Question

In: Finance

The following facts apply to a convertible bond making semiannual payments:      Conversion price $ 47...

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.)

Solutions

Expert Solution

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


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