Question

# A company has liabilities of \$1,000 due in 6 months and \$1,000 due in one year....

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. \$1,854

2. \$1,870

3. \$1,906

4. \$1,929

5. \$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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