Question

You have been hired to value a new 30-year callable, convertible bond, with a $1,000 par value. The bond has a coupon rate of 5.3 percent, payable annually. The conversion price is $99, and the stock currently sells for $38.40. The stock price is expected to grow at 10 percent per year. The bond is callable at $1,200, but, based on prior experience, it won’t be called unless the conversion value is $1,300. The required return on this bond is 7 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

Straight Value of bond :

N = 30 , PMT = $53, FV = $1000, r = 7%

Present Value = [ PMT/r * 1 - 1/ (1+r)^N] + FV/(1+R)^N

PV = [53/0.07 * 1 - 1/(1.07)^30] + 1000/(1.07)³⁰

PV = 657.67 + 131.37

=$789.04

Converstion Ratio (CV) = FV/CP

= 1000/$99

= $10.10

Converstion Value = Price * CR

= 38.4 * 10.10

= $387.88

Current Converstion Value = $387.88

Bond will be called when Coversion price = $1300

387.88 * 1.10^{t =} 1300

ln (1.10)^t = ln( 1300/387.88)

t ln (1.10) = 1.2094

t = 12.6906 years

Present Value = [ 53/0.07 * 1 - 1/ (1.08)^12.6906] + 1300/(1.08)^12.6906

= 472.029 + 489.53

PV = $961.56

Current Value of Bond = $961.56