A construction firm is facing three liabilities of 1000, due at times 1, 2, and 3 in years. There are three bonds available to match these liabilities, as follows:

Bond I: A bond due at the end of period 1 with a coupon rate of 1% per year, valued at a annual effective yield rate of 14%.

Bond II: A bond due at the end of period 2 with a coupon rate of 2% per year, valued at a annual effective yield rate of 15%.

Bond III: A zero-coupon bond due at time 3 valued at a periodic effective yield rate of 18%.

Calculate the face value of each bond that should be purchased to exactly match the liabilities.

	Bond I	Bond II	Bond III
(A)	970.68	980.39	1000.00
(B)	970.68	1000.00	980.39
(C)	980.39	970.68	1000.00
(D)	1000.00	980.39	970.68
(E)	1000.00	1000.00	1000.00

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

Only Bond III can match the liability at time 3. The bond must mature for 1000. Only Bond II can match the liability at time 2. The face value and coupon must total 1000. If X is the face value, then X + 0.02X = 1000 and thus X = 980.39. Only Answer A has these to values. To check, Bond II also provides a coupon of 0.02(980.39) = 19.61 at time 1. Therefore, Bond I must provide the remaining 980.39 from its coupon and redemption value. If Y is the face value, then Y + 0.01Y = 980.39 for Y = 970.68.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.