Suppose that a $1000 par value bond has 4 years and 3 months left until maturity

Question

Suppose that a $1000 par value bond has 4 years and 3 months left until maturity. It has a coupon rate of 6% that is paid in semi-annual interest payments, and it has a required rate of return equivalent to 5%.

a.What is the intrinsic value of the bond?

b-A 9% annual coupon bond will mature in 5 years, and it has a YTM of 6%. What is the duration of this bond?

c-Using the bond information from the prior problem, calculate the modified duration of the bond.

d-Based on your answer from the prior problem, what percentage change in the market price of this bond would you expect to see for a 1% increase in market interest rates?

Explanation / Answer

Solution:

a. Given that Face value, FV = 1000, Coupon payment, C = 0.06/2*1000 = 30, YTM = 5%/2 = 2.5% and Number of years, n = 4.25*2 = 8.50

The intrinsic value of bond, P is

P = C (PVIFA @ YTM, n) + FV (PVIF @YTM, n)

P = 30 (PVIFA @ 2.5%, 8.5) + 1000 (PVIF @ 2.5%, 8.5)

P = 30 [(1.025^8.5-1)/(0.025*1.025^8.5)] + 1000 (1/1.025^8.5)

P = 30 (7.5730) + 1000 (0.8107)

P = $1,037.87

b.

Duration = 4829.513/1127.371 = 4.29 years

c. Modified duration = Duration/(1 + ytm)

Modified duration = 4.29/(1.06)

Modified duration = 4.045 years

d. % change in price = Modified duration x % increase in market rate

% change in price = -4.045 x 1%

% change in price = - 4.045%

Year CF PVIF @ 6% CF*PVIF PVxYear 1 90 0.9433962 84.90566 84.90566 2 90 0.8899964 80.09968 160.1994 3 90 0.8396193 75.56574 226.6972 4 90 0.7920937 71.28843 285.1537 5 1090 0.7472582 814.5114 4072.557 1126.371 4829.513

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