Bonds and Their Valuation

1. Chapter 7 Bonds and Their Valuation

2. What is a 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. • Indenture - A formal agreement between the issuer and the bondholders. • Bonds are issued by corporations and government agencies that are looking for long-term debt capital. • Primarily traded in the over-the-counter (OTC)market.

3. What is a bond? (cont’d….) • Fixed income securities are often classified according to maturity, as follows: • Less than one year – Bills or “Paper” • 1 year < Maturity < 7 years – Notes • > 7 years – Bonds Different types of bonds:

4. Key Features of a Bond • Par value: face amount of the bond (i.e. face value), which is paid at maturity. • Coupon interest rate: the annual percentage interest paid on the bond’s face value; to calculate the dollar value of the annual coupon, multiply the coupon rate by the face value. - If the coupon is paid twice a year, divide the annual coupon by two Example: A $1,000 bond with an 8% coupon rate will have an $80 coupon if paid annually or a $40 coupon if paid semiannually - Fixed-Rate Bond, Floating-Rate Bond, Zero Coupon Bond, Original Issue Discount (OID) Bond • Maturity date: A specified date on which the par value of a bond must be repaid.. • Issue date: when the bond was issued. • Yield to maturity: rate of return earned on a bond held until maturity (also called the “promised yield”).

5. Key Features of a Bond (cont’d….) • Call provision:Allows issuer to refund the bond issue if rates decline. • Other Features (i) Convertible bonds are bonds that are exchangeable into shares of common stock at a fixed price at the option of the bondholder.

6. Bond value rd = the market rate of interest on the bond. This is the discount rate used to calculate the present value of the cash flows, which is also the bond’s price. N = the number of years before the bond matures. INT = dollars of interest paid each year = Coupon rate x Par value M = the par, or maturity, value of the bond. This amount must be paid at maturity.

7. Bond value (cont’d....)

8. 0 1 2 N VB = ? 100 100 100 + 1,000 What is the value of a 10-year, 10% annual coupon bond, if rd = 10%? 10% ...

9. BOND YIELDS • Yield to Maturity (YTM): The rate of return earned on a bond if it is held to maturity. • Yield to maturity is simply the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the price of the bond. Finding YTM: (i) Exact formula- all you need to do is solve for rd from the above equation. (ii) Approximate formula-

10. BOND YIELDS Suppose you were offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. What rate of interest would you earn on your investment if you bought the bond, held it to maturity, and received the promised interest and maturity payments? The answer would be approximately 5%.

11. BOND YIELDS (cont’d....) • Current yield: is the yield on the bond’s current market price provided by the annual coupon

12. Changes in Bond Value over Time • What would happen to the value of these three bonds if the required rate of return remained at 10%? VB 1,184 1,000 816 13% coupon rate 10% coupon rate 7% coupon rate Years to Maturity 10 5 0

13. Bond Values over Time • At maturity, the value of any bond must equal its par value. • If rd 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. • The value of a par bond stays at $1,000.

14. Bond Values over Time Bond Price-Yield Curve: When interest rates increase, bond prices fall

15. BONDS WITH SEMIANNUAL COUPONS Although some bonds pay interest annually, the vast majority actually make payments semiannually. To adjust for semi-annual coupons, we must make three changes: 1. Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each six months. 2. Multiply the years to maturity, N, by 2 to determine the number of semi-annual periods. 3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic (semiannual) interest rate. On a time line, there would be twice as many payments, but each would be half as large as with an annual payment bond.

16. Interest Rate (price) Risk • Price risk is the concern that rising rd will cause the value of a bond to fall. rd1-yearChange10-yearChange 5% $1,048 $1,386 10% 1,000 1,000 15% 956 749 • The 10-year bond is more sensitive to interest rate changes, and hence has more price risk. • Interest rate risk is higher on bonds that have long maturities than on bonds that will mature in the near future. + 4.8% – 4.4% +38.6% –25.1%

17. Reinvestment risk Reinvestment risk is the concern that rd 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. 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 for 10 years, assuming the bond is not callable.

18. Default Risk • If an issuer defaults, investors receive less than the promised return. • Influenced by the issuer’s financial strength and the terms of the bond contract. Bond ratings

19. Importance of Bond Ratings Bond ratings are important to both firms and investors. • A bond’s rating is an indicator of its default risk, the rating has a direct, measurable influence on the bond’s interest rate and the firm’s cost of debt. • Most bonds are purchased by institutional investors rather than individuals and many institutions are restricted to investment-grade securities.

20. Various Types of Corporate Bonds • Mortgage bonds: A bond backed by fixed assets. • Debentures: A long-term bond that is not secured by a mortgage on specific property. • Subordinated debentures: A bond having a claim on assets only after the senior debt has been paid off in the event of liquidation. • Investment-grade bonds: Bonds rated triple-B or higher. • Junk bonds: A high-risk, high-yield bond.