A company has liabilities of $1,000 due in 6 months and $1,000 due in one year.
The assets available are:
Bond A: A one-year $1,000 par bond with 4% coupons paid semiannually, with an annual effective yield of 6%
Bond B: A 6 month $1,000 par bond with 6% coupon paid semiannually, with an annual effective yield of 8%
What is the total purchase price of the portions of each bond that must be bought to exactly match the liabilities?
$1,854
$1,870
$1,906
$1,929
$1,954
step - 1:
First we need to find out semi annual rate for given effective annual rate
EAR = (1+r)^n - 1
where r = rate per period
n = number of periods
For Bond A:
6% = (1+r)^2 - 1
(1+r)^2 = 1.06
r = 2.956%
For Bond B:
8% = (1+r)^2 - 1
(1+r)^2 = 1.08
r = 3.923%
pressent value = future value / (1 + yield)^n
Total purchase price = 1000 / (1+3.923%) + 1000 / (1 + 2.956%)^2
= 962.25 + 943.40
= 1905.65
so total Purchase Price = $1906 (rounded to nearest dollar)
Third option is correct.
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