Interest Rate and Bond Valuation What is Bond

Interest Rate and Bond Valuation

What is Bond? • When a corporation or government wishes to borrow money from public, it usually does so by issuing, or selling bonds • When investors buy a bond, they lend money to the bond issuer, the government or corporation • As a lender, investors expect to be paid back the original amount (principle) and interest over some specified period time • As a borrower, the bond issuer must repay principle and interest to buyers over some specified period time Interest Rate and Bond Valuation 2

Key Features • Par value (face value, F) • Amount borrowed by issuers (sellers) from investors (buyers) at the beginning • Re-paid at the end of loan • Assume $1, 000 for corporate bonds • Annual Coupon (C) • Annual interest payments to buyers • Coupon Rate = Annual coupon/Par Value = C/F Interest Rate and Bond Valuation 3

Key Features • Maturity (T): • Number of years until par value is repaid by issuers (sellers) • Yield to maturity (YTM): • Discount rate used to value a bond • Quoted as an annual rate • Market rate of return Interest Rate and Bond Valuation 4

Annual Coupon Bond Price Interest Rate and Bond Valuation 5

Annual Coupon Bond Price • The cash flows from investing on this bond are 15 years $100 plus $1, 000 in the end of year 15 0 1 P=? 100 2 … 100 14 15 100 1, 000 • How much will investors pay to buy the bond? • Present value of this stream of cash flows • Two Parts – 1) Annuity + 2) PV of $1000 Interest Rate and Bond Valuation 6

Annual Coupon Bond Price Interest Rate and Bond Valuation 7

Annual Coupon Bond Price Interest Rate and Bond Valuation 8

Annual Coupon Bond Price Interest Rate and Bond Valuation 9

Example 1) Bond Prices § Lycan, Inc. , has 7. 6% coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 9. 6%, what is the current bond price? Interest Rate and Bond Valuation 10

Example 1 -Bond Prices N I/YR = 9. 6 PV =? PMT = 76 FV Interest Rate and Bond Valuation =9 = - 882. 97 = 1000 11

Example 1 -Bond Prices § Solution II: Interest Rate and Bond Valuation 12

Semiannual Coupon Bond Price Interest Rate and Bond Valuation 13

Semiannual Coupon Bond Price Interest Rate and Bond Valuation 14

Example 2) Bond Prices § App Store Co. issued 20 -year bonds one year ago at a coupon rate of 6. 1%. The bonds make semiannual payments. If the YTM on these bonds is 5. 3%, what is the current bond price? Interest Rate and Bond Valuation 15

Example 2 -Bond Prices N I/YR = 2. 65 PV =? PMT = 30. 5 FV Interest Rate and Bond Valuation = 38 = - 1095. 07 = 1000 16

Example 2 -Bond Prices Interest Rate and Bond Valuation 17

Example 3) Finding Bond YTM Interest Rate and Bond Valuation 18

Example 3 - Solution N I/YR PV PMT FV Interest Rate and Bond Valuation = 30 =? = 7. 45 = -1278 = 98 = 1000 19

Example 4) Finding Bond YTM Interest Rate and Bond Valuation 20

Example 4 - Solution N I/YR PV PMT FV Interest Rate and Bond Valuation = 60 =? = 3. 73 (Semi-Annual) =3. 73 x 2=7. 47 (Annual) = -1278 = 49 = 1000 21

Example 5) Coupon Rate § Merton Enterprises has bonds on the market making annual payments, with 14 years to maturity, and selling for $953. At this price, the bonds yield 9. 4%. What must the coupon rate be on Merton’s bonds? Interest Rate and Bond Valuation 22

Example 5 - Solution N = 14 I/YR = 9. 4 PV PMT FV Interest Rate and Bond Valuation = -953 =? = 87. 8/1000=8. 78% = 1000 23

Example 6) § Volbeat Corporation has bonds on the market with 12 years to maturity, a YTM of 9. 7%, and a current price of $948. The bonds make semiannual payments. What must the coupon rate be on the bonds? Interest Rate and Bond Valuation 24

Example 6 - Solution N I/YR = 4. 85 PV = -948 PMT FV Interest Rate and Bond Valuation = 24 =? = 44. 78 (Semi) or 44. 78 x 2=89. 56 (Ann. ) = 89. 56/1000=8. 96% = 1000 25

More About Bonds § Graphical Relationship Between Price and YTM Interest Rate and Bond Valuation 26

