CFA 53: Introduction to Fixed-Income Valuation

A portfolio manager is considering the purchase of a bond with a 5.5% coupon rate that pays interest annually and matures in three years. If the required rate of return on the bond is 5%, the price of the bond per 100 of par value is closest to: 98.65. 101.36. 106.43. B is correct. The bond price is closest to 101.36. The price is determined in the following manner: PV=PMT(1+r)1+PMT(1+r)2+PMT+FV(1+r)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=5.5(1+0.05)1+5.5(1+0.05)2+5.5+100(1+0.05)3 PV = 5.24 + 4.99 + 91.13 = 101.36 A bond with two years remaining until maturity offers a 3% coupon rate with interest paid annually. At a market discount rate of 4%, the price of this bond per 100 of par value is closest to: 95.34. 98.00. 98.11. C is correct. The bond price is closest to 98.11. The formula for calculating the price of this bond is: PV=PMT(1+r)1+PMT+FV(1+r)2 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=3(1+0.04)1+3+100(1+0.04)2=2.88+95.23=98.11 An investor who owns a bond with a 9% coupon rate that pays interest semiannually and matures in three years is considering its sale. If the required rate of return on the bond is 11%, the price of the bond per 100 of par value is closest to: 95.00. 95.11. 105.15. A is correct. The bond price is closest to 95.00. The bond has six semiannual periods. Half of the annual coupon is paid in each period with the required rate of return also being halved. The price is determined in the following manner: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT(1+r)5+PMT+FV(1+r)6 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=4.5(1+0.055)1+4.5(1+0.055)2+4.5(1+0.055)3+4.5(1+0.055)4+4.5(1+0.055)5+4.5+1 00(1+0.055)6 PV = 4.27 + 4.04 + 3.83 + 3.63 + 3.44 + 75.79 = 95.00 A bond offers an annual coupon rate of 4%, with interest paid semiannually. The bond matures in two years. At a market discount rate of 6%, the price of this bond per 100 of par value is closest to: 93.07. 96.28. 96.33. B is correct. The bond price is closest to 96.28. The formula for calculating this bond price is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT+FV(1+r)4 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=2(1+0.03)1+2(1+0.03)2+2(1+0.03)3+2+100(1+0.03)4 PV = 1.94 + 1.89 + 1.83 + 90.62 = 96.28 A bond offers an annual coupon rate of 5%, with interest paid semiannually. The bond matures in seven years. At a market discount rate of 3%, the price of this bond per 100 of par value is closest to: 106.60. 112.54. 143.90. B is correct. The bond price is closest to 112.54.The formula for calculating this bond price is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT+FV(1+r)14 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=2.5(1+0.015)1+2.5(1+0.015)2+2.5(1+0.015)3+⋯+2.5(1+0.015)13+2.5+100(1+0.01 5)14 PV = 2.46 + 2.43 + 2.39 + ... + 2.06 + 83.21 = 112.54 A zero-coupon bond matures in 15 years. At a market discount rate of 4.5% per year and assuming annual compounding, the price of the bond per 100 of par value is closest to: 51.30. 51.67. 71.62. B is correct. The price of the zero-coupon bond is closest to 51.67. The price is determined in the following manner: PV=100(1+r)N where: PV = present value, or the price of the bond r = market discount rate, or required rate of return per period N = number of evenly spaced periods to maturity PV=100(1+0.045)15 PV = 51.67 Consider the following two bonds that pay interest annually: Bond Coupon Rate Time-to-Maturity A 5% 2 years B 3% 2 years At a market discount rate of 4%, the price difference between Bond A and Bond B per 100 of par value is closest to: 3.70. 3.77. 4.00. B is correct. The price difference between Bonds A and B is closest to 3.77. One method for calculating the price difference between two bonds with an identical term to maturity is to use the following formula: PV=PMT(1+r)1+PMT(1+r)2 where: PV = price difference PMT = coupon difference per period r = market discount rate, or required rate of return per period In this case the coupon difference is (5% - 3%), or 2%. PV=2(1+0.04)1+2(1+0.04)2=1.92+1.85=3.77 Bond Price Coupon Rate Time-to-Maturity A 101.886 5% 2 years B 100.000 6% 2 years C 97.327 5% 3 years Which bond offers the lowest yield-to-maturity? Bond A Bond B Bond C A is correct. Bond A offers the lowest yield-to-maturity. When a bond is priced at a premium above par value the yield-to-maturity (YTM), or market discount rate is less than the coupon rate. Bond A is priced at a premium, so its YTM is below its 5% coupon rate. Bond B is priced at par value so its YTM is equal to its 6% coupon rate. Bond C is priced at a discount below par value, so its YTM is above its 5% coupon rate. Bond Price Coupon Rate Time-to-Maturity A 101.886 5% 2 years B 100.000 6% 2 years C 97.327 5% 3 years Which bond will most likely experience the smallest percent change in price if the market discount rates for all three bonds increase by 100 basis points? Bond A Bond B Bond C B is correct. Bond B will most likely experience the smallest percent change in price if market discount rates increase by 100 basis points. A higher-coupon bond has a smaller percentage price change than a lower-coupon bond when their market discount rates change by the same amount (the coupon effect). Also, a shorter-term bond