FIN 7020_Chapter 7_Lecture Notes (1).docx

d∂FIN 7020 Dr. Amine Khayati **Chapter 7 Lecture Notes** =========================== **Interest Rates and Bond Valuation** ===================================== **I- Bonds and bond valuation:** Bonds are long-term debt securities issued by corporations and by federal, state, and local governmen...

d∂FIN 7020 Dr. Amine Khayati **Chapter 7 Lecture Notes** =========================== **Interest Rates and Bond Valuation** ===================================== **I- Bonds and bond valuation:** Bonds are long-term debt securities issued by corporations and by federal, state, and local governments. A bond is normally an interest-only loan: the borrower will pay the interest every period and the principal will be repaid at the end of the loan. It is commonly called [level-coupon bond]. **Bond Features:** Example: ABC Corporation wants to borrow \$1,000 for 30 years. The interest rate on similar debt issued by similar corporations is 12%. So, ABC corp. will pay 1,0000.12= \$120 every year for 30 years and at the end of the 30 years, it will repay the \$1,000. - Coupon: the stated interest payment made on a bond: \$120 - Coupon rate: the annual coupon divided by the face value of a bond: 12% - Face value: also called the par value is the principal amount of a bond that is repaid at the end of the term: \$1,000. - Maturity date: is the date on which the principal amount of a bond is paid and is also the day of the last coupon payment. - Time to maturity is the number of years until the face value is paid. Once the bond has been issued, the number of years to maturity declines as time goes by. **Bond Values and Yields:** \- The cash flows from a bond stay the same during the life of the bond. However, as time passes, interest rates change in the markets which affect the present value of the bond. When interest rates increase, the present value of the bond decrease and when interest rates fall, the bond is worth more. \- There is an *inverse relationship* between interest rates and bond prices. \- The value of a bond is the present value of the future coupon payments plus the present value of the principal payment, discounted at the appropriate opportunity rate for bonds of similar characteristics (Yield to maturity). \- To estimate the bond current market value we need to know the face value, the coupon, the number of periods remaining until maturity and the market interest rate for bonds with similar features (maturity and risk). This interest rate required in the market on a bond is called the bond's *Yield to maturity* (YTM). YTM is also defined as the rate implied by the current bond price. \- Notice that the yield to maturity, the required return, and market rate are used synonymously; the coupon rate is set by the issuer at the time of the issuance to simply determine the size of the dollar coupon payment. \- Current yield of a bond is defined as the annual coupon divided by the market price. Example 1: consider a bond with a coupon rate of 10% and coupons paid annually. The par value is \$1,000 and the bond has 20 years to maturity. The yield to maturity is 11%. What is the value of the bond? PV = 920.37 Example 2: same as example 1 except that the yield to maturity is 9%. PV = 1,091.28 **Bond prices: Relationship between coupon rate and yield to maturity.** - If YTM = coupon rate, then the bond price = the face value. - If YTM \> coupon rate, then the bond price \< the face value and the bond is selling at discount also called discount bond. - If YTM \< coupon rate, then the bond price \> the face value and the bond is selling at a premium also called premium bond. - A par value bond is a bond that has a market price equal to the face value and a yield to maturity that equals to the coupon rate. - A discount bond sells for a price below the par value and has a yield to maturity that exceeds the coupon rate. - A premium bond sells for a price higher than the par value and has a coupon rate that exceeds the yield to maturity. **Interest Rate Risk:** The risk that arises for bond owners from fluctuating interest rates is called interest rate risk. The sensitivity of a bond price to interest rate changes depends on two things: the time to maturity and the coupon rate. 1. All else equal, the longer the time to maturity, the greater the interest rate risk. 2. All else equal, the lower the coupon rate, the greater the interest rate risk. **II- More on Bond Features:** A bond is a promise to repay Principal (the original amount of the loan) plus interest, at a specified time to the lender (or creditor). The firm is the debtor or borrower, and the debt owe is a liability. From a financial view point, the main differences between debt and equity are the following: +-----------------------------------+-----------------------------------+ | **Debt** | **Equity** | +===================================+===================================+ | - Not an ownership interest. | - Ownership interest. | | | | | - Creditors do not have voting | - Common stockholders vote to | | rights | elect the board of directors | | | and on other issues. | | - Interest is considered as an | | | expense and is | - Dividends are not considered | | tax-deductible. | an expense and are not tax | | | deductible. | | - Creditors have legal recourse | | | if interest or principal | - Dividends are not liability | | payments are missed. | to the firm until declared. | | | Stockholders have no legal | | - Excess