More About Bonds § Current Yield: § Coupon portion of bond return § Current Yield = Annual Coupon / Bond Price § Example: § In Example 6 we found interest payment of the bond is $89. 56 and price of the bond (PV) is $948 § Current yield= 89. 56/948=0. 095 or 9. 5% Interest Rate and Bond Valuation 27

Bond Sold at Par § Price = Par value § When are bonds sold at par? § Example: § 30 -year annual coupon bonds with $100 face value and 5% coupon rate § If YTM is 5%, how much is the bond? § § Issuer promises $5 annual coupon (interest payment) Bondholders expect $5 return Actual interest payment = Expected return Investors are willing to lend $100 to the issuer, so pay $100 to buy the bond Interest Rate and Bond Valuation 28

Discount Bond § Price < Par value § Example: § 30 -year annual coupon bonds with $100 face value and 5% coupon rate § If YTM is 10%, how much is the bond? § § § Issuer promises $5 annual coupon (interest payment) Bondholders expect $10 return Actual interest payment < Expected return Investors are not willing to lend $100 to the issuer Investors will pay less than $100 to buy Bond price is $52. 87 < $100 Interest Rate and Bond Valuation 29

Premium Bond § Price > Par value § Example § 30 -year annual coupon bonds with $100 face value and 5% coupon rate § If YTM is 3%, how much is the bond? § § § Issuer promises $5 annual coupon (interest payment) Bondholders expect $3 return Actual interest payment > Expected return Investors would like to pay more than $100 to buy Investors will lend more than $100 to the issuer Bond price is $139. 20 > $100 Interest Rate and Bond Valuation 30

Current Yields of Discount and Premium Bonds Interest Rate and Bond Valuation 31

Important Price Relations Interest Rate and Bond Valuation 32

Risks in Investing Bonds – Interest Rate Risk § Interest rate movements affect investors’ expectation on bond return, so do bond price § Interest rate risk refers to the sensitivity of bond price to interest rate variations § Two features determine interest rate risk § Maturity § Coupon Rate Interest Rate and Bond Valuation 33

Interest Rate Risks – Price Risk • Price Risk: • Change in price due to changes in interest rates. • Rule 1) The longer the maturity, the greater the interest rate risk • Bond with longer maturity has more distant cash flows, which are more adversely affected by the increasing of interest rate • Rule 2) The lower the coupon rate, the greater the interest rate risk • Bond with lower coupon rate proportionally depends more on the present value of par value, so its price is more adversely affected by the increasing of interest rate Interest Rate and Bond Valuation 34

Example 7) § Both Bond Bill and Bond Ted have 12. 4% coupons, make annual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. If interest rates suddenly rise by 3%, what is the percentage change in the price of these bonds? Interest Rate and Bond Valuation 35

Answer – Interest Rates Rise by 3% Interest Rate and Bond Valuation 36

Answer - Interpretation • The only difference between Bond Bill and Ted is coupon rate: Ted has a longer maturity • % decline in price for Bond Ted is greater than % decline for Bill, so Bond Ted price is more sensitive to interest rate changes Interest Rate and Bond Valuation 37

Example 8) § Bond J has a coupon rate of 4. 5%. Bond S has a coupon rate of 14. 5%. Both bonds have eight years to maturity, make annual payments, and have a YTM of 10%. If interest rates suddenly rise by 3%, what is the percentage change in the price of these bonds? What does this problem tell you about the interest rate risk of lower-coupon bonds? Interest Rate and Bond Valuation 38

Answer – Interest Rates Rise by 3% Interest Rate and Bond Valuation 39

Answer - Interpretation • The only difference between Bond J and S is time to maturity: S has a greater coupon rate • % decline in price for Bond S is smaller than % decline for S, so Bond S price is less sensitive to interest rate changes Interest Rate and Bond Valuation 40

Interest Rate Risks – Reinvestment Rate Risk • Reinvestment Rate Risk. • Uncertainty concerning rates at which cash flows can be reinvested. • Rules: (Mirror image of Price Risks) • Rule 1) Short-term bonds have more reinvestment rate risk than long-term bonds. • Rule 2) High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds. Interest Rate and Bond Valuation 41

