9.6 Term-to-Maturity Sensitivity (Cash Flows)
Once again, we see that the longer the term to the cash flows, the greater the volatility (the first derivative). This is illustrated below for 10% and 12 % discounts, and 5 versus 30 years.
| Term-to-Maturity | Present Value of $1 @ .10 | Present Value of $1 @ .12 | Percentage Difference (The First “Derivative”) |
|---|---|---|---|
| 5 | .6209 | .5674 | -.0862 |
| 30 | .0573 | .0334 | -.4171 |
Note that the “percentage difference” column represents how much less the 12% discount value is in comparison to the 10%. For 5 years, the calculation is: (0.5674 ÷ 0.62.09) – 1 = – 0.0862. The 12% discount multiplier is about 8.6% less. Were it more, the result would yield a positive number.
Conclusions / Implications
- The longer the average term of the cash flow, the more sensitive its present value. (i.e., dollar value/price) is to changes in the discount rate.
- Price volatility increases with term-to-maturity.
- The lower the coupon, the longer the ALCF, the greater the price volatility. A Zero-coupon bond (“Zero”) has the longest ALCF – equal to the maturity. Again, A Zero-coupon bond shall be our base case.
Note:
The present value difference of 2% itself compounds (discounts) over time.
