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Bonds Definition : A bond is a type of annuity

v2 Feb 12. Bonds Definition : A bond is a type of annuity 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

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Bonds Definition : A bond is a type of annuity

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  1. MGT 326 Ch 6: Bonds (bdh) v2 Feb 12 • Bonds • Definition: • A bond is a type of annuity • 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: rcpn , 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

  2. MGT 326 Ch 6: Bonds (bdh) More Terms: • 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 • Coupon Interest Rate • This is the cost of debt to the issuer (borrower) • A coupon bond pays periodic interest • A zero-coupon bond pays interest only once (simple interest) (more on this later); applies mainly to short-term bonds • For both types of bonds, the principle is repaid at maturity • Coupon Payment Example: a $10k face value bond has a coupon rate of 5.0000% per annum, paid annually. How much is the coupon payment? CPN(Cpn) = Face Value(rcoupon/m) = $10k(0.05/1) = $500 Example: a $10k face value bond has a coupon rate of 5% per annum, paid semiannually. How much is the coupon payment? CPN(Cpn) = Face Value(rcoupon/m) = $10k(0.05/2) = $250

  3. MGT 326 Ch 6: Bonds (bdh) Bond Ratings: • Bonds from companies with similar risk characteristics are grouped together into categories as shown below Risk / rd Lower Higher Higher risk, higher rd • Each of the rating categories above will have a different term structure of interest rates (see next slide) • Standard & Poors, Moody’s and Fitch are the main firms that provide these bond ratings • Each category has sub-ratings: • Moody’s: 1, 2, 3 • S&P: -, no symbol, + • Fitch: a, aa, aa3 • 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” from Ch 3) • The current market interest rate is also called the “spot rate” • 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

  4. MGT 326 Ch 6: Bonds (bdh) Example: Interest Rate Term Structure for Different Bond Ratings Bonds in different rating category but with the same maturity will have a different rd. Why? WSJ Bond Yields (as of 22 Feb 2012)

  5. MGT 326 Ch 6: Bonds (bdh) • The Market Interest Rate (rd) is the Required ROR for all bonds of the same rating and maturity • 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 • 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)

  6. MGT 326 Ch 6: Bonds (bdh) • Bond Retail Price: Zero-Coupon Bonds • Recall that a zero-coupon bond pays interest only at maturity (simple interest), it does not pay periodic interest • this is true for some 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 significantly lower than par value • At issue, the coupon rate is usually equal to rd • Bonds are valuated using the TVM principles and techniques we learned in Ch 4 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 rd for 1-year BB bonds is 3.0000%? FV = $1000 rd = 3% 0 1 VB = ? N=1, I/YR=3, FV=1000; PV (VB) = $970.87

  7. MGT 326 Ch 6: Bonds (bdh) • Bond Valuation: Coupon Bonds • 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 Ch 4 version cash flow diagram for a bond looks like this: M = Face Value = $1,000 ≠ Future Value 0 1 2 3 4 5 Note: In Ch 4, the interest payments were implied PV = ? In this chapter, the bond cash flow diagram looks like this: Bond Buyer’s (Holder, Lender) Perspective Face Value (M) ≠ Future Value Coupon (Interest) Payments (CPN or INT) 1 0 2 3 4 5 Fair Market Value or VB or Vd = PV • 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 (there’s only 1 payment each period, not 2 as is the case for an annuity as described in Ch 4) • It is necessary to do this in order to do more complicated analysis on bonds which is beyond the scope of this course Bond Seller’s (Issuer, Borrower) Perspective Fair Market Value or VB or Vd = PV 1 0 2 3 4 5 Face Value (M) ≠ Future Value Coupon (Interest) Payments (CPN or INT)

  8. MGT 326 Ch 6: Bonds (bdh) Bond Valuation (continued) • 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(rcoupon): 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(rCPN/m) • rd: 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

