CFA Level 1 - Fixed Income Session 16 - Reading 57 (Notes, Practice Questions, Sample Questions) 1. By purchasing a noncallable, nonputable, U.S. Government 30-year bond, an investor is entitled to: A)full recovery of face value at maturity or when the bond is retired.B)annuity of coupon payments. C)annuity of coupon payments plus recovery of principal at maturity <Explanation> Bond investors are entitled to two distinct types of cashflows: (1) the periodic receipt of coupon income over the life of thebond, and (2) the recovery of principal (or face value) at the end of thebond’s life 2. Answering an essay question on a midterm examination, a finance student writes these two statements:Statement 1: The value of a fixed income security is the sum of the presentvalues of all its expected future coupon payments.Statement 2: The steps in the bond valuation process are to estimate thebond’s cash flows, determine the appropriate discount rate, and calculatethe present value of the expected cash flows.With respect to the student's statements: A)only one is correct. B)both are correct.C)both are incorrect. <Explanation> Statement 1 is incorrect. The value of a fixed incomesecurity is the sum of the present values of its expected future couponpayments and its future principal repayment. Statement 2 is correct.The three steps in the bond valuation process are to estimate the cash
flows over the life of the security; determine the appropriate discountrate based on the risk of the cash flows; and calculate the presentvalue of the cash flows using the appropriate discount rate 3. Assume a city issues a $5 million bond to build a new arena. The bond pays 8% semiannual interest and will mature in 10 years. Current interestrates are 9%. What is the present value of this bond and what will thebond's value be in seven years from today? Present Value Value in 7 Years from Today A) 4,674,802 4,871,053 B) 4,674,802 4,931,276 C) 5,339,758 4,871,053 <Explanation> Present Value:Since the current interest rate is above the coupon rate the bond willbe issued at a discount. FV = $5,000,000; N = 20; PMT = (0.04)(5million) = $200,000; I/Y = 4.5; CPT → PV = -$4,674,802 Value in 7 Years:Since the current interest rate is above the coupon rate the bond willbe issued at a discount 4. A corporate bond with the following data is issued: ● $1,000 par value. ● 8% coupon payments. ● 5 years to maturity with semiannual coupon payments. ● Market interest rates are 10%. What is the total interest expense?
A)923.B)545. C)477. <Explanation> Total interest expense is the difference between theamount paid by the issuer and the amount received from thebondholder.Present value of the bond is computed as follows: FV = 1,000; PMT =[(1,000)(0.08)] / 2 = 40; I/Y = 5; N = 10; CPT → PV = -923 [($40 coupon payments)(10 periods) + $1,000 par value] – $923present value of the bond = 477 5. A bond is issued with the following data: ● $10 million face value. ● 9% coupon rate. ● 8% market rate. ● 3-year bond with semiannual payments. What is the present value of the bond? A)$10,138,754.B)$10,000,000. C)$10,262,107. <Explanation> FV = 10,000,000; PMT = 450,000; I/Y = 4; N = 6; CPT → PV = -10,262,107 6. It is easier to value bonds than to value equities because: A)the future cash flows of bonds are more stable. B)Both of these choices are correct. C)there is no maturity value for common stock
<Explanation> Bonds pay out a specified periodic cash flow (couponpayment) throughout the life of the bond and pay out a lump sum atthe maturity date. Common stocks don't have a maturity date and havemore volatility than bond 7. A Treasury bill has a $10,000 face value and matures in one year. If the current yield to maturity on similar Treasury bills is 4.1% annually, whatwould an investor be willing to pay now for the T-bill? A)$9,799.12.B)$9,899.05. C)$9,606.15. <Explanation> The investor would pay the present value of the$10,000 one year away at a discount rate of 4.1%. To value the T-bill,enter FV = $10,000; N = 1; PMT = 0; I/Y = 4.1%; CPT → PV = -$9,606.15 8. The value of a 10-year zero-coupon bond with a $1,000 maturity value, compounded semiannually, and has an 8% discount rate is closest to: A)$200.00. B)$456.39. C)$463.19 <Explanation> V = (maturity value)/(1 + i)number of years x 2 =$1,000/(1.04)10 x 2 = $1,000/2.1911 = $456.39orn = 20, i = 4, FV = 1,000, compute PV = 456.39 9. Anne Warner wants to buy zero-coupon bonds in order to protect herself from reinvestment risk. She plans to hold the bonds for fifteen years andrequires a rate of return of 9.5%. Fifteen-year Treasuries are currentlyyielding 4.5%. If interest is compounded semiannually, the price Warner iswilling to pay for each $1,000 par value zero-coupon bond is closest to:
A)$256.B)$498. C)$249. <Explanation> Note that because the question asks for how muchWarner is willing to pay, we will want to use her required rate ofreturn in the calculation.N = 15 × 2 = 30, FV = $1,000, I/Y = 9.5 / 2 = 4.75, PMT = 0; CPT → PV = -248.53.The difference between the bond’s price of $249 that Warner would bewilling to pay and the par value of $1,000 reflects the amount ofinterest she would earn over the fifteen year horizon 10. Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Suppose the term structure of interest ratesis flat at 6%. How much does the bond price change if the term structure ofinterest rates shifts down by 1% instantaneously? A)-2.67.B)0.00. C)2.67. <Explanation> This value is computed as follows: Bond Price Change =New Price – Old Price = 100 – (5/1.06 + 5/1.062 + 105/1.063) = 2.67.-2.67 is the correct value but the wrong sign. The value 0.00 isincorrect because the bond price is not insensitive to interest ratechanges 11. A year ago a company issued a bond with a face value of $1,000 with an 8% coupon. Now the prevailing market yield is 10%. What happens to thebond? The bond: A)is traded at a market price higher than $1,000. B)is traded at a market price of less than $1,000.
