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Valuation and Characteristics of Bonds

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Principles Used Principle 1: The Risk-Return Trade-off – We Won’t Take on Additional Risk Unless We Expect to Be Compensated with Additional Return. Principle 2: The Time Value of Money – A Dollar Received Today is Worth More Than a Dollar Received in the Future Principle 3: Cash-Not Profits-Is King.

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BOND VALUATION Type of debt or long-term promissory note, issued by a borrower, promising to its holder a predetermined and fixed amount of interest on specific dates and principal upon maturity.

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**BOND CHARACTERISTICS Par Value Coupon Rate Maturity Date**

Call Provision Convertible Bonds Income Bonds. Indexed bond

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**BOND CHARACTERISTICS Par Value: Maturity Date:**

Face value of the bond, returned to the bondholder at maturity Maturity Date: The length of time until the bond issuer returns the par value to the bondholder and terminates or redeems the bond.

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**BOND CHARACTERISTICS Coupon Rate: Interest Payment:**

Rate of interest paid as a percentage of the par value. Fixed Rate Vs Floating Rate Zero Coupon Bonds – Issued at a deep discount and do not pay interest. Interest Payment: = Coupon rate X Par Value

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BOND CHARACTERISTICS Call Provision – The borrower may redeem the bond early. Usually includes a call premium. Sinking Fund Provision – Requires borrower to regularly retire a portion of the bond by either calling it or buying it on the open market.

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**BOND CHARACTERISTICS Convertible Bonds: Income Bonds: Indexed bond:**

Bonds may be converted into common stock at a fixed price. Income Bonds: Only pays interest if the company makes a profit. Indexed bond: Interest based on an inflation index.

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**TYPES OF BONDS US Government Bonds Municipal Bonds Corporate Bonds**

EuroBonds Junk Bonds

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**U.S. Government Bonds Treasury Bills Treasury Notes**

No coupons (zero coupon security) Face value paid at maturity Maturities up to one year Treasury Notes Coupons paid semiannually Maturities from 2-10 years 6 6

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**U.S. Government Bonds Treasury Bonds Treasury Strips**

Coupons paid semiannually Face value paid at maturity Maturities over 10 years The 30-year bond is called the long bond. Treasury Strips Zero-coupon bond Created by “stripping” the coupons and principal from Treasury bonds and notes. 7 7

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**CORPORATE BONDS Mortgage Bonds – Bonds secured with real property.**

Debentures – Unsecured bonds.

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Eurobonds Securities (bonds) issued in a country different from the one in whose currency the bond is denominated Example: a U.S. dollar-denominated bond issued by a non-U.S. entity outside the U.S. A eurodollar bond that is denominated in U.S. dollars and issued in Japan by an Australian company would be an example of a eurobond. The Australian company in this example could issue the eurodollar bond in any country other than the U.S.

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**Junk Bonds (High-Yield Bonds)**

Junk Bond is a bond that is rated below investment grade at the time of purchase. High risk debt with ratings of BB or below by Moody’s and Standard & Poor’s High yield — typically pay 3%-5% more than AAA grade long-term bonds These bonds have a higher risk of default or other adverse credit events, but typically pay higher yields than better quality bonds in order to make them attractive to investors.

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BOND RATINGS Bonds are rated as to their riskiness by several firms. (Moody’s Investment Service and Standard & Poor’s) Bonds with the highest rating are rated AAA. As bonds become riskier their ratings drop. Riskiness is the chance of default. Investment grade bonds must be rated at least BBB.

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Bond Ratings 13 13

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**Bond Valuation The value of a bond is a combination of:**

The amount and timing of the cash flows to be received by investors maturity The investor’s required rate of return

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BOND VALUATION VB = Present Value of the Interest Payments plus the Present Value of the Maturity Value (Par Value).

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**BOND VALUATION Interest Payment ($) BOND VALUE Par Value**

Number of Periods Interest Rate

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BOND VALUATI0N A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 10%. What is the value of the bond? Par Value = 1,000 Interest Rate (r) = 10% Interest Payment = 10% x 1,000 = $100 No. of periods = 3 years

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**BOND VALUATION Present Value of the Interest Payments**

10% ~ .10

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**Bond Valuation 1 2 3 $100 $100 $100 $91 $83 $75 $249 r=10%**

Present Value of the Interest Payments 1 2 3 r=10% $ $ $100 100 ( )1 100 ( )2 $91 100 ( )3 $83 $75 $249 18

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**Bond Valuation Present Value of the Maturity Value $1,000 3 yrs**

10% ~ .10 18

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Bond Valuation Present Value of the Maturity Value 1 2 3 r=10% $1,000 $1,000 ( )3 $751 18

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**Bond Valuation 1 2 3 $100 $100 $100 $1,000 $91 $83 $75 $249 $751**

Present Value of the Interest Payments plus the Present Value of the Maturity Value 1 2 3 $ $ $100 $1,000 100 ( )1 100 ( )2 $1,000 ( )3 $91 100 ( )3 $83 $75 $249 $751 $1,000 = Vb When the coupon rate and i are equal the value of the bond will always be the par value. 18

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**Review Questions In your groups calculate the value of the bonds.**

A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 5%. What is the value of the bond? A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 5%. The required rate of return on the bond is also 10%. What is the value of the bond? TAKE TEN MINUTES

