A bond with 3 years remaining to maturity has an annual coupon rate of 8.5%, and
ID: 2383383 • Letter: A
Question
A bond with 3 years remaining to maturity has an annual coupon rate of 8.5%, and a face value of $1,000. Assume the yield to maturity is 7.00% and answer the questions below. (You may use a financial calculator to get the PV of the bond in this problem – but show your calculator entries, i.e., 1000 FV, etc).
a) What is the duration of this bond?
b) If interest rates fall 0.15% from the given YTM, by what percent will the bond change in value? Show this 2 ways (using modified duration and the capital gains formula method).
Explanation / Answer
A)
Determination of the duration of the bond is as follows:
Year
Cash flow
Discount factor@7%
Discounted cash flows
Weight
Duration
1
85
0.934579439
79.44
0.076431
0.076431
2
85
0.873438728
74.24
0.07143
0.142861
3
85
0.816297877
69.39
0.066757
0.200272
3
1000
0.816297877
816.30
0.785382
2.356145
1,039.36
2.775708
Thus, the duration of the bond is 2.77 years.
B)
Computation of the % of fall in bond price if interest rate falls to 8.35%:
Under modified duration method:
If the interest falls by 0.15%, the price of the bond comes to 1,035; which represents in 0.38% decrease of the price of the bond.
Year
Cash flow
Discount factor@7%
Discounted cash flows
Weight
Duration
1
85
0.934579439
79.44
0.076431
0.076431
2
85
0.873438728
74.24
0.07143
0.142861
3
85
0.816297877
69.39
0.066757
0.200272
3
1000
0.816297877
816.30
0.785382
2.356145
1,039.36
2.775708
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