- Variable Interest Rates 221
higher because so is the price at which we sell the bonds after three years.Year 0 1 2 3
Rate 12% 10% 10% 10%
PV of coupon 1 $8. 87 $10. 00
PV of coupon 2 $7. 87 $9. 05 $10. 00
PV of coupon 3 $6. 98 $8. 19 $9. 05 $10. 00
PV of coupon 4 $6. 19 $7. 41 $8. 19 $9. 05
PV of face value $61. 88 $74. 08 $81. 87 $90. 48
Bond price $91. 78 $98. 73 $99. 11 $99. 53
Cashed coupons $108. 96 $119. 99 $132. 10
Additional bonds 1. 10 1. 21
Number of bonds 10. 90 12. 00 13. 21
Value of investment $1, 000. 00 $1, 184. 65 $1, 309. 25 $1, 446. 94- If the rate increases to 14% and stays there, the bonds will be cheaper than
in Scenario 1. The final value of the investment will be disappointing.
Year 0 1 2 3
Rate 12% 14% 14% 14%
PV of coupon 1 $8. 87 $10. 00
PV of coupon 2 $7. 87 $8. 69 $10. 00
PV of coupon 3 $6. 98 $7. 56 $8. 69 $10. 00
PV of coupon 4 $6. 19 $6. 57 $7. 56 $8. 69
PV of face value $61. 88 $65. 70 $75. 58 $86. 94
Bond price $91. 78 $88. 53 $91. 83 $95. 63
Cashed coupons $108. 96 $121. 26 $134. 46
Additional bonds 1. 23 1. 32
Number of bonds 10. 90 12. 13 13. 45
Value of investment $1, 000. 00 $1, 073. 53 $1, 234. 85 $1, 420. 41As a motivation for certain theoretical notions, consider the above invest-
ment, with the same possible scenarios, but involving a specially designed se-
curity, a coupon bond with annual coupons paying $32, all other parameters
remaining unchanged. The results are as follows:
Scenario Value after 3 years
12%, 12%, 12%, 12% $1,433.33
12%, 10%, 10%, 10% $1,433.68
12%, 14%, 14%, 14% $1,433.78It is remarkable that any change in interest rates improves the result of our
investment. We do not lose if the rates change unfavourably. On the other