debt can lead to | recourse if dividends are not | | financial distress and | declared. | | bankruptcy. | | | | - An all-equity firm cannot go | | - The return is limited to the | bankrupt. | | interest paid. | | | | - Has a residual claim. | | | | | | - There is no limit on the | | | dividend that can be paid. | +-----------------------------------+-----------------------------------+ **Long-Term Debt: The basics** \- The maturity of a long-term debt instrument is the length of time the debt remains outstanding. \- Short-term debt has a maturity of less than one year, while long-term securities have maturities greater than one year. Typically, corporate debt securities are either: notes, debentures, or bonds. Strictly speaking, a bond is secured by a mortgage on specific property, whereas a debenture is unsecured; however, the word "Bond" is often used generically. - A debenture is an unsecured (for which no specific property has been pledged as security) debt which generally matures in ten years or more. - A note is an unsecured debt that generally matures in less than ten years. A public issue is a debt issue which is sold to the general public. In a private issue, terms are negotiated directly between borrower and lender, and the security is issued directly to the lender. **The Indenture:** Indenture is the written agreement between the corporation (the borrower) and its creditors (the lenders) detailing the terms of the debt issue. It generally includes the following provisions: 1. the basic terms of the bonds 2. The total amount of bonds issued. 3. A description of property used as security. 4. The repayment arrangements. 5. The call provisions. 6. Details of the protective covenants. - When interest payments on a bond are made directly to the owner of record, the bond is said to be in registered form. The company's appointed registrar mails interest payments directly to the owners of registered bond. However, when interest payments are made to whoever holds the bond, the bond is said to be in bearer form. Bearer bonds have dated coupons attached and the bondholder detaches a coupon and mails it to the firm, which then makes the payment. - Collateral is a general term that frequently means securities (for example, bonds and stocks) that are pledged as security for payment of debt. However, the term collateral is commonly used to refer to any asset pledged on a debt. - Mortgage securities are secured by a mortgage on the real property of the borrower, usually real estate, land or buildings. - Seniority indicates priority of payment to creditors in the event of bankruptcy. If a debt is subordinated, it means that other creditors must be paid first in the event of bankruptcy. **Repayments:** Bonds can be repaid at maturity or they may be repaid in part or in entirely before maturity. Early repayment is more typical and is often handled through a sinking fund. - A sinking fund is an account managed by the bond trustee for the purpose of redeeming bonds early. A sinking fund requires the corporation to make annual payments to the bond trustee, who then either repurchases bonds in the open market or selects by lottery and redeems bonds at specified price. - Call provision is the right of the bond issuer to repurchase the bond at a predetermined price prior to maturity. - The call premium is the amount by which the call price exceeds the par value. - A deferred call provision is the provision that prohibits a bond issuer from repurchasing a bond for a period of time after issue. - A call protected bond is a bond that currently cannot be redeemed by the issuer. **Protective Covenants:** - Protective covenants are the stipulations in a bond indenture agreement which limit the actions a firm can take while the bond issue is still outstanding. 1. The firm must limit the amount of dividend it pays 2. The firm cannot issue additional long-term debt. 3. The firm cannot merge with another firm. **Bond Ratings:** Firms frequently pay to have their debt rated. The two-leading bond-rating firms are Moody's and Standard and Poor's (S&P). Bonds are rated according to the likelihood of default and the protection creditors have in the event of default. Bond ratings are concerned [only] with the possibility of default. - The highest ratings are AAA, AA for S&P and Aaa, Aa for Moody's: indicate a very low probability of default. - Bonds that are rated at least BBB (S&P) or Baa (Moody's) are considered *investment grade*. While lower rated bonds are referred to as low-grade, high-yield or junk bonds. **III- Some Different types of bonds:** **Government bonds:** [1- Treasury securities]: The federal government borrows by issuing Treasury bonds, notes and bills. T-bills are pure discount bonds with original maturity of one year or less. T-notes are coupon debt with original maturity between one and ten years. T-bonds are coupon debt with original maturity greater than ten years. \- The U.S. Treasury issues, unlike essentially all other bonds, have [no default risk]. \- Treasury issues are exempt from state income taxes but still subject to federal income taxes. \- The U.S. Treasury market is the largest securities market in the world. [2- Municipal securities]: State and local governments also borrow money by selling notes and bonds, called municipal bonds or notes or just "munis" for short. \- Municipal issues have varying degrees of default risk and are rates much like corporate issues. \- Municipal issues coupon payments are exempt from federal income taxes which makes them very attractive to high-income, high-tax bracket investors. \- Due to the tax break, yields on municipal bonds are much lower than the yields on taxable bonds. Example: A taxable bond has a yield of 8% and a municipal bond has a yield of 6%. \- If you are in a 40% tax bracket, which bond do you prefer? Taxable bond return = R (1 -- Tax rate) = 8% ( 1 -- 0.40) = 4.8% Municipal bond return = 6% You would prefer municipal bond 6% \> 4.8% \- At what tax rate would you be indifferent between these two bonds? 