# 1 Bond Valuation Learning Module. 2 Definitions Par or Face Value - Par or Face Value - The amount of money that is paid to the bondholders at maturity.

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1 Bond Valuation Learning Module

2 Definitions Par or Face Value - Par or Face Value - The amount of money that is paid to the bondholders at maturity. For most bonds this amount is \$1,000. It also generally represents the amount of money borrowed by the bond issuer. The amount of money that is paid to the bondholders at maturity. For most bonds this amount is \$1,000. It also generally represents the amount of money borrowed by the bond issuer. Coupon Rate - Coupon Rate - The coupon rate, which is generally fixed, determines the periodic coupon or interest payments. It is expressed as a percentage of the bond's face value. It also represents the interest cost of the bond to the issuer. The coupon rate, which is generally fixed, determines the periodic coupon or interest payments. It is expressed as a percentage of the bond's face value. It also represents the interest cost of the bond to the issuer.

3 Definitions Coupon Payments - Coupon Payments - The coupon payments represent the periodic interest payments from the bond issuer to the bondholder. The annual coupon payment is calculated by multiplying the coupon rate by the bond's face value. Since most bonds pay interest semiannually, generally one half of the annual coupon is paid to the bondholders every six months. The coupon payments represent the periodic interest payments from the bond issuer to the bondholder. The annual coupon payment is calculated by multiplying the coupon rate by the bond's face value. Since most bonds pay interest semiannually, generally one half of the annual coupon is paid to the bondholders every six months. Maturity Date - Maturity Date - The maturity date represents the date on which the bond matures, i.e., the date on which the face value is repaid. The last coupon payment is also paid on the maturity date. The maturity date represents the date on which the bond matures, i.e., the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.

4 Definitions Original Maturity - Original Maturity - The time from when the bond was issued until its maturity date. The time from when the bond was issued until its maturity date. Remaining Maturity - Remaining Maturity - The time currently remaining until the maturity date. The time currently remaining until the maturity date. Call Date - Call Date - For bonds which are callable, i.e., bonds which can be redeemed by the issuer prior to maturity, the call date represents the earliest date at which the bond can be called. For bonds which are callable, i.e., bonds which can be redeemed by the issuer prior to maturity, the call date represents the earliest date at which the bond can be called.

5 Definitions Call Price - Call Price - The amount of money the issuer has to pay to call a callable bond (there is a premium for calling the bond early). When a bond first becomes callable, i.e., on the call date, the call price is often set to equal the face value plus one year's interest. The amount of money the issuer has to pay to call a callable bond (there is a premium for calling the bond early). When a bond first becomes callable, i.e., on the call date, the call price is often set to equal the face value plus one year's interest. Required Return - Required Return - The rate of return that investors currently require on a bond. The rate of return that investors currently require on a bond.

6 Definitions Yield to Maturity - Yield to Maturity - The rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity. Alternatively, it represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price. The rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity. Alternatively, it represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price. Yield to Call - Yield to Call - The rate of return that an investor would earn if he bought a callable bond at its current market price and held it until the call date given that the bond was called on the call date. The rate of return that an investor would earn if he bought a callable bond at its current market price and held it until the call date given that the bond was called on the call date.

7 Bond Valuation Bonds are valued using time value of money concepts. Bonds are valued using time value of money concepts. Their coupon, or interest, payments are treated like an equal cash flow stream (annuity). Their coupon, or interest, payments are treated like an equal cash flow stream (annuity). Their face value is treated like a lump sum. Their face value is treated like a lump sum.

8 Example Assume Hunter buys a 10-year bond from the KLM corporation on January 1, 2003. The bond has a face value of \$1000 and pays an annual 10% coupon. The current market rate of return is 12%. Calculate the price of this bond today. Assume Hunter buys a 10-year bond from the KLM corporation on January 1, 2003. The bond has a face value of \$1000 and pays an annual 10% coupon. The current market rate of return is 12%. Calculate the price of this bond today. 1. Draw a timeline \$100 \$1000 + ? ?

