Question

A corporate bond has 2 years to maturity, a coupon rate of 8%, a face value of $1,000 and pays coupons semiannually. The market interest rate for similar bonds is 9.5%. Duration is 1.886 years, NPV is 973.25.

a. If yields fall by 0.8 percentage points, what is the new expected bond price based on its duration (in $)?

b. What is the actual bond price after the change in yields (in $)?

c. What is the difference between the two new bond prices (in absolute $)?

Answer 1

(a)

Change in yield = -0.8%

Duration = 1.886

% change in bond price = - Change in yield * Duration = - (-0.8)*1.886 = 1.5088%

Hence, New Price = 973.25 * (1 + 0.015088) = $987.93

(b)

Number of periods = n = 2*2 = 4 semiannual periods

New Semiannual Yield r = (0.095-0.008)/2 = 0.0435

Semiannual Payment P = 8%*1000/2 = $40

Face Value FV = $1000

Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ

= P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ = 40(1 - 1.0435^-4)/0.0435 + 1000/1.0435⁴ = $987.40

(c) Difference = 987.93 - 987.40 = $0.53