Solution to Case 8Bond Analysis and Valuation Corporate Bonds −They are More Complex Than You Think! 1. How should Jill go about explaining the relationship between coupon rates and bond prices? Why do the coupon rates for the various bonds vary so much? Jill could explain the relationship between coupon rates and bond prices by calculating the prices of bonds, which have similar features except for their coupon rates, under different assumptions regarding the yield to maturity. [For example, the 0%, AAA-rated, 20-year ABC Energy bond and the 5%, AAA-rated. 20-year ABC Energy bond.] Bond ABC Energy ABC Energy ABC Energy Coupon Rate 5% 5% 5% Maturity 20 20 20 Face Value $1,000 $1,000 $1,000 Rating AAA AAA AAA Yield 2% 5% 8% Price $1,490.54 $1,000.00 $705.46 % Change 49.05% 0.00% -29.45% ABC Energy ABC Energy ABC Energy 0% 0% 0% 20 20 20 $1,000 $1,000 $1,000 AAA AAA AAA 2% 5% 8% $672.97 $376.89 $214.55 78.56% 0.00% -43.07% The table shows that the 5% coupon bond has a wider fluctuation in price than the zerocoupon bond for equivalent changes in yields. 1 4.2. N = 40. depending on the firm’s preference for the coupon rate that will be paid. the yields demanded by investors will change based on economic and company-specific factors. investors are demanding a higher rate of return than what the company is currently paying via the coupon payment. would be “just right” and not really a bargain or overpriced.03% 2 . During the presentation one of the clients is puzzled why some bonds sell for less than their face value while others sell for a premium. the bond becomes less attractive and therefore its required rate of return goes up. Each of these rating agencies has a committee that evaluates the risk level of a company’s bond issue and accordingly assigns a rating ranging from AAA or Aaa (best rating) down to D (default). PMT = $25. the price has to vary in line with the consensus yield demanded by investors. When ratings get adjusted downward. Thus. Face Value = $1000.1. 3. FV = $1000. Price = $703. leading to a drop in price and vice-versa. at par. CPT I = 8. whether at a discount or a premium from face value. Thus. She asks whether the discount bonds are a bargain? How should Jill respond? Jill should explain that bonds can be issued at a discount. however.1 (semiannual coupons) PV = -$703. How are the ratings of these bonds determined? What happens when the bond ratings get adjusted downwards? The ratings are determined by professional rating agencies such as Standard & Poor’s and Moody’s. To calculate a bond’s YTM we must use the following inputs: For example: ABC Energy. or even at a premium from face value. as long as the yields are a true reflection of the risk level of the bond (which would happen in efficient markets). and receives the face value when it matures. The vast majority of bonds are sold at par ($1000) with the coupon rate being set equal to the yield that is commensurate with its rating and maturity. The YTM of a bond is also known as its promised yield. If the yield exceeds the coupon rate. 20 year. reducing its price. The ratings are periodically re-evaluated whenever there is any significant development in a company’s capital structure or earnings performance. bond prices. reinvests the coupons. After being issued. but the coupon rate is fixed. 5%. What does the term “yield to maturity” mean and how is it to be calculated? The “yield to maturity” (YTM) of a bond is the rate of return that an investor expects to earn when he or she buys the bond at its current price. there is generally a deferred call period of about 5 years.1601% 8.092.000 $1. the existence of a call provision presents a risk to the bond investor that their investment horizon on that bond may be prematurely ended.2023% The nominal yield to maturity on the bonds is calculated by multiplying the semi-annual yield by 2. it is best to compare similar risk bonds on the basis of their nominal YTMs.00%. The effective annual YTM would be calculated as ((1+. For this calculation.9927% 8.30 $1. In the case of callable bonds.9923% 5.0310% 8.206.0001% 7. the semi-annual YTM is 4. The company does pay a premium (typically equal to one extra coupon) when the bond is called. during which the bond cannot be called.2026% 9. How should she go about explaining the effects of the call provision on bond risk and return potential. 