1. Ch 7. Interest Rate and Bond Valuation

2. 1. Goals To discuss the types of bonds
To understand the terms of bonds
To understand the types of risks to issuers and investors
To understand the changes of value

3. I. Bonds
A bond: a long term contract under which a borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond.
E.g) 3 year corporate bond with 6% coupon rate.
1. Characteristics of Bonds
Face value or Par value: the stated face value of the bond. Ex) $1000 or multiples of $1000
Coupon rate: coupon payment / par value. (usually coupon is paid semiannually)

4. (3) Maturity: a specific date on which the par value of the bond must be paid.
(4) Yield to Maturity (YTM): the rate required in the market on a bond.

5. 2. Bond valuation:
It is based on the cash flows to investors.
Two types of cash flows: Coupon payment & Par value
Bond value = discounted coupon payments (PV of annuity) + discounted par value

6. Formula:
Yield To Maturity (YTM):
The discount rate (rd) that will match current market bond price with the above formula.
Promised rate of return that investors will receive if all promised payments are made.

7. E. g) 5 year bond with 6% coupon rate. Coupon is paid annually
E.g) 5 year bond with 6% coupon rate. Coupon is paid annually. If yield to maturity is 10%, what is the bond price?
60*(1-1/(1.1^5))/ /(1.1^5)
E.g) 5 year bond with 6% coupon rate. Coupon is paid semi-annually. If yield to maturity is 10%, what is the bond price?
30*(1-1/(1.05^10))/ /(1.05^10)

8. E. g) 6 year bond with 5% coupon rate
E.g) 6 year bond with 5% coupon rate. Currently, it is priced at $1100 in the market. Coupon is paid annually. What is yield to maturity of the bond?

9. Coupon rate and Bond price:
(1) if the coupon rate equals to discount (interest) rates, a bond price is par value
(2) if the coupon rate > discount (interest) rates, premium bond
(3) if the coupon rate < discount (interest) rates, discount bond
(4) As maturities approach, the premium/discount bonds’ prices approach to par value

10. Yield to Call: The rate of return earned on a bond if it is called before its maturity date. (in the formula, par value is replaced with call price).
Current Yield = annual coupon payment/ current bond price
Bond valuation with semi-annual coupon rate.
3. Riskiness of Bonds
Interest rate risk:
The risk of a decline in a bond’s price due to an increase in interest rates.

11. The longer the maturity of the bond, the greater the interest rate risk.
The lower coupon rate, the greater the interest rate risk.
2) Reinvestment Rate Risk:
The risk that a decline in interest rates will lead to a decline in income from a bond portfolio.
The shorter maturity, the higher the reinvestment rate risk.

12. 4.The indenture: written agreement between the corporation and the lender detailing terms of debt issue.
Basic terms of bonds.
Total amounts of bonds issued.
Description of property used as security.
Repayment arrangements.
Call provisions.
Protective covenants.

13. 1) form of bond issue
Registered form: the form of bond issue in which the registrar of the company records ownership of each bond; payment is made directly to the owner of record.
Bearer form: the form of bond issue in which the bond is issued without record of the owner’s name; payment is made to whomever holds the bond.

14. (2) Security: collateral (e. g. stocks) and mortgages (e. g
(2) Security: collateral (e.g. stocks) and mortgages (e.g. real property) used to protect the bondholder.
- debenture: an unsecured debt, usually with a maturity of 10 years or more.
- note: an unsecured debt, usually with a maturity under 10 years.
- blank mortgage pledges all property owned by the company.
(3) Seniority: senior debt holders have priority to receive money back.

15. (4) Repayment: Bond may be repaid in part or in entirety before maturity.
- sinking fund: an account managed by the bond trustee for early bond redemption – buying bonds from market or call back bonds.
(5) Call provision: A provision that gives the issuer the right to redeem the bonds prior to the maturity date. In this case, call premium (difference between call price and par value) is offered. But a bond is often not callable until several years after issues (deferred call provision). This bond are said to be “ call protected bond.”

16. “Make-whole” call: bond holders receive approximately what the bond is worth if it is called.
(6) Protective covenant: a part of the indenture limiting certain actions that might be taken during the term of the loan, usually to protect the lender’s interest.
-negative covenant (thou shalt not): limiting or prohibiting actions a company may take.
-positive covenant (thou shalt): specifying actions that a company agrees.

17. 5. Bond rating
Two leading bond-rating firms: Moody’s and Standard &Poor’s.
Bond rating only concerns the possibility of default.
Investment-graded rating is BBB. Bonds below BBB is called junk bonds.
5B or split rating: one agency gives BBB and another one gives BB.
Fallen angels: bonds down-graded to junk bonds.

