Answer:
a.
Percentage change in Bill Price = (91.8486 - 100) / 100 = -0.0815 or -8.15%
Percentage change in Bill Price = (78.1448 - 100) / 100 = -0.2186 or -21.86%
b.
Percentage change in Bill Price = (109.0298 - 100) / 100 = 0.0903 or 9.03%
Percentage change in Bill Price = (132.0946 - 100) / 100 = 0.3209 or 32.09%
Explanation:
To calculate the percentage change in the price of both the bonds, we assume that the par value of both the bonds is $100 each.
a.
To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,
Coupon Payment (C) both Bill and Ted = 100 * 0.058 * 6/12 = $2.9
Total periods (n) - Bill= 5 * 2 = 10
Total periods (n) - Ted= 25 * 2 = 50
As the bonds were previously price at par, the YTM or market interest rate would have been same as the coupon rate. Thus, the old market interest rate was 5.8%. Now as the interest rates have risen by 2% new interest rate will be = 5.8 + 2 = 7.8%
New r or YTM - both Bill and Ted = 7.8% * 6/12 = 3.9% or 0.039
The formula to calculate the price of the bonds today is attached.
Bond Price - Bill = 2.9 * [( 1 - (1+0.039)^-10) / 0.039] + 100 / (1+0.039)^10
Bond Price - Bill = $91.8486
Percentage change in Bill Price = (91.8486 - 100) / 100 = -0.0815 or -8.15%
Bond Price - Ted = 2.9 * [( 1 - (1+0.039)^-50) / 0.039] + 100 / (1+0.039)^50
Bond Price - Ted = $78.1448
Percentage change in Bill Price = (78.1448 - 100) / 100 = -0.2186 or -21.86%
b.
As the bonds were previously price at par, the YTM or market interest rate would have been same as the coupon rate. Thus, the old market interest rate was 5.8%. Now as the interest rates have fallen by 2% new interest rate will be = 5.8 - 2 = 3.8%
New r or YTM - both Bill and Ted = 3.8% * 6/12 = 1.9% or 0.019
The formula to calculate the price of the bonds today is attached.
Bond Price - Bill = 2.9 * [( 1 - (1+0.019)^-10) / 0.019] + 100 / (1+0.019)^10
Bond Price - Bill = $109.0298
Percentage change in Bill Price = (109.0298 - 100) / 100 = 0.0903 or 9.03%
Bond Price - Ted = 2.9 * [( 1 - (1+0.019)^-50) / 0.019] + 100 / (1+0.019)^50
Bond Price - Ted = $132.0946
Percentage change in Bill Price = (132.0946 - 100) / 100 = 0.3209 or 32.09%