C)price is not affected by the change in market yield, and will continue totrade at $1,000 <Explanation> A bonds price/value has an inverse relationship withinterest rates. Since interest rates are increasing (from 8% whenissued to 10% now) the bond will be selling at a discount. Thishappens so an investor will be able to purchase the bond and still earnthe same yield that the market currently offers 12. A 2-year option-free bond (par value of $1,000) has an annual coupon of 6%. An investor determines that the spot rate of year 1 is 5% and theyear 2 spot rate is 8%. Using the arbitrage-free valuation approach, thebond price is closest to: A)$992. B)$966. C)$1,039. <Explanation> The arbitrage free valuation approach is the process ofvaluing a fixed income instrument as a portfolio of zero coupon bonds.We can calculate the price of the bond by discounting each of theannual payments by the appropriate spot rate and finding the sum ofthe present values. Bond price = [60 / (1.05)] + [1,060 / (1.08)2] =$966. Or, in keeping with the notion that each cash flow is a separatebond, sum the following transactions on your financial calculator:N = 1; I/Y = 5.0; PMT = 0; FV = 60; CPT → PV = 57.14 N = 2; I/Y = 8.0; PMT = 0; FV = 1,060; CPT → PV = 908.78 Price = 57.14 + 908.78 = $966 13. A three-year bond with a 10% annual coupon has cash flows of $100 at year 1, $100 at year 2, and pays the final coupon and the principal for a cashflow of $1,100 at year 3. The spot rate for year 1 is 5%, the spot rate foryear 2 is 6%, and the spot rate for year 3 is 6.5%. What is the arbitrage-freevalue of the bond?
A)$1,050.62.B)$975.84. C)$1,094.87. <Explanation> Spot interest rates can be used to price coupon bondsby taking each individual cash flow and discounting it at theappropriate spot rate for that year’s payment. To find thearbitrage-free value:Bond value = [$100 / (1.05)] + [$100 / (1.06)2] + [$1,100 / (1.065)3] =$95.24 + $89.00 + $910.63 = $1,094.87 14. A 3-year option-free bond (par value of $1,000) has an annual coupon of 9%. An investor determines that the spot rate of year 1 is 6%, the year 2spot rate is 12%, and the year 3 spot rate is 13%. Using the arbitrage-freevaluation approach, the bond price is closest to: A)$912. B)$1,080.C)$968. <Explanation> We can calculate the price of the bond by discountingeach of the annual payments by the appropriate spot rate and findingthe sum of the present values. Price = [90 / (1.06)] + [90 / (1.12)2] +[1,090 / (1.13)3] = 912. Or, in keeping with the notion that each cashflow is a separate bond, sum the following transactions on yourfinancial calculator:N = 1; I/Y = 6.0; PMT = 0; FV = 90; CPT → PV = 84.91 N = 2; I/Y = 12.0; PMT = 0; FV = 90; CPT → PV = 71.75 N = 3; I/Y = 13.0; PMT = 0; FV = 1,090; CPT → PV = 755.42 Price = 84.91 + 71.75 + 755.42 = $912.08 15. The arbitrage-free bond valuation approach can best be described as the:
A)use of a series of spot interest rates that reflect the current termstructure. B)use of a single discount factor.C)geometric average of the spot interest rates <Explanation> The use of multiple discount rates (i.e., a series of spotrates that reflect the current term structure) will result in moreaccurate bond pricing and in so doing, will eliminate any meaningfularbitrage opportunities. That is why the use of a series of spot rates todiscount bond cash flows is considered to be an arbitrage-freevaluation procedure 16. Which of the following statements concerning the arbitrage-free valuation of non-Treasury securities is CORRECT? The credit spread is: A)only a function of the bond's term to maturity. B)a function of default risk and the term to maturity. C)only a function of the bond's default risk <Explanation> For valuing non-Treasury securities, a credit spread isadded to each treasury spot yields. The credit spread is a function ofdefault risk and the term to maturity 17. You are considering the purchase of a three-year annual coupon bond with a par value of $1,000 and a coupon rate of 5.5%. You have determinedthat the spot rate for year 1 is 5.2%, the spot rate for year two is 5.5%, andthe spot rate for year three is 5.7%. What would you be willing to pay forthe bond now? A)$937.66. B)$995.06. C)$1,000.00. <Explanation> You need the find the present value of each cash flowusing the spot rate that coincides with each cash flow.
