99
192.
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
193.
An institute has provided an early retirement incentive package to a 60-year-old retiree that pays
12,000 per year at the end of each year up to and including age 65, plus a lump sum payment of
150,000 at age 65. All payments are guaranteed whether or not the retiree is alive at age 65.
The institute will create a portfolio of two five-year bonds to exactly match the payments under
this package.
The first bond has a face amount of 100,000 and an annual coupon rate of 10%.
Determine which of the following second bonds will exactly match the liability.
(A) A bond with a price of 42,015, an annual coupon rate of 4% and annual effective yield of
8%.
(B) A bond with a price of 50,000, an annual coupon rate of 4% and annual effective yield of
8%.
(C) A bond with a price of 41,588, an annual coupon rate of 8% and annual effective yield of
10%.
(D) A bond with a price of 50,000, an annual coupon rate of 8% and annual effective yield of
10%.
(E) A bond with a price of 55,451, an annual coupon rate of 8% and annual effective yield of
10%.