台湾大学：《财务管理》（英文版） Chapter 4 Valuing Bonds

Fundamentals of Corporate Finance Third edition Chapter 4 Valuing Bonds Brealey Myers Marcus ndamentals of Corporate Finan Brealey Myers Marcus slides by Matthew will IrwinMcGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 1 Irwin/McGraw-Hill Chapter 4 Fundamentals of Corporate Finance Third Edition Valuing Bonds Brealey Myers Marcus slides by Matthew Will Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc.,2001

4-2 Topics Covered S Bond characteristics reading the financial pages SBond prices and yields )Bond prices and interest rates → YTM VS. current yield 少 Rate of return iNterest rate risk 少 The Yield Curve Nominal and real rates of Interest → Default risk Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 2 Irwin/McGraw-Hill Topics Covered Bond Characteristics ➔reading the financial pages Bond Prices and Yields ➔Bond prices and interest rates ➔YTM vs. current yield ➔Rate of Return ➔Interest Rate Risk ➔The Yield Curve ➔Nominal and Real Rates of Interest ➔Default Risk

Bonds Terminology O Bond- Security that obligates the issuer to make specified payments to the bondholder S Coupon- The interest payments made to the bondholder OFace Value(Par Value or Maturity Value)-Payment at the maturity of the bond COupon rate- Annual interest payment, as a percentage of face value Irwin/McGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 3 Irwin/McGraw-Hill Bonds Terminology Bond - Security that obligates the issuer to make specified payments to the bondholder. Coupon - The interest payments made to the bondholder. Face Value (Par Value or Maturity Value) - Payment at the maturity of the bond. Coupon Rate - Annual interest payment, as a percentage of face value

4-4 Bonds WARNING The coupon rate IS NOT the discount rate used in the Present value calculations The coupon rate merely tells us what cash flow the bond will produce Since the coupon rate is listed as a %o, this misconception is quite common Irwin/McGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 4 Irwin/McGraw-Hill Bonds WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations. The coupon rate merely tells us what cash flow the bond will produce. Since the coupon rate is listed as a %, this misconception is quite common

4-5 Bond pricing The price of a bond is the present value of all cash flows generated by the bond (i.e coupons and face value) discounted at the required rate of return cpn con cpn+ par PV= +,, (1+r)(1+r)2 (1+r) Irwin/McGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 5 Irwin/McGraw-Hill Bond Pricing The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return. PV cpn r cpn r cpn par r t = + + + + + + ( ) ( ) + .... ( ) 1 1 (1 ) 1 2

4-6 Bond pricing Example What is the price ofa 6% annual coupon bond with a$1,000 face value, which matures in 3 years? Assume a required return of 5.6%0 60 60 1.060 Py (1.056)(1.056)2(1.056)3 PV=$1,010.77 Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 6 Irwin/McGraw-Hill Bond Pricing Example What is the price of a 6 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 5.6%. $1,010.77 (1.056) 1,060 (1.056) 60 (1.056) 60 1 2 3 = = + + PV PV

4-7 Bond pricing Example(continued) What is the price of the bond if the required rate of return is 690? (1.06)(M3× 60 60 060 PV= 1.06) PV=S1.000 Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 7 Irwin/McGraw-Hill Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 6 %? $1,000 (1.06) 1,060 (1.06) 60 (1.06) 60 1 2 3 = = + + PV PV

4-8 Bond pricing Example(continued) What is the price of the bond if the required rate of return is15 %0? 60 60 1.060 PV= (1.15)(1.5)3× 5)2(1.15) P=$794.51 Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 8 Irwin/McGraw-Hill Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 15 %? $794.51 (1.15) 1,060 (1.15) 60 (1.15) 60 1 2 3 = = + + PV PV

4-9 Bond pricing Example(continued) What is the price of the bond if the required rate of return is 5.6%o AND the coupons are paid semi 30 30 30 1.030 Py ..+ (1.028)(1.028) (1.028)3(1.028)° PV=$1010.91 Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 9 Irwin/McGraw-Hill Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 5.6% AND the coupons are paid semi￾annually? $1,010.91 (1.028) 1,030 (1.028) 30 ... (1.028) 30 (1.028) 30 1 2 5 6 = = + + + + PV PV

4-10 Bond pricing Example(continued) Q: How did the calculation change, given semi annual coupons versus annual coupon payments ie periods Discount rate Paying coupons twice a Since the time periods are year, instead ofonce now halt years, the doubles the total number of discount rate is also cash flows to be discounted changed from the annual in the Py formula rate to the half year rate Irwin/McGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 4- 10 Irwin/McGraw-Hill Bond Pricing Example (continued) Q: How did the calculation change, given semi￾annual coupons versus annual coupon payments? Time Periods Paying coupons twice a year, instead of once doubles the total number of cash flows to be discounted in the PV formula. Discount Rate Since the time periods are now half years, the discount rate is also changed from the annual rate to the half year rate