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Valuation of Stocks and Bonds

Valuation of Stocks and Bonds. 3. 1 Bonds and Bonds Valuation. What is Bond ?. A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

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Valuation of Stocks and Bonds

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  1. Valuation of Stocks and Bonds 3.1 Bonds and Bonds Valuation

  2. What is Bond ? • A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond. • A bond is a security that obligates the issuer to make specified interest and principal payments to the holder on specified dates. • Coupon rate • Face value (or par) • Maturity (or term) • Bonds are sometimes called fixedincome securities. • Bond is normally an interest-only loan, meaning that the borrower will pay the interest every period, but none of the principal will be repaid until the end of the loan.

  3. Key Features of a Bond • Par value or face value – face amount of the bond, which is paid at maturity (assume $1,000). • Bond that sells for its par value is called a par value bond • Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest. • Because the coupon is constant and paid every year, the type of bond we are describing is sometimes called a level coupon bond. • Maturity date – years until the bond must be repaid. • Issue date – when the bond was issued. • Yield to maturity (YTM) - rate of return earned on a bond held until maturity (also called the “promised yield”).

  4. $I $I $I $I $I $I+$M . . . 1 2 n 0 Characteristics of Bonds • Bonds pay fixed coupon (interest) payments at fixed intervals (usually every 6 months) and pay the par value at maturity. example: AT&T 9s of 2018 par value = $1000 coupon = 9% of par value per year. = $90 per year ($45 every 6 months). maturity = 20 years. issued by AT&T.

  5. $45 $45 $45 $45 $45 $45+$1000 . . . 1 2 20 0 Example: AT&T 9s of 2018 par value = $1000 coupon = 9% of par value per year. = $90 per year ($45 every 6 months). maturity = 20 years. issued by AT&T.

  6. Types of Bonds • Pure Discount or Zero-Coupon Bonds (Zeroes) • Pay no coupons prior to maturity. • Pay the bond’s face value at maturity. • Priced at a deep discount. • Coupon Bonds • Pay a stated coupon at periodic intervals prior to maturity. • Pay the bond’s face value at maturity. • Perpetual Bonds (Consols) • No maturity date. • Pay a stated coupon at periodic intervals.

  7. Types of Bonds • Self-Amortizing Bonds • Pay a regular fixed amount each payment period over the life of the bond. • Principal repaid over time rather than at maturity. • Debentures – • unsecured bonds. • Subordinated debentures – • unsecured “junior” debt. • Mortgage bonds – • secured bonds. • Junk bonds – • speculative or below-investment grade bonds; rated BB and below.

  8. Types of Bonds • Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas). • example - suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country. Why do this? • If borrowing rates are lower in France, • To avoid SEC regulations.

  9. Other types (features) of bonds • Convertible bond – may be exchanged for common stock of the firm, at the holder’s option. • Warrant – long-term option to buy a stated number of shares of common stock at a specified price. • Putable bond – allows holder to sell the bond back to the company prior to maturity. • Income bond – pays interest only when income is earned by the firm. • Indexed bond – interest rate paid is based upon the rate of inflation.

  10. Bond markets • Bond market is bigger in value than stock market. • Largest securities market in the world is not NYSE but U.S. Treasury Market. • Primarily traded in the over-the-counter (OTC) market. • This means that there’s no particular place where buying and selling occur. • Instead dealers around the country (and around the world) stand ready to buy and sell and they are connected electronically. • Most bonds are owned by and traded among large financial institutions. • Full information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE.

  11. Bond markets (contd…) • Because Bond market is almost entirely OTC, it has little or no transparency. • It is near to impossible to get the information on price and quantity of transactions because transactions are privately negotiated between parties, and there is little of no centralized reporting of transactions.

  12. Bond Issuers • Federal Government and its Agencies • Local Municipalities • Corporations

  13. U.S. Government Bonds • Treasury Bills • No coupons (zero coupon security) • Face value paid at maturity • Maturities up to one year • Treasury Notes • Coupons paid semiannually • Face value paid at maturity • Maturities from 2-10 years • Treasury Bonds • Coupons paid semiannually • Face value paid at maturity • Maturities over 10 years • The 30-year bond is called the long bond.

  14. Agencies Bonds • Mortgage-Backed Bonds • Bonds issued by U.S. Government agencies that are backed by a pool of home mortgages. • Self-amortizing bonds. • Maturities up to 20 years.

