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Answer:
1.1 Inflow (Coupon payment ) = $1000 * 7.5% = $75
Year Inflows Pvf at 5% Present value
1 75 0.952381 71.43
2 75 0.907029 68.03
3 75 0.863838 64.79
4 75 0.822702 61.70
4 1000 0.822702 822.70
Total 1,088.65
Price of Bond, when yield to maturity is 5% = $1088.65
1.2 Year Inflows Pvf at 5.2% Present value
1 75 0.95057 71.29
2 75 0.9035839 67.77
3 75 0.85892 64.42
4 75 0.816464 61.23
4 1000 0.816464 816.46
Total 1,081.18
Price of Bond, when yield to maturity is 5.2% =$1081.18
1.3 Change in price of Bond = (Decrease in price of bond / price of bond ) * 100
= $7.47 / 1088.65 *100
= 0.69%
Change in price of Bond when yield increases by 0.2%( i.e Decrease in price of bond)
= $1088.65 - $ 1081.18
= $7.47
1.4 Year Inflows Pvf at 5% P. value Year*P. value
1 75 0.9523809 71.43 71.43
2 75 0.907029 68.03 136.05
3 75 0.863838 64.79 194.36
4 75 0.822702 61.70 246.81
4 1000 0.822702 822.70 3,290.81
Total 1,088.65 3,939.47
Modified duration = Bond duration / ( 1+YTM)
= 3.6187 / ( 1+0.05)
= 3.446
Bond Duration = Sum of (PV of inflows) / Sum of (Year*PV of inflows)
= $3,939.47 / $1088.65
= $3.6187
1.5 % Change in price of bond = (-1 * Modified duration * % change in YTM in term of basis point)
= ( -1 * 3.446 * 0.2)
= -0.69 %