5.9 Solution to Problem #2
Solution
| Given: | Coupon | = 0% |
| Discount Rate | = 8% | |
| Maturity | 3 Years | |
| Face Value: | $100,000 | |
| Compounding Frequency | Semi-Annual |
| End of Period | Coupon Interest | Interest Expense | Amortization | Debt Balance |
|---|---|---|---|---|
| 0 | $79,030 | |||
| 1 | 0 | $3,161 | $3,161 | $82,190 |
| 2 | 0 | $3,289 | $3,289 | $85,480 |
| 3 | 0 | $3,419 | $3,419 | $88,900 |
| 4 | 0 | $3,556 | $3,556 | $92,460 |
| 5 | 0 | $3,699 | $3,699 | $96,150 |
| 6 | 0 | $3,846 | $3,846 | $100,000 |
| Total | $20,970 | $20,970 | ||
Here, the solution has been stated in hundreds of thousands.
Analytic comment:
The Amortization for a zero-coupon bond can be calculated in two different ways. One involves extrapolating the relevant Present Value factors from our rate tables and multiplying by dollars in order to determine the increasing debt balances. From these numbers, we can subtract the period-by-period absolute differences in the factors, adjusting for dollars. To illustrate, going from period zero to period one: (0.8219 – 0.7903) ($100,000) = $3,160 (with a small rounding error). Remember: for a Zero, amortization adds to the balance.
The other method for calculating the amortization is by multiplying the discount rate and the balance. To illustrate, 0.04) ($79,030) = 3,161.
Both methods yield the same result. That’s cool!