6.000 Coupon Rate 5% 0% 10% 11% Rating AAA AAA AA AA Quoted Years until Sinking maturity Fund Price $703.00 $1.04)2)-1 = .000 $1. Moreover. investors should calculate the yield to first call of the bonds and decide accordingly. What is the difference between the “nominal” and effective yields to maturity for each bond listed in Table 1? Which one should the investor use when deciding between corporate bonds and other securities of similar risk? Please explain.40 20 20 20 30 Yes Yes Yes No 3 Years NA 5 Years 5 Years 8. there is reinvestment risk associated with callable bonds.206.0816 or 8. Jill should explain to the audience that call provisions are attached to bonds so as to allow companies to refinance their debt at lower rates when interest rates drop. For example… On the ABC Energy 5%. Jill knows that the call period and its implications will be of particular concern to the audience. Thus.092.1597% 8. since the bonds are called when rates are low.30 $1.9997% 9.10 $208. 20 year bond. The effective YTM is calculated by compounding the semi-annual yield for two periods.00 $1.000 $1. Since the YTM is merely a promised yield with the actual yield being dependent on the reinvestment rate that each investor is able to earn.000 $1.0001% 8.1597% 9.000 $1.Issuer ABC Energy ABC Energy TransPower Telco Utilities Face Value $1.40 20 20 20 30 Yes Yes Yes No Yield to maturity 8.16%. the future 3 . Nominal Years until Sinking Call Yield to Effective Issuer Face Value Coupon Rate Rating Quoted Price maturity Fund Period maturity YTM ABC Energy ABC Energy TransPo wer Telco Utilities $1.9998% 8.000 $1.10 $208. Furthermore.000 5% 0% 10% 11% AAA AAA AA AA $703. CPT FV = $1. reinvest any coupons received at the rate of 5% per year and hold them until they mature.06% 6. but the highest price risk.06 $1. and the maturity is assumed to be the number of years until the bond becomes freely callable.54 FV of Coupon+ Face Vaue $2.2026% 9.00 $4. Nominal Yield to maturity 8. no reinvestment risk. 7.13 $8. PV = 0.9998% FV of Coupon $1.0001% 7.82% 8. (reinvestment rate). maturity risk.4 Years until Sinking maturity Fund 20 20 20 30 Yes Yes Yes No Call Period 3 Years NA 5 Years 5 Years Effective YTM 8. the zero coupon bond has no call risk. 5% coupon bond the realized return is calculated as follows: Future Value of Reinvested Coupons: PMT = -$25 (semiannual).1597% 9. Among the AAA bonds.685.06 Realized Return = [{(1685.3 1092 1206.685.1 208.370.00 $3.0001% 7.2023% Risk Rank (1=low) 1 2 3 4 The bond ratings provide a general guide as to the credit risk associated with each bond.9997% 9.3 1092 1206.9997% 9. Callability makes a bond have higher reinvestment risk.1601% 8.82% Note: The number of bonds purchased does not affect the realized return 4 . Telco Utilities’ bond has a longer maturity and no sinking fund making it the riskiest of the lot.685.1}]1/40 – 1 = 3. investors need to be aware of call risk.1 Issuer ABC Energy ABC Energy TransPower Telco Utilities Coupon Face Value Rate 1000 1000 1000 1000 5% 0% 10% 11% Quoted Price 703.41%*2= 6. Within each rating though. How should Jill go about explaining the riskiness of each bond? Rank order the bonds in terms of their relative riskiness.479.9998% Issuer ABC Energy ABC Energy TransPower Telco Utilities Face Value 1000 1000 1000 1000 Coupon Rate 5% 0% 10% 11% Rating AAA AAA AA AA Quoted Price 703. reinvestment risk.13 $7. i/y = 2.value is set equal to $1000 + 1 year’s coupon.61% In the case of the ABC Energy.1 208. and the sinking fund provision’s effect on risk. n = 40.54 Realized Return 6.06 $0.0001% 8.000.0001% 8. One of Jill’s best clients poses the following question.479. “ If I buy 10 of each of these bonds.4 Years until Call maturity Period 20 20 20 30 3 Years NA 5 Years 5 Years Nominal Yield to maturity 8.370. Among the AA bonds.00% 7. 8.06+1000)/703.5%. what will my realized return be on each bond investment?” How should she proceed? Realized Return = [{Future Value of reinvested coupons + Face Value}/Price of Bond ]1/n .