return: Single Period

HPR = [ I + ( P 1 – P 0 )] / P 0

where

I

= interest payment

P 1

= price in one period

P 0

= purchase price 10-19

Yield to Maturity Example 950 

t

2 0   1 35 ( 1 +

r

)

t

+ 1000 ( 1 +

r

)

T

10 yr Maturity Coupon Rate = 7% Price = $950 Solve for r = semiannual rate r = 3.8635%

10-20

Yield Measures Bond Equivalent Yield 7.72% = 3.86% x 2 Effective Annual Yield (1.0386) 2 - 1 = 7.88% Current Yield Annual Interest / Market Price $70 / $950 = 7.37 % Yield to Call 10-21

Figure 10.4 Bond Prices: Callable and Straight Debt 10-22

Realized Yield versus YTM Reinvestment Assumptions – YTM will equal the realized return over the life of the bond if reinvestment of all funds is at the YTM rate Holding Period Return – Changes in rates affect returns – Reinvestment of coupon payments – Change in price of the bond 10-23

Figure 10.5 Growth of Invested Funds 10-24

10.4 BOND PRICES OVER TIME

10-25

Premium and Discount Bonds Premium Bond – Coupon rate exceeds yield to maturity – Bond price will decline to par over its maturity Discount Bond – Yield to maturity exceeds coupon rate – Bond price will increase to par over its maturity 10-26

Figure 10.6 Premium and Discount Bonds over Time 10-27

Figure 10.7 The Price of a Zero Coupon Bond over Time 10-28

10.5 DEFAULT RISK AND BOND PRICING

10-29

Default Risk and Ratings Rating companies – Moody’s Investor Service – Standard & Poor’s – Fitch Rating Categories – Investment grade – Speculative grade 10-30

Figure 10.8 Definitions of Each Bond Rating Class 10-31

Factors Used by Rating Companies Coverage ratios: Earnings/Fixed Costs Leverage ratios: Debt/Equity Liquidity ratios – Current Ratio: Current Assets/Current Liabilities – Quick Ratio: Current Assets Less Inventories/Current Liabilities Profitability ratios – Return on Assets: Earnings before Interest and Tax/Total Assets, aka EBIT/Total Assets – Return on Equity: Net Income/Equity Cash flow to debt 10-32

Protection Against Default Sinking funds: Firms save a bit each period to pay back principal, by buying back bonds each period.

Subordination of future debt Dividend restrictions Collateral.

– Mortgage bond – collateral is house – Collateral Trust Bond – collateral is securities held by firm – Equipment Obligation Bond – collateral is equipment (railroads) – General Debentures – unsecured; no specific collateral. In case of default, owners of these bonds are general creditors of firm.

10-33

Figure 10.9 Callable Bond Issued by Mobil 10-34

10.6 THE YIELD CURVE

10-35

Term Structure of Interest Rates Relationship between yields to maturity and maturity Yield curve - a graph of the yields on bonds relative to the number of years to maturity – Usually Treasury Bonds – Have to be similar risk or other factors would be influencing yields 10-36

Figure 10.10 Yields on Long-Term Bonds 10-37

Figure 10.11 Treasury Yield Curves 10-38

Theories of Term Structure Expectations – Long term rates are a function of expected future short term rates – Upward slope means that the market is expecting higher future short term rates – Downward slope means that the market is expecting lower future short term rates Liquidity Preference – Upward bias over expectations – The observed long-term rate includes a risk premium 10-39

Figure 10.12 Returns to Two 2-year Investment Strategies 10-40

Forward Rates Implied in the Yield Curve ( 1 +

y n

)

n

 ( 1 +

y n

1 )

n

1 ( 1 + ( 1 .

12 ) 2  ( 1 .

11 ) 1 ( 1 .

1301 )

f n

) For example, using a 1-yr and 2-yr rates Longer term rate, y(n) = 12% Shorter term rate, y(n-1) = 11% Forward rate, a one-year rate in one year = 13.01% 10-41

Figure 10.13 Illustrative Yield Curves 10-42

Figure 10.14 Term Spread 10-43