  9. MGT 326 Ch 6: Bonds (bdh) Finding the Retail Price a 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:VB or Vd • Basic Approach: Find Present Value of an Annuity • Basic Valuation Equation: VB = CPN/(1 + rd /m)1 + CPN/(1 + rd/m)2 …….+ CPN/(1 + rd/m)n-1 + CPN/(1 + rd/m)n + M/(1 + rd /m)n Note: There’s an additional term to account for the maturity value (face value, redemption value) • rd changes all the time due to factors we’ve preciously discussed • Since rd changes all the time, a bond’s Fair Market Value changes all the time Why? Answer: rd is the rate at which we will discount all future cash flows to find PV. If the discount rate changes, PV must change. M + VB CPN CPN CPN CPN 0 1 2 n - 1 n

  10. MGT 326 Ch 6: Bonds (bdh) • Finding the Retail Price a Bond (continued) • When the bond is issued, the Cpn Rate is generally equal to the market interest rate (rd) 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, rd) for a 4-year loan for all BB rated firms at the time. The current market interest rate (rd) 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 (VB) of these bonds? (The coupon due at t = 2 was paid yesterday) Cash Flow Diagram When the Bond Was Issued: Cpn Rate = rcpn = 6%; Current Mkt Interest Rate = rd = 6% Cpn Pmt = M(rd/m) =$1000(0.06/1) = $60.00 M = Face Value = $1000 CPN = $60.00 3 4 0 1 2 PV =VB = $1000.00 M = Face Value = $1000 Cash Flow Diagram Current Situation: Cpn Rate = rcpn = 6% Current Mkt Interest Rate = rd = 5% Cpn Pmt = M(rcpn/m) =$1000(0.06/1) = $60.00 CPN = $60.00 0 1 2 PV =VB = ?

  11. MGT 326 Ch 6: Bonds (bdh) Finding the Retail Price a Bond (continued) Example 1: (continued) Numerical Solution: 1) Find CPN: CPN = Face Value(rcpn/m) = $1k(0.06/1) = $60 2) Find VB: VB = CPN/(1 + rd /m)1 + CPN/(1 + rd /m)2…+ CPN/(1 + rd /m)n + M(1 + rd /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 rd? Why is the current market price greater than the face value? • Financial Function Solution: • 1) Find CPN: CPN = Face Value(rcpn/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: • Enter N [2, N] • Enter discount rate (rd) [5, I/Y] • Enter CPN payment [60, PMT] • Enter 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” • Find VB [CPT,PV] and voila! PV(VB) = $1.018.59

  12. MGT 326 Ch 6: Bonds (bdh) Finding the Retail Price a Bond (continued) Example 1 (cont) Here’s an accounting explanation of what happens at each time period 0 2 1 rCpn = 6% = $60 + $60 x 0.06 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 M = Face Value Future Value • More Bond Terms: • Premium Bond: a bond whose current market value is greater than its par value (rd < Cpn Rate) • Discount Bond: a bond whose current market value is less than its par value (rd > 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

  13. MGT 326 Ch 6: Bonds (bdh) 0 1 2 3 4 5 6 Finding the Retail Price a Bond (continued) Example 2: (other than 1 compounding period per year): What is the retail price (VB) 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 (rd) for this bond is 7.0000%. $10,000 CPN? Coupon Rate = 6% rd = 7% rperiodic = ? m = 2 T = 3 years n = m x T = 6 1 2 3 yrs VB = ?

  14. MGT 326 Ch 6: Bonds (bdh) • Yield to Maturity (YTM) • Definition: • The average rate of return earned on a particular bond if it is bought at its current price and held to maturity. • The ROR or “Internal ROR” based on its current price • It 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. VB = 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

  15. MGT 326 Ch 6: Bonds (bdh) 0 1 2 3 4 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) CPN M = $10,000 rcpn = 5% rd = YTM = ? Price = 9,913.89 • Financial Calculator Solution: • 1) Find CPN: CPN = Face Value(rcpn/m) = $10k(0.05/1) = $500 • 2) Enter parameters: • Set payments per year [2nd, P/Y, 1] • Enter number of periods [ 4, N] • Enter Price [-9913.89, PV] • Enter CPN payment [500, PMT] • Enter Face Value [10000, FV] • Find YTM [CPT,I/Y] and voila! YTM (rd) = 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 (rd) so….. YTM should be equal to the current market interest rate (rd)

  16. MGT 326 Ch 6: Bonds (bdh) 0 1 2 3 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? m =2 T= 2 n = m x T = 2 x 2 = 4 M = $1,000 CPN rcpn = 6.25% rd = YTM = ? Price = $973.23

