Consider three bonds with 5.0% coupon rates, all making annual coupon payments a
ID: 2729880 • Letter: C
Question
Consider three bonds with 5.0% coupon rates, all making annual coupon payments and all selling at a face value of $1,000. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.
What will be the price of each bond if their yields increase to 6.0%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
What will be the price of each bond if their yields decrease to 4.0%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Consider three bonds with 5.0% coupon rates, all making annual coupon payments and all selling at a face value of $1,000. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.
Explanation / Answer
Given data
Coupon Rate = 5%
Face Value = Maturity Value = $1000
Interest = $1000 * 5% = $50
Requirement a:
Yield to Maturity = 6%
Price of Bond having maturity period of 4 years:
Price of Bond = PV of Interest + PV of Maturity Value
= [Interest * PVAF (6%, 4)] + [Maturity Value * PVIF (6%, 4)]
= [50 *3.465] + [1000 * 0.792]
= 173.25 + 792
= 965.25
Price of Bond having maturity period of 8 years:
Price of Bond = PV of Interest + PV of Maturity Value
= [Interest * PVAF (6%, 8)] + [Maturity Value * PVIF (6%, 8)]
= [50 *6.210] + [1000 * 0.627]
= 310.5 + 627
= 937.5
Price of Bond having maturity period of 30 years:
Price of Bond = PV of Interest + PV of Maturity Value
= [Interest * PVAF (6%, 30)] + [Maturity Value * PVIF (6%, 30)]
= [50 *13.765] + [1000 * 0.174]
= 688.25 + 174
= 862.25
4 years
8 years
30 years
Bond Price
965.25
937.5
862.25
Requirement b:
Yield to Maturity = 4%
Price of Bond having maturity period of 4 years:
Price of Bond = PV of Interest + PV of Maturity Value
= [Interest * PVAF (4%, 4)] + [Maturity Value * PVIF (4%, 4)]
= [50 *3.63] + [1000 * 0.855]
= 181.5 + 855
= 1036.5
Price of Bond having maturity period of 8 years:
Price of Bond = PV of Interest + PV of Maturity Value
= [Interest * PVAF (4%, 8)] + [Maturity Value * PVIF (4%, 8)]
= [50 *6.733] + [1000 * 0.731]
= 336.65 + 731
= 1067.65
Price of Bond having maturity period of 30 years:
Price of Bond = PV of Interest + PV of Maturity Value
= [Interest * PVAF (4%, 30)] + [Maturity Value * PVIF (4%, 30)]
= [50 * 17.292] + [1000 * 0.308]
= 864.6 + 308
= 1172.6
4 years
8 years
30 years
Bond Price
1036.5
1067.65
1172.6
Requirement c:
Long term bonds are more affected than short term bonds by a rise in interest rates.
Requirement d:
Long term bonds are more affected by a fall in interest rates.
4 years
8 years
30 years
Bond Price
965.25
937.5
862.25