Question

BALA FINANCE grants a bullet loan to mary for a term of three years carrying a coupon of 10% p.a annualy. the face (par) value of the loan is rs 5000 which is also its current market value because the loans current YTM is 10% p.a. what is this loans duration?

Answer 1

Duration = [(1+YTM/2)/YTM] - [(1+YTM/2) + M(C-YTM)]/YTM + C[(1+YTM/2)^2M - 1]

C = annual coupon rate i.e.10%; YTM = yield to maturity i.e. 10%; M = loan term i.e. 3 years

Duration = [(1+0.10/2)/0.10] - [(1+0.10/2) + 3(0.10-0.10)]/0.10 + 0.10[(1+0.10/2)^2*3 - 1]

Duration = [(1+0.05)/0.10] - [(1+0.05) + 3(0)]/0.10 + 0.10[(1+0.05)⁶ - 1]

Duration = (1.05/0.10) - (1.05 + 0)/0.10 + 0.10[(1.05)⁶ - 1]

Duration = 10.5 - 1.05/0.10 + 0.10(1.340095640625 - 1) = 10.5 - 10.5 + 0.10*0.340095640625 = 10.5 - 10.5 + 0.0340095640625 = 0.034 years