A convertible bond is selling for $800. It has 10 years to maturity, a $1000 face value, and a 10% coupon paid semi-annually. Similar nonconvertible bonds are priced to yield 14%. The conversion price is $50 per share. The stock currently sells for $31.375 per share. Determine the bond's option premium.

The bond's option premium is $11.88

Explanation:

Acording to the data we have the following:

The Maturity Value of Bond=$1000

The Coupon Rate = 10%

Hence, there is an interest of $100 Per year but it is semi anually , Therefore there is an interest of $50 received per year .

Also, the YTM = 14% , which means 7% for 6 months

Therefore, to calculate the  bond's option premium, we have to use first the formula to calculate the fair value of bond.

The Fair Value of Bond = PVAF( 7% , 20 )*50 + PV( 7% , 20 )*1000

                                       = 50*10.594 + 1000*0.2584

                                       = $529.70 + $258.419

                                      =$788.119

Hence, The bond's option premium = $800 - $788.119 = $11.88

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