Question 16.5: Let us analyze the following two alternatives for a 20-year ...
Let us analyze the following two alternatives for a 20-year bond. The stock price is now $40.
| Interest Rate | Shares | Conversion Premium | Conversion Price | |
| Alternative 1 | 0.08 | 25 | \frac{\$1,000 − 25 (\$40)}{25 (\$40)}=0 | $40 |
| Alternative 2 | 0.10 | 20 | \frac{\$1,000 − 20 (\$40)}{20 (\$40)}=0.25 | $50 |
Which alternative is better for the issuing firm?
Alternative 2 has an extra $20-per-year interest on a $1,000 bond. But it saves five shares at the time of conversion. If the stock price is $40 or less and conversion does not take place, alternative 2 leads to an extra $20-per-year (before-tax) cost and zero benefits. The bonds are not converted with either alternative. Alternative 2 is inferior to alternative 1.
If the stock price goes to P_{n} where P_{n} is larger than $50, then alternative 2 saves five shares worth P_{n} each. For the issuing firm, we have a NPV of
NPV = −20 B(n, ki) + 5 (P_{n}) (1 + ki)^{-n} .
If the stock price is between $40 and $50, then at time n alternative 1 costs 25P_{n} while alternative 2 costs $1,000.
The NPV of alternative 2 compared to alternative 1 is
NPV = −20 B(n, ki) + (25P_{n} – \$1,000) (1 + ki)^{-n} .
If P_{n} = $40, the NPV is a negative 20 B(n,ki) and alternative 1 is preferred. If P_{n} = $50, n = 20, and k_{i} = 0.10, we have
NPV = −20(8.5136) + ($1,250 − $1,000)(0.1486) = −170 + 37 = −133.
Alternative 1 is better than alternative 2.
With n = 20, Pn has to be at least as large as $229 for alternative 2 to be better:
NPV = −20 (8.5136) + 5P_{n} (0.1486) = 0
5P_{n} = \frac{\$170}{0.1486} = \$1,144
P_{n}= $229.
The analysis can also be done for different values of n and different call strategies. An earlier conversion will increase the importance of the extra five shares.