Question

The following facts apply to a convertible bond making semiannual payments:

  

Conversion price	$	43	/share
Coupon rate		6.8	%
Par value	$	1,000
Yield on nonconvertible debentures of same quality		8	%
Maturity		20	years
Market price of stock	$	42	/share

  

What is the minimum price at which the convertible should sell? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

Bond Price =∑ [(6.8*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^20x2

k=1

Bond Price = 881.24

Conversion price = Bond par value/conversion ratio

43 = 1000/Conversion ratio

Conversion ratio = 23.26

Conversion value = Conversion ratio*current share price

Conversion value = 23.2558139534884*42

Conversion value = 976.74

Minimum price = min (881.24,976.74) = 881.24