Problem: 4-1 Bond A Bond B Coupon Rate 5% 14% Years-to-Maturity 10 10 Yield-to-M
ID: 2643309 • Letter: P
Question
Problem: 4-1
Bond A Bond B
Coupon Rate 5% 14%
Years-to-Maturity 10 10
Yield-to-Maturity 7% 7%
Interest Payments Semi- Semi-
Annual Annual
A] What is the current price of these bonds?
B] If the interest rates rise by 2%, what is the percentage price change of these bonds?
C] If the interest rates fall by 2%, what is the percentage price change of these bonds?
D] What does this problem tell you about the interest rate risk of lower-coupon bonds?
Explanation / Answer
The price of a bond is the sum of the present values of all expected coupon payments plus the present value of the par value at maturity.
From the above table, Current Price of Bond A = $85.79
Current Price of Bond B = $149.74
When interest rate increases,
Price of Bond A = $73.98
Change in Price = -$11.80
Percentage change in price = -(11.80/85.79)*100 = -13.76%
Price of Bond B = $132.52
Change in Price = -$17.22
Percentage change in price = -(17.22/149.742)*100 = -11.50%
When interest rate decreases,
Price of Bond A = $100
Change in Price = $14.21
Percentage change in price = (14.21/85.79)*100 = 16.57%
Price of Bond B = $170.15
Change in Price = $20.40
Percentage change in price = (20.40/149.742)*100 = 13.62%
Bond A Semi-annual Payment
Bond B PV Factor
YTM = 7% Present Value
Bond A
YTM = 7% Present Value
Bond B
YTM = 7% PV Factor
YTM = 9% Present Value
Bond A
YTM = 9% Present Value
Bond B
YTM = 9% PV Factor
YTM = 5% Present Value
Bond A
YTM = 5% Present Value
Bond B
YTM = 5% 1 2.5 7 0.966184 2.415459 6.763285 0.956938 2.392344 6.698565 0.97561 2.439024 6.829268 1 2.5 7 0.933511 2.333777 6.534575 0.91573 2.289325 6.41011 0.951814 2.379536 6.662701 2 2.5 7 0.901943 2.254857 6.313599 0.876297 2.190742 6.134076 0.928599 2.321499 6.500196 2 2.5 7 0.871442 2.178606 6.100096 0.838561 2.096403 5.869929 0.905951 2.264877 6.341655 3 2.5 7 0.841973 2.104933 5.893812 0.802451 2.006128 5.617157 0.883854 2.209636 6.18698 3 2.5 7 0.813501 2.033752 5.694505 0.767896 1.919739 5.37527 0.862297 2.155742 6.036078 4 2.5 7 0.785991 1.964977 5.501937 0.734828 1.837071 5.143799 0.841265 2.103163 5.888857 4 2.5 7 0.759412 1.898529 5.315881 0.703185 1.757963 4.922296 0.820747 2.051866 5.745226 5 2.5 7 0.733731 1.834327 5.136117 0.672904 1.682261 4.710331 0.800728 2.001821 5.605099 5 2.5 7 0.708919 1.772297 4.962432 0.643928 1.609819 4.507494 0.781198 1.952996 5.468389 6 2.5 7 0.684946 1.712364 4.79462 0.616199 1.540497 4.313391 0.762145 1.905362 5.335013 6 2.5 7 0.661783 1.654458 4.632483 0.589664 1.47416 4.127647 0.743556 1.85889 5.204891 7 2.5 7 0.639404 1.59851 4.475829 0.564272 1.410679 3.949901 0.72542 1.813551 5.077943 7 2.5 7 0.617782 1.544454 4.324473 0.539973 1.349932 3.77981 0.707727 1.769318 4.95409 8 2.5 7 0.596891 1.492227 4.178234 0.51672 1.291801 3.617043 0.690466 1.726164 4.833259 8 2.5 7 0.576706 1.441765 4.036941 0.494469 1.236173 3.461285 0.673625 1.684062 4.715375 9 2.5 7 0.557204 1.393009 3.900426 0.473176 1.182941 3.312235 0.657195 1.642988 4.600365 9 2.5 7 0.538361 1.345903 3.768528 0.4528 1.132001 3.169603 0.641166 1.602915 4.488161 10 2.5 7 0.520156 1.300389 3.64109 0.433302 1.083254 3.033113 0.625528 1.563819 4.378694 10 102.5 107 0.502566 51.513 53.77455 0.414643 42.50089 44.36679 0.610271 62.55277 65.29899 85.7876 149.7434 73.98413 132.5198 100 170.1512
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