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2 chapter 42 Why shall we know the valuation of long-term securities? Make investment decisions Determine the value of the firm

3 chapter 43 Chapter 4: The valuation of long-term securities Study objectives Distinctions among valuation concepts Bond valuation Preferred stock valuation Common stock valuation Rates of Return

4 chapter 44 Why shall we know the valuation of long-term securities? Make investment decisions Determine the value of the firm

5 Bonds are simply long-term that represent claims against a firm’s assets. Bonds are a form of debt Bonds are often referred to as fixed-income investments. Bond Basics

6 Key Features of a Bond Debt instrument issued by a corp. or government.

7 Key Features of a Bond Par value = face amount of the bond, which is paid at maturity (assume $1,000). =

8 Key Features of a Bond Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.

9 Key Features of a Bond Maturity date – when the bond must be repaid. Yield to maturity (Discount Rate)- rate of return earned on a bond held until maturity. Required market rate

Bond Valuation Bond Value = Present Value of Cash Flows Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lump sum Remember, as interest rates increase present values decrease So, as interest rates increase, bond prices decrease and vice versa

The Bond-Pricing Equation Bond Value = PV annuity + PV single sum

12 Different Types of Bonds perpetual bond A perpetual bond is a bond that never matures. It has an infinite life. (1 + k d ) 1 (1 + k d ) 2  (1 + k d )  V = III =   t=1 (1 + k d ) t I  or I (PVIFA k d,  ) Ik d V = I / k d [Reduced Form]

13 Perpetual Bond Example perpetual bond Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? perpetual bond Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? I$80 I = $1,000 ( 8%) = $80. k d 10% k d = 10%. VIk d V = I / k d [Reduced Form] $8010% $800 = $80 / 10% = $800. I$80 I = $1,000 ( 8%) = $80. k d 10% k d = 10%. VIk d V = I / k d [Reduced Form] $8010% $800 = $80 / 10% = $800.

14 chapter 414 Bonds with a Finite Maturity Typical coupon bonds (limited outstanding period, annually paid interest) V=I(PVIFA r,n )+MV(PVIF r,n )

15 chapter 415 Example The Brothers determines to issue 10,000 $1000-par- value bonds with 10% coupons. The bonds will be retired in 9 years. The Brothers decides to issue the bond at $1020. If Mr. White wants to buy the bond and his required rate of return is 8%, should Mr. White buy the bond?

16 chapter 416 Zero-coupon bond A zero-coupon bond is a bond that pays no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation The interest of a zero-coupon bond is the remainder of the face value less issuing price V=MV/(1+r) n

17 chapter 417 Example Suppose that Pace Enterprises issues a zero-coupon bond having a 10-year maturity and a $1000 face value. If the investor’s required return is 12%, then V=$1000/(1+.12) 10 =$322

18 chapter 418 Seminal compounding of interest Although some bonds (typically those issued in European Markets) make interest payments once a year, most bonds issued in America pay interest twice a year. As a result, it is necessary to modify our bond valuation model V=(I/2)(PVIFA r/2,2n )+MV(PVIF r/2,2n ), here I is the interest of the bond and n is the years that the bond exists

Valuing a Bond - Examples 1) Consider a bond with a coupon rate of 10%, par value is $1000 and 20 years to maturity. The yield to maturity is 11%. What is the value of the bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.11) 20 ] / / (1.11) 20 B = = ) A bond has a 10% annual coupon and $1000 face value and 20 years to maturity. The yield to maturity is 8%. What is the price of this bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.08) 20 ] / / (1.08) 20 B = =

Bond Prices: Relationship Between Coupon and Yield If :YTM > coupon rate then bond price < par value Selling at a discount, called a discount bond If:YTM < coupon rate then bond price > par value Selling at a premium, called a premium bond If: YTM = coupon ratethen par value = bond price Selling at par

Example 7.1 p196 A $1000 bond has coupon rate of 14% with semiannual coupons, YTM is quoted as 16% and maturity 7 years. What is the price of the bond? How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? B = 70[1 – 1/(1.08) 14 ] / / (1.08) 14 =

Interest Rate Risk Change in value due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds

Quiz Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $ Will the yield be more or less than 10%? Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $ Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?

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