1. 1 Bond Valuation Corporate Finance Dr. A. DeMaskey

2. 2 Learning Objectives  Questions to be answered: What is a bond? Who issues bonds? What are the key characteristics of bonds? How are bonds valued? What is the rate of return on a bond? What types of risk are bondholders exposed to?

3. 3 Types of Bonds  Treasury Bonds  Corporate Bonds  Municipal Bonds  Foreign Bonds

4. 4 Basic Terminology  Bond  Par Value  Coupon Interest Payment  Coupon Interest Rate  Maturity Date  Bond’s Market Rate of Interest, k d

5. 5 Financial Asset Valuation  PV= CF 1+k... + 1+k 1n 1 2 2 1 k n. 012n k CF 1 CF n CF 2 Value... ++ +

6. 6 Required Rate of Return  The discount rate (k i ) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk. k i = k * + IP + LP + MRP + DRP

7. 7 Default Risk  Risk that issuer will not make interest or principal payments. Increases required rate of return Bond ratings provide one measure of default risk Defaulting on bonds may result in bankruptcy and/or reorganization

8. 8  V kk B dd  $100$1, 1 000 1 110... + $100 1 + k d 100 01210 10% 100 + 1,000 V = ?... = $90.91 +... + $38.55 + $385.54 = $1,000. ++ ++ Value of Bond

9. 9 Annual Coupon Bonds

10. 10 Semiannual Coupon Bonds  Multiply years by 2 to get periods = 2n.  Divide nominal rate by 2 to get periodic rate = k d /2.  Divide annual INT by 2 to get PMT = INT/2.

11. 11 General Observations About Bond Values  If coupon rate < k d, bond sells at a discount.  If coupon rate > k d, bond sells at a premium.  If coupon rate = k d, bond sells at its par value.  If k d rises, price falls; if k d falls, price rises.  At maturity, the value of a bond equals par.

12. 12 Changes in Bond Values Over Time  At maturity, the value of any bond must equal its par value.  The value of a premium bond would decrease to $1,000.  The value of a discount bond would increase to $1,000.  A par bond stays at $1,000 if k d remains constant.

13. 13 M Bond Value ($) Years remaining to Maturity 1,372 1,211 1,000 837 775 3025 20 15 10 5 0 k d = 7%. k d = 13%. k d = 10%. Time Path of Bond Value

14. 14 Bond Yields  Yield-to-Maturity (YTM)  Effective Annual Return on Bond  Yield-to-Call  Current Yield

15. 15 Yield-to-Maturity  YTM is the rate of return earned on a bond held to maturity, also called “promised yield.”  It is the discount rate that equates the present value of the interest and principal payments to the price of the bond. Annualized YTM = 2 x six-month yield Effective YTM = (1 + six-month yield) 2 - 1

16. 16 Total Return or Yield on Bond  The effective annual return on a bond is equal to its current yield and capital gains yield. Current yield Capital gains yield YTM = Current yield + Capital gains yield  Effective annual yield (1 + semiannual return) 2 -1

17. 17 Yield-to-Call  Call Provision Callable bonds Call premium Refunding operation  YTC is the average annual return an investor will receive if the bond is held until its expected call date.

18. 18 Current Yield  Annual interest payment/Current value of bond  Provides information about cash income on bond.  Does not provide accurate measure of total expected return on bond.

19. 19 kdkd 1-yearChange10-yearChange 5%$1,048$1,386 10%1,000 4.8% 1,000 38.6% 15%956 4.4% 749 25.1% Interest Rate Risk  Rising interest rates have an adverse effect on bond values.  The longer the maturity of a bond, the greater the exposure to interest rate risk.

20. 20 0 500 1,000 1,500 0%5%10%15% 1-year 10-year kdkd Value Interest Rate Risk

21. 21 Reinvestment Rate Risk  The risk that CFs will have to be reinvested in the future at lower rates, reducing income.  The shorter the maturity of the bond, the greater the risk of a decrease in interest rates.