CHAPTER 14

Bond Prices and Yields

• Face or par value• Coupon rate– Zero coupon bond

• Compounding and payments– Accrued Interest

• Indenture

Bond Characteristics

Different Issuers of Bonds

• U.S. Treasury– Notes and Bonds

• Corporations• Municipalities• International Governments and Corporations• Innovative Bonds– Floaters and Inverse Floaters– Asset-Backed– Catastrophe

1 (1 )(1 )

T

TB tt

ParValueCPrr

PB = Price of the bond

C = interest or coupon paymentsT = number of periods to maturityr = semi-annual discount rate or the semi-annual yield to maturity

Bond Pricing

C = 40 (SA)P = 1000T = 20 periodsr = 3% (SA)

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

77.148,1$

)03.1(

1000

03.1

140

20

20

1

P

Pt

t

• 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

Bond Prices and Yields

Figure 14.3 The Inverse Relationship Between Bond Prices and Yields

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

Yield to Maturity

• Interest rate that makes the present value of the bond’s payments equal to its price

Solve the bond formula for r

1 (1 )(1 )

T

Ttt

BParValueCP

rr

Yield to Maturity Example

)1(1000

)1(35950

20

1 rrT

tt

10 yr Maturity Coupon Rate = 7%

Price = $950

Solve for r = semiannual rate r = 3.8635%

Yield Measures

Bond Equivalent Yield7.72% = 3.86% x 2

Effective Annual Yield(1.0386)2 - 1 = 7.88%

Current YieldAnnual Interest / Market Price$70 / $950 = 7.37 %

Yield to Call

Figure 14.4 Bond Prices: Callable and Straight Debt

Realized Yield versus YTM

• Reinvestment Assumptions• Holding Period Return– Changes in rates affect returns– Reinvestment of coupon payments– Change in price of the bond

Figure 14.5 Growth of Invested Funds

Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds

Holding-Period Return: Single Period

HPR = [ I + ( P0 - P1 )] / P0

whereI = interest paymentP1 = price in one period

P0 = purchase price

Holding-Period Return Example

CR = 8% YTM = 8% N=10 yearsSemiannual Compounding P0 = $1000

In six months the rate falls to 7%P1 = $1068.55

HPR = [40 + ( 1068.55 - 1000)] / 1000 HPR = 10.85% (semiannual)

Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to

Maturity of 10%

• Rating companies– Moody’s Investor Service– Standard & Poor’s– Fitch

• Rating Categories– Investment grade– Speculative grade/Junk Bonds

Default Risk and Ratings

Figure 14.8 Definitions of Each Bond Rating Class

• Coverage ratios• Leverage ratios• Liquidity ratios• Profitability ratios• Cash flow to debt

Factors Used by Rating Companies

Default Risk and Yield

• Risk structure of interest rates• Default premiums– Yields compared to ratings– Yield spreads over business cycles

Figure 14.11 Yields on Long-Term Bonds, 1954 – 2006