9.42 Dedication Mechanics for Coupon Bonds: A Complex Example
Dedication mechanics for coupon bonds requires that we use a reverse-order algorithm, starting with the last (i.e., the three-year) bond first. (Note that the prices of the two-and three-year coupon bonds are indicated in the right-hand margin.) We will then compare the bonds to the Zero-coupon example above.
- Cash Needs in Third Year: [adjusted for price of bond dedicated to it.]
| $4,430,000 ÷ 1.1075 |
= $4,000,000 |
| Cost: $4,000,000 × 1.00 |
= $4,000,000 (Par Bond) |
| (Coupon) Cash flow of three-year bond in earlier years, which will serve to (partially) fund those payments: |
| Years 1 & 2: $4,000,000 × 1.075 |
= $430,000 |
| Year 3 (P & I) |
= $4,430,000 |
| $8,200,000 – $430,000 |
= $7,770,000 |
| This can be covered with face value of: |
| $7,770,000 ÷ 1.11 |
= $7,000,000 |
| Cost: $7,000,000 × 1.009 |
= $7,063,000 (Premium) |
| The two-year bond produces interest as well: |
| Year two (P & I): $7,000,000 × 1.11 |
= $7,770,000 |
| Year one |
= $770,000 |
| Combined CFs of Two-and Three- Year bond |
| Year Three: |
= $4,430,000 |
| Year Two: $7,770,000 + $4,430,000 |
= $8,200,000 |
| Year One: $430,000 + $770,000 |
= $1,200,000 |
| $5,200,000 – $1,200,000 |
= $4,000,000 |
| Cost: $4,000,000 × 0.90 |
= $3,636,000 (The zero is discounted) |
| $3,636,000+ $7,063,000 + $4,000,000 |
= $14,699,000 |
| Less Zero-Coupon Dedication |
= $14,703,000 (From pervious example) |
| Advantage of Coupon Dedication |
= $4,000 |
Note:
With more precise pricing than used herein, the two alternatives may exactly equal out. The choice then becomes a matter of reinvestment risk.
