Bond Valuation Case Study 3 Fundamentals of financial management BEAM047 Alexander Pereverzev Yana Shkrebenkova Verónica Deambrosi Dina Sharipova Bond Bond - a long-term contract under which a borrower agrees to make payments of interest and principal on specific dates to the holders of the bond. Grouping based on the issuer Treasury bonds Corporate bonds Municipal bonds Foreign bonds A Bond’s Key features • Par Value – the face value of a bond • Coupon Interest Rate - the stated annual interest rate on a bond: • Fixed-Rate Bond - a bond whose interest rate is fixed for its entire life • Floating-Rate Bond - a bond whose interest rate fluctuates with shifts in the general level of interest rates • Zero Coupon Bond – a bond that pays no annual interest but is sold at a discount below par, thus compensating investors in the form of capital appreciation. • Original Issue Discount (OID) Bond - any bond originally offered at a price below its par value. • Maturity Date - a specified date on which the par value of a bond must be repaid. Original Maturity - the number of years to maturity at the time a bond is issued. B Provisions and sinking fund provisions Call Provision – a provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date: • immediately callable bonds • deferred call provision bond Refunding operation: valuable to the firm but detrimental to long-term investors Sinking Fund Provision – a provision in a bond contract that requires the orderly retirement of the issue. Sinking funds are considered to protect investors as bonds are going to be retired in an orderly fashion These funds work to the detriment of bondholders if the bond’s coupon rate > the current market rate On balance bonds with a sinking fund are regarded as being safer than those without such a provision → so at the time they are issued, coupon rate of sinking fund bonds < similar bonds without sinking funds. Types of Bonds • Convertible Bond – a bond that can be exchanged into shares of common stock at a fixed price at the option of the bondholder. • Warrant - a long-term option to buy a stated number of shares of common stock at a stated price. • Putable Bond - a bond with a provision that gives the right to its investors to require the company to buy it prior to maturity at a prearranged price. • Income Bond – a bond that pays interest only if the issuer has enough earnings to pay the interest. • Indexed (Purchasing Power) Bond - a bond that has interest payments is related to an inflation index so as to protect the holder from inflation. Valuation The present value: PV = N Bond value = t=1 FV (1+ )t C F + t (1 + rd ) (1 + rd )N Price of callable bond= C N t=1 (1+r )t d 1 Bond value = 1− 1+ + Call price (1+rd )N + (1 + ) Bond value = present value of the coupons + present value of the face amount D How is a bond’s value determined? What is the value of a 10-year, $1,000 par value bond with a 10% annual coupon if its required return is 10%? • The general way of bond valuation: Calculate the present value of a bond’s cash flows and then add these up to yield a fair price of the bond • 3 STEPS: • Estimate the bond’s cash flows = the coupon payments and the return of the principal • Determine the appropriate discount rate based on the risk of the cash flows • Calculate the present value of the cash flows, and their sum D How is a bond’s value determined? What is the value of a 10-year, $1,000 par value bond with a 10% annual coupon if its required return is 10%? Period CF PVF 10% PV Y0 (?) 1 (?) Y1-Y10 100 6.145* 6145 Y10 1000 0.386 386 Total The value of the debt = 6145+386= =(1000) 0 IF bond has coupon rate = the interest rate=> price of the bond=par value Hence Bond offers current yield = YTM => zero capital gain E1 What is the value of a 13% coupon bond that is otherwise identical to the bond described in Part D? Would we now have a discount or a premium bond? Period CF PVF @ 10% PV Y0 ? 1 ? Y1-Y10 130 6.145 798.85 Y10 1000 0.386 386 Total 0 Premium Bond sells more (1184.34) than its face value (1000) B=798.85+386 B=(1184.34) E2 What is the value of a 7% coupon bond with these characteristics? Would we now have a discount or a premium bond? Period CF PVF @ 10% PV Y0 ? 1 ? Y1-Y10 70 6.145 430.15 Y10 1000 0.386 386 Total B= 430.15+386 B=(816.15) 0 Discount bond sells for less (816.15) than its par value (1000) E3 What would happen to the values of the 7%, 10%, and 13% coupon bonds over time if the required return remained at 10%? (Hint: With a financial calculator, enter PMT, I/YR, FV, and N; then change (override) N to see what happens to the PV as it approaches maturity.) 13% 10 % 7% F. (1) What is the yield to maturity on a 10-year, 9% annual coupon, $ 1,000 par vale bond that sells for $ 887.00? • That sells for $ 1,134.20? • YTM = 7.08% (Excel function) What does the fact that it sells at a discount or at a premium tell you about the relationship between rd and the coupon rate? • Whenever the bond sells at a discount it means that the going rate of interest is above the coupon rate, i.e. bond sells for $ 887.00, coupon rate is 9% while rd is 10.91%. • On the other hand, whenever the bond sells at a premium the going rate of interest is below the coupon rate, i.e. bond sells for $ 1,134.20, coupon rate is 9% while rd is 7.08%. F. (2) What are the total return, the current yield, and the capital gains yield for the discount bond? Assume that it is held to maturity and the company does not default on it. • Current yield = Coupon interest divided by the bond’s price. Current yield = 90/887 = 10.15% • Capital gains = Difference between the purchase price and the selling price divided by the current price. Capital Gains Yield = (1,000 – 887)/887 = 12.74% • Total Return = Current Yield + Capital Gains Yield. Total Return = 10.15% + 12.74% = 22.89% G. What is the interest rate (or price) risk? • The risk of a decline in a bond’s price due