Module IV· Debt RatiosIntermediate
Question
What is the average life of an amortizing debt tranche and how do you calculate it?
Answer
Mechanics
Average life = the weighted average time until the debt is repaid. Important for pricing and risk assessment.
Formula
```
Average Life = Σ (time × amortization_t) / Σ amortization_t
```
Deep diveShow more details
Example — TLA $100m, 5-year, step-up amortization
| Year | Amortization | Time × amortization |
|---|---|---|
| 1 | 5 | 5 |
| 2 | 10 | 20 |
| 3 | 15 | 45 |
| 4 | 25 | 100 |
| 5 | 45 | 225 |
| Total | 100 | 395 |
`Average Life = 395 / 100 = 3.95 years`
Comparison (bullet vs amortizing)
| Structure | Average life |
|---|---|
| 5-year bullet | 5.0 years |
| 5-year amortizing 20%/yr | 3.0 years |
| 7-year TLB (bullet) | 7.0 years |
| 7-year TLB 1%/yr + bullet | ~6.75 years |
Consequence
- Lower average life = lower risk = lower coupon
- Higher average life (e.g. 7-year bullet) = higher coupon premium (~50-100bps)
- In the pricing model, important for the yield-to-maturity calculation
Pitch tip
Question: "What is the average life of your TLB?"
Answer: "The TLB is a 7-year bullet, so average life ≈ 7. That explains the 75-100bps premium over a TLA with 3-4 years average life. Relevant in a pricing comparison"