generally has a smaller percentage price change than a longer-term bond when their market discount rates change by the same amount (the maturity effect). Bond B will experience a smaller percent change in price than Bond A because of the coupon effect. Bond B will also experience a smaller percent change in price than Bond C because of the coupon effect and the maturity effect. Bond Price Coupon Rate Time-to-Maturity A 101.886 5% 2 years B 100.000 6% 2 years C 97.327 5% 3 years Suppose a bond's price is expected to increase by 5% if its market discount rate decreases by 100 basis points. If the bond's market discount rate increases by 100 basis points, the bond price is most likely to change by: 5%. less than 5%. more than 5%. B is correct. The bond price is most likely to change by less than 5%. The relationship between bond prices and market discount rate is not linear. The percentage price change is greater in absolute value when the market discount rate goes down than when it goes up by the same amount (the convexity effect). If a 100 basis point decrease in the market discount rate will cause the price of the bond to increase by 5%, then a 100 basis point increase in the market discount rate will cause the price of the bond to decline by an amount less than 5%. Bond Coupon Rate Maturity (years) A 6% 10 B 6% 5 C 8% 5 All three bonds are currently trading at par value. Relative to Bond C, for a 200 basis point decrease in the required rate of return, Bond B will most likely exhibit a(n): equal percentage price change. greater percentage price change. smaller percentage price change. B is correct. Generally, for two bonds with the same time-to-maturity, a lower coupon bond will experience a greater percentage price change than a higher coupon bond when their market discount rates change by the same amount. Bond B and Bond C have the same time-to-maturity (5 years); however, Bond B offers a lower coupon rate. Therefore, Bond B will likely experience a greater percentage change in price in comparison to Bond C. Bond Coupon Rate Maturity (years) A 6% 10 B 6% 5 C 8% 5 All three bonds are currently trading at par value. Which bond will most likely experience the greatest percentage change in price if the market discount rates for all three bonds increase by 100 basis points? Bond A Bond B Bond C A is correct. Bond A will likely experience the greatest percent change in price due to the coupon effect and the maturity effect. For two bonds with the same time-to- maturity, a lower-coupon bond has a greater percentage price change than a higher- coupon bond when their market discount rates change by the same amount. Generally, for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount. Relative to Bond C, Bond A and Bond B both offer the same lower coupon rate of 6%; however, Bond A has a longer time-to-maturity than Bond B. Therefore, Bond A will likely experience the greater percentage change in price if the market discount rates for all three bonds increase by 100 basis points. An investor considers the purchase of a 2-year bond with a 5% coupon rate, with interest paid annually. Assuming the sequence of spot rates shown below, the price of the bond is closest to: Time-to-Maturity Spot Rates 1 year 3% 2 years 4% 101.93. 102.85. 105.81. A is correct. The bond price is closest to 101.93. The price is determined in the following manner: PV=PMT(1+Z1)1+PMT+FV(1+Z2)2 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, for Period 1 Z2 = spot rate, or the zero-coupon yield, for Period 2 PV=5(1+0.03)1+5+100(1+0.04)2 PV = 4.85 + 97.08 = 101.93 A 3-year bond offers a 10% coupon rate with interest paid annually. Assuming the following sequence of spot rates, the price of the bond is closest to: Time-to-Maturity Spot Rates 1 year 8.0% 2 years 9.0% 3 years 9.5% 96.98. 101.46. 102.95. B is correct. The bond price is closest to 101.46. The price is determined in the following manner: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, or zero rate, for period 1 Z2 = spot rate, or the zero-coupon yield, or zero rate, for period 2 Z3 = spot rate, or the zero-coupon yield, or zero rate, for period 3 PV=10(1+0.08)1+10(1+0.09)2+10+100(1+0.095)3 PV = 9.26 + 8.42 + 83.78 = 101.46 Bond Coupon Rate Time-to-Maturity Time-to-Maturity Spot Rates X 8% 3 years 1 year 8% Y 7% 3 years 2 years 9% Z 6% 3 years 3 years 10% All three bonds pay interest annually. Based upon the given sequence of spot rates, the price of Bond X is closest to: 95.02. 95.28. 97.63. B is correct. The bond price is closest to 95.28. The formula for calculating this bond price is: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, or zero rate, for period 1 Z2 = spot rate, or the zero-coupon yield, or zero rate, for period 2 Z3 = spot rate, or the zero-coupon yield, or zero rate, for period 3 PV=8(1+0.08)1+8(1+0.09)2+8+100(1+0.10)3 PV = 7.41 + 6.73 + 81.14 = 95.28 Bond Coupon Rate Time-to-Maturity Time-to-Maturity Spot Rates X 8% 3 years 1 year 8% Y 7% 3 years 2 years 9% Z 6% 3 years 3 years 10% All three bonds pay interest annually. Based upon the given sequence of spot rates, the price of Bond Y is closest to: 87.50. 92.54. 92.76. C is correct. The bond price is closest to 92.76. The formula for calculating this bond price is: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity,