Your firm has a convertible bond with 3 years to maturity and a $1000 face value. The annual coupon rate is equal to 9%. Similar nonconvertible bonds are priced to yield 12%. The current price of the convertible bond is 15% more than the price of the nonconvertible bond. Each bond can be converted into 25 shares of stock. If stock price is $26, find the bond's option premium. Will the bond holder convert the bond? Explain. If any assumptions had to be made, please indicate the assumptions

Bond's option premium = $139.19

The Bond holder will not convert the bond in Stock shares.

We have to calculate Price of convertible bond.

But we have some details about non-convertible price, hence we will calculate price of non-convertible bond as under-

Face Value = $1,000

Years to maturity = 3 years

Required rate of return (Yield rate) = 12%

Coupon Rate = 9%, hence coupon amount = $1,000*9% = $90

Non-convertible Bond Price = Coupon Amount * PVAF(12%, 3 years) + Face Value*PVIF(12%, 3 years)

Non-convertible Bond Price = $90* 2.4018 + $1000*0.71178

Non-convertible Bond Price = $216.16 + $711.78

Non-convertible Bond Price = $927.94

Price of convertible bond is 15% more than price of non-convertible bond

Hence, Price of convertible bond = $927.94+15% = $1,067.13

However, bond's option premium would be calculated as under-

Price of convertible Bond = Price of Non-convertible Bonds + Bond's Option Premium

Bond's option premium = Price of convertible Bond - Price of Non-convertible Bonds

Bond's option premium = $1,067.13 - $927.94

Bond's option premium = $139.19 (Answer)

(We can say 15% of Price of Non-convertible Bond is the Bond's Option premium = 927.94*15% = $139.19)

Stock price = $26 per share

Option for Convertible bond can be converted into 25 stock shares

Hence, value of conversion = $26*20 Shares = $650

Convertible Bond Price is higher of $1,067.13 than value of conversion into Stock of $650. Hence, Bond holder is not having benefit to convert bonds in stock. The Bond holder will not convert the bond in Stock shares.

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