Bond Features - Example Term Interest Rate and Bond Valuation Amount of issue $550 million Date of issue 01/15/2012 Maturity 01/15/2022 Face value $2, 000 Annual coupon 3. 875 Offer price (%) 99. 189 Coupon payment dates 01/15, 07/15 Security None Sinking fund None Call provision At any time Call price Treasure rate plus 0. 35% Rating Moody’s Baa 3, S&P BBB 42

A Bond Issued by Macy’s Interest Rate and Bond Valuation 43

Security • The issuer may pledge some of their assets for the bond. With these assets, the bondholders are secured when the company cannot repay its obligations • • Collateral: Financial securities that are pledged as security for payment of bond Mortgage: Real property (real estate, like land or buildings) Debentures: Unsecured bond for which no specific pledge of property is made Notes: Unsecured debt with original maturity less than 10 year • Macy’s bond Security: None • The bonds are not secured by specified assets Interest Rate and Bond Valuation 44

Sinking Fund • Usually, the bondholders receive the face value at maturity, but sometimes they may be repaid in part or in entirely before maturity • Early repayment is often handled through a sinking fund • A sinking fund is an account managed by the bond trustee for the purpose of repaying the bond • The company makes annual payment to the trustee • The trustee uses the funds to retire a portion of the bonds: Buying up some of the bonds or calling in a fraction of the outstanding bonds • Macy’s bond Sinking Fund: None • The bonds have no sinking fund Interest Rate and Bond Valuation 45

Call Provision • A call provision allows the company to repurchase part or all of the bond issue at stated price over specified time • Deferred call provision: the company can be prohibited from calling its bonds for the first part of a bond’s life (say the first 10 years) • During this period of prohibition, the bond is said to be call protected • Macy’s bond Call Provision: At any time • The bonds can be called at any time before maturity • The bond do not have deferred call Interest Rate and Bond Valuation 46

Call Price • Stated price in call provision • Price the company used to call the bonds from the market • Call price > face value, why? • The company would like to call the bond when the market interest rate is lower than the bond’s coupon • When the company calls the bond, it hurts bondholders’ benefit, so the bond has to be called at a price greater than face value • Call premium = Call price – face value • Macy’s Call Price: Treasury rate plus 0. 35% • The discount rate (YTM) used to compute Macy’s call price is treasury rate at calling time + 0. 35% Interest Rate and Bond Valuation 47

Protective Covenants • Negative covenants • Limit certain actions a company might otherwise wish to take during the term of the loan • Example: The firm cannot pledge any assets to other lenders • Positive covenants • Specify an action that the company agree to take or a condition the company must abide by • Example: The firm must maintain any collateral or security in good condition Interest Rate and Bond Valuation 48

Bond Indenture (Deed of Trust) • Contract between issuing company and bondholders • Includes: • • • Basic terms of the bonds Total amount of bonds issued Secured versus Unsecured Sinking fund Call provisions • Deferred call • Call premium • Details of protective covenants Interest Rate and Bond Valuation 49

Bond Ratings – Investment Quality • Measure bond default risk • High Grade • Moody’s Aaa and S&P AAA: Capacity to pay is extremely strong • Moody’s Aa and S&P AA: Capacity to pay is very strong • Medium Grade • Moody’s A and S&P A: Capacity to pay is strong, but more susceptible to changes in circumstances • Moody’s Baa and S&P BBB: Capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay • Macy’s bond Credit Rating: Baa 3 BBB • This bond has moderate credit risk at the bottom of investment grade Interest Rate and Bond Valuation 50

Bond Ratings – Low Quality • Low and Very Low Grade • Moody’s: Ba, B, Caa, C • S&P: BB, B, CCC, C • Considered speculative with respect to capacity to pay. The “BB” and “Ba” ratings are the lowest degree of speculation • Although such bond is likely to have some quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures to adverse conditions • Default • Moody’s D and S&P D – in default with principal and interest in arrears Interest Rate and Bond Valuation 51

Primary vs. Secondary Market • Primary Market • Original sale of securities by governments or corporations • Public offerings • Private placements • Secondary Market • Securities are bought and sold after the original sale • Provide the means for transferring ownership of corporate securities • Dealer markets and auction markets Interest Rate and Bond Valuation 52

Dealer and Dealer Market • Dealers • Maintains an inventory • Buy and sell for themselves, at their own risk • Used car dealer; local college bookstore • Dealer Market • • Most of buying and selling is done by dealers No central location Most trading in debt securities takes place over the counter (OTC) in old days Many dealers are connected electronically now Interest Rate and Bond Valuation 53

