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Chapter 7 Interest Rates and Bond Valuation Bond Features Bond - evidence of debt issued by a corporation or a governmental body. A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legaI claim on future cash flows of the borrower. The issuer promises to: Make regular coupon payments every period until the bond matures, and Pay the face/par/maturity value of the bond when it matures. Default - since the above mentioned promises are contractual obligations, an issuer who fails to keep them is subject to legal action on behalf of the lenders (bondholders). Bond Value = Present Value of the Coupons + Present Value of the Face Value Bond Value = INT [1 – (1/(1 + rd)N)]/rd + M * 1/(1 + rd)N where: INT = the promised coupon payment M = the promised face value N = number of periods until the bond matures rd = the market’s required return, YTM If a bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time 0 1 2 3 4 5 Coupons $80 $80 $80 $80 $80 Face Value $ 1000 Market Price $____ How much is this bond worth? It depends on the level of current market interest rates. If the going rate on bonds like this one is 10%, then this bond is worth $924.18. 1 5N 10 I/Y 80 PMT 1000 FV CPT PV (-924.18) Suppose a bond currently sells for $932.90. It pays an annual coupon of $70, and it matures in 10 years. It has a face value of $1000. What are its coupon rate, current yield, and yield to maturity (YTM)? 1. The coupon rate (or just “coupon”) is the annual dollar coupon as a percentage of the face value: Coupon rate = $70 /$1000 = 7% 2. The current yield is the annual coupon divided by the current market price of the bond: Current yield = $70 /932.90 = 7.5% 3. The yield to maturity (or “YTM”) is the rate that makes the price of the bond just equal to the present value of its future cash flows. It is the unknown r in: Value of Bond = Coupon Payment [1 –(1/(1 + rd)10]/rd + Face Value /(1 + rd )10 $932.90 = $70 [1 – (1/(1 + rd)10)]/rd + $1000/(1 + rd )10 The only way to find the YTM is trial and error: a. Try 10%: $70 * [(1 - 1/(1.10)10]/.10 + $1000/(1.10)10 = $816 b. Try 9%: $70 * [1 - 1/(1.09)10]/.09 + $1000/(1.09)10 = $872 c. Try 8%: $70 * [1 - 1/(1.08)10]/.08 + $1000/(1.08)10 = $933 ( ) The yield to maturity is closest to 8%. Or using the BA II Plus Calculator 10 N 70 PMT - 932.90 PV 1000 FV CPT I/Y Valuing a Bond 2 Assume you have the following information. Barnhart, Inc. bonds have a $1000 face value The promised annual coupon is $100 The bonds mature in 20 years The market’s required return on similar bonds is 10% Calculate the present value of the face value = $1000 X [1/1.1020 ] = $1000 X .14864 = $148.64 Calculate the present value of the coupon payments = $100 [1 - (1/1.1020)]/.10 = $100 8.5136 = $851.36 The value of each bond = $148.64 + 851.36 = $1000 Or 20 N 10 I/Y 100 PMT 1000 FV CPT PV (-1000) Assume you have the following information. Barnhart, Inc. bonds have a $1000 face value The promised annual coupon is $100 The bonds mature in 20 years The market’s required return on similar bonds is 12% Calculate the present value of the face value = $1000 [1/(1.12)20 ] = $1000 .10366 = $103.66 Calculate the present value of the coupon payments = $100 [1 - (1/1.1220)]/.12 = $100 7.4694 = $746.94 3 The value of each bond = $103.66 + 746.94 = $850.60 Or 20 N 12 I/Y 100 PMT 1000 FV CPT PV (-850.60) Example: A Premium Bond Assume you have the following information. Barnhart, Inc. bonds have a $1000 face value The promised annual coupon is $100 The bonds mature in 20 years The market’s required return on similar bonds is 8% 20 N 8 I/Y 100 PMT 1000 FV CPT PV (-1196.36) Calculate the present value of the face value = $1000 x [1/1.0820 ] = $1000 .21455 = $214.55 Calculate the present value of the coupon payments = $100 x [1 - (1/1.0820)]/.08 = $100 9.8181 = $981.81 The value of each bond = $214.55 + 981.81 = $1,196.36 Why do the bonds in this and the preceding example have prices that are different from par? Bond Value = Present Value of the Coupons + Present Value of the Face Value Bond Value = INT [1 – (1/(1 + rd)N)]/rd + M * 1/(1 + rd)N where: INT = the promised coupon payment M = the promised face value N = number of periods until the bond matures rd = the market’s required return, YTM 4 SEMI ANNUAL COUPON PAYMENTS Most bonds pay coupon payments semi-annually. So a bond with a 10% coupon rate and a face value of $1000 has annual coupon payment Annual Coupon Payment = $1000 *.10 = $100 If the bond has 10 years to maturity and a yield to maturity of 12% The bond will pay a $50 coupon every six months ($100/2). If the bond has 10 years to maturity and a yield to maturity of 12% 0 1 2 3 4 10 [-----[----[-----[-----[-----[------[-----[------[-----------------------------[ 50 50 50 50 50 50 50 50 50 $1000 10*2 = 20 N 12/2 = 6 I/Y 100/2 = 50 PMT 1000 FV CPT PV (-885.30) Value of Bond = 100/2 [1 - 1/(1 + (.12/2)2*10]/.12/2 + 1000 * 1/(1 + .12/2)2*10 885.30 Reznik Corporation has bonds on the market with 12.5 years to maturity, a yield-to-maturity of 8 percent, and a current price of $875. The bonds make semiannual payments. What must the coupon rate be on the bonds? Total number of coupon payments = 12.5 * 2 = 25 Yield-to-maturity per period = 8% / 2 = 4% Maturity value = F = $1000 1. Callaghan Motors' bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity of 9 percent. What is the current market price of these bonds? 