9.41 Dedication Mechanics Using a Zero-Coupon Bond: “Cash Flow Matching.”
Given:
A company has the following future (explicit or contingent) liability payment schedule:
| Amount Due | |
|---|---|
| Year 1 | $5,200,000 |
| Year 2 | $8,200,000 |
| Year 3 | $4,430,000 |
| Total: | $17,830,000 |
Problem 1:
Using the following Zero-Coupon Bonds, each of which matures precisely on the respective liability payment dates, what is the total cost (i.e., present value) of Dedication? In other words, how much money will the firm need to invest today – in Zeros – in order to fund its future liabilities?
| Price | Yield | |
|---|---|---|
| Year 1 | 90.9 | 10.0 |
| Year 2 | 81.9 | 10.5 |
| Year 3 | 73.6 | 10.75 |
Solution:
| $5,200,000 × .909 | = $4,726,800 |
| $8,200,000 × .819 | = $6,715,800 |
| $4,430,000 × .736 | = $3,260,480 |
| $14,703,000 |