Bond Market • Dealer market • Extremely large number of bond issues • A corporation typically has only 1 common stock, but could have a dozen or more bond issues • Federal, state, and local governments can have a wide variety of bonds outstanding • Little or no transparency • Getting up-to-date prices difficult, particularly on small company issues • Little centralized reporting of transactions, which are privately negotiated between parties Interest Rate and Bond Valuation 54

Corporate Bond Quotations • Corporate bond dealers are now required to report trade information through Trade Reporting and Compliance Engine (TRACE) • One site that provides bond information is www. finra. org/industry/trace/corporatebond-data • Database that provides bond information is Bloomberg Interest Rate and Bond Valuation 55

Treasury Quotations Interest Rate and Bond Valuation 56

Treasury Quotations Maturity Coupon 5/15/2030 6. 250 Interest Rate and Bond Valuation Bid Asked 150. 7188 150. 7500 Chg. 8906 Asked Yield 2. 713 57

Treasury Quotations Maturity Coupon 5/15/2030 6. 250 Bid Asked 150. 7188 150. 7500 Chg. 8906 Asked Yield 2. 713 • Ask price goes up by 0. 8906% since the previous day • Two bond prices correspond to two YTM. Asked Yield is the YTM (=2. 713%) used to compute Asked Price (=$1, 507. 5) Interest Rate and Bond Valuation 58

Quoted Price vs. Invoice Price • Quoted bond prices = “clean” price. • Net of accrued interest. • Invoice Price = “dirty” or “full” price. • Price actually paid. • Includes accrued interest. • Accrued Interest. • Interest earned since last coupon payment is owed to bond seller at time of sale Interest Rate and Bond Valuation 59

Clean Price Interest Rate and Bond Valuation 60

Dirty Price Interest Rate and Bond Valuation 61

Example 9) § You purchase a bond with an invoice price of $1, 095. The bond has a coupon rate of 9. 9%, semiannual coupons, and there are two months to the next coupon date. What is the clean price of the bond? Interest Rate and Bond Valuation 62

Answer • Accrued interest = $99/2 × 4/6 Accrued interest = $33. 00 • And we calculate the clean price as: • Clean price = Dirty price – Accrued interest Clean price = $1, 095 – 33. 00 • • Clean price = $1, 062. 00 Interest Rate and Bond Valuation 63

Example 10) § You purchase a bond with a coupon rate of 9 percent, semiannual coupons, and a clean price of $840. If the next coupon payment is due in three months, what is the invoice price? Interest Rate and Bond Valuation 64

Answer • Accrued interest = $90/2 × 3/6 Accrued interest = $22. 50 • And we calculate the dirty price as: Dirty price = Clean price + Accrued interest Dirty price = $840 + 22. 50 • Dirty price = $862. 50 Interest Rate and Bond Valuation 65

Real Rates and Nominal Rates • Nominal rate on an investment is the % change in the number of $ • Real rate on an investment is the % change in purchasing power • Difference between nominal and real rate is inflation • Inflation is the % in the price level of average basket of goods • The price level (and the nominal wage rate) depend on the level of the money supply. The rate of inflation depends on the rate of growth of the money supply. • When the government had a large fiscal deficit, it would print money to finance it. Interest Rate and Bond Valuation 66

Fisher Effect Interest Rate and Bond Valuation 67

Example 11) § An investment offers a total return of 14 percent over the coming year. Bill Bernanke thinks the total return on this investment will be only 8. 1 percent. What does Bill believe the inflation rate will be over the next year? • The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) h = [(1 +. 14) / (1 +. 081)] – 1 • h =. 0546, or 5. 46% Interest Rate and Bond Valuation 68

Term Structure of Interest Rates • The graphical representation of the relationship between YTM and maturity of default-free, pure discount bonds is called the time structure of interest rates • Tells the pure time value of money for different length of time • Three components determine the shape of term structure • Real rate of interest • Inflation • Interest rate risk Interest Rate and Bond Valuation 69

Normal Case: Upward-Sloping Interest Rate and Bond Valuation 70

Inverted Case: Downward Sloping Interest Rate and Bond Valuation 71

Risk and Reward for Holding Bonds • Anything else that affects the risk of the cash flows (bond payments) to the bondholders will affect the bond yield to maturity (YTM) • Bond YTM is the return required in the market to compensate those risks of investing in bond Interest Rate and Bond Valuation 72

Thanks! 73