Question

Philip Morris has issued bonds that pay annually with the following characteristics:

Coupon	Yield to Maturity	Maturity	Macaulay Duration
8%	8%	15 Years	15 Years

a. Calculate modified duration using the information above.

b. Explain why the modified duration is a better measure than maturity when calculating the bond’s sensitivity to changes in interest rates.

c. Identify the direction of change in modified duration if:

i. The coupon of the bond was 4%, not 8%.

ii. The maturity of the bond was 7 years, not 15 years.

Short answer

a. 9.26 Years

b. Modified duration includes factors such as the size and timing of coupon payments, yield to maturity, etc. maturity considers only the final cash flow

c. (i) increase (ii) decrease

Step-by-step solution

Calculation of modified duration

Given,

Macaulay duration = 10 Years

YTM = 8%

Therefore

Modified duration = Macaulay duration / 1 + YTM

= 10 / 1 + 0.8

= 10/ 1.08

= 9.26 Years

Explanation of modified duration

Because while modified duration includes factors such as the size and timing of coupon payments, yield to maturity, etc. maturity considers only the final cash flow.

Calculation of direction of change to modified duration

(i) This would lead to an increase in Modified duration as the coupon has decreased from 8% to 4%.

(ii) This would lead to a decrease in Modified duration as maturity has decreased.