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Chapter 14. Bond Prices and Yields. Bond Characteristics. Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture. Different Issuers of Bonds. U.S. Treasury Notes and Bonds Corporations Municipalities

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chapter 14

Chapter 14

Bond PricesandYields

bond characteristics
Bond Characteristics
  • Face or par value
  • Coupon rate
    • Zero coupon bond
  • Compounding and payments
    • Accrued Interest
  • Indenture
different issuers of bonds
Different Issuers of Bonds
  • U.S. Treasury
    • Notes and Bonds
  • Corporations
  • Municipalities
  • International Governments and Corporations
  • Innovative Bonds
    • Indexed Bonds
    • Floaters and Reverse Floaters
provisions of bonds
Provisions of Bonds
  • Secured or unsecured
  • Call provision
  • Convertible provision
  • Put provision (putable bonds)
  • Floating rate bonds
  • Sinking funds
default risk and ratings
Default Risk and Ratings
  • Rating companies
    • Moody’s Investor Service
    • Standard & Poor’s
    • Duff and Phelps
    • Fitch
  • Rating Categories
    • Investment grade
    • Speculative grade
factors used by rating companies
Factors Used by Rating Companies
  • Coverage ratios
  • Leverage ratios
  • Liquidity ratios
  • Profitability ratios
  • Cash flow to debt
protection against default
Protection Against Default
  • Sinking funds
  • Subordination of future debt
  • Dividend restrictions
  • Collateral
bond pricing
Bond Pricing

PB = Price of the bond

Ct = interest or coupon payments

T = number of periods to maturity

y = semi-annual discount rate or the semi-annual yield to maturity

solving for price 10 yr 8 coupon bond face 1 000

20

1

1

=

+

P

40

1000

B

t

20

(1+.03)

(1+.03)

t

=1

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

PB = $1,148.77

Ct = 40 (SA)

P = 1000

T = 20 periods

r = 3% (SA)

bond prices and yields
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
yield to maturity
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

yield to maturity example
Yield to Maturity Example

10 yr Maturity Coupon Rate = 7%

Price = $950

Solve for r = semiannual rate

r = 3.8635%

yield measures
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 %

realized yield versus ytm
Realized Yield versus YTM
  • Reinvestment Assumptions
  • Holding Period Return
    • Changes in rates affects returns
    • Reinvestment of coupon payments
    • Change in price of the bond
holding period return single period
Holding-Period Return: Single Period

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

where

I = interest payment

P1 = price in one period

P0 = purchase price

holding period example
Holding-Period Example

CR = 8% YTM = 8% N=10 years

Semiannual Compounding P0 = $1000

In six months the rate falls to 7%

P1 = $1068.55

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

HPR = 10.85% (semiannual)

holding period return multiperiod
Holding-Period Return: Multiperiod
  • Requires actual calculation of reinvestment income
  • Solve for the Internal Rate of Return using the following:
    • Future Value: sales price + future value of coupons
    • Investment: purchase price