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WESTERN MONEY MANAGEMENT INC.BOND VALUATION Robert Black and Carol Alvarez are vice presidents of Western Money Management and codirectors of the companys pension fund management division. A major new client, the California League of Cities, has requested that Western present an investment seminar to the mayors of the represented cities. Black and Alvarez, who will make the presentation, have asked you to help them by answering the following questions.a. What are a bonds key features?b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky?c. How is the value of any asset whose value is based on expected future cash flows determined?d. How is a bonds 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%?e. (1) 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?(2) What is the value of a 7% coupon bond with these characteristics? Would we now have a discount or premium bond?(3) What would happen to the values of the 7%, 10%, and 13% coupon bonds over time if the required return remained at 10%?f. (1) What is the yield to maturity on a 10-year, 9%, annual coupon, $1,000 par value bond that sells for $887.00? that sells for $1,134.20? What does the fact that it sells at a discount or at a premium tell you about the relationship between rdand the coupon rate?(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.g. What is interest rate (or price) risk? Which has more interest rate risk, an annual payment 1-year bond or a 10-year bond? Why?h. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond?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%.j. 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? If $1,000 is the proper price for the semiannual bond, what is the equilibrium price for the annual payment bond?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.(1) What is the bonds nominal yield to call (YTC)?(2) If you bought this bond, would you be more likely to earn the YTM or the YTC? Why?l. Does the yield to maturity represent the promised or expected return on the bond? Explain.m. These bonds were rated AA- by S&P. Would you consider them investment-grade or junk bonds?n. What factors determine a companys bond rating?o. 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?
Solution: WESTERN MONEY MANAGEMENT INC. a) Fixed income securities such as bonds are a promise to pay a stream of semi-annual payments for a given number of years and then repay the loan amount at the maturity date. Let us consider a straight (Option-free) bond. For Example, a Treasury bond that has a 6% coupon and matures five years from today in the amount of $1000 is a promise by the issuer (U.S. Treasury) to pay 6% of the $1000 par value ($60) each year for five years and to repay the $1000 five years from today. With treasury bonds and almost all U.S. corporate bonds, the annual interest is paid in two semi-annual instalments. Therefore, this bond will make nine coupon payments (one every six months) of $30 and a final payment of $1030 (par value plus the final coupon payment) at the end of five years. This stream of payment is fixed when the bonds are issued and does not change over the life of the bond. Each Semi-annual payment is one-half the coupon rate (which is always expressed as an annual rate) times the par value, which is sometimes called the face value or the maturity value. An 8% treasury note with a face value of $100000 will make a coupon payment of $4000 every six months and a final payment of $104000 at maturity. A U.S. treasury bond is determined in U.S. dollars. Bonds can be issued in other currencies as well. The currency denomination of a bond issued by the Mexican government will likely be Mexican pesos. Bonds can be issued that promise to make…

