Question

You have been hired to value a new 20-year callable, convertible bond. The bond has a coupon rate of 8.4 percent, payable semiannually, and its face value is $1,000. The conversion price is $67, and the stock currently sells for $54. |

a. |
What is the minimum value of the bond? Comparable nonconvertible
bonds are priced to yield 9 percent. |

b. |
What is the
conversion premium for this bond? (Enter your answer as a
percent rounded to 2 decimal places, e.g., 32.16.) |

Answer #1

á). Conversion Ratio = Par Value / Conversion Price = $1,000 / $67 = 14.93

Conversion Value = Stock Price x Conversion Ratio = $54 x 14.93 = $805.97

Straight Bond Value = $42[PVIFA_{4.5%,40}] +
$1,000/1.045^{40} = $772.87 + $171.93 = $944.80

The minimum bond price is the greater of the straight bond value or the conversion value, which is conversion value of $805.97

b). Conversion Premium = [Current Stock Price - Conversion Price] / Current Stock Price

= [$54 - $67] / $54 = -$13 / $54 = -0.24.07, or 24.07%

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