Question

You have been hired to value a new 20-year callable, convertible bond. The bond has a coupon rate of 2.8 percent, payable semiannually, and its face value is $1,000. The conversion price is $59, and the stock currently sells for $46. a. What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 3 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) 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

The minimum bond price is the greater of the straight bond value or the conversion value. The straight bond value is:

Straight bond value = [$14.00(PVIFA_{1.5%,40})] +
$1,000/1.015^{40}

Straight bond value = $418.82 + $551.26 = $970.08

The conversion ratio is the par value divided by the conversion price, so:

Conversion ratio = $1,000/$59 = 16.95

The conversion price is the conversion ratio times the stock price, so:

Conversion value = 16.95($46) = $779.66

The minimum value for this bond is the straight bond value of $970.08

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

= [$59 - $46] / $46 = $13 / $46 = 28.26%

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