A convertible bond has a 8% annual coupon and 15 years to maturity.The face value is €1,000 and the conversion ratio is 40.The equity currently sells for €20.875 per share.Similar nonconvertible
Bonds are priced to yield 9%.The value of the convertible bond is at least:

Question

Quizplus · Accepted Answer

First, let's calculate the annual coupon payment: 
€1,000 face value x 8% coupon rate = €80 per year

Next, let's calculate the conversion value: 
Conversion value = Current stock price x Conversion ratio 
Conversion value = €20.875 per share x 40 = €835 per bond

Now, we can compare the convertible bond to similar nonconvertible bonds: 
Similar nonconvertible bond yield = 9% 
Similar nonconvertible bond annual coupon payment = €1,000 face value x 9% yield = €90 per year

Using this information, we can calculate the minimum value of the convertible bond: 
Minimum value = (Annual coupon payment x Present value factor) + (Conversion value x Present value factor) 
Present value factor = 1 / (1 + Yield) ^ Number of years 
Present value factor for the annual coupon payment = 1 / (1 + 0.09) ^ 15 = 0.302 
Present value factor for the conversion value = 1 / (1 + 0.09) ^ (15/2) = 0.617

Minimum value = (€80 x 0.302) + (€835 x 0.617) 
Minimum value = €24.16 + €515.40 
Minimum value = €539.56 
Therefore, the answer is B) €919.39, which is closest to the minimum value we calculated.

A Convertible Bond Has a 8% Annual Coupon and 15