  15. U.S. Government Bonds • No default risk. Considered to be riskfree. • Exempt from state and local taxes. • Sold regularly through a network of primary dealers. • Traded regularly in the over-the-counter (OTC) market.

  16. Municipal Bonds (Munis) • Maturities from one month to 40 years. • Exempt from federal, state, and local taxes. • Riskier than U.S. Government bonds. • Rated much like corporate issues. • They are almost always callable.

  17. Corporate Bonds • Secured Bonds (Asset-Backed) • Secured by real property • Ownership of the property reverts to the bondholders upon default. • Debentures • General creditors • Have priority over stockholders, but are subordinate to secured debt.

  18. Common Features of Corporate Bonds • Senior versus subordinated bonds • Convertible bonds • Callable bonds • Putable bonds • Sinking funds

  19. Convertibility • Some bonds may be converted to common stock. • Can be swapped for a fixed number of shares of stock anytime before maturity at the holder’s option. • Is this a benefit to the investor? Yes !

  20. Effect of a call provision • Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor). • Borrowers are willing to pay more, and lenders require more, for callable bonds. • Most bonds have a deferred call and a declining call premium.

  21. What is a sinking fund? • Provision to pay off a loan over its life rather than all at maturity. • Similar to amortization on a term loan. • Reduces risk to investor, shortens average maturity. • But not good for investors if rates decline after issuance.

  22. Security Valuation • In general, The intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return. • Can the intrinsic value of an asset differ from the market value? YES

  23. 0 1 2 n r ... Value CF1 CF2 CFn The value of financial assets

  24. Bond Valuation • Determining the value of a bond requires: • An estimate of expected cash flows • An estimate of the required return • Assumptions: • The coupon interest rate is fixed for the term of the bond • The coupon payments are made annually and the next coupon payment is receivable exactly a year from now • The bond will be redeemed at par on maturity. • The bond is non-callable.

  25. Bond Valuation (contd…)

  26. Example 1 Consider a 10 year, 12 % coupon bond with a par value of Rs 1000. Let the required yield on this bond is 13%. The cash flows for this bond are as follows: • 10 annual coupon payment of Rs 120 • Rs 1000 principal repayment 10 years from now

  27. Bond Values with Semi-Annual Interest

  28. What is the market price of a U.S. Treasury bond that has a coupon rate of 9%, a face value of $1,000 and matures exactly 10 years from today if the required yield to maturity is 10% compounded semiannually? Example 2 0 6 12 18 24 ... 120 Months 45 45 45 45 1045

  29. Bond Valuation (contd…) • To determine the value of a bond at a particular point in time, we need to know: • Number of periods remaining until maturity • The Face Value of the Bond • The Coupon (Interest) • The market interest rate for bond with similar features. (Yield To Maturity – YTM) • Interest rate required in the market on particular bond type is called the bond’s YTM or simply YIELD of the bond.

  30. Bond Yields and PricesThe case of coupon bonds • Suppose you purchase the U.S. Treasury bond described earlier (Example 2) and immediately thereafter interest rates fall so that the new yield to maturity on the bond is 8% compounded semiannually. What is the bond’s new market price? • Suppose the interest rises, so that the new yield is 12% compounded semiannually. What is the market price now? • Suppose the interest equals the coupon rate of 9%. What do you observe?

  31. New Semiannual yield = 8%/ 2 = 4% • What is the price of the bond if the yield to maturity is 8% compounded semiannually? • Similarly: • If r=12%: P =$ 827.95 • If r= 9%: P =$ 1,000.00 Bonds Yields and Prices

  32. Exercise • S’pose our firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate. • What would be a fair price for these bonds?

  33. 1000 120 120 120 . . . 120 0 1 2 3 . . . 20 Period/Yr = 1 N = 20 r% per year = 12 FV = 1,000 Coupon = 120 Solution: P = $1,000 Note: If the coupon rate = yield, the bond will sell for par value.

  34. Exercise (contd…) • Suppose interest rates fall immediately after we issue the bonds. The required return on bonds of similar risk drops to 10% i.e. Yield falls to 10 % • What would happen to the bond price?

  35. Period/Yr = 1 N = 20 r% per Year = 10 Coupon = 120 FV = 1000 Solution: P = $1,170.27 Note: If the coupon rate > yield, the bond will sell for a premium.

