Question

You have been hired to value a new 25-year callable, convertible bond, with a $1,000 par value. The bond has a coupon rate of 5.6 percent, payable annually. The conversion price is $102, and the stock currently sells for $52.10. The stock price is expected to grow at 10 percent per year. The bond is callable at $1,100, but, based on prior experience, it won’t be called unless the conversion value is $1,200. The required return on this bond is 9 percent.

  

What value would you assign to this bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Solution :-

Straight Bond :-

Time to Maturity ( N ) = 25

Pmt = $1,000 * 5.6% = $56

FV = $1,000

r = 9%

Now Price = $56 * PVAF ( 25 , 9% ) + $1,000 * PVF ( 25 , 9% )

= ( $56 * 9.823 ) + ( $1,000 * 0.11597 )

= $666.03

Now Conversion Ratio = $1,000 / $102 = 9.8039

Now Conversion Value = $52.10 * 9.8039 = $510.78

Bond will Called at Price $1,200

Therefore

$510.78 * ( 1 + 0.10 )^t = 1,200

t * Log (1.10) = Log ( 2.3493 )

t = 8.9616 Years

Now Current Value of Convertible Bond

= $56 * PVAF ( 8.9616 , 9% ) + $1,200 * PVF ( 8.9616 , 9% )

= ( $56 * 5.9783 ) + ( $1,200 * 0.46189 )

= $889.06

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