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# Chap 9 bonds

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### Chap 9 bonds

1. 1. FinancialManagement Chapter 9 Theory and Practice Tenth Edition Bonds and their Valuation Eugene F. BrighamMichael C. Ehrhardt Instructor: Sanam Taimoor Institute of Business Management
2. 2. Topics• Bonds and bond’s characteristics• Types of bonds• Bond Valuation• Yield to Maturity• Calculating YTM• Bond Price and Yield relationship
3. 3. BOND• A long term contract under which a borrower agrees to make payments of interest and principal on specific date, to the holders of the bond• Bond Indenture – Is a legal document that specifies both the rights of the bondholders and duties of the issuing corporation
4. 4. Types of Bonds• Treasury Bonds – Issued by the government• Corporate Bonds – Issued by companies• Municipal Bonds – Issued by local governments• Foreign Bonds – Issued by foreign governments or companies
5. 5. Characteristics of a Bond• Par Value – the stated face value of a bond• Coupon Interest Rate – the fixed “rate of interest” which remains the same throughout the life of the bond• Maturity Date – Specified maturity date on which par value must be paid• Call Option – It gives the issuer the opportunity to repurchase the bonds prior to maturity
6. 6. Other Types of Bonds• Floating Rate Bonds• Zero Coupon Bonds• Perpetual Bonds• Convertible Bonds
7. 7. Bond Valuation VB INT PVIFA kd , N M PVIF kd , NINT = Coupon InterestM = Par valueKd = Market rate of interestN = Number of years before the bond matures
8. 8. Example• Bond C has a \$1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond? – VB = \$80 (PVIFA10%, 30) + \$1,000 (PVIF10%, 30) = \$80 (9.427) + \$1,000 (.057) = \$754.16 + \$57.00 = \$811.16.
9. 9. Perpetual Bond Example• Bond P has a \$1,000 face value and provides an 8% coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? I VB kd VB = \$80 / 10% = \$800
10. 10. Zero Coupon Bond Example• Bond Z has a \$1,000 face value and a 30-year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond? M VB n M PVIF kd , N 1 kdV = \$1,000 (PVIF10%, 30) = \$1,000 (.057) = \$57.00
11. 11. Semi Annual Compounding• Some Bonds pay interest twice a year• Adjustments needed – Divide kd by 2 – Multiply N by 2 – Divide INT by 2
12. 12. Semi Annual Compounding Example• Bond C has a \$1,000 face value and provides an 8% semiannual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond? – VB = \$40 (PVIFA5%, 30) + \$1,000 (PVIF5%, 30) = \$40 (15.373) + \$1,000 (.231) = \$614.92 + \$231.00 = \$845.92
13. 13. Yield to Maturity• The rate of return (Kd) that investors earn if they buy a bond at a specified price and hold it until maturity• In other words it is the rate of interest that sets the present value of the bond’s expected future cash-flow stream equal to the bond’s current market price
14. 14. Calculating YTM Consider a \$1,000 par value bond with thefollowing characteristics : a current market price of \$ 761; 12 years until maturity and an 8% coupon rate . What is the YTM?
15. 15. Calculating YTMTry 10%:\$761 = \$80(PVIFA10%,12) + \$1,000(PVIF10%,12)\$761 = \$80(6.814) + \$1,000(.319)\$761 = \$545.12 + \$319 = \$864.12 [Rate is too low!]
16. 16. Calculating YTMTry 15%\$761 = \$80(PVIFA 15%,12) + \$1,000(PVIF 15%, 12)\$761 = \$80(5.421) + \$1,000(.187)\$761 = \$433.68 + \$187 = \$620.68 [Rate is too high!]
17. 17. Calculating YTM• YTM Solution (Interpolate) b a A YTM a A B a = Lower interest rate b = Higher interest rate A = Value at lower rate B = Value at higher rate• Answer: 12.90%
18. 18. Calculating YTM• Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The bonds have a current market value of \$1,250.• 7.40%
19. 19. Bond Price- Interest Rate Relationship• A bond’s price and interest rates are inversely related; – When interest rates rise, bond’s price falls – When interest rates fall, bond’s prices rises
20. 20. Bond Price- Interest Rate Relationship 1600BOND PRICE (\$) 1400 1200 1000 5 Year 600 15 Year 0 0 2 4 6 8 10 12 14 16 18 Coupon Rate MARKET REQUIRED RATE OF RETURN (%)
21. 21. Bond Price- Interest Rate Relationship• Assume that the required rate of return on a 15-year, 10% coupon-paying bond rises from 10% to 12%. What happens to the bond price?• When interest rates rise, then the market required rates of return rise and bond prices will fall
22. 22. Bond Price- Interest Rate Relationship 1600 1400BOND PRICE (\$) 1200 1000 5 Year 600 15 Year 0 0 2 4 6 8 10 12 14 16 18 Coupon Rate MARKET REQUIRED RATE OF RETURN (%)
23. 23. Bond Price- Interest Rate Relationship• Assume that the required rate of return on a 15-year, 10% coupon-paying bond falls from 10% to 8%. What happens to the bond price?• When interest rates fall, then the market required rates of return fall and bond prices will rise.
24. 24. Bond Price- Interest Rate Relationship 1600 1400BOND PRICE (\$) 1200 1000 Par 5 Year 600 15 Year 0 0 2 4 6 8 10 12 14 16 18 Coupon Rate MARKET REQUIRED RATE OF RETURN (%)
25. 25. Bond Price- Interest Rate Relationship• Discount Bond -- The market required rate of return exceeds the coupon rate (Par > P0 ).• Premium Bond -- The coupon rate exceeds the market required rate of return (P0 > Par).• Par Bond -- The coupon rate equals the market required rate of return (P0 = Par).