  36. Exercise (contd…) • Suppose interest rates rise immediately after we issue the bonds. The required return on bonds of similar risk rises to 14%. • What would happen to the bond price?

  37. Period/Yr = 1 N = 20 r% per year = 14 Coupon = 120 FV = 1000 Solution: P = $867.54 Note: If the coupon rate < yield, the bond will sell for a discount.

  38. Relationship Between Bond Prices and Yields • Bond prices are inversely related to interest rates (or yields). • A bond sells at par only if its coupon rate equals the required yield. • A bond sells at a premium if its coupon rate is above the required yield. • A bond sells at a discount if its coupon rate is below the required yield.

  39. Volatility of Coupon Bonds • Consider two bonds with 10% annual coupons with maturities of 5 years and 10 years. • The yield is 8% • What are the responses to a 1% yield change? • The sensitivity of a coupon bond increases with the maturity

  40. Bond Prices and Yields Longer term bonds are more sensitive to changes in (yields) Interest rates than shorter term bonds. Bond Price Premium Par Discount Yield 10% 12% 14%

  41. Bond Yields and PricesThe problem • Consider the following two bonds: • Both have a maturity of 5 years • Both have yield of 8% • First has 6% coupon, other has 10% coupon, compounded annually. • Then, what are the price sensitivities of these bonds to a 1% increase (decrease) in bond yields? • Lesser coupon rate bonds are more sensitive to change in yield.

  42. Interest Rate (Price) Risk • The risk that arises for bond owners from fluctuating interest rates is called interest rate risk. • How much interest rate risk a bond has, depends on how sensitive its price is to interest rate changes. • This sensitivity directly depends on two things: • The time to maturity • The coupon rate. • All other things being equal, the longer the time to maturity, the greater the interest rate risk. • All other things being equal, the lower the coupon rate, the greater the interest rate risk.

  43. What is interest rate (or price) risk? Interest rate risk is the concern that rising r will cause the value of a bond to fall. % change 1 yr r 10yr % change +4.8% $1,048 5% $1,386 +38.6% $1,000 10% $1,000 -4.4% $956 15% $749 -25.1% The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

  44. Interest Rate Risk (contd…) • Reason that longer-term bonds have greater interest rate sensitivity: • A large portion of a bond’s value comes from the discounting of face value at maturity, • The PV of this amount isn’t greatly affected by a small change in interest rates if the amount is to be received in smaller years to maturity, • Even a small change in the interest rate, however, once it is compounded for greater years to maturity, can have a significant effect on the present value. • Interest rate risk, increases at a decreasing rate. • Diff of interest rate risk betn 1 yr bond and 10 yr bond is greater, but this diff is not that greater between 20 yr bond and 30 yrs bond

  45. Interest Rate Risk (contd…) • Reasons that the bonds with lower coupons have greater interest rate risk: • Value of the bond depends on the PV of coupons and the PV of the face value. • Value of one with the lower coupon is proportionately more dependent on the discounted value of face value. • The bond with higher coupon has a larger cash flow early in its life, so its value is less sensitive to the changes in the discount rate.

  46. What is reinvestment rate risk? • Reinvestment rate risk is the concern that r will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest.

  47. Reinvestment rate risk example • You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. • If you choose the 1-year bond strategy: • After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. • If you choose the 10-year bond strategy: • You can lock in a 10% interest rate, and $50,000 annual income.

  48. Conclusions about interest rate and reinvestment rate risk Low High High Low CONCLUSION: Nothing is riskless!

  49. Bond values over time • At maturity, the value of any bond must equal its par value (assuming that there’s no risk of default) • A bond that is redeemable for Rs 1,000 (which is its par value) after 5 years when it matures, will have a price of Rs 1,000 at maturity, no matter what the current price is. • If r (yield) remains constant: • The value of a premium bond would decrease over time, until it reached $1,000. • The value of a discount bond would increase over time, until it reached $1,000. • A value of a par bond stays at $1,000.

  50. P 1,372 1,211 1,000 837 775 r = 7%. r= 10%. r = 13%. Years to Maturity 30 25 20 15 10 5 0 The price path of a bond • What would happen to the value of this bond if its required rate of return remained at 10%, or at 13%, or at 7% until maturity?

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