9 Example 2. First, find the value of the coupon stream Remember to follow the same approach you use in time value of money calculations. Remember to follow the same approach you use in time value of money calculations. You can find the PV of a cash flow stream You can find the PV of a cash flow stream PV = \$100/(1+.12) 1 + \$100/(1+.12) 2 + \$100/(1+.12) 3 + \$100/(1+.12) 4 + \$100/(1+.12) 5 + \$100/(1+.12) 6 + \$100/(1+.12) 7 + \$100/(1+.12) 8 + \$100/(1+.12) 9 + \$100/(1+.12) 10 PV = \$100/(1+.12) 1 + \$100/(1+.12) 2 + \$100/(1+.12) 3 + \$100/(1+.12) 4 + \$100/(1+.12) 5 + \$100/(1+.12) 6 + \$100/(1+.12) 7 + \$100/(1+.12) 8 + \$100/(1+.12) 9 + \$100/(1+.12) 10 Or, you can find the PV of an annuity Or, you can find the PV of an annuity PVA = \$100 * {[1-(1+.12) -10 ]/.12} PVA = \$100 * {[1-(1+.12) -10 ]/.12} PV = \$565.02 PV = \$565.02

10 Example 3. Find the PV of the face value PV = CF t / (1+r) t PV = CF t / (1+r) t PV = \$1000/ (1+.12) 10 PV = \$1000/ (1+.12) 10 PV = \$321.97 PV = \$321.97 4. Add the two values together to get the total PV \$565.02 + \$321.97 = \$886.99 \$565.02 + \$321.97 = \$886.99 Alternatively, on your calculator Alternatively, on your calculator PMT = 100 FV = 1000 n = 10 i = 12 PV = ? PMT = 100 FV = 1000 n = 10 i = 12 PV = ? Note that if the payments had been semiannual, PMT=50, FV=1000, n=20, i=6, PV=?=\$885.30. Note that if the payments had been semiannual, PMT=50, FV=1000, n=20, i=6, PV=?=\$885.30.

11 Realized Return Sometimes you will be asked to find the realized rate of return for a bond. Sometimes you will be asked to find the realized rate of return for a bond. This is the return that the investor actually realized from holding a bond. This is the return that the investor actually realized from holding a bond. Using time value of money concepts, you are solving for the required rate of return instead of the value of the bond. Using time value of money concepts, you are solving for the required rate of return instead of the value of the bond.

12 Example Doug purchased a bond for \$800 5-years ago and he sold the bond today for \$1200. The bond paid an annual 10% coupon. What is his realized rate of return? Doug purchased a bond for \$800 5-years ago and he sold the bond today for \$1200. The bond paid an annual 10% coupon. What is his realized rate of return? n PV =  [CF t / (1+r) t ] PV =  [CF t / (1+r) t ] t=0 t=0 \$800 = [\$100/(1+r) + \$100/(1+r) 2 + \$100/(1+r) 3 + \$100/(1+r) 4 + \$100/(1+r) 5 ] + [\$1200/(1+r) 5 ] \$800 = [\$100/(1+r) + \$100/(1+r) 2 + \$100/(1+r) 3 + \$100/(1+r) 4 + \$100/(1+r) 5 ] + [\$1200/(1+r) 5 ] To solve, you need use a “trail and error” approach. You plug in numbers until you find the rate of return that solves the equation. To solve, you need use a “trail and error” approach. You plug in numbers until you find the rate of return that solves the equation. The realized rate of return on this bond is 19.31%. The realized rate of return on this bond is 19.31%.

13 Example This is much easier to find using a financial calculator: This is much easier to find using a financial calculator: n = 5 PV = -800 FV = 1200 PMT = 100 i = ?, this is the realized rate of return on this bond n = 5 PV = -800 FV = 1200 PMT = 100 i = ?, this is the realized rate of return on this bond Note that if the payments had been semiannual, n=10, PV=-800, FV=1200, PMT=50, i=?=9.47%. Thus, the realized return would have been 2 * 9.47% = 18.94%. Note that if the payments had been semiannual, n=10, PV=-800, FV=1200, PMT=50, i=?=9.47%. Thus, the realized return would have been 2 * 9.47% = 18.94%.

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