2. Thatcher Corporation's bonds will mature in 10 years. The bonds have a face value of $1,000 and an 8 percent coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds are callable in 5 years at a call price of $1,050. What is the yield to maturity? What is the yield to call? 3 Nungesser Corporation has issued bonds that have a 9 percent coupon rate, payable semi- annually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5 percent. What is the price of the bonds? 5 4. A bond that matures in 10 years sells for $985. The bond has a face value of $1,000 and and a 7% coupon rate.. a.. What is the bond's yield to maturity (YTM)? b. Assume that the yield to maturity remains constant for the next 3 years. What will be the price of the bond 3 years from today? 5. A bond that matures in 7 years sells for $1,020. The bond has a face value of $1,000 and a yield to maturity of 10.5883 percent. The bond pays coupons semiannually. What is the bond's current yield? Factors Affecting Bond Yields * The real rate of interest Expected future inflation Interest rate risk Default risk premium Taxability premium Liquidity premium Features of a May Department Stores Bond Term Explanation Amount of issue $125 million The company will issue $125 million worth of bonds. Date of issue 2/28/86 The bonds were sold on 2/28/86. Maturity 3/1/16 The principal will be paid in 30 years. Face Value $1,000 The denomination of the bonds is $1,000. Annual coupon 9.25 Each bondholder will receive $92.50 per bond per year (9.25% of the face value). Offer price 100 The offer price will be 100% of the $1,000 face value per bond. Term Explanation 6 Coupon payment dates 3/1, 9/1 Coupons of $92.50/2 = $46.25 will be paid on these dates. Security None The bonds are debentures. Sinking fund Annual, The firm will make annual payments beginning 3/1/97 toward the sinking fund. Call provision Not callable The bonds have a deferred call feature. before 2/28/93 Rating Moody’s A2 This is one of Moody’s higher ratings. The bonds have a low probability of default. Call price 106.48 initially, After 2/28/93, the company can buy declining to 100 back the bonds for $1,064.80 per bond, declining to $1,000 on 2/28/05. The Bond Indenture The bond indenture is a three-party contract between the bond issuer, the bondholders, and the trustee. The trustee is hired by the issuer to protect the bondholders’ interests. (What do you think would happen if an issuer refused to hire a trustee?) The indenture includes The basic terms of the bond issue The total amount of bonds issued A description of the security The repayment arrangements The call provisions Details of the protective covenants 7 Bond Ratings Low Quality, speculative, Investment-Quality Bond Ratings and/or “Junk” Standard & Poor’s AAA AA A BBB BB B CCC CC C D Moody’s Aaa Aa A Baa Ba B Caa Ca C C Moody’s S&P Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong. Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rating, this group comprises the high- grade bond class. A A Debt rated A has a strong capacity to pay interest and repayrincipal, although it is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than debt in high rated categories. Baa BBB Debt rated Baa and BBB is regarded as having an adequate capacity to pay interest and repay principal. Whereas it normally exhibits adequate protection parameters, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity to pay interest and repay principal for debt in this category than in higher rated categories. These bonds are medium-grade obligations. Ba, B BB, B Debt rated in these categories is regarded, on balance, as Ca, CCC, C predominantly speculative with respect to capacity to pay interest and repay principal in accordance with the terms of the obligation. BB and Ba indicate the lowest degree of speculation, and CC and Ca the highest degree of speculation. Although such debt will likely have some quality and protective characteristics, these are out-weighed by large uncertainties or major risk exposures to adverse conditions. Some issues may be in default. D D Debt rated D is in default, and payment of interest and/or repayment of principal is in arrears 8 NEW YORK EXCHANGE BONDS Quotations as of 4 p.m. Eastern Time Thursday, March 5, 1998 CORPORATION BONDS Volume, $15,786,000 Co Cp Mat YTM Vol Price CHG Rate ATT 4 3/4 98 4.8 10 99 9/16 ... ATT 7 1/8 02 6.9 10 104 1/8 ATT 6 3/4 04 6.6 118 102 5/8 +1/8 ATT 7 1/2 06 7.0 30 107 3/8 ... ATT 8 1/8 22 7.6 72 107 1/8 1/4 ATT 8 1/8 24 7.6 78 106 1/2 + 5/8 ATT 8 5/8 31 7.9 24 108 7/8 1/2 TREASURY BONDS, NOTES & BILLS Bid Ask Cp Rate MAT Price Price CHG YTM 53/8 Jan 00n 99:17 99:18 +1 5.62 73/4 Jan 00n 103:24 103:26 +1 5.61 77/8 Nov 04n 111:07 111:11 . . . . 5.80 . . . . . . . . . . . . . . . 9 Nov 18 133:10 133:16 4 6.12 8 7/8 Feb 19 131:31 132:05 6 6.13 8 1/8 Aug 19 123:13 123:19 5 6.13 8 3/4 May 20 131:09 131:15 8 6.13 8 3/4 Aug 20 131:14 131:20 7 6.14 7 7/8 Feb 21 121:00 121:06 6 6.14 9