  17. MGT 326 Ch 6: Bonds (bdh) • 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 (rd) • 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 What Happens When rd = Cpn Rate? • When the market interest rate (rd) equals the coupon interest rate (rcpn) the market value of a bond equals its face value (VB = M) • Example: What is the current fair market value (VB) of a 2-year, $1,000 Face Value bond that has a coupon rate of 6% APR and has annual coupon payments? The current market interest rate (rd) for this bond is 6%. (rcpn = rd). Answer: $1,000 • VB = CPN/(1 + rd)1 + CPN/(1 + rd)2…+ CPN/(1 + rd)n + M/(1 + rd)n • =$1,000(0.06)/(1 + 0.06)1 + $1,000(0.06)/(1 + 0.06)2 + $1,000/(1 + 0.06)2 • = $60/1.06 + $60/1.1236 + $1,000/1.1236 • = $56.6038 + $53.3998 + $899.9964 • = $1,000 • When the fair market value of a bond equals its face value, the bond is said to be “trading at par” (recall: face value = par value) • When the bond is first issued, the Cpn Rate is generally = to rd in order to sell the bond at or very close to par value

  18. MGT 326 Ch 6: Bonds (bdh) • 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 (rd 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 Ch 5 8 6 4 2 0 Interest Rate (%) 1 5 10 20 Maturity • 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

  19. MGT 326 Ch 6: Bonds (bdh) 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 yield curve is: 5 4 3 2 1 0 4.3700% 4.0600% 3.5500% 2.5400% Interest Rate (%) 0 1 2 3 4 Maturity 1) Find CPN: CPN = Face Value(rcpn/m) = $1k(0.03/1) = $30 2) Find VB: VB = CPN1/(1 + rd,1 /m)1 + CPN2/(1 + rd,2 /m)2+ CPN3/(1 + rd,3 /m)3 + + CPN4/(1 + rd,4 /m)4 + M(1 + rd,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

  20. MGT 326 Ch 6: Bonds (bdh) 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(rcpn/m) = $1k(0.03/1) = $30 • 2) Find VB(Using Calculator Financial Functions: • N=4, I/Y= 3.15, PMT=30, FV=1000; CPT PV, VB = $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)

  21. MGT 326 Ch 6: Bonds (bdh) Relationship Between rd and VB: • When rd goes down (over time), VB goes up [rd↓, VB↑] • When rd goes up (over time), VB goes down [rd↑, VB↓] Example: A $1,000 bond issued by Home Depot paying a semi-annual coupon rate of 6.2500% APR with 2 years left to maturity has a current rd of 7.7200%. a) What is the VB of this bond? Answer: $973.23 b) What is the VB of this bond if rd fell to 4.5000%? Answer: $1,033.12 c) What is the VB of this bond if rd rose to 8.5000%? Answer: $959.40 Cpn Rate = 6.25% @ rd = 6.25%, this bond trades at par (VB = $1,000) Value @ rd > 6.25%, VB < $1,000 @ rd < 6.25%, VB > $1,000 rd (YTM)

  22. MGT 326 Ch 6: Bonds (bdh) What happens to the Price (Value) of a bond over time? Example: A $1,000 face value bond with an annual coupon rate of 5.0000% p.a., paying annual coupon payments and a maturity of 5 years is issued at t = 0. What is its value at t = 1 if it’s trading at par? CPN M = $1,000 Cpn Rate = 5% rd = 5% 0 1 2 3 4 5 VB1 = ? • VB1 = $1,000 (rd = Cpn Rate, it’s trading at par) • What is the bond’s value at t = 1 if market interest rates have dropped to 2.8000%? Answer: VB1 = $1,082.17 • What is the value of the bond with only 3 years remaining until maturity (t=2) if the market rate is 2.8000%? Answer: VB2 = $1,062.47 • What is the value of the bond with only 1 year remaining until maturity (t=4) if the market rate is 2.8000% ? Answer: VB4 = $1,021.40 • As time goes on, the fair market value of a bond approaches (converges) to its par value (M, FV, etc) • As a bond approaches maturity, value fluctuation due to changes in rd decreases • the value of a premium bond would decrease towards $1,000. • the value of a discount bond would increase towards $1,000. • At maturity, the value of any bond must equal its par value (after the last coupon payment is paid)

