Please help me with part B. Can you show me how to get the first and the second
ID: 2383393 • Letter: P
Question
Please help me with part B. Can you show me how to get the first and the second answer using formulas( modified duration and the capital gains formula)! Thank you
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).
Answer to A and part of B
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.
Comment
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
Explanation / Answer
Present value of cash flow is 943.26 in case of 8.35% interest rate as compared to 938.67 at 8.5% interest rate.
Years Cash flow PV of cash flows @ 8.5% Time weighted PV of cash flows 1 85 78.34101382 78.34101382 2 85 72.20369938 144.4073988 3 85 66.54718837 199.6415651 3 1000 721.5742843 2164.722853 938.67 2,587.11 Cashflows divided by the PV = 2,587.113/938.67 = 2.756 2.756 years