Question

Joe must pay liabilities of 1,000 due one year from now and another 2,000 due three years from now. There are two available investments: Bond I: A one-year zero-coupon bond that matures for 1,000. The yield rate is 6% per year Bond II: A two-year zero-coupon bond with face amount of 1,000. The yield rate is 7% per year. At the present time the one-year forward rate for an investment made two years from now is 6.5%. Joe plans to buy amounts of each bond. He plans to reinvest the proceeds from Bond II in a one-year zero-coupon bond. Assuming the reinvestment earns the forward rate, calculate the total purchase price of Bond I and Bond II where the amounts are selected to exactly match the liabilities.
1. 2,584
2. 2,697
3. 2,801
4. 2,907
5. 3,000

Answer 1

Answer:

1. 2,584

Explanation:

future payments: $1,000 in 1 year and $2,000 in 3 years

the present value of alternative I (one year bond):

$1,000 / 1.06 = $943.40

the present value of alternative II (first 2 years and then 1 year):

$2,000 / 1.065 = $1,877.93 ⇒ PV at year 2

PV at year 0 = $1,877.93 / 1.07² = $1,640.26

the total present value of both options = $943.40 + $1,640.26 = $2,583.66 ≈ $2,584