Question

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

  

Conversion price	$	47	/share
Coupon rate		8.4	%
Par value	$	1,000
Yield on nonconvertible debentures of same quality		9	%
Maturity		20	years
Market price of stock	$	46	/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

The minimum price at which the convertible should sell is the higher of the straight value of the bond or the conversion price of the bond

(a)-Straight Value of the Bond

-The Straight Value of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value/Par Value.

-The Price of the Bond is normally calculated either by using EXCEL Functions or by using Financial Calculator.

-Here, the calculation of the Bond Price using financial calculator is as follows

Variables	Financial Calculator Keys	Figures
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 8.40% x ½]	PMT	42
Market Interest Rate or Yield to maturity on the Bond [9.00% x ½]	1/Y	4.50
Maturity Period/Time to Maturity [20 Years x 2]	N	40
Bond Price/Current market price of the Bond	PV	?

Here, we need to set the above key variables into the financial calculator to find out the Price of the Bond. After entering the above keys in the financial calculator, we get the Price of the Bond (PV) = $944.80

The Straight Value of the Bond will be $944.80.

(b)-Conversion Price of the Bond

The Conversion Price of the Bond = [$1,000 / $47 per share] x $46 per share

= $978.72.

(c)- The minimum price at which the convertible should sell

The minimum price at which the convertible should sell is the higher of the straight value of the bond or the conversion price of the bond.

= Higher of Straight value of the Bond or the Conversion Price

= Higher of $944.80 or $978.72

= $978.72.

Therefore, the minimum price at which the convertible should sell will be $978.72