to an increase in interest rates. • For example, 15-year bond, par value of $ 1,000, 10% annual coupon. Bond Price at moment 0 is $ 1,000. • If the going interest rate rises to 15%, by using the formula • • • • C = coupon payment n = number of payments i = interest rate, or required yield M = value at maturity, or par value we calculate the PV of the bond at this time to be $ 707.63. Which has more interest rate risk, an annual payment 1year bond or a 10-year bond? Why? • Interest rate risk is higher on bonds that have long maturities than on bonds that will mature in the near future. Therefore, a 10year bond has more interest rate risk than a 1-year bond. • This is because the longer the maturity, the longer before the bond will be paid off and the bondholder can replace it with another bond with a higher coupon. H. What is reinvestment rate risk? • The risk that a decline in interest rates will lead to a decline in income from a bond portfolio. Which has more reinvestment rate risk, a 1-year bond or a 10-year bond? • Reinvestment risk is higher in a 1-year bond. This is because the shorter the bond’s maturity, the fewer the years before the relatively high old-coupon bonds will be replaced with the new low-coupon issues. I. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10% coupon bond if nominal rd = 13%. Equation for valuing bond with annual payments: = =1 (1+ ) + (1+ ) Equation for valuing bond with semi-annual payments: = /2 2 =1 (1+ /2) + (1+ /2)2 => Divide the interest rate and coupons by 2, increase the number of periods by 2. (NB! Annual coupon rate is assumed) Ex.: n=10; YTM=13%; q=10%; N=100 = 10/2 2∗10 =1 (1+13%/2) + 100 (1+13%/2)10∗2 = 83.47 J (1). Suppose for $1,000 you could buy a 10%, 10-year, annual payment bond or a 10%, 10-year, semiannual payment bond. They are equally risky. Which would you prefer? Let’s assume N=900 1000 = 90 10 =1 (1+) 1000 = 90/2 2∗10 =1 (1+/2) + 900 (1+)10 + => YTM=8.32% annually 900 (1+/2)10∗2 => YTM=8.51% annually Thus, we will prefer semiannual payments. In fact, the effective rate of semiannual payments will always be higher than effective rate of annually paid CFs. E.g.: If a bond’s annual YTM=10%, the effective YTM rate of that bond paid semiannually = (1+10%/2)2-1=10.25%. Remember about the opportunity of received coupon payments’ reinvesting! J (2). If $1,000 is the proper price for the semiannual bond, what is the equilibrium price for the annual payment bond? Let’s assume semiannual bond with following characteristics: q=10%; YTM=13%; N=1200; n=10; Price=1000. Annual bond’s Price will be: = 100 10 =1 (1+13%) 1000 + (1+13%)10 = 1003 => The annual bond’s price must be higher at this YTM rate. K. Suppose a 10-year, 10%, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a nominal yield to maturity of 8%. However, it can be called after 4 years for $1,050. What is the bond’s nominal yield to call (YTC)? If you bought this bond, would you be more likely to earn the YTM or the YTC? Why? The yield to call is the yield to maturity assuming that the bond is called on its first callable date for the callable value. 1 2 3 4 5 6 7 8 CF 50 50 50 50 50 50 50 1100 Total PV 48,28 46,61 45,01 43,46 41,96 40,51 39,12 830,95 1135,90 Thus, YTC for this bond will equal to 7.14%, which is lower than nominal YTM. => It is cheaper for the issuer to call the bond and issue another one with lower nominal YTM afterwards. So, we should expect YTC rather than YTM. Does the yield to maturity represent the promised or expected return on the bond? Explain. The yield to maturity can be viewed as the bond’s promised rate of return, which is the return that investors will receive if all the promised payments are made. The yield to maturity equals the expected rate of return only if: • The probability of default is zero • The bond cannot be called. These bonds were rated AA- by S&P. Would you consider them investment-grade or junk bonds? What factors determine a company’s bond rating? 1.Various ratios 9.Antitrust 2.Mortgage provisions 10.Overseas operations 3.Subordination provisions 11.Environmental factors 4.Guarantee provisions 12.Product liability 5.Sinking fund 13.Pension liabilities 6.Maturity 14.Labor unrest 7.Stability 15.Accounting policies 8.Regulation If this firm were to default on the bonds, would the company be immediately liquidated? Would the bondholders be assured of receiving all of their promised payments? • Liquidation or reorganization • The reorganization plan call for restructuring => reduce the financial charges • Liquidation – if company worth more dead than alive => assets are auctioned off and the cash obtained is distributed Suppose a firm will need $100,000 20 years from now to replace some equipment. It plans to make 20 equal payments, starting today, into an investment fund. It can buy bonds that mature in 20 years or bonds that mature in 1 year. Both types of bonds currently sell to yield 10%, i.e., rd = YTM = 10%. The company’s best estimate of future interest rates is that they will stay at current levels, i.e., they may rise or they may fall, but the expected rd is the current rd. How much should the firm plan to invest each year? • 100,000 = 20 =1 (1+10%) => • To obtain $100,000 at the end of every year, the company will have to invest the sum equal to $11,745.96 If the company decides to invest enough right now to produce the future $100,000, how much must it put up? • Let’s assume a zero-coupon bond. Thus, to obtain $100,000 at the end of the 20 year period, the company has to invest the sum equal to 100,000/(1+0,1)20=$14,864.36 right away. Can you think of any other type of bond that might be useful for this company’s purposes? • The best type of bonds to be invested in is putable one. That is the bond with embedded option to be redeemed at a date chosen with a pre-specified price by a bond holder. 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