Question

The following facts apply to a convertible bond making semiannual payments: Conversion price $ 37 /share Coupon rate 2.6 % Par value $ 1,000 Yield on nonconvertible debentures of same quality 5 % Maturity 25 years Market price of stock $ 34 /share

a. 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
Face Value [-$1,000]	FV	-1,000
Coupon Amount [$1,000 x 2.60% x ½]	PMT	13
Market Interest Rate or Required Rate of Return [5.00% x ½]	1/Y	2.50
Time to Maturity [25 Years x 2]	N	50
Bond Price	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 = $659.65

“Hence, the Straight Value of the Bond will be $659.65”

(b)-Conversion Price of the Bond

Conversion Ratio = Par Value of the Bond / Conversion price per share

= $1,000 / $37.00 per share

= 27.02703

Therefore, the Conversion Price of the Bond = Conversion Ratio x Market Price per share

= 27.02703 x $34.00 per share

= $918.92

(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 $659.65 or $918.92

= $918.92

“Therefore, the minimum price at which the convertible should sell will be $918.92”