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Chapter 10

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Chapter 10

Bond Prices and Yields

- Face or par value
- Coupon rate
- Zero coupon bond

- Compounding and payments
- Accrued Interest
- invoice price versus quoted price

- Indenture

- Secured or unsecured (debenture)
- Call provision
- refunding
- call price
- deferred callable bond
- coupon rates and promised ytm at issuance

- Convertible provision
- conversion ratio
- market conversion value
- conversion premium
- coupon rate & ytm at issuance
- Convertible example
- conversion ratio = 25
- market price of stock = $42
- callable bond price = $1150

- Put provision (putable bonds)
- coupon rate & ytm at issuance

- Floating rate bonds
- changing credit condition of issuer

- Sinking funds

- Pay in kind bonds (pik)
- reverse floaters
- indexed bonds (TIPS -Treasury Inflation Protection bonds)

- Rating companies
- Moody’s Investor Service
- Standard & Poor’s
- Duff and Phelps
- Fitch

- Rating Categories
- Investment grade
- Speculative grade

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

- Sinking funds
- Subordination of future debt
- Dividend restrictions
- Collateral
- mortgage bond
- equipment obligation
- collateral trust

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

20

1

1

=

+

P

40

1000

B

t

20

(1+.03)

(1+.03)

t

=1

PB = $1,148.77

Ct= 40 (SA)

P= 1000

T= 20 periods

r= 3% (SA)

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

Price

Yield

YTM = the discount rate that makes the present value of the bond’s promised payments equal to its price.

Bond is priced at $1067.95, it has a coupon rate of 9% paid semiannually, a par value of $1000, and 10 years to maturity. Find the bond’s ytm.

What is the current yield?

Bond is priced at $945.40 , it has a coupon rate of 6% paid semiannually, a par value of $1000, and 14 years to maturity. Find the bond’s ytm.

What is the current yield?

- Bond selling at par
- coupon = YTM = current yield

- Bond selling at a premium
- coupon > current > YTM

- Bond selling at a discount
- coupon < current < YTM

- Similar to YTM, but use time to first call date and call price as future value.
- Bond with 15 years to maturity, par of $1000, a coupon rate of 8% (paid semiannually), price of $1025, callable in 5 years at $1080. Find YTC.

- YTM will equal the realized return over the life of the bond if all payments are reinvested at an interest rate equal to the bond’s yield.
- Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $1067.10.

- Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $1067.10.
- What is its ytm?
- Realized compound yield if you reinvest at ytm?
- RCY if you reinvest at 3 percent?

- Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $1067.10. Note: ytm = 8%
- Suppose you hold the bond one year and interest rates decline to 7 percent. Calculate your HPR.
- Suppose instead that rates had risen to 9 percent. What is your HPR?

- Consider a 10 year Treasury strip with a yield of 5 percent and face of $10,000.
- Price = $6,139.13
- After one year (yield = 5%)
- P = $6,446.09
- Difference = implicit interest = $306.96
- If you sold the strip for $6,500, then you would have interest income of $306.96 and capital gain of $53.91

- 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

Yields

Upward Sloping

Downward Sloping

Maturity

- Expectations
- Liquidity Preference
- Upward bias over expectations

- Market Segmentation
- Preferred Habitat