Refer to Table 3.5. Suppose the spot interest rates change to the following down
ID: 2819279 • Letter: R
Question
Refer to Table 3.5. Suppose the spot interest rates change to the following downward-sloping term structure: r1 = 4.6%, r2 = 4.4%, r3 = 4.2%, and r4 = 4.0%.
a. Calculate the discount factors for each of the bonds listed in the table. (Do not round intermediate calculations. Round your answers to 4 decimal places.)
Year Discount Factors
1 .9560
2 .9175
3 .8839
4 .8548
b. Calculate bond prices and yields to maturity for each of the bonds listed in the table. (Do not round intermediate calculations. Round your "Bond Price" to 2 decimal places. Enter your "YTM" as a percent rounded to 3 decimal places.)
Bond Price (PV) YTM (%)
Bond A $ 1067.37 4.407 %
Bond B ? ?
Bond C ? ?
Year (t) Bond Price (PV) Yield to Maturity (y, %) 0.06 0.7921 0.03 Spot rates Discount factors Bond A (8% coupon) 0.04 0.9246 0.05 0.8638 0.9709 Payment (Ct) PV (Ct) $80.001,080.00 $77.67 998.52 $1,076.19 3.96 Bond B (8% coupon) Payment (Ct) PV (Ct) $80.00 $77.67 80.001,080.00 73.96 932.94 $1,084.58 4.90 Bond C (8% coupon) Payment (Ct) PV (C) $80.00 $77.67 80.00 73.96 80.00 1,080.00 69.11 855.46 $1,076.20 5.81 TABLE 3.5 The law of one price applied to government bonds.Explanation / Answer
Discount Factors:
1/(1+4.6%)=0.9560
1/(1+4.4%)^2=0.9175
1/(1+4.2%)^3=0.8839
1/(1+4%)^4=0.8548
Bond Price:
A=80*0.9560+1080*0.9175=1067.38
B=80*0.9560+80*0.9175+1080*0.8839=1104.492
C=80*0.9560+80*0.9175+80*0.8839+1080*0.8548=1143.776
YTM:
A:0=-1067.38+80/(1+ytm)+1080/(1+ytm)^2
=>ytm=4.407%
B:0=-1104.492+80/(1+ytm)+80/(1+ytm)^2+1080/(1+ytm)^3
=>ytm=4.219%
C:0=-1143.776+80/(1+ytm)+80/(1+ytm)^2+80/(1+ytm)^3+1080/(1+ytm)^4
=>ytm=4.036%