nts in any currency. b) Call provision: If a particular security has a call provision, the issuer has the option to retire the debt early if circumstances are in his favour. If interest rates fall the issuer can exercise the call option and call the bonds so as to reissue the bonds again at the then available lower market rates. As the option lies with the issuer, the issuer must offer higher yields on callable bonds as compared to non-callable bonds. The advantage with callable bonds is that if interest rates drop, the issuer can call the issue by refunding at the lower market rates. The disadvantage faced by the investor is that he has to invest the amount received by the issuer at the lower market rates. Thus, due to this re-investment risk, callable bonds are a risky option. Sinking Fund: Sinking fund is a fund created by an organization by setting aside some amount of money over a period of time to fund future expenses or for the repayment of debt. Because money is set aside, there is less default risk and thus lower coupon rate on the bonds. The advantage of a sinking fund structure is that the corporation can plan the solutions as how to address the debt. Thus, having a sinking fund provision definitely makes a bond less risky. c) The general procedure for valuing fixed income securities (or any security) is to take the present value of all the expected cash flows and add them up to get the value of the security. d) There are three steps in the bond valuation process: 1. Estimate the cash flows over the life of the security. For a bond, there are two types of cash flows: 1) the coupon payments and 2) return of principal. 2. Determine the appropriate discount rate based on the risk of (uncertainty) about receipt of the estimated cash flows. 3. Calculate the present value of the estimated cash flows by multiplying the bonds expected cash flows by the appropriate discount factors. Par value = $1000 Coupon payment = $100 Required rate of return = 10% Number of years = 10 Value of the bond = 100/ (1.10) ^1 + 100/ (1.10) ^2 + .. (1000+100)/ (1.10) ^10 = $1000 When Coupon rate = required return (YTM), Market price = Par value. e. e). 1) Par value = $1000 Coupon = 13% (1000*0.13) = $130 Required return = 10% Number of years = 10 Value of the bond = 130/ (1.10) ^1 + 130/ (1.10) ^2 + .. (1000+130)/ (1.10) ^10 = $1184. Because Coupon rate > Discount rate, the bond is trading at a premium. Bond prices and yields have a negative relationship with each other. e.2) Par value = $1000 Coupon = 7% (1000*0.07) = $70 Required return = 10% Number of years = 10 Value of the bond = 70/ (1.10) ^1 + 70/ (1.10) ^2 + .. (1000 + 70)/ (1.10) ^10 = $815.66 Because Coupon rate < Discount rate, the bond is trading at a discount. Bond prices and yields have a negative relationship with each other. e.3) The 13% bond is trading at a premium to the par value. Over time, if the required rate of return remained at 10%, the value of this bond will move towards its Par Value. This is also known as Pull to Par concept. The value of this bond will decrease from the higher price of $1184 to its Par value of $1000. The 10% bond is trading at its Par Value and will remain at its par value over the life of the bond. The 7% bond is trading at a discount to the par value. Over time, if the required rate of return remained at 10%, the value of this bond will move towards its Par Value. This is also known as Pull to Par concept. The value of this bond will increase from the lower price of $815.66 to its Par value of $1000. f. f) 1.) Par value = $1000 Coupon = 9% (1000*0.09) = $90 Required return (YTM) = r Number of years = 10 Value of the bond = $887.00 887.00 = 90/ (1+r) ^1 + 90/ (1+r) ^2 + .. (1000+90)/ (1+r) ^10 Solving for r, we get 10.91% If it sells for $1134.20 1134.20 = 90/ (1+r) ^1 + 90/ (1+r) ^2 + .. (1000+90)/ (1+r) ^10 Solving for r, we get 7.08% When the bond is trading at a discount, the required return is greater than the coupon rate. (10.91% > 9%) When the bond is trading at a premium, the required return is less than the coupon rate. (7.08% < 9%) f. 2) Par value = $1000 Coupon = 7% (1000*0.07) = $70 Required return = 10% Number of years = 10 Value of the bond = 70/ (1.10) ^1 + 70/ (1.10) ^2 + .. (1000 + 70)/ (1.10) ^10 = $815.66 Current Yield = Annual coupon/Current price = 70 / 815.66 = 8.58% Capital gains yield = Price at the end / Price at the beginning - 1 = 1000/815.66 1 = 22.60% Total Return: If the bonds are held to maturity, we assume that the coupon payments are re-invested at the YTM. FV of the coupon payments = 70 * [(1.10) ^10 1]/0.10 = $1115.62 Horizon price will be the par value returned at maturity = $1000 Price today = $815.66 Total return = (1000+1115.62)/815.66 1 = 159.37% g) Interest rate risk refers to the sensitivity of bond prices to changes in interest rates. If the interest rates in the market rise, the price of the bond decreases as the return offered in the market is more than what is being offered on the bond thus, reducing the attractiveness of the bond to the investor. A 