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, we can calculate the annual coupon payment as 8% of €1,000, which is €80. Then, we can calculate the conversion value as 40 shares multiplied by the current stock price of €20.875, which is €835.

To calculate the bond's value, we need to consider two scenarios:

1. If the bond is kept as a bond and not converted into equity:
The present value of the bond can be calculated using the formula:
PV = (C/r) * (1 - 1/(1+r)^n) + FV/(1+r)^n
where:
C = annual coupon payment = €80
r = yield to maturity = 9%
n = number of years to maturity = 15
FV = face value = €1,000
Using this formula, we get:
PV = (80/0.09) * (1 - 1/(1+0.09)^15) + 1,000/(1+0.09)^15
PV = €704.63

2. If the bond is converted into equity:
The conversion value is €835 and the current market value of the equity is €20.875 per share. So, the number of shares that the bond can be converted into is:
40 shares = €835 / €20.875 per share
The convertible bond can be converted into 40 shares of equity, which are currently valued at:
40 shares x €20.875 = €835
Since the conversion value is higher than the present value of the bond, the bondholder would choose to convert the bond into equity.

Therefore, the minimum value of the convertible bond is the present value of the bond, which is €704.63.

A Convertible Bond Has a 8% Annual Coupon and 15