  23. MGT 326 Ch 6: Bonds (bdh) 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 VB just after the most recent coupon was paid

  24. MGT 326 Ch 6: Bonds (bdh) • 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, rd) for a 4-year loan for all BB rated firms at the time. The current market interest rate (rd) is 5.0000%. What is the value of the bond? $1000.00 $60.00 $60.00 $60.00 $60.00 3 4 0 1 2 PV =VB = ? VB = CPN/(1 + rd /m)1 + CPN/(1 + rd /m)2…+ CPN/(1 + rd /m)n + M(1 + rd /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 rd = 5% and rcpn = 6%, the bonds won’t sell at par) Now exactly two years go by. The coupon due at year 2 will be paid today. What is the value of the bond is rd = 5%? $1000.00 $60.00 $60.00 $60.00 0 1 2 PV =VB = ? VB = 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 rd = 5%? $1000.00 $60.00 $60.00 0 1 2 PV =VB = $1,018.59 (as previously computed on p. 11)

  25. MGT 326 Ch 6: Bonds (bdh) Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued) 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 rd = 5%? $1000.00 $60.00 $60.00 0 1 PV =VB = ? VB = 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 rd = 5%? $1000.00 $60.00 0 1 PV =VB = ? VB = 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 VB’s looks like this: This is why the line in the diagram on p. 23 is jagged $1,078.59 $1,069.52 $1,018.59 $1,009.52

  26. MGT 326 Ch 6: Bonds (bdh) Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued) 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? 1 Oct ‘10 PV =VB = ? 1 Jun ’11 $35.00 1 Dec ’10 $35.00 1 Dec ’11 $35.00 1 Jun ’12 $35.00 + $1000.00 1 Jun ‘10 122 days + 61 days = 183 days • The seller is entitled to accrued interest on the next coupon payment • The Hard Way: • Step 1: Find CPN: CPN = Face Value(rcpn/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 3: Find the accrued interest (prorated cpn pmt) owed to the seller • Accrued interest: $35(122 / (122 + 61)) = $35(122 / 183) = $23.3333 • Step 4: Compute VB (Settlement Value) • VB = $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. 11) • Clean Price = Dirty Price – Accrued Interest on upcoming coupon

  27. MGT 326 Ch 6: Bonds (bdh) Adjusting Bond FMV By Prorating the Upcoming Coupon Pmt (continued) 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? 1 Oct ‘10 PV =VB = ? 1 Jun ’11 $35.00 1 Dec ’10 $35.00 1 Dec ’11 $35.00 1 Jun ’12 $35.00 + $1000.00 1 Jun ‘10 122 days + 61 days = 183 days • The Easy Way: Use the Bond Worksheet • 1) Access Bond Worksheet: [2nd, BOND] • 2) Clear the worksheet [2nd, CLR WORK] • 3) Enter parameters: • Enter settlement date SDT (PV date)[10.01.10, ENTER↓] • Enter coupon rate (not coupon payment) CPN [7, ↓] • Enter redemption (maturity) date RDT [6.01.12, ENTER] • Enter YLD (yield to maturity) {press down arrow until YLD appears} [6.197, ENTER, ↓] • Find VB (redemption value as a % of face value); {press down arrow unit PR = 0.000000 appears} CPT, PRI(VB) = 101.2413% • multiply PRI by 10 → VB = $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

  28. MGT 326 Ch 6: Bonds (bdh) 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

  29. MGT 326 Ch 6: Bonds (bdh) Increasing rd Decreasing rd 30 25 20 15 10 5 0 Risk of Long-term Bonds vs Short-term Bonds Value Fluctuation Due to Changes in rd rd < Coupon Rate Value M Price Range rd > Coupon Rate Years to Maturity • As time goes on, the fair market value of a bond approaches (converges) to its par value (M, FV, etc) • The price range of a 30-year bond is much greater than that of shorter maturity bonds • The prices of bonds with longer remaining maturity are much more influenced by a change in rd than the price of bonds with shorter remaining maturity Why? • Price volatility of long maturity bonds is greater than that of short maturity bonds • Longer term bonds are more sensitive to change in rd than shorter term bonds • Long maturity bonds are riskier than shorter maturity bonds; this is reflected by the higher rd

