A pension plan needs to make a $3,000,000 payment in 3 years. They can buy 1 year bonds with a duration of 1 and 5 year bonds with a duration of 4.2 years. With a 10% yield-to-maturity, the immunized amount invested in 1 year bonds should be

Question

Quizplus · Accepted Answer

To immunize the portfolio, the total present value of liabilities should be equal to the total present value of assets. 
Liability PV= $2,000,000 
If we invest x amount in bonds with 10% yield to maturity, then the present value of these bonds would be x/ (1.1) 
Using algebra: x/ (1.1) = $2,000,000
x = $2,200,000

Therefore, we need to invest $2,200,000 in bonds to immunize the portfolio. 
For a 10% yield-to-maturity, the amount to be invested in 1-year bonds would be: 
$2,200,000 x 0.5 = $1,100,000

Hence, the answer is B.

A Pension Plan Needs to Make a $3,000,000 Payment in 3