18. 4. Other types of bonds, depending on characters
(1) Government bonds: No default and highly liquid.
- Treasury notes, bills and bonds – state tax exemption.
- Municipal bonds (state or local) – federal tax exemption.
(2) Zero Coupon Bonds: A bond that pays no annual interest but is sold at a discount below par. Any bond originally offered at a price significantly below its par value is called an original issue discount (OID) bond.
- For tax purpose, the issuer would deduct interest every year – implicit interest is determined by amortizing the loan. Table 7.2.

19. E. g) $1000 face value zero coupon bond. 5 year maturity is assumed
E.g) $1000 face value zero coupon bond. 5 year maturity is assumed. Semi-annual coupon payment is assumed. YTM is 14%. Initial price is $ After one year, bond value is $ (=1000/(1.07^8)). Implicit interest at the first year is $73.66 (= ). At the second year, interest is = here (666.34=1000/(1.07^6)).

20. (3) Floating rate bond: bonds whose coupon payment will vary with market rates such as T-Bill or Bond rates or inflation. e.g) Treasury Inflation-Protected Securities (TIPS)-coupon payment is adjusted with inflation.
(4) Convertible bond: A bond that is exchangeable for common stocks of issuing firm at a fixed price.
(5) Income bond: A bond that pays interest only if the interest is earned.
(6) Putable bond: a bond with provisions that allow its investor to sell it back to the company prior to maturity at a pre-arranged price.

21. 7) warrant: the right to purchase shares of stock in the company at a fixed price.
8) CoCo (coupon payment) or NoNo bonds (no coupon payment)– contingent convertible, putable, callable, subordinated bonds.
9) Sukuk – Islamic law does not permit charging or paying riba or interests. Islamic bond (sukuk) having partial ownership in a debt or asset has been created. E.g) there is a binding promise to repurchase a certain asset by the issuer at maturity.

22. 6. Bond market
Bonds are traded in OTC (over the counter) market.
Trading information of corporate bonds is reported to TRACE (trade report and compliance engine).
Treasury price is quoted at the percentage of face value or 32nd (Treasury)

23. - bid price: a dealer is willing to pay for a security.
- asked price: a dealer is willing to take (sell) a security.
- bid-ask spread: difference between the bid price and the asked price.
- clean price: the price of bond net of accrued interest. It is the price typically quoted.
- dirty price: the price of a bond including accrued interest, also known as the full or invoice price. This is the price the buyer actually pays.

24. E. g) Suppose you buy a bond with a 12% annual coupon rate
E.g) Suppose you buy a bond with a 12% annual coupon rate. You actually pay $1,080. Coupon is paid semiannually. When you buy this bond, next coupon payment is due in 4 months.
Dirty price = $1,080.
Clean price = 1,080 – 20 (=60*2/6)

25. 7. Inflation and interest rate
Inflation reduces the purchasing power of currency. Quoted rate is nominal rate.
1) Fisher effect
(1+R)=(1+r)*(1+h)
R: nominal interest rate not adjusted for inflation
r: real interest rate adjusted for inflation
H: inflation rate

26. E. g) if nominal rate is 15. 50%. Inflation rate is 5%
E.g) if nominal rate is 15.50%. Inflation rate is 5%. What is the real rate?
=(1+r)*(1+0.05)
r=10%
2) Present Value Calculation
Discount nominal cash flows at a nominal rate or discount real cash flows at a real rate.

27. E.g) You want to withdraw $25000 (purchasing power) each year for next three years. Currently inflation rate is 4%. What is the present value of this withdrawal plan if a nominal rate is 10%?
- Discount nominal cash flows by a nominal rate.
Considering a 4% inflation,
C1 = 25000*1.04
C2=25000*1.04^2 and C3=25000*1.04^3

28. Using a 10% nominal rate, PV= C1/1. 1 + C2/(1. 1^2) + C3/(1
- Discounting real cash flows by a real discount rate.
Estimating a real interest rate.
(1+0.1) =(1+r)*(1+0.04)
r=0.0577
PV = 25000/ /(1.0577^2)+25000/(1.0577^3)
=25000*(1-1/( )^3)/0.0577 =

29. Using a growing annuity,
PV = 26000*[1-(1.04/1.1)^3]/( )
= 67,111.65

30. 8. Determinants of bond yield
Term structure of interest rates: relationship between nominal interest rates on default-free, pure discount securities and time to maturity.
1) Treasury yield curve
= real interest rate + inflation premium + interest rate risk premium
(inflation premium: compensation for expected future inflation. Interest rate risk premium: compensation for bearing interest rate risk)

31. 2) Corporate bond yield curve
= real interest rate + inflation premium + interest rate risk premium + default risk premium + taxability premium + liquidity premium
(Default risk premium: compensation for the possibility of default. Taxability premium: compensation for unfavorable tax status. Liquidity premium: compensation for lack of liquidity)