A 12-year, 8 percent annual coupon bond with $100 par value currently sells at par. The bond is callable at 102. What is the effective duration of the bond assuming interest rates change by 100 basis points?
A. 5.85.
B. 7.55.
C. 10.50.
D. 4.58.
Answer:D
Since the bond is selling at par, its yield = coupon rate = 8%.
V0 = Par = 100.
I/Y = 7.00; FV = 100; N = 12; PMT = 0.08 x 100 = 8; PV = V- = 107.94.
Since the call price is 102 which is lower than 107.94, we use V- = 102
I/Y = 9.00; FV = 100; N = 12; PMT = 0.08 x 100 = 8; PV = V+ = 92.84
D = Duration = (V- - V+)/2V0(Δy)
= (102-92.84)/(200x0.01)
= 4.58