Vital Silence Corp. has just issued a 30-year callable, convertible bond with a coupon rate of 6.4 percent and annual coupon payments. The bond has a conversion price of $93.40. The company's stock is selling for $28.60 per share. The owner of the bond will be forced to convert if the bond's conversion value is ever greater than or equal to $1,140. The required return on an otherwise identical nonconvertible bond is 7.4 percent. Assume a par value of $1,000. a. What is the minimum value of the bond?
b. If the stock price were to grow by 10.8 percent per year forever, how long would it take for the bond's conversion value to exceed $1,140?

a. $880.74

b. 13 years

Explanation:

a.  Conversion ratio = Current Value of bond / Conversion price  = 1,000 / 93.4 = 10.71

Conversion price of bond = 10.71 × 28.60  = $306.31

Coupon = Par value of bond * Coupon rate  = $1,000 * 6.4% = $64

Present value of straight debt is calculated below:

Present Value = $64 × [1-(1+7.4%)^-30 / 7.4%] + [$1,000 / (1+7.4%)^30]

= $64*11.93 + $117.46

= $763.28 + $117.46

= $880.74 .

Therefore, the minimum value of bond is $880.74

b. Conversion ratio = 10.71

Current stock price = $28.6

Suppose number of year the stock will take to reach above $1,140 is t.

Conversion value = Current stock price * Conversion ratio*(1+10.8%)^t

$1,140 = $28.6 * 10.71 * (1.108)^t

(1.108)^t = 3.7218

t = 12.8145 year.

t = 13 years

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