8% ( 1 -- Tax rate) = 6%, solve for the tax rate → tax rate = 25% [3- Zero coupon bonds: ] [4- Floating rate Bonds:] [5- Other Types of bonds:] **IV- Bond Markets:** **How Bonds are bought and sold:** Most bond transactions take place over the counter (OTC). Bond dealers are connected electronically. There is an extremely large number of bond issues, but generally low daily volume in single issue. Corporate bonds trade less frequently than common stocks and thus obtaining current bond values can be difficult sometimes. **Bond Price Reporting:** - Bid price is the price at which you can sell a bond to the dealer, and asked price is the price a dealer is willing to take for a security. - Bid-Ask spread is the profit that a dealer earns on the purchase and subsequent resale of a bond. **Corporate bond quotations:** Company (ticker) coupon Maturity last price last yield ESTspread UST EST vol (000's) GM 8.375 Jul 15, 2033 100.641 8.316 362 30 763,528 Company: General Motors Coupon rate: 8.375%; coupon payment per year = \$83.75 Bond matures on July 15, 2033 Current yield = 8.32%; computed as annual coupon divided by current price Trading volume = \$765,528 Quoted price: 100.641% of face value, so if face value is 1,000, the price is \$1,006.41. It is important to emphasize that bond pr ices are quoted as a percent of par, just as the coupon is quoted as a percent of par. The bond's yield is 362 basis points (3.62%) above the 30-year Treasury bond yield. **Treasury bond quotations:** Highlighted quote in Figure 6.4: 9.000 Nov 18 145:25 145:26 22 4.51 What is the coupon rate on the bond? 9% When does the bond mature? November 2018 What is the bid price? 25/32=0.78125 so the bid price is 145.78125% of a \$1,000 which is \$1,457.81 What is the ask price? 26/32=0.8125 so the ask price is 145.8125% of a \$1,000 which is \$1,458.125 - Treasury prices are quoted in 32nds, the smallest possible price change is 1/32 which is called the "tick" size. **A Note on Bond price Quotes:** When you buy a bond between coupon payment dates, the price you pay is usually more than the quoted price because the price you actually pay includes the accrued interest. - The clean price of a bond is the price excluding any accrued interest. It is the quoted price. - The dirty price is the price including any accrued interest to date. It is also called the full or invoice price, the price the buyer actually pays. Example: You buy a bond with a 12% annual coupon, payable semiannually. You paid \$1,080 for the bond and the next coupon is due in four months. What are your dirty price and your clean price? Dirty price = \$1,080 Accrued interest: if the next coupon is due in four months on a semiannually bond, it means that you sold the bond two months after the last coupon payment. So, you will charge the buyer two months of interest. Two months worth of interest is: (120/12)×2 = \$20 Dirty price = clean price + Accrued Interest Clean price = \$1,060 **V- Inflation and interest rates:** **Real versus Nominal Rates:** - Real rates are interest rates that have been adjusted for return. - The real rate of return indicates the actual change in purchasing power. - The nominal rate is the rate you earn on an investment before adjusting for inflation. **The Fisher Effect:** **1 + R = (1 + r) (1 + h)** Where: R is the nominal rate r is the real rate h is the inflation rate **VI- Determinants of Bond yields:** **The term structure of Interest rates:** *The term structure of interest rates* is the relationship between [nominal interest rates] on [default-free pure discount] securities and time to maturity; that is, the pure time value of money. These rates are pure interest rates because they involve no risk of default. The nominal rates reflected in the term structure (or in its graphical representation, the yield curve) comprise (a) the real rate of return, (b) the inflation premium, and (c) the interest rate risk premium. **\ Upward-sloping term structure:** **Download sloping term structure:**  - The yield curve is the graphical representation of the term structure. - The Treasury yield curve is the curve that results from plotting the yields of treasury notes and bonds in relation to their respective times to maturity. - Inflation premium is the compensation investors require to offset expected future prices. - Interest rate risk premium is the compensation investors require for their assumption of the risk related to changes in interest rates. - Default risk premium is the portion of a bond yield that compensates investors for the possibility that the bond's interest or principal might not be paid. - Taxability premium is the compensation that investors demand for a corporate bond over that of a comparable municipal bond. - Liquidity premium is the portion of a nominal interest rate that represents compensation of the lack of the ability to sell the bond at its fair value in a timely manner.