Bond Valuation

1. Bond Valuation Corporate Finance Dr. A. DeMaskey

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. Types of Bonds • Treasury Bonds • Corporate Bonds • Municipal Bonds • Foreign Bonds

4. Basic Terminology • Bond • Par Value • Coupon Interest Payment • Coupon Interest Rate • Maturity Date • Bond’s Market Rate of Interest, kd

5. 0 1 2 n Value CF1 CF2 CFn Financial Asset Valuation k ... CF CF CF 1 2 n + + + PV = . . . .       1 2 n 1 + k 1 + k 1 + k

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

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. 0 1 2 10 Value of Bond 10% ... 100 + 1,000 V = ? 100 100 $100 $100 $1 , 000 V  . . . + + + B 1 10 10       1 k 1 k 1 k + + + d d d = $90.91 + . . . + $38.55 + $385.54 = $1,000.

9. Annual Coupon Bonds

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

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

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 kd remains constant.

13. Bond Value ($) kd = 7%. 1,372 1,211 kd = 10%. M 1,000 837 kd = 13%. 775 30 25 20 15 10 5 0 Years remaining to Maturity Time Path of Bond Value

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

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. 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. 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. 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. 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. kd 1-year Change 10-year Change 5% $1,048 $1,386 4.8% 38.6% 10% 1,000 1,000 4.4% 25.1% 15% 956 749

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

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.