CFA 53: Introduction to Fixed-Income Valuation

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+100(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+0.015)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