A convertible bond has an 7% annual coupon and 10 years to maturity.The face value is €1,000 and the conversion ratio is 35.The equity currently sells for €27.375 per share.Similar nonconvertible
Bonds are priced to yield 9%.The value of the convertible bond is at least:

Question

Quizplus · Accepted Answer

The annual coupon payment is €70 (€1,000 face value x 7%).  The conversion price is €28.57 (€1,000 face value / 35 conversion ratio) and the stock is currently selling for €27.375 per share. This means that the conversion value of the bond is €959.81 (€27.375 stock price x 35 conversion ratio).

To find the minimum value of the convertible bond, we use the following formula: 
Minimum value = straight bond value + conversion value

The straight bond value is calculated by multiplying the annual coupon payment by the present value of an annuity factor for 10 years at 9% yield.

PV of annuity factor = (1 - (1 / (1 + r)^n)) / r

where r is the yield and n is the number of periods.

PV of annuity factor = (1 - (1 / (1 + 0.09)^10)) / 0.09 
PV of annuity factor = 6.4177

Straight bond value = annual coupon payment x PV of annuity factor 
Straight bond value = €70 x 6.4177 
Straight bond value = €448.24

Therefore, the minimum value of the convertible bond is: 
Minimum value = €448.24 + €959.81 
Minimum value = €1,408.05

However, we know that the value of the convertible bond cannot be higher than the straight bond value because investors would simply buy the nonconvertible bond instead (since it has a higher yield). Therefore, the minimum value of the convertible bond is €448.24.

Hence, the answer is B (€958.13).

A Convertible Bond Has an 7% Annual Coupon and 10