Philip Morris has issued bonds that pay semiannually with the following characteristics: Coupon Yield to Maturity Maturity Macaulay Duration
8% 8% 15 years 10 years

Required:
a. Calculate modified duration using the preceding information.
b. Explain why modified duration is a better measure than maturity when calculating the bondâs sensitivity to changes in interest rates.
c. Identify the direction of change in modified duration if

1. the coupon of the bond were 4 percent, not 8 percent.
2. the maturity of the bond were 7 years, not 15 years.

a)  ≈  9.6 years

b)   Modified duration is a better measure because Modified duration consider the concept of negative convexity

c) i) coupon of bond = 4%

  Modified duration will increase since the coupon rate of payment decreased

ii) Maturity of bond = 7

 Modified duration will decline as Maturity period has declined to 7 years

Explanation:

A) Calculate modified duration using the preceding information

modified duration = Macaulay duration / ( 1 + (yield to maturity / 2 ))

                             = 10 / ( 1 + ( 0.08 / 2 ))

                             = 9.615 years

B) Modified duration is a better measure because Modified duration consider the concept of negative convexity while Macaulay methods shows the inverse relationship between the duration of the bond and coupon payment .

C) Determine Direction of change in modified duration if

i) coupon of bond = 4%

  Modified duration will increase since the coupon rate of payment decreased

ii) Maturity of bond = 7

 Modified duration will decline as Maturity period has declined to 7 years