Question

Both Bond Bill and Bond Ted have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 3 years to maturity, whereas Bond Ted has 20 years to maturity. Both bonds have a par value of 1,000.

a.	If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	If rates were to suddenly fall by 3 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

using Financial Calculator Please

Answer 1

(a) Bond Bill: Face Value = $ 1000, Price = $ 1000, Coupon = 10%, Yield = Coupon = 10 % (as bonds are priced at par), Coupon Frequency: Semi-Annual, Tenure = 3 years

Semi-Annual Coupon = 0,1 x 0.5 x 1000 = $ 50

Post rise in Interest Rates, New Yield = 10 + 3 = 13%

Therefore, New Bond Price = 50 x (1/0.065) x [1-{1/(1.065)^(6)}] + 1000 / (1.065)^(6) = $ 927.38

% Change in Bond Price = [(1000-927.38) / 1000] = 7.26 %

Bond Ted:

Face Value = $ 1000, Price = $ 1000, Coupon = 10%, Yield = Coupon = 10 % (as bonds are priced at par), Coupon Frequency: Semi-Annual, Tenure = 20 years

Semi-Annual Coupon = 0,1 x 0.5 x 1000 = $ 50

Post rise in Interest Rates, New Yield = 10 + 3 = 13%

Therefore, New Bond Price = 50 x (1/0.065) x [1-{1/(1.065)^(40)}] + 1000 / (1.065)^(40) = $ 787.82

% Change in Bond Price = [(1000-787.82) / 1000] = 21.22 %

(b)

Bond Bill: Face Value = $ 1000, Price = $ 1000, Coupon = 10%, Yield = Coupon = 10 % (as bonds are priced at par), Coupon Frequency: Semi-Annual, Tenure = 3 years

Semi-Annual Coupon = 0,1 x 0.5 x 1000 = $ 50

Post fall in Interest Rates, New Yield = 10 - 3 = 7 %

Therefore, New Bond Price = 50 x (1/0.035) x [1-{1/(1.035)^(6)}] + 1000 / (1.035)^(6) = $ 1079.93

% Change in Bond Price = [(1079.93-1000) / 1000] = 7.99%

Bond Ted:

Face Value = $ 1000, Price = $ 1000, Coupon = 10%, Yield = Coupon = 10 % (as bonds are priced at par), Coupon Frequency: Semi-Annual, Tenure = 20 years

Semi-Annual Coupon = 0,1 x 0.5 x 1000 = $ 50

Post fall in Interest Rates, New Yield = 10 - 3 = 7%

Therefore, New Bond Price = 50 x (1/0.035) x [1-{1/(1.035)^(40)}] + 1000 / (1.035)^(40) = $ 1320.33

% Change in Bond Price = [(1320.32-1000) / 1000] = 32.0326 % ~ 32.03 %