Question

g You have been hired to value a new 25-year callable, convertible bond with a par value of $1,000. The bond has a coupon rate of 6 percent, payable annually. The conversion price is $180 and the stock currently sells for $42.10. 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 8 percent. What value would you assign to this bond

Answer 1

The value that would be assigned to this bond is $1,209.36.

Step-by-step explanation:

From the question, we have:

n = Number of years = 25

FV = Future value = $1,000

PMT = Coupon payment = Coupon rate * FV = 6% * $1000 = $60

r = required return rate = 8%, or 0.08

CP = Conversion price = $180

P = Current selling price = $42.10

t = number of years the bond will be called = ?

PV = [(PMT / r) * (1 - (1 / (1 + r)^n))] + (FV / (1 + r)^n) = [(60 / 0.08) * (1 - (1 / (1 + 0.08)^25))] + (1000 / (1 + 0.08)^25) = $786.50

Therefore, we have:

PV = Current value of the bond = $786.50

CR = Conversion ratio = FV/CP = 1000 / 180

CV = Conversion value = P * CR = $42.10 * (100 / 180) = $23.39

CCP = Current conversion price = CV = $23.39

CPB = Conversion price at which Bond will be called = $1,300

Therefore. we have:

CCP * CR^t = CPB ................... (1)

Substitute relevant values into equation (1) and solve for t, we have:

$23.39 * (1000 / 180)^t = $1,300

23.39 * 5.56^t = 1,300

5.56^t = 1,300 / 23.39

t = ln(1,300 / 23.39) / ln(5.56)

t = 2.34 years

Therefore, we have:

Value assigned to the bond = PV = [(PMT / r) * (1 - (1 / (1 + r)^t))] + (CPB / (1 + r)^t) = [(60 / 0.08) * (1 - (1 / (1 + 0.08)^2.34))] + (1300 / (1 + 0.08)^2.34) = $1,209.36