1. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 1 The Components of an Interest Rate: This is how the major factors that influence the cost of money are quantified and factored into interest rates Nominal Interest Rate  r = r* + IP + DRP + LP + MRP r = Nominal Rate in a particular market 1 ; also called the “Quoted Rate” r* = Real Interest Rate (Real Risk-Free Rate )  Compensates the lender for his opportunity costs, regardless of inflation or any other risks →Production Opportunities →Time Preference for Consumption  No one really knows what the real risk-free rate is  A commonly accepted value for the real risk-free rate can be found by subtracting current inflation rate from the current 30-day Treasury-bill rate. (See Nominal Risk-free Rate next page)  r* is not constant; it changes over time IP = Inflation Premium  Compensates the lender for loss in value over time due to inflation.  This is computed as the average expected inflation rate over the life of the loan (more on this later)  The IP that is often applied is derived from government economic forecasts. No one really knows what the current inflation rate is but the one the U.S. Government reports is the commonly accepted value  No one ever really knows what the inflation rate will be in the future (but we have some indication of what it might be; more on this later) Note 1: we will talk about different loan markets later Risk Premium Ch 3 Part 2: Term Structure of Interest Rates & Bonds

2. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 2 The Components of an Interest Rate: (continued) DRP = Default Risk Premium  Compensates the lender for possible default.  This is kind of like an “insurance payment”  30-day Treasury bills (T-bills; $1,000 face value very short term bonds) have a DRP of 0% Why? Answer: T-bills are considered “riskless”. LP = Liquidity Premium:  Accounts for the ability of a borrower to repay a loan with the firm’s assets.  If these assets are not very liquid (i.e. real estate, buildings, equipment, etc.), LP will be higher  Although it’s very difficult to calculate LP, it tends to differ 2 to 5 percent between the most liquid and least liquid financial assets MRP = Maturity Risk Premium  “Maturity” is the length of the loan  Compensates for Interest Rate Risk. The longer the term (time till maturity), the greater the interest rate risk, thus a higher MRP. (We will talk more about interest rate risk later in the semester)  Compensates for Reinvestment (Rate) Risk.  When a loan matures, the interest rate might be lower than when the loan was issued  Therefore the lender can’t reinvest the repaid principle at the same rate at which he originally loaned it. Nominal Risk-Free Rate (r RF ):  Since no one really knows what r* is, the financial world uses a commonly accepted formula: r* ≈ r RF - Current Inflation Rate  The above equation can be re-written as r RF ≈ r* + IP This is the “Nominal” or “Quoted” Risk-Free Rate (r RF )  The yield (interest rate) on a 30-day T-bill is usually used for r RF  A short-term T-bill is also considered a “riskless asset” (see Ch 5)

3. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 3 Real Interest Rate vs. Nominal Interest Rates The real interest rate accounts for inflation and expresses the “real” rate of return r real = r nominal – I Example: Given the nominal rate for the realized return on a one-year investment was 7.8500% p.a. and the inflation for the previous year was 1.8700%, what was the real ROR on that investment? r real = r nominal – I = 7.8500% - 1.8700% = 5.9800% Note: the real interest rate is not often used in the financial world The Term Structure of Interest Rates  Term Structure: the relationship between interest rates (yields) and different loan lengths (maturities). U.S. Treasury Bond Interest Rate Term Structure Term to Interest Rate Maturity Mar. 1980 Mar. 1999 Jan. 2006 6 months 15.0% 4.6% 4.16% 1 year 14.0% 4.9% 4.23% 5 years 13.5% 5.2% 4.34% 10 years 12.8% 5.5% 4.38% 20 years 12.5% 5.9% 4.46% Why do bonds of longer maturity have higher interest rates?  A graph of the term structure is called a yield curve. It graphically portrays the relationship between interest rates and maturities The shape of the yield curve indicates what the debt market thinks interest rates are likely to do in the future  upward sloping: interest likely to increase  downward sloping: interest rates likely to decrease  flat: interest rates likely to be stable

4. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 4 Bonds  Definition:  A bond is a long or short term debt instrument (a loan) issued by corporations and municipal, state and federal agencies.  A bond is a contract; it’s an IOU  When a corporation or government agency issues bonds (request a loan, borrows money), it is said to be issuing debt  When you buy a bond, you become a creditor to the issuing agency which, in turn, becomes a debtor to you  Bonds are issued in uniform denominations (i.e. $1,000, $10,000, etc.); most corporate and gov’t bonds are for $1,000  Bonds are traded (bought and sold); mostly OTC  Bonds are the most predominate method for financing business and government projects  Bonds are a fundamental investment class Some Terms:  Principal, Face Value, Maturity Value, and Par Value: The amount of money the firm borrows and promises to repay at some future date, usually at the maturity date  Coupon Interest Rate: r cpn, the stated annual rate of interest paid on a bond.  Coupon Payment:  the specified number of dollars of interest paid each period. Bonds most commonly pay semiannual interest.  it’s called a “coupon” because……..  Original Maturity: The number of years (or months) to maturity at the time the bond is issued. Also referred to as the “term”. Some bonds have been issued with 100 year original maturity  Maturity Date: A specified date on which the par value of a bond must be repaid.  “Maturity” or “term”: The time left until a bond matures. What do you call a 10-year original maturity bond that was issued 8 years ago and thus has only 2 years left to maturity? Answer: a 2-year bond

5. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 5 Bond Ratings:  Bonds from companies with similar risk characteristics are grouped together into categories as shown below Risk / r d Higher Lower  Standard & Poors, Moody’s and Fitch are the main firms that provide these bond ratings :  A firm’s bond rating can change over time and are influenced by:  Financial health/strength of the issuing company  Mortgage (collateral) provisions  Seniority of the debt  Restrictive covenants  Sinking fund or deferred call  Litigation possibilities  Regulation effects on issuer Higher risk, higher r d Moody'sS&PFitch Rating description Long-termShort-termLong-termShort-termLong-termShort-term Aaa P-1 AAA A-1+ AAA F1+ Prime Investment- grade Aa1AA+ High grade Aa2AA Aa3AA− A1A+ A-1 A+ F1 Upper medium grade A2AA A3 P-2 A− A-2 A− F2 Baa1BBB+ Lower medium grade Baa2 P-3 BBB A-3 BBB F3 Baa3BBB− Ba1 Not prime BB+ B B Non-investment grade Ba2BB speculative aka high- yield bonds Ba3BB− aka junk bonds B1B+ Highly speculative B2BB B3B− Caa1CCC+ CCCCC Substantial risks Caa2CCC Extremely speculative Caa3CCC− Default imminent with little Ca CC prospect for recovery C C D/ DDD /In default / DD D

6. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 6 Bond Market Interest Rate (r d ):  This is the current cost of debt for all loans of the same maturity and same level of risk  Each of the rating categories on the previous slide will have a different and unique term structure of interest rates  Each rating category is also referred to as a “bond market” (i.e. all AAA bonds of the same maturity are traded in the AAA “bond market”)  The cost of debt for a particular term in a particular bond market is called the “market interest rate”  All bonds in the same bond market and having the same maturity have the same market interest rate (“Law of One Price”)  The current market interest rate is also called the “spot rate” The Market Interest Rate (r d ) is the Required ROR for all bonds of the same rating and maturity AA+ Bonds Maturity (yrs)rdrd 14.25% 24.56% 35.02% 45.54% 56.13% 107.17% 208.93% B- Bonds Maturity (yrs)rdrd 15.75% 26.06% 36.52% 47.04% 57.63% 108.67% 2010.43% Example: Interest Rate Term Structure for Different Bond Ratings Bonds in different rating category but with the same maturity will have a different r d. Why?

7. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 7 Main Types of Credit Market Instruments: 1. Zero-coupon Bonds (Discount Bond):  Promises a single future payment which includes a single coupon payment (interest) and face value (principle)  These are usually short-term bonds 2. Coupon Bonds:  Promises a series of periodic coupon payments and repay the face value at maturity (the end of the loan)  These are usually long-term bonds  Coupons are typically paid semiannually 3. Consols: Make periodic interest payments in perpetuity and never repay the principle amount loaned (see Ch 3 Part 1 for perpetuities) 4. Fixed-payment Loans (Fully Amortized Loan): i.e. car loans, home mortgages, etc. 5. Simple Loan: a loan with only one interest payment due at the end of the loan Main Types of Bonds (By Issuers):  Treasury Bonds: issued by the U.S. Government; also known as “treasuries” or “government bonds”; three types (by maturity):  T-bills: orig. maturity of 1 year or less  Treasury Notes: 1 > orig. maturity < 10 years  Treasury Bonds: 10 > maturity; the maximum maturity currently available for new bonds is 30 years  Corporate Bonds: issued by private firms  Municipal Bonds:  issued by state and local govt’s; called “munis”;  interest earned on most munis is tax deductible  Foreign Bonds:  Subject to all risk/reward characteristics of domestic bonds  Additional risk due to currency exchange rate fluctuation

8. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 8 Pricing Bonds Zero-coupon Bonds:  Promises  Recall that a zero-coupon bond pays interest only at maturity (simple interest), it does not pay periodic interest  this is true for most types of zero-coupon bonds  In reality most zero-coupon bonds pay no interest  they are, instead, sold at a discount; they are issued as Original Issue Discount (OID) bonds  the cost of borrowing money using a zero-coupon bond is reflected by the issue price, which is lower than the face value value  At issue, the coupon rate is usually equal to r d Example 1: A firm with a BB bond rating wants to issue a 1-year $1,000 zero- coupon bond. This will be an OID bond What is the price of the bond at issue if r d for 1-year BB bonds is 3.0000%? Bond Issue(s) or Series  Companies don’t issue one bond at a time  They issue several million $ worth at a time with each bond usually having a $1,000 Face/Maturity Value  Example: Intel issues $50m worth of bonds on 1 Sep 2004, each bond has a Maturity Value of $1,000; that equates to 50,000 bonds  This single grouping of bonds is called a bond “issue” or “series”  All bonds in a series have the same bond rating and YTM (more on YTM later) 01 FV = $1000 V B = ? r d = 3% N=1, I/YR=3, FV=1000; PV (V B ) = $970.87

9. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 9 Finding the Retail Price a Coupon Bond  Coupon Bonds can be modeled as simple present value problems Example: Consider a $1,000 face value bond that pays annual interest and has a maturity of 5 years. Draw the Cash Flow diagram. The true TVM cash flow diagram for a bond looks like this: Bond Buyer’s (Holder, Lender) Perspective Bond Seller’s (Issuer, Borrower) Perspective Coupon (Interest) Payments (CPN or INT) Fair Market Value or V B or V d = PV PV = ? 012345 Note: the interest payments were implied In this chapter, the bond cash flow diagram looks like this: 0 1 2345  The interest payments are implied, but we will treat them as if they were specified; thus the bond looks an annuity (in arrears)  We will treat and analyze bonds as though they are annuities but they really aren’t  It is necessary to do this in order to do more complicated analysis on bonds which is beyond the scope of this course Face Value (M) ≠ Future Value Coupon (Interest) Payments (CPN or INT) Fair Market Value or V B or V d = PV 0 1 2345 Face Value (M) = $1,000 ≠ Future Value

10. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 10  m: the number of compounding periods/payments per year  T: the number of years left until maturity  n: the number of years or months or days, etc. (number of compounding periods/payments) until the bond matures; n = m x T  M: Face Value; the principle; the Par Value  Coupon Rate(r coupon ): This is the interest the borrower promises to pay the lender. It is an APR.  Coupon Payment (CPN): This is the interest payment (periodic or simple) CPN = Face Value(r CPN /m)  r d : The current market interest rate  it is the current cost of money for all bonds of the same maturity and risk category (bond rating)  it is the current ROR for all bonds of the same maturity and risk category thus it is an opportunity cost/best investment opportunity WRT risk, i.e. it is the Opportunity Cost of Capital (from Ch’s 3 & 5)  since our investment will grow at this rate we must also use it as the discount rate to compute PV  Things that will not change during the life of a bond: → M (the face value) → the Coupon Rate (promised interest rate) → the Coupon Payment (promised interest payment) → these are contractual obligations Finding the Retail Price a Coupon Bond

11. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 11 Finding the Retail Price a Coupon Bond  We want to know how to determine the appropriate current market price of bonds so we know how much to pay for or charge for that bond  This is the current “market price” or “retail price” or “settlement price” of a bond  Symbols: V B or V d  Basic Approach: Find Present Value of an Annuity  Basic Valuation Equation: V B = CPN/(1 + r d /m) 1 + CPN/(1 + r d /m) 2 …….+ CPN/(1 + r d /m) n-1 + CPN/(1 + r d /m) n + M/(1 + r d /m) n Note: There’s an additional term to account for the maturity value (face value, redemption value)  r d changes all the time due to factors we’ve preciously discussed  Since r d changes all the time, a bond’s Fair Market Value changes all the time Why? Answer: r d is the rate at which we will discount all future cash flows to find PV. If the discount rate changes, PV must change. 0 CPNVBVB n12n - 1 CPN M +

12. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 12 Finding the Retail Price a Bond (continued)  When the bond is issued, the Cpn Rate is generally equal to the market interest rate (r d ) at that time in order to sell the bond at par value Example 1: Two years ago Jamaica Jim’s Cruise Lines (BB bond rating) issued $100m worth of $1,000 bonds with an original maturity of 4 years and annual coupon payments. The bonds have a CPN Rate of 6.0000% since that was the cost of debt (market interest rate, r d ) for a 4-year loan for all BB rated firms at the time. The current market interest rate (r d ) for BB bonds with 2 year maturity is 5.0000%. (i.e. the current cost of a 2-year loan for all BB rated firms is 5.0000%). What is the current retail price (V B ) of these bonds? (The coupon due at t = 2 was paid yesterday) CPN = $60.00 M = Face Value = $1000 012 PV =V B = $1000.00 Cash Flow Diagram When the Bond Was Issued: Cpn Rate = r cpn = 6%; Current Mkt Interest Rate = r d = 6% Cpn Pmt = M(r d /m) =$1000(0.06/1) = $60.00 43 CPN = $60.00 M = Face Value = $1000 012 PV =V B = ? Cash Flow Diagram Current Situation: Cpn Rate = r cpn = 6% Current Mkt Interest Rate = r d = 5% Cpn Pmt = M(r cpn /m) =$1000(0.06/1) = $60.00

13. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 13 Finding the Retail Price a Bond (continued) Example 1: (continued) Numerical Solution: 1) Find CPN: CPN = Face Value(r cpn /m) = $1k(0.06/1) = $60 2) Find V B : V B = CPN/(1 + r d /m) 1 + CPN/(1 + r d /m) 2 …+ CPN/(1 + r d /m) n + M(1 + r d /m) n = 60/(1 + 0.05) 1 + 60/(1 + 0.05) 2 + 1000/(1 + 0.05) 2 = 60/(1.05) + 1060/(1.05) 2 = 60/1.05 + 1060/1.1025 = 57.1429 + 961.4512 = $1,018.59 Why do we discount the cash flows using r d ? Why is the current market price greater than the face value? Financial Function Solution: 1) Find CPN: CPN = Face Value(r cpn /m) = $1k(0.06/1) = $60 2) Clear your calculator: [2nd, CLR TVM] 3) Set/ensure 1 payment per year [2nd, P/Y, 1, ENTER] 4) Set payment timing to end of year: [2nd, BGN, 2nd, SET] (Note: the “BGN” should NOT appear in the display) 5) Enter parameters: óEnter N [2, N] óEnter discount rate (r d ) [5, I/Y] óEnter CPN payment [60, PMT] óEnter Face Value [1000, FV] Note: the FV(Future Value) of two payments of $60 over two years is not $1,000! When working with bonds, the FV key on the TI BA II PLUS can be interpreted as meaning “Face Value” óFind V B [CPT,PV] and voila! PV(V B ) = $1.018.59

14. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 14 0 1 2 r Cpn = 6% Beginning Balance: $0.00 $0.00 $60.00 Interest Earned: $0.00 $60.00 $63.60 Repay Principle: $1,000.00 Ending Balance: $0.00 $60.00 $1,123.60 Future Value = $60 + $60 x 0.06 M = Face Value Finding the Retail Price a Bond (continued) Example 1 (cont) Here’s an accounting explanation of what happens at each time period More Bond Terms:  Premium Bond: a bond whose current market value is greater than its par value (r d < Cpn Rate)  Discount Bond: a bond whose current market value is less than its par value (r d > Cpn Rate)  When a bond is first issued it is referred to as a new issue  Once a bond has been on the market a while, it’s referred to as a seasoned issue or an outstanding bond

15. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 15 Finding the Retail Price a Bond (continued) Example 2: (other than 1 compounding period per year): What is the retail price (V B ) of a 3-year, $10,000 Face Value bond that has a coupon rate of 6.0000% p.a. and has semiannual coupon payments? The current market interest rate (r d ) for this bond is 7.0000%. 0456123 123 yrs $10,000 CPN? Coupon Rate = 6% r d = 7% r periodic = ? V B = ? m = 2 T = 3 years n = m x T = 6

16. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 16 Finding the No Arbitrage Price / Theoretical Value / Fair Market Value of a Bond  The “Retail Price” of a bond as we discussed earlier is determined using one discount rate (r d or YTM) to discount all future cash flows to t = 0 and then adding them up  The “No Arbitrage Price” of a bond is found the same way (by discounting all future cash flows to t = 0 and adding them up). However, a different discount rate is used for each future cash flow Recall the topic of yield curves from MGT 326  The yield curves we discussed were “spot rate” yield curves; they don’t tell you what interest rates will be in the future  There is another type of yield curve called a “forward rate” yield curve; this does provide an estimate of what interest rates will be in the future 8642086420 Interest Rate (%) 1 51020 Years in the Future  Note that the market interest rate is different at each year of maturity  This means that at each different future point in time when the coupon is paid, the opportunity cost of capital will be different  To accurately determine the No Arbitrage Price / Theoretical Value / Fair Market Value, we must discount each future coupon payment at the appropriate opportunity cost of capital Forward Rate Yield Curve

17. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 17 Finding the No Arbitrage Price / Theoretical Value / Fair Market Value of a Bond (continued) Example: Consider a four-year U.S. Treasury $1,000 face value note paying 3.0000% p.a. coupon. What is the no arbitrage price of this bond? (The most recent coupon payment was yesterday). The current U.S Treasuries Forward Rate yield curve is: 543210543210 Interest Rate (%) Years in the Future 01234 2.5400% 3.5500% 4.0600% 4.3700% 1) Find CPN: CPN = Face Value(r cpn /m) = $1k(0.03/1) = $30 2) Find V B : V B = CPN 1 /(1 + r d,1 /m) 1 + CPN 2 /(1 + r d,2 /m) 2 + CPN 3 /(1 + r d,3 /m) 3 + + CPN 4 /(1 + r d,4 /m) 4 + M(1 + r d,4 /m) 4 = 30/(1 + 0.0254/1) 1 + 30/(1 + 0.0355/1) 2 + 30/(1 + 0.0406/1) 3 + 30/(1 + 0.0437/1) 4 + 1,000/(1 + 0.0437/1) 4 = 30/(1.0254) + 30/(1.0723) + 30/(1.1268) + 30/(1.1866) + 1000/(1.1866) = 29.2569 + 27.9783 + 26.6238 + 25.2824 + 842.7471 = $951.89 = No Arbitrage Price / Theoretical Value / Fair Market Value

18. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 18 Finding the No Arbitrage Price / Theoretical Value / Fair Market Value of a Bond (continued) Example (continued): Consider a four-year U.S. Treasury $1,000 face value note paying 3.0000% p.a. coupon. It’s YTM is 3.1500%. What is the retail price of this bond? (The most recent coupon payment was yesterday). 1) Find CPN: CPN = Face Value(r cpn /m) = $1k(0.03/1) = $30 2) Find V B (Using Calculator Financial Functions: N=4, I/Y= 3.15, PMT=30, FV=1000; CPT PV, V B = $994.44 Point:  Licensed bond brokers/traders (bond market insiders) sell bonds to each other at the No Arbitrage Price / Theoretical Value / Fair Market Value (i.e. at $951.89)  Bond brokers sell bonds to you and me (bond market outsiders) at the retail price plus what ever extra profit current market conditions will allow (i.e. at least $994.44)

19. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 19 What happens to the Value of a bond over time? (continued) As time goes on, the fair market value of a bond approaches (converges) to its par value (M, FV, etc) Adjusting Bond FMV by Prorating the Upcoming Coupon Pmt  Notice that the lines for the coupon bonds are not smooth  This is because the bond value drops by exactly the value of the coupon payment just after the coupon is paid  Then the value of the bond slowly rises until the next coupon is paid. This is because we have to adjust FMV for the upcoming coupon payment  This was not done in previous examples because we calculated V B just after the most recent coupon was paid

20. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 20 Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued)  Consider the bond from Example 1 again: Jamaica Jim’s Cruise Lines (BB bond rating) issued $100m worth of $1,000 bonds with an original maturity of 4 years and annual coupon payments. The bonds have a CPN Rate of 6.0000% since that was the cost of debt (market interest rate, r d ) for a 4-year loan for all BB rated firms at the time. The current market interest rate (r d ) is 5.0000%. What is the value of the bond? $60.00 $1000.00 012 PV =V B = ? 43 V B = CPN/(1 + r d /m) 1 + CPN/(1 + r d /m) 2 …+ CPN/(1 + r d /m) n + M(1 + r d /m) n = 60/(1+0.05) 1 + 60/(1+0.05) 2 + 60/(1+0.05) 3 + 60/(1+0.05) 4 + 1000/(1+0.05) 4 = 60/(1.05) + 1060/(1.05) 2 + 60/(1.05) 3 + 60/(1.05) 4 + 1000/(1.05) 4 = 60/1.05 + 60/1.1025 + 60/1.1576 + 60/1.2155 + 1000/1.2155 = 57.1429 + 54.4218 + 51.8303 + 49.3621 + 822.7025 = $1,035.46 (Note: since r d = 5% and r cpn = 6%, the bonds won’t sell at par) $60.00 Now exactly two years go by. The coupon due at year 2 will be paid today. What is the value of the bond is r d = 5%? $60.00 $1000.00 012 PV =V B = ? $60.00 V B = 60 + 60/(1+0.05) 1 + 60/(1+0.05) 2 + 1000/(1+0.05) 2 = 60 + 60/(1.05) + 1060/(1.05) 2 + 1000/(1.05) 2 = 60 + 60/1.05 + 60/1.1025 + 1000/1.1025 = 60 + 57.1429 + 54.4218 + 907.0295 = $1,078.59 What is the value of the bond the day after the coupon at year 2 was paid if r d = 5%? $60.00 $1000.00 012 PV =V B = $1,018.59 (as previously computed on p. 13) $60.00

21. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 21 Now exactly one more year goes by. The coupon due at year 3 will be paid today. What is the value of the bond is r d = 5%? $60.00 $1000.00 01 PV =V B = ? $60.00 V B = 60 + 60/(1+0.05) 1 + 1000/(1+0.05) 1 = 60 + 60/(1.05) + 1000/(1.05) 1 = 60 + 60/1.05 + 1000/1.05 = 60 + 57.1429 + 952.3810 = $1,069.52 What is the value of the bond the day after the coupon at year 3 was paid if r d = 5%? $60.00 $1000.00 01 PV =V B = ? V B = 60/(1+0.05) 1 + 1000/(1+0.05) 1 = 60/(1.05) + 1000/(1.05) 1 = 60/1.05 + 1000/1.05 = 57.1429 + 952.3810 = $1,009.52 A plot of the V B ’s looks like this: This is why the line in the diagram on p. 19 is jagged $1,009.52 $1,069.52 $1,018.59 $1,078.59 Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued)

22. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 22 Computing the Retail Price of a Bond Between Coupon Payments (The “Clean Price”) Example: A $1,000 face value Smithfields Foods bond matures 1 Jun 2012. It has a 7.0000% coupon rate and pays coupons semiannually. Its YTM as of 1 Oct 2010 was 6.1970%. What was this bond’s FMV as of 1 Oct 2010? The seller is entitled to accrued interest on the next coupon payment The Hard Way: Step 1: Find CPN: CPN = Face Value(r cpn /m) = $1k(0.07/2) = $35 Step 2: Discount all future cash flows back to 1 Dec 2010 $35 + [P/Y=2, N=3, I/Y=6.1970, PMT=35, FV=1000; CPT PV] PV = $35 + $1,011.3354 = $1,046.3354 Step 3: Discount this value back to 1 Oct 2010 a) Compute n: n = 61/183 = 0.3333 b) Find PV: N=0.3333, I/Y=6.1970, FV=1,046.3354; CPT PV, PV = $1,035.7465 Step 4: Find the accrued interest (prorated cpn pmt) owed to the seller Accrued interest: $35(122 / (122 + 61)) = $35(122 / 183) = $23.3333 Step 5: Compute V B (Settlement Value) V B = $1,035.7465 - $23.3333 = $1,012.41 = “Clean Price” Summary:  The “Dirty Price” is the retail price computed just after a coupon is issued (i.e. Example 1 on p. 13)  Clean Price = Dirty Price – Accrued Interest on upcoming coupon 1 Dec ’10 $35.00 1 Oct ‘10 PV =V B = ? 1 Jun ‘10 1 Jun ’11 $35.00 1 Dec ’11 $35.00 1 Jun ’12 $35.00 + $1000.00 122 days + 61 days = 183 days Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued)

23. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 23 Computing the Value of a Bond Between Coupon Payments (The “Clean Price”) Example (repeated): A $1,000 face value Smithfields Foods bond matures 1 Jun 2012. It has a 7.0000% coupon rate and pays coupons semiannually. Its YTM as of 1 Oct 2010 was 6.1970%. What was this bond’s FMV as of 1 Oct 2010? The Easy Way: Use the Bond Worksheet 1) Access Bond Worksheet: [2nd, BOND] 2) Clear the worksheet [2nd, CLR WORK] 3) Enter parameters: óEnter settlement date SDT (PV date)[10.0110, ENTER↓] óEnter coupon rate (not coupon payment) CPN [7, ↓] óEnter redemption (maturity) date RDT [6.0112, ENTER] óEnter YLD (yield to maturity) {press down arrow until YLD appears} [6.197, ENTER, ↓] óFind V B (redemption value as a % of face value); {press down arrow unit PR = 0.000000 appears} CPT, PRI(V B ) = 101.2413% multiply PRI by 10 → V B = $1,012.41 = “Clean Price” Point:  Very few bonds get traded right after a coupon payment  Most bonds get traded somewhere between coupon payments; therefore the retail price must be computed as the clean price 1 Dec ’10 $35.00 1 Oct ‘10 PV =V B = ? 1 Jun ‘10 1 Jun ’11 $35.00 1 Dec ’11 $35.00 1 Jun ’12 $35.00 + $1000.00 122 days + 61 days = 183 days Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued)

24. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 24 Computing the Value of a Bond Between Coupon Payments Example: A $5,000 face value Diamond Jim’s Corporation bond matures 1 Sep 2013. It has a 6.2500% coupon rate and pays coupons semiannually. Its YTM as of 1 Oct 2010 was 5.8250%. What was this bond’s FMV as of 1 Oct 2010? Use the Bond Worksheet

25. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 25 Yield to Maturity (YTM)  The rate of return (ROR) of a bond will not necessarily equal the coupon rate of the bond  YTM is the average ROR earned on a particular bond if it is bought at its current price and held to maturity.  Technically, YTM is the discount rate that will cause the sum of the PVs of all future cash flows to equal the current market price of the bond. V B = CPN/(1 + YTM /m) 1 + CPN/(1 + YTM /m) 2 ……+ CPN/(1 + YTM /m) n-1 + CPN/(1 + YTM /m) n + M(1 + YTM /m) n

26. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 26 Yield to Maturity (YTM) (continued) Example: (finding YTM): The current retail price of a 4-year, $10,000 AA bond issued by GM paying an annual coupon rate of 5.0000% p.a. is $9,913.89. What is the yield to maturity (YTM) of this bond? Approach: Given all the normal bond parameters (i.e. face value, coupon rate and maturity) and the current price of the bond, find YTM (this is like solving for r of an annuity) 01234 M = $10,000 Price = 9,913.89 r d = YTM = ? r cpn = 5% CPN Financial Calculator Solution: 1) Find CPN: CPN = Face Value(r cpn /m) = $10k(0.05/1) = $500 2) Enter parameters: óSet payments per year [2 nd, P/Y, 1] óEnter number of periods [ 4, N] óEnter Price [-9913.89, PV] óEnter CPN payment [500, PMT] óEnter Face Value [10000, FV] óFind YTM [CPT,I/Y] and voila! YTM (r d ) = 5.2442% Interpretation:  If you buy this bond today it will earn 5.2442% p.a. until it matures.  This bond has an Internal ROR of 5.2442%  The price is based on the current market interest rate (r d ) so….. YTM should be equal to the current market interest rate (r d )

27. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 27 01234 M = $1,000 Price = $973.23 r d = YTM = ? r cpn = 6.25% CPN m =2 T= 2 n = m x T = 2 x 2 = 4 Yield to Maturity (YTM) (continued) Example: (finding YTM w/ other-than-annual cpn payments): The current FMV of a $1,000 BB bond issued by Home Depot paying a semi-annual coupon rate of 6.2500% APR with 2 years left to maturity is $973.23. What is the yield to maturity of this bond?

28. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 28 Why would we want to know a bond’s YTM? Answer: to determine if the bond is selling at an appropriate market price  Each bond issue/series from a particular firm has a particular YTM  All BB bonds of the same maturity will have the same market interest rate and thus the prices of all these bonds should be equal or very close to each other (Law of One Price)  Thus the YTMs for all BB rated bonds of similar maturity will be equal to the market interest rate (r d )  However, the price of a particular firm’s bonds is a result of market perception of that firm’s financial health  If a bond’s reported YTM is higher than that of other bonds in the same bond market it means the bond is selling for less than FMV Current Yield  Current yield is the coupon payment divided by the price paid Current yield = Coupon Payment / Price Paid  Measures the part of the bond’s return due solely from the coupon payments; it ignores the capital gains yield/loss that occurs if you sell the bond prior to its maturity  This is not used much in the bond world

29. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 29 Holding Period Return (HPR) or Realized Total Yield  This is the total return from interest and capital gains when you sell a bond  Comprised of two factors: HPR = ROR of the Coupon Pmt + Realized Capital Gains Yield  Expressed as an annual rate Realized Capital Gains Yield  This is how much you earn if/when you sell a bond  It is capital gain(loss) due to changes in r d  It’s a rate (percentage)  It’s like computing Rate of Return (ROR) Example: At the beginning of the year, a $1,000 bond paying 8.25% APR semiannually bought for $1,048 (FMV). At the end of the year, this bond was sold for $1,059 (FMV). What is the capital gains yield on this bond? Capital Gains Yield = (V B1 – V B0 )/V B0 = (Ending Value - Beginning Value)/ Beginning Value = ($1,059 - $1,048)/$1,048 = 0.010496 = 1.0496% ROR of the Coupon Payment  This is the profit from interest on the loan expressed as a rate of return  Your book sez to use Current Yield for this  A better method is to use the EAR of coupon rate  assumes interest payments are reinvested at the coupon rate and thus TVM is applied  current yield factor in the price paid for the bond; this is already accounted for in cap. gains yield

30. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 30 Holding Period Return (HPR) or Realized Total Yield (continued) Example: One year ago you bought a AA rated $1,000 face value bond which pays 8.2500% coupon rate semiannually and has an 8 year term. You purchased the bond immediately after it issued its most recent coupon and at that time, the market interest rate for all AA rated bonds of 8 year maturity was 8.6000%. You sold this bond today, immediately after it paid its most recent coupon at par. What is the total return on this bond? 1) Find EAR Cpn Rate : [2nd, ICONV, 8.25, ENTER, ↓, ↓, 2, ENTER, ↓, ↓, CPT] = 8.4202% p.a. 2) Find Realized Capital Gains Yield: a) (V B1 – V B0 )/V B0 i) Find V B0 (the beginning value) T=8, m=2; n=T x m = 8 x 2 = 16 Cpn = FV(r cpn /m) = $1,000(0.0825/2) = $41.25 P/Y=2, N=16, I/Y=8.6, PMT=41.25, FV=1000; CPT PV: PV(V B0 ) = $980.0525 ii) Find V B1 (the ending value) Since the bond sold at par, V B1 = $1,000 iii) (V B1 – V B0 )/V B0 = ($1,000 - $980.0525) / $980.0525 = 2.0354% p.a. 3) Find Holding Period Return: 8.4202% + 2.0354% = 10.4556% p.a.

31. MGT 470 Ch 3 Part 2 Bonds & Term Structure of Int. Rates(me8ed) v1.0 Dec 15 31 1-yr Bond 20-yr Bond FV = $1,000 r coupon = 7.50% Annual Coupon r d = r coupon thus V B = FV Investment Implications of Bond Sensitivity to a change in r d  When market interest rates are falling, it’s good to have an inventory of long-term bonds to sell:  when r d decreases, bond values rise  since long-term bond prices are more sensitive (react more) to changes in r d, the profits from selling them will be greater than for short term bonds  When market interest rates bottom out and start to rise, it’s better to deal in (buy, hold, sell) short-term bonds:  when r d increases, bond prices fall  shorter-term bonds are less sensitive to changes in r d and will have lower int. rate (price) and reinvestment risk  if you have to liquidate your investment, you will lose much less money than if you had invested in long-term bonds Can we foresee what interest rates might do? Note: Coupon pmts are not prorated Price Sensitivity of Lt Bonds vs St Bonds wrt Changing r d