Bond X is a premium bond making semiannual payments. The bond pays a coupon rate
ID: 2733536 • Letter: B
Question
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 7 percent, has a YTM of 5 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 5 percent, has a YTM of 7 percent, and also has 13 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of Bond X $ Price of Bond Y $ If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In four years? In nine years? In 11 years? In 13 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of bond Bond X Bond Y One year $ $ Four years $ $ Nine years $ $ 11 years $ $ 13 years $ $
Explanation / Answer
Solution:
Calculation of the price of each bond today:
P = C (PVIFAR%, t) + 1,000 (PVIFR%, t)
Bond X:
C = 1,000 * 7% * 1/2 = 35
P0 = 35 (PVIFA2.5%, 26) + 1,000 (PVIF2.5%, 26)
= 35 (18.9506) + 1,000 (0.5262)
= 663.271 + 526.20
= 1,189.47
Bond Y:
C = 1,000 * 5% * 1/2 = 25
P0 = 25 (PVIFA3.5%, 26) + 1,000 (PVIF3.5%, 26)
= 25 (16.8904) + 1,000 (0.4088)
= 422.26 + 408.80
= 831.06
Calculation of the price of these bonds to be one year from now, In four years, In nine years, In 11 years and In 13 years:
Bond X:
P1 = 35 (PVIFA2.5%, 24) + 1,000 (PVIF2.5%, 24)
= 35 (17.885) + 1,000 (0.5529)
= 1,178.88
P4 = 35 (PVIFA2.5%, 18) + 1,000 (PVIF2.5%, 18)
= 35 (14.3534) + 1,000 (0.6412)
= 1,143.57
P9 = 35 (PVIFA2.5%, 8) + 1,000 (PVIF2.5%, 8)
= 35 (7.1701) + 1,000 (0.8207)
= 1,071.65
P11 = 35 (PVIFA2.5%, 4) + 1,000 (PVIF2.5%, 4)
= 35 (3.762) + 1,000 (0.906)
= 1,037.67
P13 = 35 (PVIFA2.5%, 0) + 1,000 (PVIF2.5%, 0)
= 35 (0) + 1,000 (1)
= 1,000
Bond Y:
P1 = 25 (PVIFA3.5%, 24) + 1,000 (PVIF3.5%, 24)
= 25 (16.0584) + 1,000 (0.438)
= 839.46
P4 = 25 (PVIFA3.5%, 18) + 1,000 (PVIF3.5%, 18)
= 25 (13.1897) + 1,000 (0.5384)
= 868.14
P9 = 25 (PVIFA3.5%, 8) + 1,000 (PVIF3.5%, 8)
= 25 (6.874) + 1,000 (0.7594)
= 931.25
P11 = 25 (PVIFA3.5%, 4) + 1,000 (PVIF3.5%, 4)
= 25 (3.6731) + 1,000 (0.8714)
= 963.23
P13 = 25 (PVIFA3.5%, 0) + 1,000 (PVIF3.5%, 0)
= 25 (0) + 1,000 (1)
= 1,000