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BOND VALUATI0N A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 5%. What is the value of the bond? Par Value = 1,000 Interest Rate (r) = 5% Interest Payment = 10% x 1,000 = $100 No. of periods = 3 years

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**Bond Valuation 1 2 3 $100 $100 $100 $1,000 $95 $91 $86 $272 $864**

Present Value of the Interest Payments plus the Present Value of the Maturity Value 1 2 3 $ $ $100 $1,000 100 ( )1 100 ( )2 $1,000 ( )3 $95 100 ( )3 $91 $86 $272 $864 $1,136 = Vb Whenever interest rates fall, bond prices go up. Sell at a premium. 18

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BOND VALUATI0N A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 5%. The required rate of return on the bond is also 10%. What is the value of the bond? Par Value = 1,000 Interest Rate (r) = 10% Interest Payment = 5% x 1,000 = $50 No. of periods = 3 years

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**Bond Valuation 1 2 3 $50 $50 $50 $1,000 $45 $41 $38 $124 $751**

Present Value of the Interest Payments plus the Present Value of the Maturity Value 1 2 3 $ $ $50 $1,000 50 ( )1 50 ( )2 $1,000 ( )3 $45 50 ( )3 $41 $38 $124 $751 $876 = Vb Whenever interest rates go up bond values fall. Sells at a discount. 18

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BOND VALUATION Interest rates change over time, so a bond’s value will fluctuate over time.

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BOND VALUATI0N (EXCEL) A company issues a 30 year bond with a par value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 10%. What is the value of the bond? Using PV formula nper = 30, rate = .10, Pmt = 100, FV = 1,000 PV = 1,000 When the coupon rate and i are equal the value of the bond will always be the par value.

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**SEMI-ANNUAL COUPONS Most bonds have semiannual coupons.**

When valuing a bond with semiannual coupons divide the Pmt by 2; multiply n by 2.

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BOND VALUATI0N A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 10%. What is the value of the bond, if interest payments are paid semi-annually? Par Value = 1,000 Interest Rate (r) = 10% per yr / 2 = 5% Interest Payment = (10%/2) x 1,000 = 50 No. of periods = 3 X 2 = 6

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BOND VALUATION nper = 6 rate = .05 Pmt = 50 FV = 1,000 PV = ???

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BOND VALUATION nper = 6 rate = .05 Pmt = 50 FV = 1,000 PV = 1,000

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Calculate the value of a bond with the following features, assuming that interest is paid semi-annually and that the face value of the bond is $1,000: Problem Coupon rate Yield to maturity Years to maturity Bond value a 8% 10% 3 b 4% 6% 1.5 c 2 d 6.25% e 2.5

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BOND YIELDS Yield to maturity – the yield you will receive if you hold the bond until it matures.

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YIELD TO MATURITY Let’s use the same example: we issue a bond with a 10% coupon. The price is $1,000 (the par value). What is the yield to maturity? nper = 30, Pmt = 100, FV = 1,000, PV = -1,000 The FV and Pmt are amounts we will receive; the PV is an amount we pay so it is a minus.

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YIELD TO MATURITY Let’s use the same example: we issue a bond with a 10% coupon. The price is $1,000 (the par value). What is the yield to maturity? nper = 30, Pmt = 100, FV = 1,000, PV = -1,000 rate = 10% The same as the Coupon rate; if FV and PV are equal the interest rate will equal the coupon rate.

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YIELD TO MATURITY Now let’s assume that 5 years go by and we pay $1, for our bond. What is the yield to maturity? nper = 25, Pmt = 100, FV = 1,000, PV = -1,225.08

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YIELD TO MATURITY Now let’s assume that 5 years go by and we pay $1, for our bond. What is the yield to maturity? nper = 25, Pmt = 100, FV = 1,000, PV = -1,225.08 rate = 7.91

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**Review Questions In your groups calculate the YTM**

The $1,000 face value EFG bond has a coupon of 10% (paid semi-annually), matures in 4 years, and has current price of $1,140. What is the EFG bond's yield to maturity? The NOP bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price of $1,200. What is the NOP's yield-to-maturity?

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**YIELD TO CALL Company’s can call bonds early.**

Company’s will generally call bonds when interest rates have fallen and new bonds can be issued with a lower coupon rate.

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YIELD TO CALL Let’s assume the bond in our example is callable 10 years after issue. Again, five years have gone by, so the bond can be called in five years. All other information remains the same.

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**YIELD TO CALL nper = 5 (years until bond can be called) Pmt = 100**

FV = 1,000 PV = -1,225.08 Rate = ????

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**YIELD TO CALL nper = 5 (years until bond can be called) Pmt = 100**

FV = 1,000 PV = -1,225.08 Rate = 4.83 The yield to call is less than the yield to maturity because we will receive fewer $100 payments.

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CURRENT YIELD The ratio of the interest payment to the bond’s current market price. The interest payment divided by the current price of the bond. In our example: Current Yield = 100/1, = 8.16%

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**Review Questions In your groups calculate the following:**

The $1,000 face value ABC bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond's value today? The KLM bond has a 8% coupon rate,with interest paid semi-annually, a maturity value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond's current price? The HIJ bond has a current price of $800, a maturity value of $1,000, and matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond's annual coupon rate?

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