10 year bond has more interest rate risk than a 1 year bond because with a 10 year bond there is enough time for the interest to go up and down which can lead to a change in bond price. Longer the maturity, higher the interest-rate risk. h) Re-investment risk refers to the fact that when market rates fall, the cash flows (both principal and interest) from fixed-income securities must be re-invested at lower rates, reducing the returns an investor will earn. A 10 year bond has more re-investment risk than a 1 year bond because the number of coupon payments to be re-invested are more in case of a longer duration bond than a shorter duration bond. i) The equation for valuing a semi-annual coupon bond is: Price = semi- annual coupon/(1 + Rate/2)^1 + semi- annual coupon/(1 + Rate/2)^2 + .. Semi- annual coupon/(1 + Rate/2)^n Where, n = 2 * number of years. Par value = $1000 Coupon = $50 (10/2 = 5% *1000) Required return = 13%/2 = 6.5% Number of years = 10*2 = 20 Value of a bond = 50/(1.065)^1 + 50/(1.065)^2 + (1000+50)^20 = $834.72 j) FV of the coupon payments = Coupon * [(1+r) ^n 1] / r For annual coupon bonds: = 100 * [(1.10) ^10 1]/0.10 = 1593.74 For Semi-annual coupon bonds = 50 * [(1.05)^20 -1 ]/ 0.05 = 1653.29 Since the FV of the Coupons is more with semi-annual bonds, we should prefer them as they would lead to greater accumulation and greater return due to the effects of compounding. If $1000 is the proper price for semi-annual bond, the equilibrium price for annual payment bond will also be $1000. k) k) 1) The bond can be called after 4 years. Number of semi-annual periods = 8 Call value = $1050 Current Value = $1135.90 Semi-annual coupon = 10%/2 = 5%*1000 = $50 1135.90 = 50/ (1+r) ^1 + (1050 + 50)/(1+r)^8 Solving for r, we get 3.56% semi-annually or 7.12% annually. k) 2) If we bought this bond, we are more likely to earn Yield to call because after four years, if the interest rates decline, the issuer will call the bond and redeem the issue thus making the investors earn the Yield to call. l) Yield to maturity represents the promised return on an investment if the bond is held till maturity. YTM is an annualized internal rate of return, based on a bonds price and its promised cash flows. For a bond with semi-annual coupon payments, the yield to maturity is stated as two times the semi-annual internal rate of return implied by the bonds price. YTM and price contain the same information. That is, given the YTM, you can calculate the price and given the price, you can calculate the YTM. m) These bonds would be Investment grade bonds. Triple A is the highest rating. Bonds with ratings of BBB- or higher are considered investment grade. Bonds with BB+ or lower are considered non-investment grade and are often called high-yield bonds and junk bonds. n) The factors determining a companys bond rating can be categorised as: Capacity, Collateral, Covenants and character. Capacity refers to a corporate borrowers ability to repay its debt obligations on time. Collateral analysis is more important foe less creditworthy companies. The market value of a companys assets can be difficult to observe directly. Covenants are the terms and conditions the borrowers have agreed to as part of a bond issue. Covenants protect lenders while leaving some operating flexibility to the borrowers to run the company. Character refers to managements integrity and its commitment to repay the loan. o) If the company were to default on its bonds, there could be two courses of action. Either the company can be re-organised or it can be liquidated. Re-organisation would be a good option if the value of the re-organised company would be more than the value of the assets sold today. In case of re-organisation, the court may appoint a committee for unsecured creditors for negotiation with the management on the terms of the re-organisation. The re-organisation plan may call for re-structuring of the firms debt such as reducing the interest payment or lengthening the term to maturity. However if things had gone beyond control and no restructuring was possible, the company would be liquidated and the general seniority for debt repayment would be: 1. First Lien or first mortgage. 2. Senior secured debt 3. Junior secured debt 4. Senior unsecured debt. 5. Senior sub-ordinate debt 6. Sub-ordinate debt. 7. Junior sub-ordinate debt.

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