Question

# You have been hired to value a new 20-year callable, convertible bond. The bond has a...

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.)

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(PVIFA1.5%,40)] + \$1,000/1.01540

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%