  30. MGT 326 Ch 6: Bonds (bdh) Risk of Long-term Bonds vs Short-term Bonds FV = $1,000 rcoupon = 7.50% Annual Coupon 20-yr Bond rd = rcoupon thus VB = FV 1-yr Bond Note: Coupon pmts are not prorated • Investment Implications of Bond Sensitivity to a change in rd • When market interest rates are falling, it’s good to have an inventory of long-term bonds to sell: • when rd decreases, bond values rise • since long-term bond prices are more sensitive (react more) to changes in rd, 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 rd increases, bond prices fall • shorter-term bonds are less sensitive to changes in rd and will have lower int. rate (price) and reinvestment risk Can we foresee what interest rates might be?

  31. MGT 326 Ch 6: Bonds (bdh) Other Risks Associated With Bonds • Interest Rate Risk (Bond Price Risk): This is the uncertainty concerning the future value of a bond due to changes in rd • Reinvestment Risk: • The risk that income from a bond portfolio will vary because cash flows have to be reinvested at current market rates • When a bond matures, the owner may not be able to reinvest the face value of that bond at a rate at least a favorable as the one currently paid by that bond. • These two types of risk are what is really being compensated by the Maturity Risk Premium (MRP) Point: Shorter term bonds have less exposure to these types of risk than longer term bonds. • That’s why MRP is smaller for short-term bonds than for long-term bonds • A possible decision criteria for selecting bond maturities

  32. MGT 326 Ch 6: Bonds (bdh) • 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 rd • It’s a 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 = (VB1 – VB0)/VB0 = (End Value - Begin. Value)/ Begin. Value = ($1,059 - $1,048)/$1,048 = 0.010496 = 1.0496% Realized Total Yield • This is the total return from interest and capital gains when you sell a bond • Usually expressed as an annual rate • Realized Total Return = EAR of Cpn Rate + Realized Cap. Gains Yield (Important Assumption: interest payments are reinvested at the coupon rate)

  33. MGT 326 Ch 6: Bonds (bdh) 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) (VB1 – VB0)/VB0 i) Find VB0 (the beginning value) T=8, m=2; n=T x m = 8 x 2 = 16 Cpn = FV(rcpn/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(VB0) = $980.0525 ii) Find VB1 (the ending value) Since the bond sold at par, VB1 = $1,000 iii) (VB1 – VB0)/VB0 = ($1,000 - $980.0525) / $980.0525 = 2.0354% p.a. 3) Find Realized Total Yield: 8.4202% + 2.0354% = 10.4556% p.a.

  34. MGT 326 Ch 6: Bonds (bdh) Types of Bond (From Ch 14) • Mortgage Bonds: A bond with some fixed asset presented as collateral • higher claim priority than unsecured bonds • usually have lower interest rates • Debentures: A long-term bond that is not secured by a mortgage on a specific property • higher interest rates than secured bonds Why? • Subordinated Debentures: A bond that is specifically designated to be of lower claim priority than other bonds Bonds with Provisions (Indentures, Restrictions): • Convertible bonds: A bond that can be converted to a fixed number of stock shares specified at time of issue (it’s like a stock option) • have a lower coupon rate than non-convertible bonds Why? • offers the holder a chance at capital gains through stock • Warrants: • Similar to a convertible bond but the price of the stock is specified at time of issue, not the number of shares • offer a chance at capital gains if stock price at time of conversion is higher than the specified stock price • Income Bond: pays interest only if the issuing firm has sufficient income to pay the interest • A real safe deal from the issuer’s stand point; this type of bond can’t bankrupt a firm • These type bonds pay high relative interest (otherwise, who would buy them?)

  35. MGT 326 Ch 6: Bonds (bdh) • Putable Bonds: a bond that can be redeemed for cash at the bond holder’s option • pay lower interest rates Why? • when would it be a good idea to redeem this bond? • Callable Bond: a bond that has a “call provision” which allows the issuer to redeem the bond for cash at the issuer’s option prior to the stated maturity date • pay higher interest rates. Why? • when would it be a good idea to redeem this bond? • Call premium: Compensation paid to the holder by the issuer if/when the bond is “called”

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