The present value of cash flow 1 is: FV = $55; PMT = 0; I/Y = 5.2%; N =1; CPT → PV = -$52.28. The present value of cash flow 2 is: FV = $55; PMT = 0; I/Y = 5.5%; N =2; CPT → PV = –$49.42. The present value of cash flow 3 is: FV = $1,055; PMT = 0; I/Y = 5.7%;N = 3; CPT → PV = –$893.36. The most you pay for the bond is the sum of: $52.28 + $49.42 +$893.36 = $995.06 18. Which of the following packages of securities is equivalent to a three-year 8% coupon bond with semi-annual coupon payments and a parvalue of 100? A three-year zero-coupon bond: A)with a par of 100 and six zero-coupon bonds with a par value of 8 andmaturities equal to the time to each coupon payment of the coupon bond.B)with a par value of 150 and six 8% coupon bonds with a maturity equalto the time to each coupon payment of the above bond. C)with a par of 100 and six zero-coupon bonds with a par value of 4and maturities equal to the time to each coupon payment of thecoupon bond <Explanation> This combination of zero-coupon bonds has exactly thesame cash flows as the above coupon bond and therefore it isequivalent to it. 19. Which of the following statements concerning arbitrage-free bond prices is NOT correct? A)It is not possible to strip coupons from U.S. Treasuries and resellthem. B)Credit spreads are affected by time to maturity.C)The determination of spot rates is usually done using risk-free securities. <Explanation> It is possible to both strip coupons from U.S. Treasuriesand resell them, as well as to aggregate stripped coupons and
reconstitute them into U.S. Treasury coupon bonds. Therefore,arbitrage arguments ensure that U.S. Treasury securities sell at orvery near their arbitrage free values. For valuing non-Treasurysecurities, a credit spread is added to each treasury spot yields. Thecredit spread is a function of default risk and the term to maturity. 20. Current spot rates are as follows: 1-Year: 6.5%2-Year: 7.0%3-Year: 9.2% Which of the following is CORRECT A)For a 3-year annual pay coupon bond, all cash flows can be discounted at9.2% to find the bond's arbitrage-free value. B)For a 3-year annual pay coupon bond, the first coupon can bediscounted at 6.5%, the second coupon can be discounted at 7.0%, andthe third coupon plus maturity value can be discounted at 9.2% to findthe bond's arbitrage-free value. C)The yield to maturity for 3-year annual pay coupon bond can be found bytaking the geometric average of the 3 spot rates. <Explanation> Spot interest rates can be used to price coupon bondsby taking each individual cash flow and discounting it at theappropriate spot rate for that year’s payment. Note that the yield tomaturity is the bond’s internal rate of return that equates all cashflows to the bond’s price. Current spot rates have nothing to do withthe bond’s yield to maturity 21. A 2-year option-free bond (par value of $10,000) has an annual coupon of 15%. An investor determines that the spot rate of year 1 is 16% and theyear 2 spot rate is 17%. Using the arbitrage-free valuation approach, thebond price is closest to: A)$8,401.
B)$11,122. C)$9,694. <Explanation> We can calculate the price of the bond by discountingeach of the annual payments by the appropriate spot rate and findingthe sum of the present values. Price = [1,500/(1.16)] +[11,500/(1.17)2] = $9,694. Or, in keeping with the notion that eachcash flow is a separate bond, sum the following transactions on yourfinancial calculator:N=1, I/Y=16.0, PMT=0, FV=1,500, CPT PV=1,293N=2, I/Y=17.0, PMT=0, FV=11,500, CPT PV=8,401Price = 1,293 + 8,401 = $9,694 22. Assume that there are no transaction costs and that securities are infinitely divisible. If an 8% coupon paying Treasury bond that has sixmonths left to maturity trades at 97.54, and there is a Treasury bill with sixmonths remaining to maturity that is correctly priced using a discount rateof 9%, is there an arbitrage opportunity? A)The coupon bond is not correctly priced but no arbitrage trade can be setup using the T-bill.B)Yes, the coupon bond price is too high. C)Yes, the coupon bond price is too low. <Explanation> The coupon bond has a cash flow at maturity of 104,which discounted at 9% results in a bond price of 99.52. Therefore,the bond is underpriced. An arbitrage trade can be set up byshort-selling 1.04 units of the T-bill at 99.52 and then using theproceeds to buy 1.02 units of the coupon bond